# coding: utf-8
# Copyright (c) Pymatgen Development Team.
# Distributed under the terms of the MIT License.
"""
This module implements a simple algorithm for extracting nearest neighbor
exchange parameters by mapping low energy magnetic orderings to a Heisenberg
model.
"""
import logging
import sys
from ast import literal_eval
import copy
import numpy as np
import pandas as pd
from monty.serialization import dumpfn
from monty.json import MSONable, jsanitize
from pymatgen.analysis.magnetism import CollinearMagneticStructureAnalyzer, Ordering
from pymatgen.analysis.graphs import StructureGraph
from pymatgen.analysis.local_env import MinimumDistanceNN
from pymatgen.symmetry.analyzer import SpacegroupAnalyzer
from pymatgen import Structure
__author__ = "ncfrey"
__version__ = "0.1"
__maintainer__ = "Nathan C. Frey"
__email__ = "ncfrey@lbl.gov"
__status__ = "Development"
__date__ = "June 2019"
[docs]class HeisenbergMapper:
"""
Class to compute exchange parameters from low energy magnetic orderings.
"""
def __init__(self, ordered_structures, energies, cutoff=0.0, tol=0.02):
"""
Exchange parameters are computed by mapping to a classical Heisenberg
model. Strategy is the scheme for generating neighbors. Currently only
MinimumDistanceNN is implemented.
n+1 unique orderings are required to compute n exchange
parameters.
First run a MagneticOrderingsWF to obtain low energy collinear magnetic
orderings and find the magnetic ground state. Then enumerate magnetic
states with the ground state as the input structure, find the subset
of supercells that map to the ground state, and do static calculations
for these orderings.
Args:
ordered_structures (list): Structure objects with magmoms.
energies (list): Total energies of each relaxed magnetic structure.
cutoff (float): Cutoff in Angstrom for nearest neighbor search.
Defaults to 0 (only NN, no NNN, etc.)
tol (float): Tolerance (in Angstrom) on nearest neighbor distances
being equal.
Parameters:
strategy (object): Class from pymatgen.analysis.local_env for
constructing graphs.
sgraphs (list): StructureGraph objects.
unique_site_ids (dict): Maps each site to its unique numerical
identifier.
wyckoff_ids (dict): Maps unique numerical identifier to wyckoff
position.
nn_interacations (dict): {i: j} pairs of NN interactions
between unique sites.
dists (dict): NN, NNN, and NNNN interaction distances
ex_mat (DataFrame): Invertible Heisenberg Hamiltonian for each
graph.
ex_params (dict): Exchange parameter values (meV/atom)
"""
# Save original copies of inputs
self.ordered_structures_ = ordered_structures
self.energies_ = energies
# Sanitize inputs and optionally order them by energy / magnetic moments
hs = HeisenbergScreener(ordered_structures, energies, screen=False)
ordered_structures = hs.screened_structures
energies = hs.screened_energies
self.ordered_structures = ordered_structures
self.energies = energies
self.cutoff = cutoff
self.tol = tol
# Get graph representations
self.sgraphs = self._get_graphs(cutoff, ordered_structures)
# Get unique site ids and wyckoff symbols
self.unique_site_ids, self.wyckoff_ids = self._get_unique_sites(
ordered_structures[0]
)
# These attributes are set by internal methods
self.nn_interactions = None
self.dists = None
self.ex_mat = None
self.ex_params = None
# Check how many commensurate graphs we found
if len(self.sgraphs) < 2:
print("We need at least 2 unique orderings.")
sys.exit(1)
else: # Set attributes
self._get_nn_dict()
self._get_exchange_df()
@staticmethod
def _get_graphs(cutoff, ordered_structures):
"""
Generate graph representations of magnetic structures with nearest
neighbor bonds. Right now this only works for MinimumDistanceNN.
Args:
cutoff (float): Cutoff in Angstrom for nearest neighbor search.
ordered_structures (list): Structure objects.
Returns:
sgraphs (list): StructureGraph objects.
