Source code for pymatgen.analysis.magnetism.analyzer

# coding: utf-8
# Copyright (c) Pymatgen Development Team.
# Distributed under the terms of the MIT License.

This module provides some useful functions for dealing with magnetic Structures
(e.g. Structures with associated magmom tags).

import warnings
import numpy as np
import os
import logging

from enum import Enum, unique
from collections import namedtuple

from scipy.stats import gaussian_kde
from scipy.signal import argrelextrema

from pymatgen.core.structure import Specie, Structure, Element, DummySpecie
from pymatgen.electronic_structure.core import Magmom
from pymatgen.symmetry.analyzer import SpacegroupAnalyzer
from pymatgen.transformations.standard_transformations import (
from pymatgen.transformations.advanced_transformations import (
from pymatgen.symmetry.groups import SpaceGroup
from monty.serialization import loadfn

from typing import Union, List, Dict, Tuple, Optional, Any
from pymatgen.util.typing import Vector3Like

This module provides some useful functions for dealing with magnetic Structures
(e.g. Structures with associated magmom tags).

__author__ = "Matthew Horton"
__copyright__ = "Copyright 2017, The Materials Project"
__version__ = "0.1"
__maintainer__ = "Matthew Horton"
__email__ = ""
__status__ = "Development"
__date__ = "Feb 2017"

MODULE_DIR = os.path.dirname(os.path.abspath(__file__))

    DEFAULT_MAGMOMS = loadfn(os.path.join(MODULE_DIR, "default_magmoms.yaml"))
except Exception:
        "Could not load default_magmoms.yaml, falling back to VASPIncarBase.yaml"
    DEFAULT_MAGMOMS = loadfn(
        os.path.join(MODULE_DIR, "../../io/vasp/VASPIncarBase.yaml")

[docs]@unique class Ordering(Enum): """ Enumeration defining possible magnetic orderings. """ FM = "FM" # Ferromagnetic AFM = "AFM" # Antiferromagnetic FiM = "FiM" # Ferrimagnetic NM = "NM" # Non-magnetic Unknown = "Unknown"
[docs]@unique class OverwriteMagmomMode(Enum): """ Enumeration defining different modes for analyzer. """ none = "none" respect_sign = "respect_sign" respect_zero = "respect_zeros" replace_all = "replace_all" normalize = "normalize"
[docs]class CollinearMagneticStructureAnalyzer: """ A class which provides a few helpful methods to analyze collinear magnetic structures. """ def __init__( self, structure: Structure, overwrite_magmom_mode: Union[OverwriteMagmomMode, str] = "none", round_magmoms: bool = False, detect_valences: bool = False, make_primitive: bool = True, default_magmoms: dict = None, set_net_positive: bool = True, threshold: float = 0.00, threshold_nonmag: float = 0.1, ): r""" If magnetic moments are not defined, moments will be taken either from default_magmoms.yaml (similar to the default magmoms in MPRelaxSet, with a few extra definitions) or from a specie:magmom dict provided by the default_magmoms kwarg. Input magmoms can be replaced using the 'overwrite_magmom_mode' kwarg. This can be: * "none" to do nothing, * "respect_sign" which will overwrite existing magmoms with those from default_magmoms but will keep sites with positive magmoms positive, negative magmoms negative and zero magmoms zero, * "respect_zeros", which will give a ferromagnetic structure (all positive magmoms from default_magmoms) but still keep sites with zero magmoms as zero, * "replace_all" which will try to guess initial magmoms for all sites in the structure irrespective of input structure (this is most suitable for an initial DFT calculation), * "replace_all_if_undefined" is the same as "replace_all" but only if no magmoms are defined in input structure, otherwise it will respect existing magmoms. * "normalize" will normalize magmoms to unity, but will respect sign (used for comparing orderings), magmoms < theshold will be set to zero Args: structure: input Structure object overwrite_magmom_mode: "respect_sign", "respect_zeros", "replace_all", "replace_all_if_undefined", "normalize" (default "none") round_magmoms: will round input magmoms to specified number of decimal places if integer is supplied, if set to a float will try and group magmoms together using a kernel density estimator of provided width, and extracting peaks of the estimator detect_valences: if True, will attempt to assign valences to input structure make_primitive: if True, will transform to primitive magnetic cell default_magmoms: (optional) dict specifying default magmoms set_net_positive: if True, will change sign of magnetic moments such that the net magnetization is positive. Argument will be ignored if mode "respect_sign" is used. threshold: number (in Bohr magnetons) below which magmoms will be rounded to zero threshold_nonmag: number (in Bohr magneton) below which nonmagnetic ions (with no magmom specified in