Mechanism of antisymmetric spin polarization in centrosymmetric multiple-$Q$ magnets based on bilinear and biquadratic spin cross products

TL;DR

This paper reveals how antisymmetric spin polarization can be engineered in centrosymmetric magnets without spin-orbit coupling by analyzing spin cross products in momentum space, with implications for spintronic applications.

Contribution

It introduces a theoretical framework linking spin cross products to antisymmetric spin polarization in centrosymmetric systems without spin-orbit coupling.

Findings

Derived a formula relating spin cross products to spin polarization.

Applied the theory to specific magnetic states like cycloidal spirals and skyrmion crystals.

Proposed a mechanism for giant spin splitting driven by magnetic phase transitions.

Abstract

We investigate how to engineer an antisymmetric spin-split band structure under spin density waves with finite ordering wave vectors in centrosymmetric systems without the relativistic spin-orbit coupling. On the basis of a perturbative analysis for the spin-charge coupled model in centrosymmetric itinerant magnets, we show that nonzero chiral-type bilinear and biquadratic spin cross products in momentum space under the magnetic orderings are related to an antisymmetric spin polarization in the electronic band structure. We apply the derived formula to the single-$Q$ cycloidal spiral and double-$Q$ noncoplanar states including the meron-antimeron and skyrmion crystals. Our results present a clue to realize a giant antisymmetric spin splitting driven by magnetic phase transitions in the centrosymmetric lattice structures without the spin-orbit coupling.