Magnetic Hedgehog Lattice in a Centrosymmetric Cubic Metal

TL;DR

This study demonstrates the stabilization of a magnetic hedgehog lattice in a centrosymmetric cubic metal through simulated annealing, revealing unique topological properties and field-dependent behaviors distinct from noncentrosymmetric systems.

Contribution

The paper introduces a theoretical model showing the stabilization of a hedgehog lattice in a centrosymmetric metal, contrasting with previous noncentrosymmetric cases, and analyzes its magnetic and topological properties.

Findings

Stabilization of a hedgehog lattice with no net scalar spin chirality.

Transition of the hedgehog lattice into trivial conical states under magnetic field.

Gradual change in ellipticity and angles of spin helices with increasing magnetic field.

Abstract

The hedgehog lattice (HL) is a three-dimensional topological spin texture hosting a periodic array of magnetic monopoles and antimonopoles. It has been studied theoretically for noncentrosymmetric systems with the Dzyaloshinskii-Moriya interaction, but the stability, as well as the magnetic and topological properties, remains elusive in the centrosymmetric case. We here investigate the ground state of an effective spin model with long-range bilinear and biquadratic interactions for a centrosymmetric cubic metal by simulated annealing. We show that our model stabilizes a HL composed of two pairs of left- and right-handed helices, resulting in no net scalar spin chirality, in stark contrast to the noncentrosymmetric case. We find that the HL turns into topologically-trivial conical states in an applied magnetic field. From the detailed analyses of the constituent spin helices, we clarify that the ellipticity and angles of the helical planes change gradually while increasing the magnetic field. We discuss the results in comparison with the experiments for a centrosymmetric cubic metal SrFeO$_3$.