default_magmoms) will be rounded to zero """ if default_magmoms: self.default_magmoms = default_magmoms else: self.default_magmoms = DEFAULT_MAGMOMS structure = structure.copy() # check for disorder if not structure.is_ordered: raise NotImplementedError( "Not implemented for disordered structures, " "make ordered approximation first." ) if detect_valences: trans = AutoOxiStateDecorationTransformation() try: structure = trans.apply_transformation(structure) except ValueError: warnings.warn( "Could not assign valences " "for {}".format(structure.composition.reduced_formula) ) # check to see if structure has magnetic moments # on site properties or species spin properties, # prioritize site properties has_magmoms = bool(structure.site_properties.get("magmom", False)) has_spin = False for comp in structure.species_and_occu: for sp, occu in comp.items(): if getattr(sp, "spin", False): has_spin = True # perform input sanitation ... # rest of class will assume magnetic moments # are stored on site properties: # this is somewhat arbitrary, arguments can # be made for both approaches if has_magmoms and has_spin: raise ValueError( "Structure contains magnetic moments on both " "magmom site properties and spin species " "properties. This is ambiguous. Remove one or " "the other." ) elif has_magmoms: if None in structure.site_properties["magmom"]: warnings.warn( "Be careful with mixing types in your magmom " "site properties. Any 'None' magmoms have been " "replaced with zero." ) magmoms = [m if m else 0 for m in structure.site_properties["magmom"]] elif has_spin: magmoms = [getattr(sp, "spin", 0) for sp in structure.species] structure.remove_spin() else: # no magmoms present, add zero magmoms for now magmoms = [0] * len(structure) # and overwrite magmoms with default magmoms later unless otherwise stated if overwrite_magmom_mode == "replace_all_if_undefined": overwrite_magmom_mode = "replace_all" # test to see if input structure has collinear magmoms self.is_collinear = Magmom.are_collinear(magmoms) if not self.is_collinear: warnings.warn( "This class is not designed to be used with " "non-collinear structures. If your structure is " "only slightly non-collinear (e.g. canted) may still " "give useful results, but use with caution." ) # this is for collinear structures only, make sure magmoms # are all floats magmoms = list(map(float, magmoms)) # set properties that should be done /before/ we process input magmoms self.total_magmoms = sum(magmoms) self.magnetization = sum(magmoms) / structure.volume # round magmoms on magnetic ions below threshold to zero # and on non magnetic ions below threshold_nonmag magmoms = [ m if abs(m) > threshold and a.species_string in self.default_magmoms else m if abs(m) > threshold_nonmag and a.species_string not in self.default_magmoms else 0 for (m, a) in zip(magmoms, structure.sites) ] # overwrite existing magmoms with default_magmoms if overwrite_magmom_mode not in ( "none", "respect_sign", "respect_zeros", "replace_all", "replace_all_if_undefined", "normalize", ): raise ValueError("Unsupported mode.") for idx, site in enumerate(structure): if site.species_string in self.default_magmoms: # look for species first, e.g. Fe2+ default_magmom = self.default_magmoms[site.species_string] elif ( isinstance(site.specie, Specie) and str(site.specie.element) in self.default_magmoms ): # look for element, e.g. Fe default_magmom = self.default_magmoms[str(site.specie.element)] else: default_magmom = 0 # overwrite_magmom_mode = "respect_sign" will change magnitude of # existing moments only, and keep zero magmoms as # zero: it will keep the magnetic ordering intact if overwrite_magmom_mode == "respect_sign": set_net_positive = False if magmoms[idx] > 0: magmoms[idx] = default_magmom elif magmoms[idx] < 0: magmoms[idx] = -default_magmom # overwrite_magmom_mode = "respect_zeros" will give a ferromagnetic # structure but will keep zero magmoms as zero elif overwrite_magmom_mode == "respect_zeros": if magmoms[idx] != 0: magmoms[idx] = default_magmom # overwrite_magmom_mode = "replace_all" will ignore input magmoms # and give a ferromagnetic structure with magnetic # moments on *all* atoms it thinks could be magnetic elif overwrite_magmom_mode == "replace_all": magmoms[idx] = default_magmom # overwrite_magmom_mode = "normalize" set magmoms magnitude to 1 elif overwrite_magmom_mode == "normalize": if magmoms[idx] != 0: magmoms[idx] = int(magmoms[idx] / abs(magmoms[idx])) # round magmoms, used to smooth out computational data magmoms = ( self._round_magmoms(magmoms, round_magmoms) if round_magmoms else magmoms ) if set_net_positive: sign = np.sum(magmoms) if sign < 0: magmoms = -np.array(magmoms) structure.add_site_property("magmom", magmoms) if