"""
# Strategy for finding neighbors
if cutoff:
strategy = MinimumDistanceNN(cutoff=cutoff, get_all_sites=True)
else:
strategy = MinimumDistanceNN() # only NN
# Generate structure graphs
sgraphs = [
StructureGraph.with_local_env_strategy(s, strategy=strategy)
for s in ordered_structures
]
return sgraphs
@staticmethod
def _get_unique_sites(structure):
"""
Get dict that maps site indices to unique identifiers.
Args:
structure (Structure): ground state Structure object.
Returns:
unique_site_ids (dict): maps tuples of equivalent site indices to a
unique int identifier
wyckoff_ids (dict): maps tuples of equivalent site indices to their
wyckoff symbols
"""
# Get a nonmagnetic representation of the supercell geometry
s0 = CollinearMagneticStructureAnalyzer(
structure, make_primitive=False, threshold=0.0
).get_nonmagnetic_structure(make_primitive=False)
# Get unique sites and wyckoff positions
if "wyckoff" in s0.site_properties:
s0.remove_site_property("wyckoff")
symm_s0 = SpacegroupAnalyzer(s0).get_symmetrized_structure()
wyckoff = ["n/a"] * len(symm_s0)
equivalent_indices = symm_s0.equivalent_indices
wyckoff_symbols = symm_s0.wyckoff_symbols
# Construct dictionaries that map sites to numerical and wyckoff
# identifiers
unique_site_ids = {}
wyckoff_ids = {}
i = 0
for indices, symbol in zip(equivalent_indices, wyckoff_symbols):
unique_site_ids[tuple(indices)] = i
wyckoff_ids[i] = symbol
i += 1
for index in indices:
wyckoff[index] = symbol
return unique_site_ids, wyckoff_ids
def _get_nn_dict(self):
"""Get dict of unique nearest neighbor interactions.
Returns:
None: (sets self.nn_interactions and self.dists instance variables)
"""
tol = self.tol # tolerance on NN distances
sgraph = self.sgraphs[0]
unique_site_ids = self.unique_site_ids
nn_dict = {}
nnn_dict = {}
nnnn_dict = {}
all_dists = []
# Loop over unique sites and get neighbor distances up to NNNN
for k in unique_site_ids:
i = k[0]
i_key = unique_site_ids[k]
connected_sites = sgraph.get_connected_sites(i)
dists = [round(cs[-1], 2) for cs in connected_sites] # i<->j distances
dists = sorted(list(set(dists))) # NN, NNN, NNNN, etc.
dists = dists[:3] # keep up to NNNN
all_dists += dists
# Keep only up to NNNN and call dists equal if they are within tol
all_dists = sorted(list(set(all_dists)))
rm_list = []
for idx, d in enumerate(all_dists[:-1]):
if abs(d - all_dists[idx + 1]) < tol:
rm_list.append(idx + 1)
all_dists = [d for idx, d in enumerate(all_dists) if idx not in rm_list]
if len(all_dists) < 3: # pad with zeros
all_dists += [0.0] * (3 - len(all_dists))
all_dists = all_dists[:3]
labels = ["nn", "nnn", "nnnn"]
dists = {l: d for (l, d) in zip(labels, all_dists)}
# Get dictionary keys for interactions
for k in unique_site_ids:
i = k[0]
i_key = unique_site_ids[k]
connected_sites = sgraph.get_connected_sites(i)
# Loop over sites and determine unique NN, NNN, etc. interactions
for cs in connected_sites:
dist = round(cs[-1], 2) # i_j distance
j = cs[2] # j index
for key in unique_site_ids.keys():
if j in key:
j_key = unique_site_ids[key]
if abs(dist - dists["nn"]) <= tol:
nn_dict[i_key] = j_key
elif abs(dist - dists["nnn"]) <= tol:
nnn_dict[i_key] = j_key
elif abs(dist - dists["nnnn"]) <= tol:
nnnn_dict[i_key] = j_key
nn_interactions = {"nn": nn_dict, "nnn": nnn_dict, "nnnn": nnnn_dict}
self.dists = dists
self.nn_interactions = nn_interactions
def _get_exchange_df(self):
"""
Loop over all sites in a graph and count the number and types of
nearest neighbor interactions, computing +-|S_i . S_j| to construct
a Heisenberg Hamiltonian for each graph.
