A microscopic model for spiral ordering along (110) on the MnSi lattice

TL;DR

This paper presents a microscopic Heisenberg model on the MnSi lattice that explains spiral magnetic ordering along (110), highlighting the effects of various interactions and anisotropies, and its potential relevance to MnSi's partially ordered state.

Contribution

The study introduces a detailed Heisenberg model capturing spiral ordering in MnSi, emphasizing the role of specific exchange interactions and anisotropies in determining magnetic order directions.

Findings

Spiral ordering along (110) is common for certain exchange parameters.

Dzyaloshinskii-Moriya interaction has limited effect on ordering direction.

Magnetic anisotropy can shift ordering from (110) to (111).

Abstract

We study an extended Heisenberg model on the MnSi lattice. In the cubic B20 crystal structure of MnSi, Mn atoms form lattices of of corner-shared equilateral triangles. We find an ubiquitous spiral ordering along (110) for J1 <0, and J2=J3 >0, where J1, J2, and J3 are 1st, 2nd and 3rd nearest neighbor Heisenberg interactions, respectively. While the ordering direction of (110) is reasonably robust to the presence of the Dzyaloshinskii-Moriya interaction, it can be shifted to the (111) direction with the introduction of a magnetic anisotropy term for small J2/|J1|. We discuss the possible relevance of these results to the partially ordered state recently reported in MnSi.