make_primitive: structure = structure.get_primitive_structure(use_site_props=True) self.structure = structure @staticmethod def _round_magmoms( magmoms: Vector3Like, round_magmoms_mode: Union[int, float] ) -> np.ndarray: """If round_magmoms_mode is an integer, simply round to that number of decimal places, else if set to a float will try and round intelligently by grouping magmoms. """ if isinstance(round_magmoms_mode, int): # simple rounding to number of decimal places magmoms = np.around(magmoms, decimals=round_magmoms_mode) elif isinstance(round_magmoms_mode, float): try: # get range of possible magmoms, pad by 50% just to be safe range_m = max([max(magmoms), abs(min(magmoms))]) * 1.5 # construct kde, here "round_magmoms_mode" is the width of the kde kernel = gaussian_kde(magmoms, bw_method=round_magmoms_mode) # with a linearly spaced grid 1000x finer than width xgrid = np.linspace( -range_m, range_m, int(1000 * range_m / round_magmoms_mode) ) # and evaluate the kde on this grid, extracting the maxima of the kde peaks kernel_m = kernel.evaluate(xgrid) extrema = xgrid[argrelextrema(kernel_m, comparator=np.greater)] # round magmoms to these extrema magmoms = [extrema[(np.abs(extrema - m)).argmin()] for m in magmoms] except Exception as e: # TODO: typically a singular matrix warning, investigate this warnings.warn( "Failed to round magmoms intelligently, " "falling back to simple rounding." ) warnings.warn(str(e)) # and finally round roughly to the number of significant figures in our kde width num_decimals = len(str(round_magmoms_mode).split(".")[1]) + 1 magmoms = np.around(magmoms, decimals=num_decimals) return magmoms
[docs] def get_structure_with_spin(self) -> Structure: """Returns a Structure with species decorated with spin values instead of using magmom site properties. """ structure = self.structure.copy() structure.add_spin_by_site(structure.site_properties["magmom"]) structure.remove_site_property("magmom") return structure
[docs] def get_structure_with_only_magnetic_atoms( self, make_primitive: bool = True ) -> Structure: """Returns a Structure with only magnetic atoms present. Args: make_primitive: Whether to make structure primitive after removing non-magnetic atoms (Default value = True) Returns: Structure """ sites = [site for site in self.structure if abs(["magmom"]) > 0] structure = Structure.from_sites(sites) if make_primitive: structure = structure.get_primitive_structure(use_site_props=True) return structure
[docs] def get_nonmagnetic_structure(self, make_primitive: bool = True) -> Structure: """Returns a Structure without magnetic moments defined. Args: make_primitive: Whether to make structure primitive after removing magnetic information (Default value = True) Returns: Structure """ structure = self.structure.copy() structure.remove_site_property("magmom") if make_primitive: structure = structure.get_primitive_structure() return structure
[docs] def get_ferromagnetic_structure(self, make_primitive: bool = True) -> Structure: """Returns a Structure with all magnetic moments positive or zero. Args: make_primitive: Whether to make structure primitive after making all magnetic moments positive (Default value = True) Returns: Structure """ structure = self.structure.copy() structure.add_site_property("magmom", [abs(m) for m in self.magmoms]) if make_primitive: structure = structure.get_primitive_structure(use_site_props=True) return structure
@property def is_magnetic(self) -> bool: """Convenience property, returns True if any non-zero magmoms present. """ return any(map(abs, self.structure.site_properties["magmom"])) @property def magmoms(self) -> np.ndarray: """Convenience property, returns magmoms as a numpy array. """ return np.array(self.structure.site_properties["magmom"]) @property def types_of_magnetic_specie(self) -> Tuple[Union[Element, Specie, DummySpecie], ...]: """Equivalent to Structure.types_of_specie but only returns magnetic species. Returns: types of Specie as a list """ if self.number_of_magnetic_sites > 0: structure = self.get_structure_with_only_magnetic_atoms() return tuple(sorted(structure.types_of_specie)) else: return tuple() @property def magnetic_species_and_magmoms(self) -> Dict[str, Any]: """Returns a dict of magnetic species and the magnitude of their associated magmoms. Will return a list if there are multiple magmoms per species. Returns: dict of magnetic species and magmoms """ structure = self.get_ferromagnetic_structure() magtypes: Dict = { str(site.specie): set() for site in structure if["magmom"] != 0 } for site in structure: if["magmom"] != 0: magtypes[str(site.specie)].add(["magmom"]) for sp, magmoms in magtypes.items(): if len(magmoms) == 1: magtypes[sp] = magmoms.pop() else: magtypes[sp] = sorted(list(magmoms)) return magtypes @property def number_of_magnetic_sites(self) -> int: """Number of magnetic sites present in structure.""" return int(np.sum([abs(m) > 0 for m in self.magmoms]))
