Compound#

class slothpy.Compound(*args, **kwargs)[source]#

Bases: object

The core object constituting the API and access to all the methods.

Methods

`animate_3d`(group, data_type, ...[, i_start, ...])	Creates animations of 3d plots dependent on field B[T] and temperature T[K].
`calculate_energy`(group, fields, grid, ...[, ...])	Calculates powder-averaged or directional Helmholtz or internal energy for a given list of temperature and field values.
`calculate_energy_3d`(group, fields, ...[, ...])	Calculates 3D Helmholtz or internal energy over a spherical grid for a given list of temperature and field values.
`calculate_g_tensor_and_axes_doublet`(group, ...)	Calculates pseudo-g-tensor components (for S = 1/2) and main magnetic axes for a given list of doublet states.
`calculate_magnetisation`(group, fields, grid, ...)	Calculates powder-averaged or directional molar magnetisation M(T,H) for a given list of temperature and field values.
`calculate_magnetisation_3d`(group, fields, ...)	Calculates 3D magnetisation over a spherical grid for a given list of temperature and field values.
`calculate_susceptibility`(group, ...[, ...])	Calculates powder-averaged or directional molar magnetic susceptibility chi(T)(H,T) for a given list of field and temperatures values.
`calculate_susceptibility_3d`(group, ...[, ...])	Calculates 3D magnetic susceptibility over a spherical grid for a given list of temperature and field values.
`calculate_susceptibility_tensor`(group, ...)	Calculates magnetic susceptibility chi(H,T) (Van Vleck) tensor for a given list of field and temperature values.
`calculate_zeeman_splitting`(group, ...[, ...])	Calculates directional or powder-averaged Zeeman splitting for a given number of states and list of field values.
`delete_group_dataset`(first[, second])	Deletes a group/dataset provided its full name/path from the .slt file.
`interactive_plot_3d`(group, data_type[, ...])	Creates interactive widget plot dependent on field and temperature values.
`magnetic_momenta_matrix`(group[, ...])	Calculates magnetic momenta matrix for a given number of SOC states.
`matrix_decomposition_in_z_pseudo_spin_basis`(...)	Calculates decomposition of a given matrix in "z" pseudo-spin basis.
`matrix_from_ito`(full_group_name, complex[, ...])	Calculates matrix from a given ITO decomposition.
`plot_3d`(group, data_type, field_i, temp_i[, ...])	Creates 3d plots of data dependent on field B[T] and temperature T[K].
`plot_energy`(group, energy_type[, show_fig, ...])	Creates graphs of Helmholtz energy F(T,H) or internal energy U(T,H) given a name of the group in .slt file, graphs can be optionally saved, color palettes can be changed.
`plot_magnetisation`(group[, show_fig, save, ...])	Creates graphs of M(H,T) given a name of the group in .slt file, graphs can be optionally shown, saved, color palettes can be changed.
`plot_susceptibility`(group[, show_fig, save, ...])	Creates graphs of chiT(H,T) or chi(H,T) depending on the content of .slt file, given a name of the group in .slt file, graphs can be optionally saved, color palettes can be changed.
`plot_zeeman`(group[, show_fig, save, ...])	Function that creates graphs of E(H,orientation) given a name of the group in .slt file, graphs can be optionally saved, color palettes can be changed.
`soc_crystal_field_parameters`(group, ...[, ...])	Calculates ITO decomposition (CFPs) of SOC matrix.
`soc_energies_cm_1`(group[, number_of_states, slt])	Returns energies for the given number of first spin-orbit states in cm-1.
`soc_zeem_in_z_angular_magnetic_momentum_basis`(...)	Calculates SOC or Zeeman matrix in "z" magnetic or total angular momentum basis.
`states_magnetic_momenta`(group[, states, ...])	Calculates magnetic momenta of a given list (or number) of SOC states.
`states_total_angular_momenta`(group[, ...])	Calculates total angular momenta of a given list (or number) of SOC states.
`total_angular_momenta_matrix`(group[, ...])	Calculates total angular momenta matrix for a given number of SOC states.
`zeeman_matrix`(group, fields, orientations[, ...])	Calculates Zeeman matrices for a given list of magnetic fields and their orientations.
`zeeman_matrix_ito_decpomosition`(group, ...)	Calculates ITO decomposition of Zeeman matrix.

delete_group_dataset(first, second=None)[source]#

Deletes a group/dataset provided its full name/path from the .slt file.

Parameters:

first (str) – A name of the group or dataset to be deleted.
second (str, optional) – A name of the particular dataset inside the group from the first argument to be deleted.

Raises:

SltFileError – If the deletion is unsuccessful.

Return type:

None

calculate_g_tensor_and_axes_doublet(group, doublets, slt=None)[source]#

Calculates pseudo-g-tensor components (for S = 1/2) and main magnetic axes for a given list of doublet states.

Parameters:

group (str) – Name of a group containing results of relativistic ab initio calculations used for the computation of g-tensors.
doublets (ndarray[int64]) – ArrayLike structure (can be converted to numpy.NDArray) of integers corresponding to doublet labels (numbers).
slt (str, optional) – If given, the results will be saved using this name to the .slt file with the suffix: _g_tensors_axes, by default None.

Returns:

The first array (g_tensor_list) contains a list g-tensors in a format [doublet_number, gx, gy, gz], the second one (magnetic_axes_list) contains respective rotation matrices.

Return type:

Tuple[ndarray[float64], ndarray[float64]]

Raises:

SltSaveError – If the name of the group already exists in the .slt file.
SltInputError – If input ArrayLike data cannot be converted to numpy.NDArrays.
SltInputError – If doublets are not one-diemsional array.
SltCompError – If the calculation of g-tensors is unsuccessful.
SltFileError – If the program is unable to correctly save results to .slt file.

Note

Magnetic axes are returned in the form of rotation matrices that diagonalise the Abragam-Bleaney tensor (G = gg.T). Coordinates of the main axes XYZ in the initial xzy frame are columns of such matrices (0-X, 1-Y, 2-Z).

calculate_magnetisation(group, fields, grid, temperatures, states_cutoff=0, number_cpu=0, number_threads=1, slt=None, autotune=False)[source]#

Calculates powder-averaged or directional molar magnetisation M(T,H) for a given list of temperature and field values.

Parameters:

group (str) – Name of a group containing results of relativistic ab initio calculations used for the computation of the magnetisation.
fields (ndarray[float64]) – ArrayLike structure (can be converted to numpy.NDArray) of field values (T) at which magnetisation will be computed.
grid (Union[int, ndarray[float64]]) – If the grid is set to an integer from 0-11 then the prescribed Lebedev-Laikov grids over hemisphere will be used (see grids_over_hemisphere documentation), otherwise, user can provide an ArrayLike structure (can be converted to numpy.NDArray) with the convention: [[direction_x, direction_y, direction_z, weight],…] for powder-averaging. If one wants a calculation for a single, particular direction the list has to contain one entry like this: [[direction_x, direction_y, direction_z, 1.]]. Custom grids will be automatically normalized.
temperatures (ndarray[float64]) – ArrayLike structure (can be converted to numpy.NDArray) of temeperature values (K) at which magnetisation will be computed.
states_cutoff (int, optional) – Number of states that will be taken into account for construction of Zeeman Hamiltonian. If set to zero, all available states from the file will be used., by default 0
number_cpu (int, optional) – Number of logical CPUs to be assigned to perform the calculation. If set to zero, all available CPUs will be used., by default 0
number_threads (int, optional) – Number of threads used in a multithreaded implementation of linear algebra libraries used during the calculation. Higher values benefit from the increasing size of matrices (states_cutoff) over the parallelization over CPUs., by default 1
slt (str, optional) – If given the results will be saved in a group of this name to .slt file with suffix: _magnetisation., by default None
autotune (bool, optional) – If True the program will automatically try to choose the best number of threads (and therefore parallel processes), for the given number of CPUs, to be used during the calculation. Note that this process can take a significant amount of time, so start to use it with medium-sized calculations (e.g. for states_cutoff > 300 with dense grids or a higher number of field values) where it becomes a necessity., by default False

Returns:

The resulting mth_array gives magnetisation in Bohr magnetons and is in the form [temperatures, fields] - the first dimension runs over temperature values, and the second over fields.

Return type:

ndarray[float64]

Raises:

SltSaveError – If the name of the group already exists in the .slt file.
SltInputError – If input ArrayLike data cannot be converted to numpy.NDArrays.
SltInputError – If fields are not a one-diemsional array.
SltInputError – If temperatures are not a one-diemsional array.
SltCompError – If autotuning a number of processes and threads is unsuccessful.
SltCompError – If the calculation of magnetisation is unsuccessful.
SltFileError – If the program is unable to correctly save results to .slt file.

Note

Here, (number_cpu // number_threads) parallel processes are used to distribute the workload over the provided field values.