Returns:
None: (sets self.ex_mat instance variable)
TODO:
* Deal with large variance in |S| across configs
"""
sgraphs = self.sgraphs
tol = self.tol
unique_site_ids = self.unique_site_ids
nn_interactions = self.nn_interactions
dists = self.dists
# Get |site magmoms| from FM ordering so that S_i and S_j are consistent?
# Large S variations is throwing a loop
# fm_struct = self.get_low_energy_orderings()[0]
# Total energy and nonmagnetic energy contribution
columns = ["E", "E0"]
# Get labels of unique NN interactions
for k0, v0 in nn_interactions.items():
for i, j in v0.items(): # i and j indices
c = str(i) + "-" + str(j) + "-" + str(k0)
c_rev = str(j) + "-" + str(i) + "-" + str(k0)
if c not in columns and c_rev not in columns:
columns.append(c)
num_sgraphs = len(sgraphs)
# Keep n interactions (not counting 'E') for n+1 structure graphs
columns = columns[: num_sgraphs + 1]
num_nn_j = len(columns) - 1 # ignore total energy
j_columns = [name for name in columns if name not in ["E", "E0"]]
ex_mat_empty = pd.DataFrame(columns=columns)
ex_mat = ex_mat_empty.copy()
if len(j_columns) < 2:
self.ex_mat = ex_mat # Only <J> can be calculated here
else:
sgraphs_copy = copy.deepcopy(sgraphs)
sgraph_index = 0
# Loop over all sites in each graph and compute |S_i . S_j|
# for n+1 unique graphs to compute n exchange params
for graph in sgraphs:
sgraph = sgraphs_copy.pop(0)
ex_row = pd.DataFrame(
np.zeros((1, num_nn_j + 1)), index=[sgraph_index], columns=columns
)
for i, node in enumerate(sgraph.graph.nodes):
# s_i_sign = np.sign(sgraph.structure.site_properties['magmom'][i])
s_i = sgraph.structure.site_properties["magmom"][i]
for k in unique_site_ids.keys():
if i in k:
i_index = unique_site_ids[k]
# Get all connections for ith site and compute |S_i . S_j|
connections = sgraph.get_connected_sites(i)
# dists = [round(cs[-1], 2) for cs in connections] # i<->j distances
# dists = sorted(list(set(dists))) # NN, NNN, NNNN, etc.
for j, connection in enumerate(connections):
j_site = connection[2]
dist = round(connection[-1], 2) # i_j distance
# s_j_sign = np.sign(sgraph.structure.site_properties['magmom'][j_site])
s_j = sgraph.structure.site_properties["magmom"][j_site]
for k in unique_site_ids.keys():
if j_site in k:
j_index = unique_site_ids[k]
# Determine order of connection
if abs(dist - dists["nn"]) <= tol:
order = "-nn"
elif abs(dist - dists["nnn"]) <= tol:
order = "-nnn"
elif abs(dist - dists["nnnn"]) <= tol:
order = "-nnnn"
j_ij = str(i_index) + "-" + str(j_index) + order
j_ji = str(j_index) + "-" + str(i_index) + order
if j_ij in ex_mat.columns:
ex_row.at[sgraph_index, j_ij] -= s_i * s_j
elif j_ji in ex_mat.columns:
ex_row.at[sgraph_index, j_ji] -= s_i * s_j
# Ignore the row if it is a duplicate to avoid singular matrix
if ex_mat.append(ex_row)[j_columns].equals(
ex_mat.append(ex_row)[j_columns].drop_duplicates(keep="first")
):
e_index = self.ordered_structures.index(sgraph.structure)
ex_row.at[sgraph_index, "E"] = self.energies[e_index]
sgraph_index += 1
ex_mat = ex_mat.append(ex_row)
# if sgraph_index == num_nn_j: # check for zero columns
# zeros = [b for b in (ex_mat[j_columns] == 0).all(axis=0)]
# if True in zeros:
# sgraph_index -= 1 # keep looking
ex_mat[j_columns] = ex_mat[j_columns].div(
2.0
) # 1/2 factor in Heisenberg Hamiltonian
ex_mat[["E0"]] = 1 # Nonmagnetic contribution
# Check for singularities and delete columns with all zeros
zeros = [b for b in (ex_mat == 0).all(axis=0)]
if True in zeros:
c = ex_mat.columns[zeros.index(True)]
ex_mat = ex_mat.drop(columns=[c], axis=1)
# ex_mat = ex_mat.drop(ex_mat.tail(len_zeros).index)
# Force ex_mat to be square
ex_mat = ex_mat[: ex_mat.shape[1] - 1]
self.ex_mat = ex_mat
[docs] def get_exchange(self):
"""
Take Heisenberg Hamiltonian and corresponding energy for each row and
solve for the exchange parameters.