[docs] def number_of_unique_magnetic_sites( self, symprec: float = 1e-3, angle_tolerance: float = 5 ) -> int: """ Args: symprec: same as in SpacegroupAnalyzer (Default value = 1e-3) angle_tolerance: same as in SpacegroupAnalyzer (Default value = 5) Returns: Number of symmetrically-distinct magnetic sites present in structure. """ structure = self.get_nonmagnetic_structure() sga = SpacegroupAnalyzer( structure, symprec=symprec, angle_tolerance=angle_tolerance ) symm_structure = sga.get_symmetrized_structure() num_unique_mag_sites = 0 for group_of_sites in symm_structure.equivalent_sites: if group_of_sites[0].specie in self.types_of_magnetic_specie: num_unique_mag_sites += 1 return num_unique_mag_sites
@property def ordering(self) -> Ordering: """Applies heuristics to return a magnetic ordering for a collinear magnetic structure. Result is not guaranteed for correctness. Returns: Ordering Enum ('FiM' is used as the abbreviation for ferrimagnetic) """ if not self.is_collinear: warnings.warn( "Detecting ordering in non-collinear structures not yet implemented." ) return Ordering.Unknown if "magmom" not in self.structure.site_properties: # maybe this was a non-spin-polarized calculation, or we've # lost the magnetic moment information return Ordering.Unknown magmoms = self.magmoms max_magmom = max(magmoms) total_magnetization = abs(sum(magmoms)) is_potentially_ferromagnetic = np.all(magmoms >= 0) or np.all(magmoms <= 0) if total_magnetization > 0 and is_potentially_ferromagnetic: return Ordering.FM elif total_magnetization > 0: return Ordering.FiM elif max_magmom > 0: return Ordering.AFM else: return Ordering.NM
[docs] def get_exchange_group_info( self, symprec: float = 1e-2, angle_tolerance: float = 5.0 ) -> Tuple[str, int]: """Returns the information on the symmetry of the Hamiltonian describing the exchange energy of the system, taking into account relative direction of magnetic moments but not their absolute direction. This is not strictly accurate (e.g. some/many atoms will have zero magnetic moments), but defining symmetry this way is a useful way of keeping track of distinct magnetic orderings within pymatgen. Args: symprec: same as SpacegroupAnalyzer (Default value = 1e-2) angle_tolerance: same as SpacegroupAnalyzer (Default value = 5.0) Returns: spacegroup_symbol, international_number """ structure = self.get_structure_with_spin() return structure.get_space_group_info( symprec=symprec, angle_tolerance=angle_tolerance )
[docs] def matches_ordering(self, other: Structure) -> bool: """Compares the magnetic orderings of one structure with another. Args: other: Structure to compare Returns: True or False """ a = CollinearMagneticStructureAnalyzer( self.structure, overwrite_magmom_mode="normalize" ).get_structure_with_spin() # sign of spins doesn't matter, so we're comparing both # positive and negative versions of the structure # this code is possibly redundant, but is included out of # an abundance of caution b_positive = CollinearMagneticStructureAnalyzer( other, overwrite_magmom_mode="normalize", make_primitive=False ) b_negative = b_positive.structure.copy() b_negative.add_site_property( "magmom", np.multiply(-1, b_negative.site_properties["magmom"]) ) b_negative = CollinearMagneticStructureAnalyzer( b_negative, overwrite_magmom_mode="normalize", make_primitive=False ) b_positive = b_positive.get_structure_with_spin() b_negative = b_negative.get_structure_with_spin() if a.matches(b_positive) or a.matches( b_negative ): # sometimes returns None (bug?) return True else: return False
def __str__(self): """ Sorts a Structure (by fractional co-ordinate), and prints sites with magnetic information. This is useful over Structure.__str__ because sites are in a consistent order, which makes visual comparison between two identical Structures with different magnetic orderings easier. """ frac_coords = self.structure.frac_coords sorted_indices = np.lexsort( (frac_coords[:, 2], frac_coords[:, 1], frac_coords[:, 0]) ) s = Structure.from_sites([self.structure[idx] for idx in sorted_indices]) # adapted from Structure.__repr__ outs = ["Structure Summary", repr(s.lattice)] outs.append("Magmoms Sites") for site in s: if["magmom"] != 0: prefix = "{:+.2f} ".format(["magmom"]) else: prefix = " " outs.append(prefix + repr(site)) return "\n".join(outs)