See also

slothpy.Compound.plot_magnetisation

slothpy.lebedev_laikov_grid: For the description of the prescribed Lebedev-Laikov grids.

calculate_magnetisation_3d(group, fields, grid_type, grid_number, temperatures, states_cutoff=0, number_cpu=0, number_threads=1, rotation=None, slt=None, autotune=False)[source]#

Calculates 3D magnetisation over a spherical grid for a given list of temperature and field values.

Parameters:

group (str) – Name of a group containing results of relativistic ab initio calculations used for the computation of the 3D magnetisation.
fields (ndarray[float64]) – ArrayLike structure (can be converted to numpy.NDArray) of field values (T) at which 3D magnetisation will be computed.
grid_type (Literal["mesh", "fibonacci"]) – Determines the type of a spherical grid used for the 3D magnetisation simulation. Two grids can be used: a classical meshgrid and a Fibonacci sphere. The latter can only be plotted as a scatter but is uniformly distributed on the sphere, avoiding accumulation points near the poles - fewer points are needed.
grid_number (int) – Controls the density (number of points) of the angular grid for the 3D magnetisation calculation. A grid of dimension (spherical_grid* 2*spherical_grid) for spherical angles, phi [0, pi] and theta [0, 2*pi] will be used for meshgrid or when Fibonacci sphere is chosen grid_number points will be distributed on the sphere.
temperatures (ndarray[float64]) – ArrayLike structure (can be converted to numpy.NDArray) of temperature values (K) at which 3D magnetisation will be computed.
states_cutoff (int, optional) – Number of states that will be taken into account for construction of Zeeman Hamiltonian. If set to zero, all available states from the file will be used., by default 0
number_cpu (int, optional) – Number of logical CPUs to be assigned to perform the calculation. If set to zero, all available CPUs will be used., by default 0
number_threads (int, optional) – Number of threads used in a multithreaded implementation of linear algebra libraries used during the calculation. Higher values benefit from the increasing size of matrices (states_cutoff) over the parallelization over CPUs., by default 1
rotation (ndarray[float64], optional) – A (3,3) orthogonal rotation matrix used to rotate momenta matrices. Note that the inverse matrix has to be given to rotate the reference frame instead. It is useful here to orient your 3D plots more conveniently., by default None
slt (str, optional) – If given the results will be saved in a group of this name to .slt file with suffix: _magnetisation_3d., by default None
autotune (bool, optional) – If True the program will automatically try to choose the best number of threads (and therefore parallel processes), for the given number of CPUs, to be used during the calculation. Note that this process can take a significant amount of time, so start to use it with medium-sized calculations (e.g. for states_cutoff > 300 with dense grids or a higher number of field values) where it becomes a necessity., by default False

Returns:

For the meshgrid the resulting mag_3d_array gives magnetisation in Bohr magnetons and is in the form [coordinates, fields, temperatures, mesh, mesh] - the first dimension runs over coordinates (0-x, 1-y, 2-z), the second over field values, and the third over temperatures. The last two dimensions are in the form of meshgrids over theta and phi, ready for 3D plots as xyz. For Fibonacci, the array has the form [fields, temperatures, points[x,y,z]] where points[x,y,z] are two-dimensional (grid_number, 3) arrays holding coordinates of grid_number points in the [x, y, z] convention.

Return type:

ndarray[float64]

Raises:

SltSaveError – If the name of the group already exists in the .slt file.
SltInputError – If input ArrayLike data cannot be converted to numpy.NDArrays.
SltInputError – If fields are not a one-diemsional array.
SltInputError – If temperatures are not a one-diemsional array.
SltInputError – If grid_type is not “mesh” or “fibonacci”.
SltInputError – If grid_number is not a positive integer.
SltCompError – If autotuning a number of processes and threads is unsuccessful.
SltCompError – If the calculation of 3D magnetisation is unsuccessful.
SltFileError – If the program is unable to correctly save results to .slt file.

Note

Here, (number_cpu // number_threads) parallel processes are used to distribute the workload over the number of points on spherical grid. Be aware that the resulting arrays and computations can quickly consume much memory (e.g. for a calculation with 100 field values 1-10 T, 300 temperatures 1-300 K, and mesh grid with grid_number = 60, the resulting array will take 3*100*300*2*60*60*8 bytes = 5.184 GB).

calculate_susceptibility(group, temperatures, fields, number_of_points=1, delta_h=0.0001, states_cutoff=0, number_cpu=0, number_threads=1, exp=False, T=True, grid=None, slt=None, autotune=False)[source]#

Calculates powder-averaged or directional molar magnetic susceptibility chi(T)(H,T) for a given list of field and temperatures values.

Parameters:

group (str) – Name of a group containing results of relativistic ab initio calculations used for the computation of the magnetisation.
temperatures (ndarray[float64]) – ArrayLike structure (can be converted to numpy.NDArray) of temeperature values (K) at which magnetic susceptibility will be computed.
fields (ndarray[float64]) – ArrayLike structure (can be converted to numpy.NDArray) of field values (T) at which magnetic susceptibility will be computed.
number_of_points (int, optional) – Controls the number of points for numerical differentiation over the magnetic field values using the finite difference method with a symmetrical stencil. The total number of used points = (2 * num_of_opints + 1), therefore 1 is a minimum value to obtain the first derivative using 3 points - including the value at the point at which the derivative is taken. In this regard, the value 0 triggers the experimentalist model for susceptibility., by default 1
delta_h (float64, optional) – Value of field step used for numerical differentiation using finite difference method. 0.0001 (T) = 1 Oe is recommended as a starting point., by default 0.0001
states_cutoff (int, optional) – Number of states that will be taken into account for construction of Zeeman Hamiltonian. If set to zero, all available states from the file will be used., by default 0
number_cpu (int, optional) – Number of logical CPUs to be assigned to perform the calculation. If set to zero, all available CPUs will be used., by default 0
number_threads (int, optional) – Number of threads used in a multithreaded implementation of linear algebra libraries used during the calculation. Higher values benefit from the increasing size of matrices (states_cutoff) over the parallelization over CPUs., by default 1
exp (bool, optional) – Turns on the experimentalist model for magnetic susceptibility., by default False
T (bool, optional) – Results are returned as a product with temperature chiT(H,T)., by default True
grid (Union[int, ndarray[float64]], optional) – If the grid is set to an integer from 0-11 then the prescribed Lebedev-Laikov grids over the hemisphere will be used (see grids_over_hemisphere documentation), otherwise, the user can provide an ArrayLike structure (can be converted to numpy.NDArray) with the convention: [[direction_x, direction_y, direction_z, weight],…] for powder-averaging. If one wants a calculation for a single, particular direction the list has to contain one entry like this: [[direction_x, direction_y, direction_z, 1.]]. If not given the average is taken over xyz directions, which is sufficient for a second rank tensor. Custom grids will be automatically normalized., by default None
slt (str, optional) – If given the results will be saved in a group of this name to .slt file with suffix: _susceptibility., by default None
autotune (bool, optional) – If True the program will automatically try to choose the best number of threads (and therefore parallel processes), for the given number of CPUs, to be used during the calculation. Note that this process can take a significant amount of time, so start to use it with medium-sized calculations (e.g. for states_cutoff > 300 with a higher number of field values and number_of_points) where it becomes a necessity., by default False

Returns:

The resulting chitht_array gives magnetic susceptibility (or product with temperature) in cm^3 (or * K) and is in the form [fields, temperatures] - the first dimension runs over field values, and the second over temperatures.

Return type:

ndarray[float64]

Raises:

SltSaveError – If the name of the group already exists in the .slt file
SltInputError – If input ArrayLike data cannot be converted to numpy.NDArrays
SltInputError – If temperatures are not a one-diemsional array.
SltInputError – If fields are not a one-diemsional array.
SltInputError – If the number of points for finite difference method is not a possitive integer.
SltInputError – If the field step for the finite difference method is not a possitive real number.
SltCompError – If autotuning a number of processes and threads is unsuccessful.
SltCompError – If the calculation of magnetic susceptibility is unsuccessful.
SltFileError – If the program is unable to correctly save results to .slt file.

Note

Here, (number_cpu // number_threads) parallel processes are used to distribute the workload over fields.size*(2*number_of_points+1) tasks.

See also

slothpy.Compound.plot_susceptibility

calculate_susceptibility_tensor(group, temperatures, fields, number_of_points=1, delta_h=0.0001, states_cutoff=0, number_cpu=0, number_threads=1, exp=False, T=True, rotation=None, slt=None, autotune=False)[source]#

Calculates magnetic susceptibility chi(H,T) (Van Vleck) tensor for a given list of field and temperature values.

