Giant anomalous Nernst effect in noncollinear antiferromagnetic Mn-based antiperovskite nitrides

Xiaodong Zhou, Jan-Philipp Hanke, Wanxiang Feng, Stefan Blügel, Yuriy Mokrousov, and Yugui Yao

Phys. Rev. Materials 4, 024408 – Published 13 February 2020

Abstract

The anomalous Nernst effect (ANE)—the generation of a transverse electric voltage by a longitudinal heat current in conducting ferromagnets or antiferromagnets—is an appealing approach for thermoelectric power generation in spin caloritronics. The ANE in antiferromagnets is particularly convenient for the fabrication of highly efficient and densely integrated thermopiles as lateral configurations of thermoelectric modules increase the coverage of heat source without suffering from the stray fields that are intrinsic to ferromagnets. In this work, using first-principles calculations together with a group theory analysis, we systematically investigate the spin-order-dependent ANE in noncollinear antiferromagnetic Mn-based antiperovskite nitrides ${Mn}_{3} X N (X = Ga$ , Zn, Ag, and Ni). The ANE in ${Mn}_{3} X N$ is forbidden by symmetry in the $R 1$ phase but amounts to its maximum value in the $R 3$ phase. Among all ${Mn}_{3} X N$ compounds, ${Mn}_{3} NiN$ presents the most significant anomalous Nernst conductivity of $1.80 A K^{- 1} m^{- 1}$ at 200 K, which can be further enhanced if strain, electric, or magnetic fields are applied. The ANE in ${Mn}_{3} NiN$ , being one order of magnitude larger than that in the famous ${Mn}_{3} Sn$ , is the largest one discovered in antiferromagnets so far. The giant ANE in ${Mn}_{3} NiN$ originates from the sharp slope of the anomalous Hall conductivity at the Fermi energy, which can be understood well from the Mott relation. Our findings provide a host material for realizing antiferromagnetic spin caloritronics that promises exciting applications in energy conversion and information processing.

Received 15 September 2019
Revised 7 January 2020
Accepted 27 January 2020

DOI:https://doi.org/10.1103/PhysRevMaterials.4.024408

Physics Subject Headings (PhySH)

Spintronics Thermoelectric effects

Antiferromagnets

First-principles calculations

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Xiaodong Zhou ¹, Jan-Philipp Hanke ², Wanxiang Feng ^1,2,*, Stefan Blügel², Yuriy Mokrousov^2,3, and Yugui Yao¹

¹Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement, Ministry of Education, School of Physics, Beijing Institute of Technology, Beijing 100081, China
²Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
³Institute of Physics, Johannes Gutenberg University Mainz, 55099 Mainz, Germany

^*wxfeng@bit.edu.cn

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Vol. 4, Iss. 2 — February 2020

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Images

Figure 1
Crystal and magnetic structures of ${Mn}_{3} X N$ . (a)–(c) Different spin orders in ${Mn}_{3} X N$ as classified by the $R 1, R 2$ , and $R 3$ phases. The yellow, blue, and purple spheres represent Mn, $X$ , and N atoms, respectively. The red arrows label the directions of the spin magnetic moments of Mn atoms, which lie on the (111) plane highlighted in green. The azimuthal angle $φ$ , defined as the spin-order parameter, measures the rotation of spins away from the face diagonals of the cube. (d)–(f) Top view of the noncollinear spin order in the (111) plane. $M_{1}, M_{2}$ , and $M_{3}$ in (d) are three mirror symmetries; ${TM}_{1}, {TM}_{2}$ , and ${TM}_{3}$ in (f) are the symmetries combining mirror and time-reversal $(T)$ operations. The $C_{3}$ rotation with respect to the $z$ axis is always present in (d)–(f).
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Figure 2
Anomalous Nernst conductivity (ANC) and Berry curvature in ${Mn}_{3} X N$ . (a) ANC as a function of the azimuthal angle $φ$ at the temperature $T = 200$ K. (b) ANC as a function of temperature when $φ = 90^{\circ} (R 3$ phase), where the shaded regions indicate the temperature regimes in which the $R 3$ phase exists in ${Mn}_{3} NiN$ and ${Mn}_{3} AgN$ . The solid lines in (a) and (b) are the polynomial fittings. (c)–(f) The Berry curvature (in arbitrary units) of ${Mn}_{3} NiN$ on the $k_{z} = 0$ plane when $T = 200$ K for the azimuthal angles of $φ = 0^{\circ}, 30^{\circ}, 60^{\circ}$ , and $90^{\circ}$ , respectively. The dashed black lines mark the first Brillouin zone.
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Figure 3
Origin of the large ANE in ${Mn}_{3} NiN$ and its tunability by various fields. (a) The ANC recorded for various ferromagnets and two antiferromagnets $({Mn}_{3} Sn$ and ${Mn}_{3} NiN)$ . Part of the data is taken from previous works [15, 37, 38, 39]. (b),(c) The AHC and ANC of ${Mn}_{3} NiN$ as a function of energy. The ANC $α_{x y}$ is calculated at the temperature $T = 200$ K using the formula of Berry curvature [Eq. (A2)] and also the generalized Mott relation [Eq. (2)]. (d) The ANC $α_{x y}$ of ${Mn}_{3} NiN$ as a function of canting angle $θ$ and strain $δ$ at $T = 200$ K. The positive and negative values of $θ$ indicate the canting of all three spins along the [111] and $[\bar{1} \bar{1} \bar{1}]$ directions, respectively.
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Figure 4
Schematics of the anomalous Nernst effect and thermopile structures. (a) Anomalous Nernst effects. (b) Thermopile made out of an array of thermoelectric modules that use the ANE in collinear ferromagnets. (c) Center panel: Unconventional thermopile based on the ANE in chiral noncollinear antiferromagnets. Left and right panels: The two noncollinear antiferromagnetic domain walls, as seen from the (111) plane of cubic ${Mn}_{3} X N$ , are mutual partners connected by time-reversal symmetry.
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