Returns:
ex_params (dict): Exchange parameter values (meV/atom).
"""
ex_mat = self.ex_mat
# Solve the matrix equation for J_ij values
E = ex_mat[["E"]]
j_names = [j for j in ex_mat.columns if j not in ["E"]]
# Only 1 NN interaction
if len(j_names) < 3:
# Estimate exchange by J ~ E_AFM - E_FM
j_avg = self.estimate_exchange()
ex_params = {"<J>": j_avg}
self.ex_params = ex_params
return ex_params
# Solve eigenvalue problem for more than 1 NN interaction
H = ex_mat.loc[:, ex_mat.columns != "E"].values
H_inv = np.linalg.inv(H)
j_ij = np.dot(H_inv, E)
# Convert J_ij to meV
j_ij[1:] *= 1000 # J_ij in meV
j_ij = j_ij.tolist()
ex_params = {j_name: j[0] for j_name, j in zip(j_names, j_ij)}
self.ex_params = ex_params
return ex_params
[docs] def get_low_energy_orderings(self):
"""
Find lowest energy FM and AFM orderings to compute E_AFM - E_FM.
Returns:
fm_struct (Structure): fm structure with 'magmom' site property
afm_struct (Structure): afm structure with 'magmom' site property
fm_e (float): fm energy
afm_e (float): afm energy
"""
fm_struct, afm_struct = None, None
mag_min = np.inf
mag_max = 0.001
fm_e_min = 0
afm_e_min = 0
# epas = [e / len(s) for (e, s) in zip(self.energies, self.ordered_structures)]
for s, e in zip(self.ordered_structures, self.energies):
ordering = CollinearMagneticStructureAnalyzer(
s, threshold=0.0, make_primitive=False
).ordering
magmoms = s.site_properties["magmom"]
# Try to find matching orderings first
if ordering == Ordering.FM and e < fm_e_min:
fm_struct = s
mag_max = abs(sum(magmoms))
fm_e = e
fm_e_min = e
if ordering == Ordering.AFM and e < afm_e_min:
afm_struct = s
afm_e = e
mag_min = abs(sum(magmoms))
afm_e_min = e
# Brute force search for closest thing to FM and AFM
if not fm_struct or not afm_struct:
for s, e in zip(self.ordered_structures, self.energies):
magmoms = s.site_properties["magmom"]
if abs(sum(magmoms)) > mag_max: # FM ground state
fm_struct = s
fm_e = e
mag_max = abs(sum(magmoms))
# AFM ground state
if abs(sum(magmoms)) < mag_min:
afm_struct = s
afm_e = e
mag_min = abs(sum(magmoms))
afm_e_min = e
elif abs(sum(magmoms)) == 0 and mag_min == 0:
if e < afm_e_min:
afm_struct = s
afm_e = e
afm_e_min = e
# Convert to magnetic structures with 'magmom' site property
fm_struct = CollinearMagneticStructureAnalyzer(
fm_struct, make_primitive=False, threshold=0.0
).get_structure_with_only_magnetic_atoms(make_primitive=False)
afm_struct = CollinearMagneticStructureAnalyzer(
afm_struct, make_primitive=False, threshold=0.0
).get_structure_with_only_magnetic_atoms(make_primitive=False)
return fm_struct, afm_struct, fm_e, afm_e
[docs] def estimate_exchange(self, fm_struct=None, afm_struct=None, fm_e=None, afm_e=None):
"""
Estimate <J> for a structure based on low energy FM and AFM orderings.