Parameters:

group (str) – Name of a group containing results of relativistic ab initio calculations used for the computation of the magnetisation.
temperatures (ndarray[float64]) – ArrayLike structure (can be converted to numpy.NDArray) of temeperature values (K) at which magnetic susceptibility tensor will be computed.
fields (ndarray[float64]) – ArrayLike structure (can be converted to numpy.NDArray) of field values (T) at which magnetic susceptibility tensor will be computed.
number_of_points (int, optional) – Controls the number of points for numerical differentiation over the magnetic field values using the finite difference method with a symmetrical stencil. The total number of used points = (2 * num_of_opints + 1), therefore 1 is a minimum value to obtain the first derivative using 3 points - including the value at the point at which the derivative is taken. In this regard, the value 0 triggers the experimentalist model for susceptibility., by default 1
delta_h (float64, optional) – Value of field step used for numerical differentiation using finite difference method. 0.0001 (T) = 1 Oe is recommended as a starting point., by default 0.0001,
states_cutoff (int, optional) – Number of states that will be taken into account for construction of Zeeman Hamiltonian. If set to zero, all available states from the file will be used., by default 0
number_cpu (int, optional) – Number of logical CPUs to be assigned to perform the calculation. If set to zero, all available CPUs will be used., by default 0
number_threads (int, optional) – Number of threads used in a multithreaded implementation of linear algebra libraries used during the calculation. Higher values benefit from the increasing size of matrices (states_cutoff) over the parallelization over CPUs., by default 1
exp (bool, optional) – Turns on the experimentalist model for magnetic susceptibility., by default False
T (bool, optional) – Results are returned as a product with temperature chiT(H,T)., by default True
rotation (ndarray[float64], optional) – A (3,3) orthogonal rotation matrix used to rotate momenta matrices. Note that the inverse matrix has to be given to rotate the reference frame instead., by default None
slt (str, optional) – If given the results will be saved in a group of this name to .slt file with suffix: _susceptibility_tensor., by default None
autotune (bool, optional) – If True the program will automatically try to choose the best number of threads (and therefore parallel processes), for the given number of CPUs, to be used during the calculation. Note that this process can take a significant amount of time, so start to use it with medium-sized calculations (e.g. for states_cutoff > 500 with a higher number of field values and number_of_points) where it becomes a necessity., by default False

Returns:

The resulting array gives magnetic susceptibility (Van Vleck) tensors (or products with temperature) in cm^3 (or * K) and is in the form [fields, temperatures, 3x3 tensor] - the first dimension runs over field values, the second over temperatures, and the last two accomodate 3x3 tensors.

Return type:

ndarray[float64]

Raises:

SltSaveError – If the name of the group already exists in the .slt file
SltInputError – If input ArrayLike data cannot be converted to numpy.NDArrays
SltInputError – If temperatures are not a one-diemsional array.
SltInputError – If fields are not a one-diemsional array.
SltInputError – If the number of points for finite difference method is not a possitive integer
SltInputError – If the field step for the finite difference method is not a possitive real number.
SltCompError – If autotuning a number of processes and threads is unsuccessful.
SltCompError – If the calculation of magnetic susceptibility tensor is unsuccessful.
SltFileError – If the program is unable to correctly save results to .slt file.

Note

Here, (number_cpu // number_threads) parallel processes are used to distribute the workload over fields.size*(2*number_of_points+1) tasks.

calculate_susceptibility_3d(group, temperatures, fields, grid_type, grid_number, number_of_points=1, delta_h=0.0001, states_cutoff=0, number_cpu=0, number_threads=1, exp=False, T=True, rotation=None, slt=None, autotune=False)[source]#

Calculates 3D magnetic susceptibility over a spherical grid for a given list of temperature and field values.

Parameters:

group (str) – Name of a group containing results of relativistic ab initio calculations used for the computation of the 3D magnetic susceptibility.
temperatures (ndarray[float64]) – ArrayLike structure (can be converted to numpy.NDArray) of temperature values (K) at which 3D magnetic susceptibility will be computed.
fields (ndarray[float64]) – ArrayLike structure (can be converted to numpy.NDArray) of field values (T) at which 3D magnetic susceptibility will be computed.
grid_type (Literal["mesh", "fibonacci"]) – Determines the type of a spherical grid used for the 3D susceptibility simulation. Two grids can be used: a classical meshgrid and a Fibonacci sphere. The latter can only be plotted as a scatter but is uniformly distributed on the sphere, avoiding accumulation points near the poles - fewer points are needed.
grid_number (int) – Controls the density (number of points) of the angular grid for the 3D susceptibility calculation. A grid of dimension (spherical_grid* 2*spherical_grid) for spherical angles, phi [0, pi] and theta [0, 2*pi] will be used for meshgrid or when Fibonacci sphere is chosen grid_number points will be distributed on the sphere.
number_of_points (int, optional) – Controls the number of points for numerical differentiation over the magnetic field values using the finite difference method with a symmetrical stencil. The total number of used points = (2 * num_of_opints + 1), therefore 1 is a minimum value to obtain the first derivative using 3 points - including the value at the point at which the derivative is taken. In this regard, the value 0 triggers the experimentalist model for susceptibility., by default 1
delta_h (float64, optional) – Value of field step used for numerical differentiation using finite difference method. 0.0001 (T) = 1 Oe is recommended as a starting point., by default 0.0001
states_cutoff (int, optional) – Number of states that will be taken into account for construction of Zeeman Hamiltonian. If set to zero, all available states from the file will be used., by default 0
number_cpu (int, optional) – Number of logical CPUs to be assigned to perform the calculation. If set to zero, all available CPUs will be used., by default 0
number_threads (int, optional) – Number of threads used in a multithreaded implementation of linear algebra libraries used during the calculation. Higher values benefit from the increasing size of matrices (states_cutoff) over the parallelization over CPUs., by default 1
exp (bool, optional) – Turns on the experimentalist model for magnetic susceptibility., by default False
T (bool, optional) – Results are returned as a product with temperature chiT(H,T)., by default True
rotation (ndarray[float64], optional) – A (3,3) orthogonal rotation matrix used to rotate momenta matrices. Note that the inverse matrix has to be given to rotate the reference frame instead. It is useful here to orient your 3D plots more conveniently., by default None
slt (str, optional) – If given the results will be saved in a group of this name to .slt file with suffix: _susceptibility_3d., by default None
autotune (bool, optional) – If True the program will automatically try to choose the best number of threads (and therefore parallel processes), for the given number of CPUs, to be used during the calculation. Note that this process can take a significant amount of time, so start to use it with medium-sized calculations (e.g. for states_cutoff > 300 with dense grids or a higher number of field values) where it becomes a necessity., by default False

Returns:

For the meshgrid the resulting chi(t)_3d_array gives susceptibility in cm^3 (or * K) and is in the form [coordinates, fields, temperatures, mesh, mesh] - the first dimension runs over coordinates (0-x, 1-y, 2-z), the second over field values, and the third over temperatures. The last two dimensions are in the form of meshgrids over theta and phi, ready for 3D plots as xyz. For Fibonacci, the array has the form [fields, temperatures, points[x,y,z]] where points[x,y,z] are two-dimensional (grid_number, 3) arrays holding coordinates of grid_number points in the [x, y, z] convention.

Return type:

ndarray[float64]

Raises:

SltSaveError – If the name of the group already exists in the .slt file.
SltInputError – If input ArrayLike data cannot be converted to numpy.NDArrays.
SltInputError – If temperatures are not a one-diemsional array.
SltInputError – If fields are not a one-diemsional array.
SltInputError – If grid_type is not “mesh” or “fibonacci”.
SltInputError – If grid_number is not a positive integer
SltInputError – If the number of points for finite difference method is not a possitive integer.
SltInputError – If the field step for the finite difference method is not a possitive real number.
SltCompError – If autotuning a number of processes and threads is unsuccessful.
SltCompError – If the calculation of 3D magnetic susceptibility is unsuccessful.
SltFileError – If the program is unable to correctly save results to .slt file.

Note

Here, (number_cpu // number_threads) parallel processes are used to distribute the workload over the number of points on spherical grid. Be aware that the resulting arrays and computations can quickly consume much memory (e.g. for calculation with 100 field values 1-10 T, 300 temperatures 1-300 K, number_of_points=3, and spherical_grid = 60, the intermediate array (before numerical differentiation) will take 7*100*300*2*60*60*8 bytes = 12.096 GB).

calculate_energy(group, fields, grid, temperatures, energy_type, states_cutoff=0, number_cpu=0, number_threads=1, slt=None, autotune=False)[source]#

Calculates powder-averaged or directional Helmholtz or internal energy for a given list of temperature and field values.

