# 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 (
AutoOxiStateDecorationTransformation,
)
from pymatgen.transformations.advanced_transformations import (
MagOrderingTransformation,
MagOrderParameterConstraint,
)
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__ = "mkhorton@lbl.gov"
__status__ = "Development"
__date__ = "Feb 2017"
MODULE_DIR = os.path.dirname(os.path.abspath(__file__))
try:
DEFAULT_MAGMOMS = loadfn(os.path.join(MODULE_DIR, "default_magmoms.yaml"))
except Exception:
warnings.warn(
"Could not load default_magmoms.yaml, falling back to VASPIncarBase.yaml"
)
DEFAULT_MAGMOMS = loadfn(
os.path.join(MODULE_DIR, "../../io/vasp/VASPIncarBase.yaml")
)
DEFAULT_MAGMOMS = DEFAULT_MAGMOMS["MAGMOM"]
[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(site.properties["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 site.properties["magmom"] != 0
}
for site in structure:
if site.properties["magmom"] != 0:
magtypes[str(site.specie)].add(site.properties["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 site.properties["magmom"] != 0:
prefix = "{:+.2f} ".format(site.properties["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 µB, 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
self.logger.info("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))
self.logger.info(
"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] = {}
# ...to 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)
self.logger.info(
"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
self.logger.info("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):
self.logger.info(
"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
self.logger.info("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
)
self.logger.info(
"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")
self.logger.info(
"Input structure not present in enumerated structures, adding..."
)
else:
self.logger.info(
"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")