Args:
fm_struct (Structure): fm structure with 'magmom' site property
afm_struct (Structure): afm structure with 'magmom' site property
fm_e (float): fm energy/atom
afm_e (float): afm energy/atom
Returns:
j_avg (float): Average exchange parameter (meV/atom)
"""
# Get low energy orderings if not supplied
if any(arg is None for arg in [fm_struct, afm_struct, fm_e, afm_e]):
fm_struct, afm_struct, fm_e, afm_e = self.get_low_energy_orderings()
magmoms = fm_struct.site_properties["magmom"]
# Normalize energies by number of magnetic ions
# fm_e = fm_e / len(magmoms)
# afm_e = afm_e / len(afm_magmoms)
m_avg = np.mean([np.sqrt(m ** 2) for m in magmoms])
# If m_avg for FM config is < 1 we won't get sensibile results.
if m_avg < 1:
iamthedanger = """
Local magnetic moments are small (< 1 muB / atom). The
exchange parameters may be wrong, but <J> and the mean
field critical temperature estimate may be OK.
"""
logging.warning(iamthedanger)
delta_e = afm_e - fm_e # J > 0 -> FM
j_avg = delta_e / (m_avg ** 2) # eV / magnetic ion
j_avg *= 1000 # meV / ion
return j_avg
[docs] def get_mft_temperature(self, j_avg):
"""
Crude mean field estimate of critical temperature based on <J> for
one sublattice, or solving the coupled equations for a multisublattice
material.
Args:
j_avg (float): j_avg (float): Average exchange parameter (meV/atom)
Returns:
mft_t (float): Critical temperature (K)
"""
num_sublattices = len(self.unique_site_ids)
k_boltzmann = 0.0861733 # meV/K
# Only 1 magnetic sublattice
if num_sublattices == 1:
mft_t = 2 * abs(j_avg) / 3 / k_boltzmann
else: # multiple magnetic sublattices
omega = np.zeros((num_sublattices, num_sublattices))
ex_params = self.ex_params
ex_params = {k: v for (k, v) in ex_params.items() if k != "E0"} # ignore E0
for k in ex_params:
# split into i, j unique site identifiers
sites = [elem for elem in k.split("-")]
sites = [int(num) for num in sites[:2]] # cut 'nn' identifier
i, j = sites[0], sites[1]
omega[i, j] += ex_params[k]
omega[j, i] += ex_params[k]
omega = omega * 2 / 3 / k_boltzmann
eigenvals, eigenvecs = np.linalg.eig(omega)
mft_t = max(eigenvals)
if mft_t > 1500: # Not sensible!
stayoutofmyterritory = """
This mean field estimate is too high! Probably
the true low energy orderings were not given as inputs.
"""
logging.warning(stayoutofmyterritory)
return mft_t
[docs] def get_interaction_graph(self, filename=None):
"""
Get a StructureGraph with edges and weights that correspond to exchange
interactions and J_ij values, respectively.
Args:
filename (str): if not None, save interaction graph to filename.
Returns:
igraph (StructureGraph): Exchange interaction graph.
"""
structure = self.ordered_structures[0]
sgraph = self.sgraphs[0]
igraph = StructureGraph.with_empty_graph(
structure, edge_weight_name="exchange_constant", edge_weight_units="meV"
)
if "<J>" in self.ex_params: # Only <J> is available
warning_msg = """
Only <J> is available. The interaction graph will not tell
you much.
"""
logging.warning(warning_msg)
# J_ij exchange interaction matrix
for i, node in enumerate(sgraph.graph.nodes):
connections = sgraph.get_connected_sites(i)
for c in connections:
jimage = c[1] # relative integer coordinates of atom j
j = c[2] # index of neighbor
dist = c[-1] # i <-> j distance
j_exc = self._get_j_exc(i, j, dist)
igraph.add_edge(
i, j, to_jimage=jimage, weight=j_exc, warn_duplicates=False
)
# Save to a json file if desired
if filename:
if filename.endswith(".json"):
dumpfn(igraph, filename)
else:
filename += ".json"
dumpfn(igraph, filename)
return igraph
def _get_j_exc(self, i, j, dist):
"""
Convenience method for looking up exchange parameter between two sites.
