amcheck is the program (and a library) to check, based on the symmetry arguments,
whether a given material is an altermagnet.
Altermagnet is a collinear magnet with symmetry-enforced zero net magnetization, where the opposite spin sublattices are coupled by symmetry operations that are not inversions or translations.
The user is supposed to provide a crystal structure and a magnetic pattern to describe the material of interest. It is implicitly assumed that the net magnetic moment is zero, i.e. if user types in a ferromagnet, the program will return an error. The underlying idea is that some pre-classification was already done and the user wants to figure out if the given material is an altermagnet or not, thus an antiferromagnet.
The code is written in python and can be installed using pip:
pip install amcheck
It has the following packages among its dependencies: ase, spglib and diophantine.
To use it as a command line tool, one provides one or more structure files (the code will internally loop over all listed files) and, when prompted, types in spin designation for each atom: 'u' or 'U' for spin-up, 'd' or 'D' for spin-down and 'n' or 'N' if the atom is non-magnetic. All atoms will be grouped into sets of symmetry-related atoms (orbits), and the user will need to provide spin designations per such a group. To mark the entire group as non-magnetic, one can use the 'nn' or 'NN' designation. Note that here, we treat spins as pseudoscalars (up and down, black and white), not as pseudovectors, and thus, no spatial anisotropy for spins is assumed.
$ amcheck FeO.vasp MnTe.vasp
==========================================================
Processing: FeO.vasp
----------------------------------------------------------
Spacegroup: P6_3/mmc (194)
Writing the used structure to auxiliary file:
check FeO.vasp_amcheck.vasp.
Orbit of Fe atoms at positions:
1 (1) [0.33333334 0.66666669 0.25 ]
2 (2) [0.66666663 0.33333331 0.75 ]
Type spin (u, U, d, D, n, N, nn or NN) for each of them (space
separated):
u d
Orbit of O atoms at positions:
3 (1) [0. 0. 0.]
4 (2) [0. 0. 0.5]
Type spin (u, U, d, D, n, N, nn or NN) for each of them (space
separated):
n n
Group of non-magnetic atoms (O): skipping.
Altermagnet? False
==========================================================
Processing: MnTe.vasp
----------------------------------------------------------
Spacegroup: P6_3/mmc (194)
Writing the used structure to auxiliary file:
check MnTe.vasp_amcheck.vasp.
Orbit of Mn atoms at positions:
1 (1) [0. 0. 0.]
2 (2) [0. 0. 0.5]
Type spin (u, U, d, D, n, N, nn or NN) for each of them (space
separated):
u d
Orbit of Te atoms at positions:
3 (1) [0.33333334 0.66666669 0.25 ]
4 (2) [0.66666663 0.33333331 0.75 ]
Type spin (u, U, d, D, n, N, nn or NN) for each of them (space
separated):
nn
Group of non-magnetic atoms (Te): skipping.
Altermagnet? True
Here is a code snippet providing an example on how to use the amcheck as a
library:
import numpy as np
from amcheck import is_altermagnet
symmetry_operations = [(np.array([[-1, 0, 0],
[ 0, -1, 0],
[ 0, 0, -1]],
dtype=int),
np.array([0.0, 0.0, 0.0])),
# for compactness reasons,
# other symmetry operations are omitted
# from this example
]
# positions of atoms in NiAs structure: ["Ni", "Ni", "As", "As"]
positions = np.array([[0.00, 0.00, 0.00],
[0.00, 0.00, 0.50],
[1/3., 2/3., 0.25],
[2/3., 1/3., 0.75]])
equiv_atoms = [0, 0, 1, 1]
# high-pressure FeO: Fe at As positions, O at Ni positions => afm
chem_symbols = ["O", "O", "Fe", "Fe"]
spins = ["n", "n", "u", "d"]
print(is_altermagnet(symops, positions, equiv_atoms, chem_symbols,
spins))
# MnTe: Mn at Ni positions, Te at As positions => am
chem_symbols = ["Mn", "Mn", "Te", "Te"]
spins = ["u", "d", "n", "n"]
print(is_altermagnet(symops, positions, equiv_atoms, chem_symbols,
spins))$ amcheck --ahc RuO2.vasp
==========================================================
Processing: RuO2.vasp
----------------------------------------------------------
List of atoms:
Ru [0. 0. 0.]
Ru [0.5 0.5 0.5]
O [0.30557999 0.30557999 0. ]
O [0.19442001 0.80558002 0.5 ]
O [0.80558002 0.19442001 0.5 ]
O [0.69441998 0.69441998 0. ]
Type magnetic moments for each atom
('mx my mz' or empty line for non-magnetic atom):
1 1 0
-1 -1 0
0 0 0
0 0 0
0 0 0
0 0 0
Assigned magnetic moments:
[[1.0, 1.0, 0.0], [-1.0, -1.0, 0.0], [0, 0, 0], [0, 0, 0],
[0, 0, 0], [0, 0, 0]]
Magnetic Space Group: {'uni_number': 584,
'litvin_number': 550, 'bns_number': '65.486',
'og_number': '65.6.550', 'number': 65, 'type': 3}
Conductivity tensor:
[[ 'xx' 'xy' '-yz']
[ 'xy' 'xx' 'yz']
[ 'yz' '-yz' 'zz']]
The antisymmetric part of the conductivity tensor
(Anomalous Hall Effect):
[['0' '0' '-yz']
['0' '0' 'yz']
['yz' '-yz' '0']]
Hall vector:
['-yz', '-yz', '0']
Andriy Smolyanyuk[1], Libor Šmejkal[2] and Igor I. Mazin[3]
[1] Institute of Solid State Physics, TU Wien, 1040 Vienna, Austria
[2] Johannes Gutenberg Universität Mainz, Mainz, Germany
[3] George Mason University, Fairfax, USA
If you're using the amcheck package, please cite the manuscript describing the underlying ideas:
A tool to check whether a symmetry-compensated collinear magnetic material is antiferro- or altermagnetic.
@misc{smolyanyuk2024tool,
title={A tool to check whether a symmetry-compensated collinear magnetic material is antiferro- or altermagnetic},
author={Andriy Smolyanyuk and Libor \v{S}mejkal and Igor I. Mazin},
year={2024},
eprint={2401.08784},
archivePrefix={arXiv},
primaryClass={cond-mat.mtrl-sci}
}