[docs]class MagneticStructureEnumerator: """Combines MagneticStructureAnalyzer and MagOrderingTransformation to automatically generate a set of transformations for a given structure and produce a list of plausible magnetic orderings. """ available_strategies = ( "ferromagnetic", "antiferromagnetic", "ferrimagnetic_by_motif", "ferrimagnetic_by_species", "antiferromagnetic_by_motif", "nonmagnetic", ) def __init__( self, structure: Structure, default_magmoms: Optional[Dict[str, float]] = None, strategies: Union[List[str], Tuple[str, ...]] = ("ferromagnetic", "antiferromagnetic"), automatic: bool = True, truncate_by_symmetry: bool = True, transformation_kwargs: Optional[Dict] = None, ): """ This class will try generated different collinear magnetic orderings for a given input structure. If the input structure has magnetic moments defined, it is possible to use these as a hint as to which elements are magnetic, otherwise magnetic elements will be guessed (this can be changed using default_magmoms kwarg). Args: structure: input structure default_magmoms: (optional, defaults provided) dict of magnetic elements to their initial magnetic moments in ┬ÁB, generally these are chosen to be high-spin since they can relax to a low-spin configuration during a DFT electronic configuration strategies: different ordering strategies to use, choose from: ferromagnetic, antiferromagnetic, antiferromagnetic_by_motif, ferrimagnetic_by_motif and ferrimagnetic_by_species (here, "motif", means to use a different ordering parameter for symmetry inequivalent sites) automatic: if True, will automatically choose sensible strategies truncate_by_symmetry: if True, will remove very unsymmetrical orderings that are likely physically implausible transformation_kwargs: keyword arguments to pass to MagOrderingTransformation, to change automatic cell size limits, etc. """ self.logger = logging.getLogger(self.__class__.__name__) self.structure = structure # decides how to process input structure, which sites are magnetic self.default_magmoms = default_magmoms # different strategies to attempt, default is usually reasonable self.strategies = list(strategies) # and whether to automatically add strategies that may be appropriate self.automatic = automatic # and whether to discard low symmetry structures self.truncate_by_symmetry = truncate_by_symmetry # other settings self.num_orderings = 64 self.max_unique_sites = 8 # kwargs to pass to transformation (ultimately to enumlib) default_transformation_kwargs = {"check_ordered_symmetry": False, "timeout": 5} transformation_kwargs = transformation_kwargs or {} transformation_kwargs.update(default_transformation_kwargs) self.transformation_kwargs = transformation_kwargs # our magnetically ordered structures will be # stored here once generated and also store which # transformation created them, this is used for # book-keeping/user interest, and # is be a list of strings in ("fm", "afm", # "ferrimagnetic_by_species", "ferrimagnetic_by_motif", # "afm_by_motif", "input_structure") self.ordered_structures: List[Structure] = [] self.ordered_structure_origins: List[str] = [] formula = structure.composition.reduced_formula # to process disordered magnetic structures, first make an # ordered approximation if not structure.is_ordered: raise ValueError( "Please obtain an ordered approximation of the " "input structure ({}).".format(formula) ) # CollinearMagneticStructureAnalyzer is used throughout: # it can tell us whether the input is itself collinear (if not, # this workflow is not appropriate), and has many convenience # methods e.g. magnetic structure matching, etc. self.input_analyzer = CollinearMagneticStructureAnalyzer( structure, default_magmoms=default_magmoms, overwrite_magmom_mode="none" ) # this workflow enumerates structures with different combinations # of up and down spin and does not include spin-orbit coupling: # if your input structure has vector magnetic moments, this # workflow is not appropriate if not self.input_analyzer.is_collinear: raise ValueError("Input structure ({}) is non-collinear.".format(formula)) self.sanitized_structure = self._sanitize_input_structure(structure) # we will first create a set of transformations # and then apply them to our input structure self.transformations = self._generate_transformations(self.sanitized_structure) self._generate_ordered_structures( self.sanitized_structure, self.transformations ) @staticmethod def _sanitize_input_structure(input_structure: Structure) -> Structure: """Sanitize our input structure by removing magnetic information and making primitive. Args: input_structure: Structure Returns: Structure """ input_structure = input_structure.copy() # remove any annotated spin input_structure.remove_spin() # sanitize input structure: first make primitive ... input_structure = input_structure.get_primitive_structure(use_site_props=False) # ... and strip out existing magmoms, which can cause conflicts # with