Args:
i (int): index of ith site
j (int): index of jth site
dist (float): distance (Angstrom) between sites
(10E-2 precision)
Returns:
j_exc (float): Exchange parameter in meV
"""
# Get unique site identifiers
for k in self.unique_site_ids.keys():
if i in k:
i_index = self.unique_site_ids[k]
if j in k:
j_index = self.unique_site_ids[k]
order = ""
# Determine order of interaction
if abs(dist - self.dists["nn"]) <= self.tol:
order = "-nn"
elif abs(dist - self.dists["nnn"]) <= self.tol:
order = "-nnn"
elif abs(dist - self.dists["nnnn"]) <= self.tol:
order = "-nnnn"
j_ij = str(i_index) + "-" + str(j_index) + order
j_ji = str(j_index) + "-" + str(i_index) + order
if j_ij in self.ex_params:
j_exc = self.ex_params[j_ij]
elif j_ji in self.ex_params:
j_exc = self.ex_params[j_ji]
else:
j_exc = 0
# Check if only averaged NN <J> values are available
if "<J>" in self.ex_params and order == "-nn":
j_exc = self.ex_params["<J>"]
return j_exc
[docs] def get_heisenberg_model(self):
"""Save results of mapping to a HeisenbergModel object.
Returns:
hmodel (HeisenbergModel): MSONable object.
"""
# Original formula unit with nonmagnetic ions
hm_formula = str(self.ordered_structures_[0].composition.reduced_formula)
hm_structures = self.ordered_structures
hm_energies = self.energies
hm_cutoff = self.cutoff
hm_tol = self.tol
hm_sgraphs = self.sgraphs
hm_usi = self.unique_site_ids
hm_wids = self.wyckoff_ids
hm_nni = self.nn_interactions
hm_d = self.dists
# Exchange matrix DataFrame in json format
hm_em = self.ex_mat.to_json()
hm_ep = self.get_exchange()
hm_javg = self.estimate_exchange()
hm_igraph = self.get_interaction_graph()
hmodel = HeisenbergModel(
hm_formula,
hm_structures,
hm_energies,
hm_cutoff,
hm_tol,
hm_sgraphs,
hm_usi,
hm_wids,
hm_nni,
hm_d,
hm_em,
hm_ep,
hm_javg,
hm_igraph,
)
return hmodel
[docs]class HeisenbergScreener:
"""
Class to clean and screen magnetic orderings.
"""
def __init__(self, structures, energies, screen=False):
"""
This class pre-processes magnetic orderings and energies for
HeisenbergMapper. It prioritizes low-energy orderings with large and
localized magnetic moments.
Args:
structures (list): Structure objects with magnetic moments.
energies (list): Energies/atom of magnetic orderings.
screen (bool): Try to screen out high energy and low-spin configurations.
Attributes:
screened_structures (list): Sorted structures.
screened_energies (list): Sorted energies.
"""
# Cleanup
structures, energies = self._do_cleanup(structures, energies)
n_structures = len(structures)
# If there are more than 2 structures, we want to perform a
# screening to prioritize well-behaved orderings
if screen and n_structures > 2:
structures, energies = self._do_screen(structures, energies)
self.screened_structures = structures
self.screened_energies = energies
@staticmethod
def _do_cleanup(structures, energies):
"""Sanitize input structures and energies.
Takes magnetic structures and performs the following operations
- Erases nonmagnetic ions and gives all ions ['magmom'] site prop
- Converts total energies -> energy / magnetic ion
- Checks for duplicate/degenerate orderings
- Sorts by energy
Args:
structures (list): Structure objects with magmoms.
energies (list): Corresponding energies.
Returns:
ordered_structures (list): Sanitized structures.
ordered_energies (list): Sorted energies.
