pymatgen.analysis.magnetism.heisenberg — pymatgen 2020.7.3 documentation

# Source code for pymatgen.analysis.magnetism.heisenberg

    # 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"

    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

        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

        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

        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

        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

        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

        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

    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

    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

        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

        @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