Parameters:

group (str) – Name of a group containing results of relativistic ab initio calculations used for the computation of the energy.
fields (ndarray[float64]) – ArrayLike structure (can be converted to numpy.NDArray) of field values (T) at which energy will be computed.
grid (ndarray[float64]) – If the grid is set to an integer from 0-11 then the prescribed Lebedev-Laikov grids over hemisphere will be used (see grids_over_hemisphere documentation), otherwise, user can provide an ArrayLike structure (can be converted to numpy.NDArray) with the convention: [[direction_x, direction_y, direction_z, weight],…] for powder-averaging. If one wants a calculation for a single, particular direction the list has to contain one entry like this: [[direction_x, direction_y, direction_z, 1.]]. Custom grids will be automatically normalized.
temperatures (ndarray[float64]) – ArrayLike structure (can be converted to numpy.NDArray) of temeperature values (K) at which energy will be computed
energy_type (Literal["helmholtz", "internal"]) – Determines which kind of energy, Helmholtz or internal, will be calculated.
states_cutoff (int) – Number of states that will be taken into account for construction of Zeeman Hamiltonian. If set to zero, all available states from the file will be used., by default 0
number_cpu (int) – Number of logical CPUs to be assigned to perform the calculation. If set to zero, all available CPUs will be used., by default 0
number_threads (int) – Number of threads used in a multithreaded implementation of linear algebra libraries used during the calculation. Higher values benefit from the increasing size of matrices (states_cutoff) over the parallelization over CPUs., by default 1
slt (str, optional) – If given the results will be saved in a group of this name to .slt file with suffix: _helmholtz_energy or _internal_energy., by default None
autotune (bool, optional) – If True the program will automatically try to choose the best number of threads (and therefore parallel processes), for the given number of CPUs, to be used during the calculation. Note that this process can take a significant amount of time, so start to use it with medium-sized calculations (e.g. for states_cutoff > 300 with dense grids or a higher number of field values) where it becomes a necessity., by default False

Returns:

The resulting eth_array gives energy in cm-1 and is in the form [temperatures, fields] - the first dimension runs over temperature values, and the second over fields.

Return type:

ndarray[float64]

Raises:

SltInputError – if energy_type is not “helmholtz” or “internal”.
SltSaveError – If the name of the group already exists in the .slt file.
SltInputError – If input ArrayLike data cannot be converted to numpy.NDArrays.
SltInputError – If fields are not a one-diemsional array
SltInputError – If temperatures are not a one-diemsional array
SltCompError – If autotuning a number of processes and threads is unsuccessful.
SltCompError – If the calculation of energy is unsuccessful.
SltFileError – If the program is unable to correctly save results to .slt file.

Note

Here, (number_cpu // number_threads) parallel processes are used to distribute the workload over the provided field values.

See also

slothpy.Compound.plot_energy

slothpy.lebedev_laikov_grid: For the description of the prescribed Lebedev-Laikov grids.

calculate_energy_3d(group, fields, grid_type, grid_number, temperatures, energy_type, states_cutoff=0, number_cpu=0, number_threads=1, rotation=None, slt=None, autotune=False, _subtract_spherical_component=False)[source]#

Calculates 3D Helmholtz or internal energy over a spherical grid for a given list of temperature and field values.

Parameters:

group (str) – Name of a group containing results of relativistic ab initio calculations used for the computation of the 3D energy.
fields (ndarray[float64]) – ArrayLike structure (can be converted to numpy.NDArray) of field values (T) at which 3D energy will be computed.
grid_type (Literal["mesh", "fibonacci"]) – Determines the type of a spherical grid used for the 3D energy simulation. Two grids can be used: a classical meshgrid and a Fibonacci sphere. The latter can only be plotted as a scatter but is uniformly distributed on the sphere, avoiding accumulation points near the poles - fewer points are needed.
grid_number (int) – Controls the density (number of points) of the angular grid for the 3D magnetisation calculation. A grid of dimension (spherical_grid* 2*spherical_grid) for spherical angles, phi [0, pi] and theta [0, 2*pi] will be used for meshgrid or when Fibonacci sphere is chosen grid_number points will be distributed on the sphere.
temperatures (ndarray[float64]) – ArrayLike structure (can be converted to numpy.NDArray) of temperature values (K) at which 3D energy will be computed.
energy_type (Literal["helmholtz", "internal"]) – Determines which kind of energy, Helmholtz or internal, will be calculated.
states_cutoff (int, optional) – Number of states that will be taken into account for construction of Zeeman Hamiltonian. If set to zero, all available states from the file will be used., by default 0,
number_cpu (int, optional) – Number of logical CPUs to be assigned to perform the calculation. If set to zero, all available CPUs will be used., by default 0
number_threads (int, optional) – Number of threads used in a multithreaded implementation of linear algebra libraries used during the calculation. Higher values benefit from the increasing size of matrices (states_cutoff) over the parallelization over CPUs., by default 1
internal_energy (bool, optional) – Turns on the calculation of internal energy., by default False
rotation (ndarray[float64], optional) – A (3,3) orthogonal rotation matrix used to rotate momenta matrices. Note that the inverse matrix has to be given to rotate the reference frame instead. It is useful here to orient your 3D plots more conveniently., by default None
slt (str, optional) – If given the results will be saved in a group of this name to .slt file with suffix: _helmholtz_energy_3d or _internal_energy_3d., by default None
autotune (bool, optional) – If True the program will automatically try to choose the best number of threads (and therefore parallel processes), for the given number of CPUs, to be used during the calculation. Note that this process can take a significant amount of time, so start to use it with medium-sized calculations (e.g. for states_cutoff > 300 with dense grids or a higher number of field values) where it becomes a necessity., by default False
_subtract_spherical_component (bool) –

Returns:

For the meshgrid the resulting energy_3d_array gives energy in cm-1 and is in the form [coordinates, fields, temperatures, mesh, mesh] - the first dimension runs over coordinates (0-x, 1-y, 2-z), the second over field values, and the third over temperatures. The last two dimensions are in the form of meshgrids over theta and phi, ready for 3D plots as xyz. For Fibonacci, the array has the form [fields, temperatures, points[x,y,z]] where points[x,y,z] are two-dimensional (grid_number, 3) arrays holding coordinates of grid_number points in the [x, y, z] convention.

Return type:

ndarray[float64]

Raises:

SltInputError – if energy_type is not “helmholtz” or “internal”.
SltSaveError – If the name of the group already exists in the .slt file.
SltInputError – If input ArrayLike data cannot be converted to numpy.NDArrays.
SltInputError – If fields are not a one-diemsional array.
SltInputError – If temperatures are not a one-diemsional array.
SltInputError – If grid_type is not “mesh” or “fibonacci”.
SltInputError – If grid_number is not a positive integer.
SltCompError – If autotuning a number of processes and threads is unsuccessful.
SltCompError – If the calculation of 3D energy is unsuccessful.
SltFileError – If the program is unable to correctly save results to .slt file.

Note

calculate_zeeman_splitting(group, number_of_states, fields, grid, states_cutoff=0, number_cpu=0, number_threads=1, average=False, slt=None, autotune=False)[source]#

Calculates directional or powder-averaged Zeeman splitting for a given number of states and list of field values.

Parameters:

group (str) – Name of a group containing results of relativistic ab initio calculations used for the computation of the Zeeman splitting.
number_of_states (int) – Number of states whose energy splitting will be given in the result array.
fields (ndarray[float64]) – ArrayLike structure (can be converted to numpy.NDArray) of field values (T) at which Zeeman splitting will be computed.
grid (ndarray[float64]) – If the grid is set to an integer from 0-11 then the prescribed Lebedev-Laikov grids over hemisphere will be used (see grids_over_hemisphere documentation) and powder-averaging will be turned on, otherwise, user can provide an ArrayLike structure (can be converted to numpy.NDArray) with the convention: [[direction_x, direction_y, direction_z, weight],…] with average = True for powder-averaging. If one wants a calculation for a list of particular directions the list has to follow the format: [[direction_x, direction_y, direction_z],…]. Custom grids will be automatically normalized.
states_cutoff (int, optional) – Number of states that will be taken into account for construction of Zeeman Hamiltonian. If set to zero, all available states from the file will be used., by default 0
number_cpu (int, optional) – Number of logical CPUs to be assigned to perform the calculation. If set to zero, all available CPUs will be used., by default 0
number_threads (int, optional) – Number of threads used in a multithreaded implementation of linear algebra libraries used during the calculation. Higher values benefit from the increasing size of matrices (states_cutoff) over the parallelization over CPUs., by default 1
average (bool, optional) – Turns on powder-averaging using a list of directions and weights in the form of ArrayLike structure: [[direction_x, direction_y, direction_z, weight],…].
slt (str, optional) – If given the results will be saved in a group of this name to .slt file with suffix: _zeeman_splitting., by default None
autotune (bool, optional) – If True the program will automatically try to choose the best number of threads (and therefore parallel processes), for the given number of CPUs, to be used during the calculation. Note that this process can take a significant amount of time, so start to use it with medium-sized calculations (e.g. for states_cutoff > 300 with dense grids or a higher number of field values) where it becomes a necessity., by default Falsee

Returns:

The resulting array gives Zeeman splitting of number_of_states energy levels in cm-1 for each direction (or average) in the form [orientations, fields, energies] - the first dimension runs over different orientations, the second over field values, and the last gives energy of number_of_states states.