later transformations otherwise since sites would end up # with both magmom site properties and Specie spins defined if "magmom" in input_structure.site_properties: input_structure.remove_site_property("magmom") return input_structure def _generate_transformations( self, structure: Structure ) -> Dict[str, MagOrderingTransformation]: """The central problem with trying to enumerate magnetic orderings is that we have to enumerate orderings that might plausibly be magnetic ground states, while not enumerating orderings that are physically implausible. The problem is that it is not always obvious by e.g. symmetry arguments alone which orderings to prefer. Here, we use a variety of strategies (heuristics) to enumerate plausible orderings, and later discard any duplicates that might be found by multiple strategies. This approach is not ideal, but has been found to be relatively robust over a wide range of magnetic structures. Args: structure: A sanitized input structure (_sanitize_input_structure) Returns: A dict of a transformation class instance (values) and name of enumeration strategy (keys) Returns: dict of Transformations keyed by strategy """ formula = structure.composition.reduced_formula transformations: Dict[str, MagOrderingTransformation] = {} # analyzer is used to obtain information on sanitized input analyzer = CollinearMagneticStructureAnalyzer( structure, default_magmoms=self.default_magmoms, overwrite_magmom_mode="replace_all", ) if not analyzer.is_magnetic: raise ValueError( "Not detected as magnetic, add a new default magmom for the " "element you believe may be magnetic?" ) # now we can begin to generate our magnetic orderings"Generating magnetic orderings for {}".format(formula)) mag_species_spin = analyzer.magnetic_species_and_magmoms types_mag_species = sorted( analyzer.types_of_magnetic_specie, key=lambda sp: analyzer.default_magmoms.get(str(sp), 0), reverse=True, ) num_mag_sites = analyzer.number_of_magnetic_sites num_unique_sites = analyzer.number_of_unique_magnetic_sites() # enumerations become too slow as number of unique sites (and thus # permutations) increase, 8 is a soft limit, this can be increased # but do so with care if num_unique_sites > self.max_unique_sites: raise ValueError("Too many magnetic sites to sensibly perform enumeration.") # maximum cell size to consider: as a rule of thumb, if the primitive cell # contains a large number of magnetic sites, perhaps we only need to enumerate # within one cell, whereas on the other extreme if the primitive cell only # contains a single magnetic site, we have to create larger supercells if "max_cell_size" not in self.transformation_kwargs: # TODO: change to 8 / num_mag_sites ? self.transformation_kwargs["max_cell_size"] = max(1, int(4 / num_mag_sites)) "Max cell size set to {}".format( self.transformation_kwargs["max_cell_size"] ) ) # when enumerating ferrimagnetic structures, it's useful to detect # symmetrically distinct magnetic sites, since different # local environments can result in different magnetic order # (e.g. inverse spinels) # initially, this was done by co-ordination number, but is # now done by a full symmetry analysis sga = SpacegroupAnalyzer(structure) structure_sym = sga.get_symmetrized_structure() wyckoff = ["n/a"] * len(structure) for indices, symbol in zip( structure_sym.equivalent_indices, structure_sym.wyckoff_symbols ): for index in indices: wyckoff[index] = symbol is_magnetic_sites = [ True if site.specie in types_mag_species else False for site in structure ] # we're not interested in sites that we don't think are magnetic, # set these symbols to None to filter them out later wyckoff = [ symbol if is_magnetic_site else "n/a" for symbol, is_magnetic_site in zip(wyckoff, is_magnetic_sites) ] structure.add_site_property("wyckoff", wyckoff) wyckoff_symbols = set(wyckoff) - {"n/a"} # if user doesn't specifically request ferrimagnetic orderings, # we apply a heuristic as to whether to attempt them or not if self.automatic: if ( "ferrimagnetic_by_motif" not in self.strategies and len(wyckoff_symbols) > 1 and len(types_mag_species) == 1 ): self.strategies += ["ferrimagnetic_by_motif"] if ( "antiferromagnetic_by_motif" not in self.strategies and len(wyckoff_symbols) > 1 and len(types_mag_species) == 1 ): self.strategies += ["antiferromagnetic_by_motif"] if ( "ferrimagnetic_by_species" not in self.strategies and len(types_mag_species) > 1 ): self.strategies += ["ferrimagnetic_by_species"] # we start with a ferromagnetic ordering if "ferromagnetic" in self.strategies: # TODO: remove 0 spins ! fm_structure = analyzer.get_ferromagnetic_structure() # store magmom as spin property, to be consistent with output from # other transformations