"""
# Get only magnetic ions & give all structures site_properties['magmom']
# zero threshold so that magnetic ions with small moments
# are preserved
ordered_structures = [
CollinearMagneticStructureAnalyzer(
s, make_primitive=False, threshold=0.0
).get_structure_with_only_magnetic_atoms(make_primitive=False)
for s in structures
]
# Convert to energies / magnetic ion
energies = [e / len(s) for (e, s) in zip(energies, ordered_structures)]
# Check for duplicate / degenerate states (sometimes different initial
# configs relax to the same state)
remove_list = []
for i, e in enumerate(energies):
e_tol = 6 # 10^-6 eV/atom tol on energies
e = round(e, e_tol)
if i not in remove_list:
for i_check, e_check in enumerate(energies):
e_check = round(e_check, e_tol)
if i != i_check and i_check not in remove_list and e == e_check:
remove_list.append(i_check)
# Also discard structures with small |magmoms| < 0.1 uB
# xx - get rid of these or just bury them in the list?
# for i, s in enumerate(ordered_structures):
# magmoms = s.site_properties['magmom']
# if i not in remove_list:
# if any(abs(m) < 0.1 for m in magmoms):
# remove_list.append(i)
# Remove duplicates
if len(remove_list):
ordered_structures = [
s for i, s in enumerate(ordered_structures) if i not in remove_list
]
energies = [e for i, e in enumerate(energies) if i not in remove_list]
# Sort by energy if not already sorted
ordered_structures = [
s for _, s in sorted(zip(energies, ordered_structures), reverse=False)
]
ordered_energies = sorted(energies, reverse=False)
return ordered_structures, ordered_energies
@staticmethod
def _do_screen(structures, energies):
"""Screen and sort magnetic orderings based on some criteria.
Prioritize low energy orderings and large, localized magmoms. do_clean should be run first to sanitize inputs.
Args:
structures (list): At least three structure objects.
energies (list): Energies.
Returns:
screened_structures (list): Sorted structures.
screened_energies (list): Sorted energies.
"""
magmoms = [s.site_properties["magmom"] for s in structures]
n_below_1ub = [len([m for m in ms if abs(m) < 1]) for ms in magmoms]
df = pd.DataFrame(
{
"structure": structures,
"energy": energies,
"magmoms": magmoms,
"n_below_1ub": n_below_1ub,
}
)
# keep the ground and first excited state fixed to capture the
# low-energy spectrum
index = list(df.index)[2:]
df_high_energy = df.iloc[2:]
# Prioritize structures with fewer magmoms < 1 uB
df_high_energy = df_high_energy.sort_values(by="n_below_1ub")
index = [0, 1] + list(df_high_energy.index)
# sort
df = df.reindex(index)
screened_structures = list(df["structure"].values)
screened_energies = list(df["energy"].values)
return screened_structures, screened_energies
[docs]class HeisenbergModel(MSONable):
"""
Store a Heisenberg model fit to low-energy magnetic orderings.
Intended to be generated by HeisenbergMapper.get_heisenberg_model().
"""
def __init__(
self,
formula=None,
structures=None,
energies=None,
cutoff=None,
tol=None,
sgraphs=None,
unique_site_ids=None,
wyckoff_ids=None,
nn_interactions=None,
dists=None,
ex_mat=None,
ex_params=None,
javg=None,
igraph=None,
):
"""
Args:
formula (str): Reduced formula of compound.
structures (list): Structure objects with magmoms.
energies (list): Energies of each relaxed magnetic structure.
cutoff (float): Cutoff in Angstrom for nearest neighbor search.
tol (float): Tolerance (in Angstrom) on nearest neighbor distances being equal.
sgraphs (list): StructureGraph objects.
unique_site_ids (dict): Maps each site to its unique numerical
identifier.
wyckoff_ids (dict): Maps unique numerical identifier to wyckoff
position.
nn_interacations (dict): {i: j} pairs of NN interactions
between unique sites.
dists (dict): NN, NNN, and NNNN interaction distances
ex_mat (DataFrame): Invertible Heisenberg Hamiltonian for each
graph.
ex_params (dict): Exchange parameter values (meV/atom).
javg (float): <J> exchange param (meV/atom).
igraph (StructureGraph): Exchange interaction graph.
