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Fourth- and sixth-order nonlinear spin current rectifier in three-dimensional h-wave and j-wave odd-parity magnets

Motohiko Ezawa

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Phys. Rev. B 114, 115404 – Published 5 August, 2026

DOI: https://doi.org/10.1103/zxcv-xcyc

Abstract

Higher-order symmetric X-wave magnets consist of two groups. One includes d-wave, g-wave, and i-wave altermagnets, while the other includes p-wave and f-wave odd-parity magnets. Recently, the possibility of h-wave magnets has been discussed. Motivated by this development, we systematically construct an X-wave magnet with (NX+1) nodes in three dimensions from an X-wave magnet with NX nodes in two dimensions by means of a dimensional extension, where NX=1,2,3,4,6 for X=p,d,f,g,i, respectively. Based on this method, we predict j-wave magnets in three dimensions. Then, we argue how to identify each of these X-wave magnets experimentally. We show that the X-wave magnet is completely identified by measuring the nonlinear spin currents. In particular, we predict that there are no spin currents other than the fourth-order ones such as σspinx3y;z in h-wave odd-parity magnets in three dimensions and the sixth-order ones such as σspinx5y;z in j-wave odd-parity magnets in three dimensions. They function as spin-current rectifiers because the spin current exhibits unidirectional flow independent of the applied electric field.

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Phys. Rev. B 114, 115404– Published 5 August, 2026
  • Received 25 March 2026
  • Revised 30 June 2026
  • Accepted 13 July 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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