Return type:

ndarray[float64]

Raises:

SltSaveError – If the name of the group already exists in the .slt file.
SltInputError – If input ArrayLike data cannot be converted to numpy.NDArrays.
SltInputError – If fields are not a one-diemsional array.
SltInputError – If number of states is not a positive integer less or equal to the states cutoff.
SltCompError – If autotuning a number of processes and threads is unsuccessful.
SltCompError – If the calculation of Zeeman splitting is unsuccessful.
SltFileError – If the program is unable to correctly save results to .slt file.

See also

slothpy.Compound.plot_zeeman

slothpy.lebedev_laikov_grid: For the description of the prescribed Lebedev-Laikov grids.

Note

Here, (number_cpu // number_threads) parallel processes are used to distribute the workload over the provided field values.

zeeman_matrix(group, fields, orientations, states_cutoff=0, rotation=None, slt=None)[source]#

Calculates Zeeman matrices for a given list of magnetic fields and their orientations.

Parameters:

group (str) – Name of a group containing results of relativistic ab initio calculations used for the computation of the Zeeman matrices.
fields (ndarray[float64]) – ArrayLike structure (can be converted to numpy.NDArray) of field values (T) for which Zeeman matrices will be computed.
orientations (ndarray[float64]) – List (ArrayLike structure) of particular magnetic field directions for which Zeeman matrices will be constructed. The list has to follow the format: [[direction_x, direction_y, direction_z],…]. The vectors will be automatically normalized.
states_cutoff (int) – Number of states that will be taken into account for construction of Zeeman Hamiltonian. If set to zero, all available states from the file will be used., by default 0
rotation (ndarray[float64], optional) – A (3,3) orthogonal rotation matrix used to rotate momenta matrices. Note that the inverse matrix has to be given to rotate the reference frame instead. It is useful here to orient your 3D plots more conveniently., by default None
slt (str, optional) – If given the results will be saved in a group of this name to .slt file with suffix: _zeeman_matrix., by default None

Returns:

The resulting array gives Zeeman matrices for each field value and orientation in the form [fields, orientations, matrix, matrix] in atomic units a.u. (Hartree).

Return type:

ndarray[complex128]

Raises:

SltSaveError – If the name of the group already exists in the .slt file.
SltInputError – If input ArrayLike data cannot be converted to numpy.NDArrays.
SltInputError – If fields are not a one-diemsional array.
SltCompError – If the calculation of Zeeman matrices is unsuccessful.
SltFileError – If the program is unable to correctly save results to .slt file.

soc_energies_cm_1(group, number_of_states=0, slt=None)[source]#

Returns energies for the given number of first spin-orbit states in cm-1.

Parameters:

group (str) – Name of a group containing results of relativistic ab initio calculations.
number_of_states (int, optional) – Number of states whose energy will be returned. If set to zero, all available states will be inculded., by default 0
slt (str, optional) – If given the results will be saved in a group of this name to .slt file with suffix: _soc_energies., by default None

Returns:

The resulting array is one-dimensional and contains the energy of first number_of_states states in cm-1.

Return type:

ndarray[float64]

Raises:

SltSaveError – If the name of the group already exists in the .slt file.
SltReadError – If the program is unable to get SOC energies from the .slt file.
SltFileError – If the program is unable to correctly save results to .slt file.

See also

slothpy.exporting.table_energy_and_g

states_magnetic_momenta(group, states=0, rotation=None, slt=None)[source]#

Calculates magnetic momenta of a given list (or number) of SOC states.

Parameters:

group (str) – Name of a group containing results of relativistic ab initio calculations used for the computation of the magnetic momenta.
states (Union[int, ndarray[int]], optional) – ArrayLike structure (can be converted to numpy.NDArray) of states indexes for which magnetic momenta will be calculated. If set to an integer it acts as a states cutoff (first n states will be given). For all available states set it to zero., by default 0
rotation (ndarray[float64], optional) – A (3,3) orthogonal rotation matrix used to rotate momenta matrices. Note that the inverse matrix has to be given to rotate the reference frame instead., by default None
slt (str, optional) – If given the results will be saved in a group of this name to .slt file with suffix: _states_magnetic_momenta., by default None

Returns:

The resulting array is one-dimensional and contains the magnetic momenta corresponding to the given states indexes in atomic units.

Return type:

ndarray[float64]

Raises:

SltSaveError – If the name of the group already exists in the .slt file.
SltInputError – If input ArrayLike data cannot be converted to numpy.NDArrays.
SltCompError – If the calculation of magnetic momenta is unsuccessful.
SltFileError – If the program is unable to correctly save results to .slt file.

states_total_angular_momenta(group, states=0, rotation=None, slt=None)[source]#

Calculates total angular momenta of a given list (or number) of SOC states.

Parameters:

group (str) – Name of a group containing results of relativistic ab initio calculations used for the computation of the magnetic momenta.
states (Union[int, ndarray[int]], optional) – ArrayLike structure (can be converted to numpy.NDArray) of states indexes for which total angular momenta will be calculated. If set to an integer it acts as a states cutoff (first n states will be given). For all available states set it to zero. , by default 0
rotation (ndarray[float64], optional) – A (3,3) orthogonal rotation matrix used to rotate momenta matrices. Note that the inverse matrix has to be given to rotate the reference frame instead., by default None
slt (str, optional) – If given the results will be saved in a group of this name to .slt file with suffix: _states_total_angular_momenta., by default None

Returns:

The resulting array is one-dimensional and contains the total angular momenta corresponding to the given states indexes in atomic units.

Return type:

ndarray[float64]

Raises:

SltSaveError – If the name of the group already exists in the .slt file.
SltInputError – If input ArrayLike data cannot be converted to numpy.NDArrays.
SltCompError – If the calculation of total angular momenta is unsuccessful.
SltFileError – If the program is unable to correctly save results to .slt file.

magnetic_momenta_matrix(group, states_cutoff=0, rotation=None, slt=None)[source]#

Calculates magnetic momenta matrix for a given number of SOC states.

Parameters:

group (str) – Name of a group containing results of relativistic ab initio calculations used for the computation of the magnetic momenta matrix.
states_cutoff (ndarray, optional) – Number of states that will be taken into account for construction of the magnetic momenta matrix. If set to zero, all available states from the file will be included., by default 0
rotation (ndarray[float64], optional) – A (3,3) orthogonal rotation matrix used to rotate momenta matrices. Note that the inverse matrix has to be given to rotate the reference frame instead., by default None
slt (str, optional) – If given the results will be saved in a group of this name to .slt file with suffix: _magnetic_momenta_matrix., by default None

Returns:

The resulting magnetic_momenta_matrix_array gives magnetic momenta in atomic units and is in the form [coordinates, matrix, matrix] - the first dimension runs over coordinates (0-x, 1-y, 2-z).

Return type:

ndarray[complex128]

Raises:

SltSaveError – If the name of the group already exists in the .slt file.
SltCompError – If the calculation of magetic momenta matrix is unsuccessful.
SltFileError – If the program is unable to correctly save results to .slt file.

total_angular_momenta_matrix(group, states_cutoff=0, rotation=None, slt=None)[source]#

Calculates total angular momenta matrix for a given number of SOC states.

Parameters:

group (str) – Name of a group containing results of relativistic ab initio calculations used for the computation of the total angular momenta matrix.
states_cutoff (ndarray, optional) – Number of states that will be taken into account for construction of the total angular momenta matrix. If set to zero, all available states from the file will be included., by default 0
rotation (ndarray[float64], optional) – A (3,3) orthogonal rotation matrix used to rotate momenta matrices. Note that the inverse matrix has to be given to rotate the reference frame instead., by default None
slt (str, optional) – If given the results will be saved in a group of this name to .slt file with suffix: _total angular_momenta_matrix., by default None

Returns:

The resulting total_angular_momenta_matrix_array gives total angular momenta in atomic units and is in the form [coordinates, matrix, matrix] - the first dimension runs over coordinates (0-x, 1-y, 2-z).

Return type:

ndarray[complex128]

Raises:

SltSaveError – If the name of the group already exists in the .slt file.
SltCompError – If the calculation of total angular momenta matrix is unsuccessful.
SltFileError – If the program is unable to correctly save results to .slt file.

matrix_decomposition_in_z_pseudo_spin_basis(group, matrix, pseudo_kind, start_state=0, stop_state=0, rotation=None, field=None, orientation=None, slt=None)[source]#

Calculates decomposition of a given matrix in “z” pseudo-spin basis.