fm_structure.add_spin_by_site(fm_structure.site_properties["magmom"]) fm_structure.remove_site_property("magmom") # we now have our first magnetic ordering... self.ordered_structures.append(fm_structure) self.ordered_structure_origins.append("fm") # we store constraint(s) for each strategy first, # and then use each to perform a transformation later all_constraints: Dict[str, Any] = {} # which we can add simple AFM cases first... if "antiferromagnetic" in self.strategies: constraint = MagOrderParameterConstraint( 0.5, # TODO: update MagOrderParameterConstraint in # pymatgen to take types_mag_species directly species_constraints=list(map(str, types_mag_species)), ) all_constraints["afm"] = [constraint] # allows for non-magnetic sublattices if len(types_mag_species) > 1: for sp in types_mag_species: constraints = [ MagOrderParameterConstraint(0.5, species_constraints=str(sp)) ] all_constraints["afm_by_{}".format(sp)] = constraints # ...and then we also try ferrimagnetic orderings by motif if a # single magnetic species is present... if "ferrimagnetic_by_motif" in self.strategies and len(wyckoff_symbols) > 1: # these orderings are AFM on one local environment, and FM on the rest for symbol in wyckoff_symbols: constraints = [ MagOrderParameterConstraint( 0.5, site_constraint_name="wyckoff", site_constraints=symbol ), MagOrderParameterConstraint( 1.0, site_constraint_name="wyckoff", site_constraints=list(wyckoff_symbols - {symbol}), ), ] all_constraints["ferri_by_motif_{}".format(symbol)] = constraints # and also try ferrimagnetic when there are multiple magnetic species if "ferrimagnetic_by_species" in self.strategies: sp_list = [str(site.specie) for site in structure] num_sp = {sp: sp_list.count(str(sp)) for sp in types_mag_species} total_mag_sites = sum(num_sp.values()) for sp in types_mag_species: # attempt via a global order parameter all_constraints["ferri_by_{}".format(sp)] = num_sp[sp] / total_mag_sites # attempt via afm on sp, fm on remaining species constraints = [ MagOrderParameterConstraint(0.5, species_constraints=str(sp)), MagOrderParameterConstraint( 1.0, species_constraints=list( map(str, set(types_mag_species) - {sp}) ), ), ] all_constraints["ferri_by_{}_afm".format(sp)] = constraints # ...and finally, we can try orderings that are AFM on one local # environment, and non-magnetic on the rest -- this is less common # but unless explicitly attempted, these states are unlikely to be found if "antiferromagnetic_by_motif" in self.strategies: for symbol in wyckoff_symbols: constraints = [ MagOrderParameterConstraint( 0.5, site_constraint_name="wyckoff", site_constraints=symbol ) ] all_constraints["afm_by_motif_{}".format(symbol)] = constraints # and now construct all our transformations for each strategy transformations = {} for name, constraints in all_constraints.items(): trans = MagOrderingTransformation( mag_species_spin, order_parameter=constraints, **self.transformation_kwargs ) transformations[name] = trans return transformations def _generate_ordered_structures( self, sanitized_input_structure: Structure, transformations: Dict[str, MagOrderingTransformation], ): """Apply our input structure to our list of transformations and output a list of ordered structures that have been pruned for duplicates and for those with low symmetry (optional). Args: sanitized_input_structure: A sanitized input structure (_sanitize_input_structure) transformations: A dict of transformations (values) and name of enumeration strategy (key), the enumeration strategy name is just for record keeping Returns: None (sets self.ordered_structures and self.ordered_structures_origins instance variables) Returns: List of Structures """ ordered_structures = self.ordered_structures ordered_structures_origins = self.ordered_structure_origins # utility function to combine outputs from several transformations def _add_structures( ordered_structures, ordered_structures_origins, structures_to_add, origin="" ): """Transformations with return_ranked_list can return either just Structures or dicts (or sometimes lists!) -- until this is fixed, we use this function to concat structures given by the transformation. """ if structures_to_add: # type conversion if isinstance(structures_to_add, Structure): structures_to_add = [structures_to_add] structures_to_add = [ s["structure"] if isinstance(s, dict) else s for s in structures_to_add ] # concatenation ordered_structures += structures_to_add ordered_structures_origins += [origin] * len(structures_to_add) "Adding {} ordered structures: {}".format( len(structures_to_add), origin ) ) return ordered_structures, ordered_structures_origins for origin, trans in self.transformations.items(): structures_to_add = trans.apply_transformation( self.sanitized_structure, return_ranked_list=self.num_orderings ) ordered_structures, ordered_structures_origins = _add_structures( ordered_structures, ordered_structures_origins, structures_to_add, origin=origin, ) # in case we've introduced duplicates, let's remove them"Pruning duplicate structures.") structures_to_remove: List[int] = [] for idx, ordered_structure in enumerate(ordered_structures): if idx not in structures_to_remove: duplicate_checker = CollinearMagneticStructureAnalyzer( ordered_structure, overwrite_magmom_mode="none" ) for check_idx, check_structure in enumerate(ordered_structures): if check_idx not in structures_to_remove and check_idx != idx: if duplicate_checker.matches_ordering(check_structure): structures_to_remove.append(check_idx) if len(structures_to_remove): "Removing {} duplicate ordered structures".format( len(structures_to_remove) ) ) ordered_structures = [ s for idx, s in enumerate(ordered_structures) if idx not in structures_to_remove ] ordered_structures_origins = [ o for idx, o in enumerate(ordered_structures_origins) if idx not in structures_to_remove ] # also remove low symmetry structures if self.truncate_by_symmetry: # by default, keep structures with 5 most symmetric space groups if not isinstance(self.truncate_by_symmetry, int): self.truncate_by_symmetry = 5"Pruning low symmetry structures.") # first get a list of symmetries present symmetry_int_numbers = [ s.get_space_group_info()[1] for s in ordered_structures ] # then count the number of symmetry operations for that space group num_sym_ops = [ len(SpaceGroup.from_int_number(n).symmetry_ops) for n in symmetry_int_numbers ] # find the largest values... max_symmetries = sorted(list(set(num_sym_ops)), reverse=True) # ...and decide which ones to keep if len(max_symmetries) > self.truncate_by_symmetry: max_symmetries = max_symmetries[0:5] structs_to_keep = [ (idx, num) for idx, num in enumerate(num_sym_ops) if num in max_symmetries ] # sort so that highest symmetry structs are first structs_to_keep = sorted( structs_to_keep, key=lambda x: (x[1], -x[0]), reverse=True ) "Removing {} low symmetry " "ordered structures".format( len(ordered_structures) - len(structs_to_keep) ) ) ordered_structures = [ordered_structures[i] for i, _ in structs_to_keep] ordered_structures_origins = [ ordered_structures_origins[i] for i, _ in structs_to_keep ] # and ensure fm is always at index 0 fm_index = ordered_structures_origins.index("fm") ordered_structures.insert(0, ordered_structures.pop(fm_index)) ordered_structures_origins.insert( 0, ordered_structures_origins.pop(fm_index) ) # if our input structure isn't in our generated structures, # let's add it manually and also keep a note of which structure # is our input: this is mostly for book-keeping/benchmarking self.input_index = None self.input_origin = None if self.input_analyzer.ordering != Ordering.NM: matches = [ self.input_analyzer.matches_ordering(s) for s in ordered_structures ] if not any(matches): ordered_structures.append(self.input_analyzer.structure) ordered_structures_origins.append("input") "Input structure not present in enumerated structures, adding..." ) else: "Input structure was found in enumerated " "structures at index {}".format(matches.index(True)) ) self.input_index = matches.index(True) self.input_origin = ordered_structures_origins[self.input_index] self.ordered_structures = ordered_structures self.ordered_structure_origins = ordered_structures_origins
MagneticDeformation = namedtuple("MagneticDeformation", "type deformation")
[docs]def magnetic_deformation( structure_A: Structure, structure_B: Structure ) -> MagneticDeformation: """Calculates 'magnetic deformation proxy', a measure of deformation (norm of finite strain) between 'non-magnetic' (non-spin-polarized) and ferromagnetic structures. Adapted from Bocarsly et al. 2017, doi: 10.1021/acs.chemmater.6b04729 Args: structure_A: Structure structure_B: Structure Returns: Magnetic deformation """ # retrieve orderings of both input structures ordering_a = CollinearMagneticStructureAnalyzer( structure_A, overwrite_magmom_mode="none" ).ordering ordering_b = CollinearMagneticStructureAnalyzer( structure_B, overwrite_magmom_mode="none" ).ordering # get a type string, this is either 'NM-FM' for between non-magnetic # and ferromagnetic, as in Bocarsly paper, or e.g. 'FM-AFM' type_str = "{}-{}".format(ordering_a.value, ordering_b.value) lattice_a = structure_A.lattice.matrix.T lattice_b = structure_B.lattice.matrix.T lattice_a_inv = np.linalg.inv(lattice_a) p =, lattice_b) eta = 0.5 * (, p) - np.identity(3)) w, v = np.linalg.eig(eta) deformation = 100 * (1.0 / 3.0) * np.sqrt(w[0] ** 2 + w[1] ** 2 + w[2] ** 2) return MagneticDeformation(deformation=deformation, type=type_str)