Large anomalous Hall effect and unusual domain switching in an orthorhombic antiferromagnetic material NbMnP

Fig. 5 Asymmetric hysteresis appearing after FC in NbMnP.

Hysteresis loops of ρzy at 10 K after different cooling processes;

a ZFC, b FC under + 0.3 T, and c FC under − 0.3 T. The numbers

indicate the order of field sweeps. The arrows of “start” show the

sweeping direction from the initial position. Asymmetric hysteresis

appeared after FC, reminiscent of the exchange bias.

(GGA) in the parametrization of Perdew, Burke, and Ernzerhof33

was used for the exchange-correlation functional, and the

pseudopotentials in the projector augmented-wave method34,35

were generated by PSLIBRARY36. The lattice constants

a = 6.1661 Å, b = 3.5325 Å, and c = 7.2199 Å from previous

experiments at 9 K19 were used. Starting from the experiment

atomic positions, until residual forces < 0.01 eV/Å were reached,

the atomic positions were fully relaxed. Next, we chose kinetic

cutoff energies of 50 and 400 Ry as the plane-wave basis set and

charge density, respectively. A k mesh of 9 × 15 × 9 had sampled

the first BZ with a Methfessel-Paxton smearing width of 0.005 Ry

to get the Fermi level. We used the PAOFLOW package37,38 to

estimate AHC. A 18 × 30 × 18 Monkhorst-Pack k-point grid

generated a tight-binding set of pseudo-atomic orbitals for

subsequent AHC calculations. Wannier9039 plotted the Berry

curvature in the BZ. The 4d and 5s orbitals of Nb, the 3d and 4s

orbitals of Mn, and the 3s and 3p of P were included for the

Wannier interpolation scheme using Wannier90 to construct

realistic tight-binding models from the first-principles band

structures40.

The AHC was calculated using the Kubo formula40.

σ αβ ¼ 

e2

dk X

ð2πÞ3

f ½εn ðkÞ  μΩn;αβ ðkÞ;

npj Quantum Materials (2023) 56

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ACKNOWLEDGEMENTS

We thank Hisatomo Harima and Youichi Yanase for valuable discussions and

comments. This work was supported by JSPS KAKENHI Grant Nos. 18H04320,

18H04321, 19H01842, 21H01789, 21H04437, 21K03446, and 23H04871, Iketani

Science and Technology Foundation, Hyogo Science and Technology Association,

and The Murata Science Foundation. A part of the numerical calculation was

performed in MASAMUNE-IMR of the Center for Computational Materials Science,

Institute for Materials Research, Tohoku University.

Published in partnership with Nanjing University

AUTHOR CONTRIBUTIONS

H.K. conceived of and designed the study. H.K., Y.K, and H.S. synthesized the single

crystal. K.T. performed the single-crystal X-ray diffraction measurements. H.K., Y.A.,

and H.T. performed the Hall resistivity measurements. V.T.N.H. and M.T.S. calculated

the Berry curvature and AHC, and provided theoretical input for the interpretation

of the results. M.M. provided information about the magnetic symmetry obtained

from the neutron scattering experiments. H.K. wrote the paper with assistance from

V.T.N.H. and M.T.S.

COMPETING INTERESTS

The authors declare no competing interests.

ADDITIONAL INFORMATION

Supplementary information The online version contains supplementary material

available at https://doi.org/10.1038/s41535-023-00587-2.

Correspondence and requests for materials should be addressed to Hisashi

Kotegawa.

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