Parameters:

group (str) – Name of a group containing results of relativistic ab initio calculations used for the construction of the matrix.
matrix (Literal["soc", "zeeman"]) – Type of a matrix to be decomposed. Two options available: “soc” or “zeeman”.
pseudo_kind (Literal["magnetic", "total_angular"]) – Kind of a pseudo-spin basis. Two options available: “magnetic” or “total_angular” for the decomposition in a particular basis.
start_state (int, optional) – Number of the first SOC state to be included., by default 0
stop_state (int, optional) – Number of the last SOC state to be included. If both start and stop are set to zero all available states from the file will be used. , by default 0
rotation (ndarray[float64], optional) – A (3,3) orthogonal rotation matrix used to rotate momenta matrices. Note that the inverse matrix has to be given to rotate the reference frame instead., by default None
field (float64, optional) – If matrix type = “zeeman” it controls a magnetic field value at which Zeeman matrix will be computed., by default None
orientation (ndarray[float64], optional) – If matrix type = “zeeman” it controls the orientation of the magnetic field and has to be in the form [direction_x, direction_y, direction_z] and be an ArrayLike structure (can be converted to numpy.NDArray)., by default None
slt (str, optional) – If given the results will be saved in a group of this name to .slt file with suffix: _magnetic/total_angular_decomposition. , by default None

Returns:

The resulting array gives decomposition in % where rows are SOC/Zeeman states and columns are associated with pseudo spin basis (from -Sz to Sz).

Return type:

ndarray[float64]

Raises:

SltSaveError – If the name of the group already exists in the .slt file.
SltCompError – If the decomposition of the matrix is unsuccessful.
SltFileError – If the program is unable to correctly save results to .slt file.

soc_crystal_field_parameters(group, start_state, stop_state, order, pseudo_kind, even_order=True, complex=False, rotation=None, slt=None)[source]#

Calculates ITO decomposition (CFPs) of SOC matrix.

Parameters:

group (str) – Name of a group containing results of relativistic ab initio calculations used for obtaining the SOC matrix.
start_state (int) – Number of the first SOC state to be included.
stop_state (int) – Number of the last SOC state to be included. If both start and stop are set to zero all available states from the file will be used.
order (int) – Order of the highest ITO (CFP) to be included in the decomposition.
pseudo_kind (Literal["magnetic", "total_angular"]) – Kind of a pseudo-spin basis. Two options available: “magnetic” or “total_angular” for the decomposition in a particular basis.
even_order (bool, optional) – If True, only even order ITOs (CFPs) will be included in the decomposition., by default True
complex (bool, optional) – If True, instead of real ITOs (CFPs) complex ones will be given., by default False
rotation (ndarray[float64], optional) – A (3,3) orthogonal rotation matrix used to rotate momenta matrices. Note that the inverse matrix has to be given to rotate the reference frame instead., by default None
slt (str, optional) – If given the results will be saved in a group of this name to .slt file with suffix: _soc_ito_decomposition., by default None

Returns:

The resulting list gives CFP - B_k_q (ITO) in the form [k,q,B_k_q].

Return type:

list

Raises:

SltSaveError – If the name of the group already exists in the .slt file.
SltReadError – If the program is unable to read SOC matrix from the file.
SltInputError – If the order exceeds 2S pseudo-spin value.
SltCompError – If the ITO decomposition of the matrix is unsuccessful.
SltFileError – If the program is unable to correctly save results to .slt file.

Note

The decomposition is obtained using a projection method described in [1] (eq. 41) employing ITOs defined in [2] (eq. 29) with a normalization factor from eq. 17.

References

[1]

L. F. Chibotaru and L. Ungur “Ab initio calculation of anisotropic magnetic properties of complexes. I. Unique definition of pseudospin Hamiltonians and their derivation” J. Chem. Phys. 137, 064112 (2012).

[2]

I. D. Ryabov “On the Generation of Operator Equivalents and the Calculation of Their Matrix Elements” J. Magn. Reson. 140, 141–145 (1999).

zeeman_matrix_ito_decpomosition(group, start_state, stop_state, field, orientation, order, pseudo_kind, complex=False, rotation=None, slt=None)[source]#

Calculates ITO decomposition of Zeeman matrix.

Parameters:

group (str) – Name of a group containing results of relativistic ab initio calculations used for obtaining the Zeeman matrix.
start_state (int) – Number of the first Zeeman state to be included.
stop_state (int) – Number of the last Zeeman state to be included. If both start and stop are set to zero all available states from the file will be used.
field (float64) – Magnetic field value at which Zeeman matrix will be computed.
orientation (ndarray[float64]) – Orientation of the magnetic field in the form of an ArrayLike structure (can be converted to numpy.NDArray) [direction_x, direction_y, direction_z].
order (int) – Order of the highest ITO (CFP) to be included in the decomposition.
pseudo_kind (Literal["magnetic", "total_angular"]) – Kind of a pseudo-spin basis. Two options available: “magnetic” or “total_angular” for the decomposition in a particular basis.
complex (bool, optional) – If True, instead of real ITOs (CFPs) complex ones will be given., by default False
rotation (ndarray[float64], optional) – A (3,3) orthogonal rotation matrix used to rotate momenta matrices. Note that the inverse matrix has to be given to rotate the reference frame instead., by default None
slt (str, optional) – If given the results will be saved in a group of this name to .slt file with suffix: _zeeman_ito_decomposition., by default None

Returns:

The resulting list gives ITOs - B_k_q in the form [k,q,B_k_q]

Return type:

list

Raises:

SltSaveError – If the name of the group already exists in the .slt file.
SltCompError – If the program is unable to calculate Zeeman matrix from the file.
SltInputError – If the order exceeds 2S pseudo-spin value
SltCompError – If the ITO decomposition of the matrix is unsuccessful
SltFileError – If the program is unable to correctly save results to .slt file.

Note

The decomposition is obtained using a projection method described in [1] (eq. 41) employing ITOs defined in [2] (eq. 29) with a normalization factor from eq. 17.

References

[1]

[2]

I. D. Ryabov “On the Generation of Operator Equivalents and the Calculation of Their Matrix Elements” J. Magn. Reson. 140, 141–145 (1999).

matrix_from_ito(full_group_name, complex, dataset_name=None, pseudo_spin=None, slt=None)[source]#

Calculates matrix from a given ITO decomposition.

Parameters:

full_group_name (str) – Full name of a group containing ITO decomposition.
complex (bool) – Determines the type of ITOs in the dataset. If True, instead of real ITOs complex ones will be used., by default False
dataset_name (str, optional) – A custom name for a user-created dataset within the group that contains list of B_k_q parameters in the form [k,q,B_k_q]., by default None
pseudo_spin (float64, optional) – Pseudo spin S value for the user-defined dataset., by default None
slt (str, optional) – If given the results will be saved in a group of this name to .slt file with suffix: _matrix_from_ito., by default None

Returns:

Matrix reconstructed from a given ITO list.

Return type:

ndarray[complex128]

Raises:

SltSaveError – If the name of the group already exists in the .slt file.
SltCompError – If the calculation of the matrix from ITOs is unsuccessful.
SltFileError – If the program is unable to correctly save results to .slt file.

Note

ITOs defined in [2] (eq. 29) with a normalization factor from eq. 17 are used.

References

[1]

I. D. Ryabov “On the Generation of Operator Equivalents and the Calculation of Their Matrix Elements” J. Magn. Reson. 140, 141–145 (1999).

soc_zeem_in_z_angular_magnetic_momentum_basis(group, start_state, stop_state, matrix_type, basis_kind, rotation=None, field=None, orientation=None, slt=None)[source]#

Calculates SOC or Zeeman matrix in “z” magnetic or total angular momentum basis.

Parameters:

group (str) – Name of a group containing results of relativistic ab initio calculations used for obtaining the SOC or Zeeman matrix.
start_state (int) – Number of the first SOC state to be included.
stop_state (int) – Number of the last SOC state to be included. If both start and stop are set to zero all available states from the file will be used
matrix_type (Literal["soc", "zeeman"]) – Type of a matrix to be decomposed. Two options available: “soc” or “zeeman”.
basis_kind (Literal["magnetic", "total_angular"]) – Kind of a basis. Two options available: “magnetic” or “total_angular” for the decomposition in a particular basis
rotation (ndarray[float64], optional) – A (3,3) orthogonal rotation matrix used to rotate momenta matrices. Note that the inverse matrix has to be given to rotate the reference frame instead., by default None
field (float64, optional) – _description_, by default None
orientation (ndarray[float64], optional) – Orientation of the magnetic field in the form of an ArrayLike structure (can be converted to numpy.NDArray) [direction_x, direction_y, direction_z]., by default None
slt (str, optional) – If given the results will be saved in a group of this name to .slt file with suffix: _{matrix_type}_matrix_in_{basis_kind}_basis., by default None

Returns:

Matrix in a given kind of basis.

Return type:

ndarray[complex128]

Raises:

SltInputError – If an unsuported type of matrix or basis is provided.
SltInputError – If there is no field value or orientation provided for Zeeman matrix.
SltSaveError – If the name of the group already exists in the .slt file.
SltCompError – If the calculation of a matrix in “z” basis is unsuccessful.
SltFileError – If the program is unable to correctly save results to .slt file.

plot_magnetisation(group, show_fig=True, save=False, save_path='.', save_name=None, color_map_name='rainbow', xlim=(), ylim=(), xticks=1, yticks=0, field='B')[source]#

Creates graphs of M(H,T) given a name of the group in .slt file, graphs can be optionally shown, saved, color palettes can be changed.

