# Magnetic hedgehog lattices in noncentrosymmetric metals

## TL;DR

This paper investigates the microscopic origins and stability of magnetic hedgehog lattices in noncentrosymmetric metals, revealing their stabilization mechanisms and phase transitions under magnetic fields through theoretical modeling.

## Contribution

It demonstrates that HLs are stabilized at zero magnetic field by spin-orbit and spin-charge interactions, providing a microscopic understanding of their origin and behavior.

## Key findings

- HLs are stabilized at zero field by spin interactions.
- Phase diagram includes topological transitions with monopole pair annihilation.
- Different types of HLs can exist even at zero magnetic field.

## Abstract

The magnetic hedgehog lattice (HL) is a noncoplanar magnetic texture with a periodic array of magnetic monopoles and anti-monopoles. Despite phenomenological and numerical studies thus far, there remain open issues on the microscopic origin, especially with respect to the recent experimental findings of two different types of HLs even at zero magnetic field. Here, we study the stability of the HLs for an effective spin model with long-range interactions arising from itinerant nature of electrons. By variational calculations and simulated annealing, we find that the HLs are stabilized in the ground state at zero magnetic field by the synergetic effect of the anti-symmetric exchange interactions generated by the spin-orbit coupling and the multiple-spin interactions generated by the spin-charge coupling. We also clarify the phase diagram in the magnetic fields, which includes topological phase transitions with pair annihilation of the monopoles and anti-monopoles depending on the field directions.