"""
self.formula = formula
self.structures = structures
self.energies = energies
self.cutoff = cutoff
self.tol = tol
self.sgraphs = sgraphs
self.unique_site_ids = unique_site_ids
self.wyckoff_ids = wyckoff_ids
self.nn_interactions = nn_interactions
self.dists = dists
self.ex_mat = ex_mat
self.ex_params = ex_params
self.javg = javg
self.igraph = igraph
[docs] def as_dict(self):
"""
Because some dicts have tuple keys, some sanitization is required for json compatibility.
"""
d = {}
d["@module"] = self.__class__.__module__
d["@class"] = self.__class__.__name__
d["@version"] = __version__
d["formula"] = self.formula
d["structures"] = [s.as_dict() for s in self.structures]
d["energies"] = self.energies
d["cutoff"] = self.cutoff
d["tol"] = self.tol
d["sgraphs"] = [sgraph.as_dict() for sgraph in self.sgraphs]
d["dists"] = self.dists
d["ex_params"] = self.ex_params
d["javg"] = self.javg
d["igraph"] = self.igraph.as_dict()
# Sanitize tuple & int keys
d["ex_mat"] = jsanitize(self.ex_mat)
d["nn_interactions"] = jsanitize(self.nn_interactions)
d["unique_site_ids"] = jsanitize(self.unique_site_ids)
d["wyckoff_ids"] = jsanitize(self.wyckoff_ids)
return d
[docs] @classmethod
def from_dict(cls, d):
"""Create a HeisenbergModel from a dict."""
# Reconstitute the site ids
usids = {}
wids = {}
nnis = {}
for k, v in d["nn_interactions"].items():
nn_dict = {}
for k1, v1 in v.items():
key = literal_eval(k1)
nn_dict[key] = v1
nnis[k] = nn_dict
for k, v in d["unique_site_ids"].items():
key = literal_eval(k)
if type(key) == int:
usids[tuple([key])] = v
elif type(key) == tuple:
usids[key] = v
for k, v in d["wyckoff_ids"].items():
key = literal_eval(k)
wids[key] = v
# Reconstitute the structure and graph objects
structures = []
sgraphs = []
for v in d["structures"]:
structures.append(Structure.from_dict(v))
for v in d["sgraphs"]:
sgraphs.append(StructureGraph.from_dict(v))
# Interaction graph
igraph = StructureGraph.from_dict(d["igraph"])
# Reconstitute the exchange matrix DataFrame
try:
ex_mat = eval(d["ex_mat"])
ex_mat = pd.DataFrame.from_dict(ex_mat)
except SyntaxError: # if ex_mat is empty
ex_mat = pd.DataFrame(columns=["E", "E0"])
hmodel = HeisenbergModel(
formula=d["formula"],
structures=structures,
energies=d["energies"],
cutoff=d["cutoff"],
tol=d["tol"],
sgraphs=sgraphs,
unique_site_ids=usids,
wyckoff_ids=wids,
nn_interactions=nnis,
dists=d["dists"],
ex_mat=ex_mat,
ex_params=d["ex_params"],
javg=d["javg"],
igraph=igraph,
)
return hmodel
def _get_j_exc(self, i, j, dist):
"""
Convenience method for looking up exchange parameter between two sites.
Args:
i (int): index of ith site
j (int): index of jth site
dist (float): distance (Angstrom) between sites +- tol
Returns:
j_exc (float): Exchange parameter in meV
"""
# Get unique site identifiers
for k in self.unique_site_ids.keys():
if i in k:
i_index = self.unique_site_ids[k]
if j in k:
j_index = self.unique_site_ids[k]
order = ""
# Determine order of interaction
if abs(dist - self.dists["nn"]) <= self.tol:
order = "-nn"
elif abs(dist - self.dists["nnn"]) <= self.tol:
order = "-nnn"
elif abs(dist - self.dists["nnnn"]) <= self.tol:
order = "-nnnn"
j_ij = str(i_index) + "-" + str(j_index) + order
j_ji = str(j_index) + "-" + str(i_index) + order
if j_ij in self.ex_params:
j_exc = self.ex_params[j_ij]
elif j_ji in self.ex_params:
j_exc = self.ex_params[j_ji]
else:
j_exc = 0
# Check if only averaged NN <J> values are available
if "<J>" in self.ex_params and order == "-nn":
j_exc = self.ex_params["<J>"]
return j_exc