Parameters:

group (str) – Name of a group from .slt file for which a plot will be created.
show_fig (bool = True) – Determines if plot is shown. Possible use: saving many plots automatically without preview.
save (bool = False) – Determines if the plot is saved.
save_path (str = ".") – Determines a path where the file will be saved if save = True.
save_name (str = None) – Determines name of the file that would be created if save = True, if left empty it will use the following format: “magnetisation_ {group}.tiff”.
color_map_name (str or list[str] = "rainbow") – Input of the color_map function.
xlim (tuple(optional: float, optional: float) = ()) – Determines the lower and upper limit of the x-axis if two floats are passed, or just the upper limit if one is passed.
ylim (tuple(optional: float, optional: float) = ()) – Determines the lower and upper limit of the y-axis if two floats are passed, or just the upper limit if one is passed.
xticks (int or float = 1) – Determines the frequency of x major ticks.
yticks (int or float = 0) – Determines the frequency of y major ticks.
field (Literal['B','H'] = 'B') – Determines the field unit - B[T] or H[kOe].

Return type:

Nothing

Raises:

SltFileError – If unable to load the data file. Most likely encountered if the group name is incorrect.
SltPlotError – If unable to create the plot.
SltSaveError – If unable to save the plot as an image.

plot_susceptibility(group, show_fig=True, save=False, save_path='.', save_name=None, color_map_name='funmat', xlim=(), ylim=(), xticks=100, yticks=0, field='B')[source]#

Creates graphs of chiT(H,T) or chi(H,T) depending on the content of .slt file, given a name of the group in .slt file, graphs can be optionally saved, color palettes can be changed.

Parameters:

group (str) – Name of a group from .slt file for which a plot will be created.
show_fig (bool = True) – Determines if plot is shown. Possible use: saving many plots automatically without preview.
save (bool = False) – Determines if the plot is saved.
save_path (str = ".") – Determines a path where the file will be saved if save = True.
save_name (str = None) – Determines name of the file that would be created if save = True, if left empty it will use the following format: “susceptibility_{group}.tiff”.
color_map_name (str or list[str] = 'funmat') – Input of color_map function.
xlim (tuple(optional: float, optional: float) = ()) – Determines the lower and upper limit of the x-axis if two floats are passed, or just the upper limit if one is passed.
ylim (tuple(optional: float, optional: float) = ()) – Determines the lower and upper limit of the y-axis if two floats are passed, or just the upper limit if one is passed.
xticks (int or float = 100) – Determines the frequency of x major ticks.
yticks (int or float = 0) – Determines the frequency of y major ticks.
field (Literal['B','H'] = 'B') – Determines the field unit - B[T] or H[kOe].

Return type:

Nothing

Raises:

SltFileError – If unable to load the data file. Most likely encountered if the group name is incorrect.
SltPlotError – If unable to create the plot.
SltSaveError – If unable to save the plot as an image.

plot_energy(group, energy_type, show_fig=True, save=False, save_path='.', save_name=None, color_map_name='PrOr', xlim=(), ylim=(), xticks=1, yticks=0, field='B')[source]#

Creates graphs of Helmholtz energy F(T,H) or internal energy U(T,H) given a name of the group in .slt file, graphs can be optionally saved, color palettes can be changed.

Parameters:

group (str) – Name of a group from .slt file for which a plot will be created.
energy_type (Literal["helmholtz", "internal"]) – Determines which kind of energy, Helmholtz or internal, will be calculated.
show_fig (bool = True) – Determines if plot is shown. Possible use: saving many plots automatically without preview.
save (bool = False) – Determines if the plot is saved.
save_path (str = ".") – Determines a path where the file will be saved if save = True.
save_name (str = None) – Determines name of the file that would be created if save = True, if left empty it will use following format: “{energy_type}_ energy_{group}.tiff”.
color_map_name (str or list[str] = 'PrOr') – Input of the color_map function.
xlim (tuple(optional: float, optional: float) = ()) – Determines the lower and upper limit of the x-axis if two floats are passed, or just the upper limit if one is passed.
ylim (tuple(optional: float, optional: float) = ()) – Determines the lower and upper limit of the y-axis if two floats are passed, or just the upper limit if one is passed.
xticks (int or float = 100) – Determines the frequency of x major ticks.
yticks (int = 0) – Determines the freqency of y major ticks.
field (Literal['B','H'] = 'B') – Determines the field unit - B[T] or H[kOe].

Return type:

Nothing

Raises:

SltFileError – If unable to load the data file. Most likely encountered if the group name is incorrect.
SltPlotError – If unable to create plot.
SltSaveError – If unable to save plot as image.

See also

slothpy.Compound.calculate_energy

plot_zeeman(group, show_fig=True, save=False, save_path='.', save_name=None, color_map_name1='BuPi', color_map_name2='BuPi_r', single=False, xlim=(), ylim=(), xticks=1, yticks=0, field='B')[source]#

Function that creates graphs of E(H,orientation) given a name of the group in .slt file, graphs can be optionally saved, color palettes can be changed.

Parameters:

group (str) – Name of a group from .slt file for which plot will be created.
show_fig (bool = True) – Determines if plot is shown. Possible use: saving many plots automatically without preview.
save (bool = False) – Determines if the plot is saved.
save_path (str = ".") – Determines a path where the file will be saved if save = True.
save_name (str = None) – Determines name of the file that would be created if save = True, if left empty it will use following format: f”zeeman_{group}.tiff” or f”zeeman_{group}_{orientation[i]}.tiff”.
color_map_name1 (str or list[str] = 'BuPi') – Input of the color_map function, determines a color of the lower set of split lines.
color_map_name2 (str or list[str] = 'BuPi_r') – Input of the color_map function, determines a color of the higher set of split lines.
single (bool = False) – Determines if all orientations are plotted together if plot is not a result of averaging.
xlim (tuple of 1-2 floats = ()) – Determines the lower and upper limit of x-axis if two floats are passed, or just the upper limit if one is passed.
ylim (tuple of 1-2 floats = ()) – Determines the lower and upper limit of y-axis if two floats are passed, or just the upper limit if one is passed.
xticks (int or float = 1) – Determines the frequency of x major ticks.
yticks (int or float = 0) – Determines the frequency of y major ticks.
field (Literal['B','H'] = 'B') – Determines the field unit - B[T] or H[kOe].

Return type:

Nothing

Raises:

SltFileError – If unable to load data file. Most likely encountered if the group name is incorrect.
SltPlotError – If unable to create the plot.
SltSaveError – If unable to save the plot as an image.

plot_3d(group, data_type, field_i, temp_i, show_fig=True, save=False, save_path='.', save_name=None, color_map_name='dark_rainbow_r_l', round_temp=3, round_field=3, lim_scalar=1.0, ticks=1.0, plot_title=None, field='B', r_density=0, c_density=0, points_size=0.2, solid_surface=False, elev=30, azim=-60, roll=0, axis_off=False, add_g_tensor_axes=False, axes_group='', axes_colors=['r', 'g', 'b'], doublet_number=None, axes_scale_factor=1.0, rotation=None)[source]#

Creates 3d plots of data dependent on field B[T] and temperature T[K].

Parameters:

group (str) – Name of a group from .slt file for which a plot will be created.
data_type (Literal["chit", "chi", "helmholtz_energy", "internal_energy",) –

“magnetisation”]
Type of the data that will be used to create plot.
field_i (int) – Index of the field from dataset that will be used for the plot.
temp_i (int) – Index of the temperature from the dataset that will be used for the plot.
show_fig (bool = True) – Determines if plot is shown. Possible use: saving many plots automatically without preview.
save (bool = False) – Determines if the plot is saved.
save_path (str = ".") – Determines path where file will be saved if save = True.
save_name (str = None) – Determines name of a file that would be created if save = True, if left empty it will use following format: f”{group}_3d_{data_type}.tiff”.
color_map_name (str or list[str] = 'dark_rainbow_r_l') – Input of the color_map function.
round_temp (int = 3) – Determines how many digits will be rounded in the graph’s title for temperature.
round_field (int = 3) – Determines how many digits will be rounded in the graph’s title for field.
lim_scalar (float = 1.) – Scalar used to set limits of the axes, smaller values magnify the plotted figure.
ticks (float = 1.) – Frequency of the ticks on all axes.
plot_title (str = None) – Determines the title of the figure, if left blank automatic title is used.
field (Literal['B','H'] = 'B') – Determines the field unit - B[T] or H[kOe].
r_density (int = 0) – Determines the rcount of a 3D plot.
c_density (int = 0) – Determines the ccount of a 3D plot.
points_size (float = 0.2) – Determines points size for Fibonacci scatter plots.
solid_surface (bool = False) – Makes surface plots using meshgrid appear as solid.
elev (int = 30) – Determines an angle between a viewing position and the xy plane.
azim (int = -60) – Determines a rotation of a viewing position in relation to z axis.
roll (int = 0) – Determines a rotation of camera around the viewing (position) axis.
axis_off (bool = False) – Determines if the axes are turned off.
add_g_tensor_axes (bool = False) – Determines if add to the plot main magnetic axes scaled by the corresponding pseudo-g-tensor values.
axes_group (str = "") – Name of a group from calculate_g_tensor_axes method from .slt file.
axes_colors (list[str] = ['r','g','b']) – Determines the colors of the magnetic axes in order of x, y, z. Accepts matplotlib colors inputs, for example HTML color codes.
doublet_number (int = None) – Number of a doublet for which axes will be added to the plot.
axes_scale_factor (float64 = 1.0) – Scale factor determining the length of the longest (main) magnetic axis concerning the maximal value of the loaded data and setting a maximal limit of the plot’s xyz axes. It should be set > 1 otherwise, some data will end up missing from the plot! The limit is max(loaded_data) * axes_scale_factor.
rotation (ndarray[float64] = None) – Has to be given if 3d data was calculated with optional rotation of the coordinate frame and add_g_tensor_axes option is turned on. One must provide the same rotation as that used for the simulation to apply it to the magnetic axes.

