Fourth-order and six-order nonlinear spin current diode in $h$-wave and $j$-wave odd-parity magnets

TL;DR

This paper predicts higher-order nonlinear spin current diodes in $h$-wave and $j$-wave odd-parity magnets, revealing unique fourth- and sixth-order spin current behaviors that enable unidirectional spin-current flow.

Contribution

It introduces a systematic method to construct and identify $X$-wave magnets with multiple nodes and predicts novel higher-order spin current diode effects in these materials.

Findings

No spin currents other than fourth-order in $h$-wave magnets.

No spin currents other than sixth-order in $j$-wave magnets.

Spin currents act as unidirectional diodes, independent of electric field direction.

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 $\left( N_{X}+1\right) $ nodes in three dimensions from an $X$-wave magnet with $N_{X}$ nodes in two dimensions by means of a dimensional extension, where $N_X=1,2,3,4,6$ 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 $\sigma _{\text{spin}}^{x^{3}y;z}$ in $h$-wave odd-parity magnets in three dimensions and the sixth-order ones such as $\sigma _{\text{spin}}^{x^{5}y;z}$ in $j$-wave odd-parity magnets in three dimensions. They function as spin-current diodes because the spin current exhibits unidirectional flow independent of the applied electric field.