Return type:

Nothing

Raises:

SltFileError – If unable to load data file. Most likely encountered if the group name is incorrect.
SltPlotError – If unable to create the plot.
SltSaveError – If unable to save the plot as an image.

animate_3d(group, data_type, animation_variable, filename, i_start=0, i_end=-1, i_constant=0, color_map_name='dark_rainbow_r_l', lim_scalar=1.0, ticks=1, plot_title=None, field='B', r_density=0, c_density=0, points_size=0.2, solid_surface=False, axis_off=False, fps=15, dpi=300, bar=True, bar_scale=False, bar_color_map_name='dark_rainbow_r', temp_rounding=0, field_rounding=0, elev=30, azim=-60, roll=0, add_g_tensor_axes=False, axes_group='', axes_colors=['r', 'g', 'b'], doublet_number=None, axes_scale_factor=1.0, rotation=None)[source]#

Creates animations of 3d plots dependent on field B[T] and temperature T[K].

Parameters:

group (str) – Name of a group from .slt file for which plot will be created.
data_type (Literal["chit", "chi", "helmholtz_energy", "internal_energy",) –

“magnetisation”]
Type of data that will be used to create plot.
animation_variable (Literal["temperature", "field"]) – Variable changing during animation, can take one of two values: temperature or field.
filename (str) – Name of the output .gif file.
i_start (int = 0) – Index of first frame’s field/temperature.
i_end (int = -1) – Index of last frame’s field/temperature.
i_constant (int) – Index of constant temperature/field.
color_map_name (str or list = 'dark_rainbow_r_l') – Input of color_map function, determines color of main figure.
lim_scalar (float = 1.) – Scalar used to set limits of axes, smaller values magnify plotted figure.
ticks (float = 1) – Determines the ticks spacing.
plot_title (str = None) – Determines the title of the figure, if left blank automatic title is used.
field (Literal['B','H'] = 'B') – Determines the field unit - B[T] or H[kOe].
r_density (int = 0) – Determines rcount of 3D plot.
c_density (int = 0) – Determines ccount of 3D plot.
points_size (float = 0.2) – Determines points size for Fibonacci scatter plots.
solid_surface (bool = False) – Makes surface plots using meshgrid appear as solid.
axis_off (bool = False) – Determines if axes are turned off.
fps (int) – Number of frames per second in animation.
dpi (int) – Dots per inch resolution of frames.
bar (bool = True) – Determines if bar representing animation variable is shown.
bar_scale (bool = False) – Determines if a scale should be shown for bar.
bar_color_map_name (str or list = 'dark_rainbow_r_l') – Input of the color_map function, determines the color of the bar.
temp_rounding (int = 0) – Determines how many decimal places are shown in bar/plot labels for temperatures.
field_rounding (int = 0) – Determines how many decimal places are shown in bar/plot labels for fields.
elev (int = 30) – Determines an angle between a viewing position and the xy plane.
azim (int = -60) – Determines a rotation of a viewing position in ralation to z axis.
roll (int = 0) – Determines a rotation of camera around the viewing (position) axis.
add_g_tensor_axes (bool = False) – Determines if add to the plot main magnetic axes scaled by the corresponding pseudo-g-tensor values.
axes_group (str = "") – Name of a group from calculate_g_tensor_axes method from .slt file.
axes_colors (list[str] = ['r','g','b']) – Determines the colors of the magnetic axes in order of x, y, z. Accepts matplotlib colors inputs, for example HTML color codes.
doublet_number (int = None) – Number of a doublet for which axes will be added to the plot.
axes_scale_factor (float64 = 1.0) – Scale factor determining the length of the longest (main) magnetic axis concerning the maximal value of the loaded data and setting a maximal limit of the plot’s xyz axes. It should be set > 1 otherwise, some data will end up missing from the plot! The limit is max(loaded_data) * axes_scale_factor.
rotation (ndarray[float64] = None) – Has to be given if 3d data was calculated with optional rotation of the coordinate frame and add_g_tensor_axes option is turned on. One must provide the same rotation as that used for the simulation to apply it to the magnetic axes.

Return type:

Nothing

Raises:

SltFileError – If unable to load data file. Most likely encountered if the group name is incorrect.
SltPlotError – If unable to create the plot.

interactive_plot_3d(group, data_type, color_map_name='dark_rainbow_r', T_slider_color='#77f285', B_slider_color='#794285', temp_bar_color_map_name='BuRd', field_bar_color_map_name='BuPi', lim_scalar=1.0, ticks=1, field='B', points_size=0.2, solid_surface=False, bar=True, bar_scale=False, temp_rounding=2, field_rounding=2, axis_off=False, add_g_tensor_axes=False, axes_group='', axes_colors=['r', 'g', 'b'], doublet_number=None, axes_scale_factor=1.0, rotation=None)[source]#

Creates interactive widget plot dependent on field and temperature values.

Parameters:

group (str) – Name of a group from .slt file for which plot will be created.
data_type (Literal["chit", "chi", "helmholtz_energy", "internal_energy",) –

“magnetisation”]
Type of the data that will be used to create the plot.
color_map_name (str or list = 'dark_rainbow_r_l') – Input of the color_map function, determines a color of the main figure.
T_slider_color (str) – Determines a color of the temperature slider.
B_slider_color (str) – Determines a color of the field slider.
temp_bar_color_map_name (str or list[str] = 'BuRd') – Input of the color_map function, determines a color map of the temperature bar.
field_bar_color_map_name (str or list[str] = 'BuPi') – Input of the color_map function, determines a color map of the field bar.
lim_scalar (float = 1.) – Scalar used to set limits of the axes, smaller values magnify the plotted figure.
ticks (float = 1) – Determines the ticks spacing.
field (Literal['B','H'] = 'B') – Determines the field unit - B[T] or H[kOe].
points_size (float = 0.2) – Determines points size for Fibonacci scatter plots.
solid_surface (bool = False) – Makes surface plots using meshgrid appear as solid.
bar (bool = True) – Determines if the bar is shown.
bar_scale (bool = False) – Determines if the bar scale is shown.
temp_rounding (int = 2) – Determines how many significant digits are shown relative to the int(value) for temperature.
temp_rounding – Determines how many significant digits are shown relative to the int(value) for temperature.
field_rounding (int = 2) – Determines how many significant digits are shown relative to the int(value) for field.
axis_off (bool = False) – Determines if the axes are turned off.
add_g_tensor_axes (bool = False) – Determines if add to the plot main magnetic axes scaled by the corresponding pseudo-g-tensor values.
axes_group (str = "") – Name of a group from calculate_g_tensor_axes method from .slt file.
axes_colors (list[str] = ['r','g','b']) – Determines the colors of the magnetic axes in order of x, y, z. Accepts matplotlib colors inputs, for example HTML color codes.
doublet_number (int = None) – Number of a doublet for which axes will be added to the plot.
axes_scale_factor (float64 = 1.0) – Scale factor determining the length of the longest (main) magnetic axis concerning the maximal value of the loaded data and setting a maximal limit of the plot’s xyz axes. It should be set > 1 otherwise, some data will end up missing from the plot! The limit is max(loaded_data) * axes_scale_factor.
rotation (ndarray[float64] = None) – Has to be given if 3d data was calculated with optional rotation of the coordinate frame and add_g_tensor_axes option is turned on. One must provide the same rotation as that used for the simulation to apply it to the magnetic axes.

Return type:

Nothing

Raises:

SltFileError – If unable to load the data file. Most likely encountered if the group name is incorrect.
SltPlotError – If unable to create the plot.

Table of Contents

Compound#