[Paper Review] Dzyaloshinskii-Moriya interaction in absence of spin-orbit coupling

Ramon Cardias, Anders Bergman+6 more|arXiv (Cornell University)|Mar 10, 2020

Magnetic properties of thin films32 references4 citations

TL;DR

This paper demonstrates that the Dzyaloshinskii-Moriya (DM) interaction can arise from non-relativistic, non-collinear spin textures rather than solely from spin-orbit coupling. Using first-principles electronic structure theory, it shows that in Mn₃Sn, non-collinearity induces significant spin-current and spin-density contributions that dominate over relativistic SOC effects, explaining the material's weak ferromagnetism and topological transport properties.

ABSTRACT

In contrast to conventional assumptions, we show that the Dzyaloshinskii-Moriya interaction can be of non-relativistic origin, in particular in materials with a non-collinear magnetic configuration, where non-relativistic contributions can dominate over spin-orbit effects. The weak antiferromagnetic phase of Mn$_{3}$Sn is used to illustrate these findings. Using electronic structure theory as a conceptual platform, all relevant exchange interactions are derived for a general, non-collinear magnetic state. It is demonstrated that non-collinearity influences all three types of exchange interaction and that physically distinct mechanisms, which connect to electron- and spin-density and currents, may be used as a general way to analyze and understand magnetic interactions of the solid state.

Motivation & Objective

• To challenge the conventional view that the Dzyaloshinskii-Moriya (DM) interaction requires spin-orbit coupling (SOC) for its origin.
• To investigate the role of non-collinear magnetic order in generating DM-like interactions through non-relativistic mechanisms.
• To disentangle contributions from charge-current, spin-current, charge-density, and spin-density in exchange interactions.
• To explain the weak ferromagnetism and large anomalous Hall effect in Mn₃Sn using a non-collinear, non-relativistic framework.

Proposed method

• Employed first-principles electronic structure theory based on the Liechtenstein-Katsnelson-Antropov-Gubanov approach, generalized to non-collinear magnetic states.
• Derived all bilinear exchange interactions (Heisenberg, DM, anisotropic symmetric) from the spin-dependent exchange tensor using linear response theory.
• Decomposed the effective exchange interactions into four physically distinct contributions: charge-current (CC), spin-current (SC), charge-density (CD), and spin-density (SD) terms.
• Used the ELK code to compute total energy differences and magnetic anisotropy, including SOC effects via perturbative treatment.
• Analyzed the angular dependence of exchange parameters (J, D, A) as a function of the magnetic twist angle θ in a model Mn₃Sn unit cell.
• Applied a generalized framework to separate relativistic and non-relativistic contributions to spin-orbit-like effects in non-collinear systems.

Experimental results

Research questions

• RQ1 Can the Dzyaloshinskii-Moriya interaction originate from non-relativistic, non-collinear spin textures without spin-orbit coupling?
• RQ2 What are the relative contributions of charge-current, spin-current, charge-density, and spin-density mechanisms to the DM interaction in non-collinear magnets?
• RQ3 How does non-collinearity influence the strength and angular dependence of exchange interactions in Mn₃Sn?
• RQ4 To what extent can non-collinear spin textures mimic or dominate over spin-orbit coupling effects in phenomena like the anomalous Hall effect or spin Hall effect?
• RQ5 Is the weak ferromagnetism in Mn₃Sn explainable by non-relativistic mechanisms rather than conventional SOC-driven mechanisms?

Key findings

• The Dzyaloshinskii-Moriya interaction in Mn₃Sn has a dominant non-relativistic origin arising from non-collinear spin textures, particularly via spin-current and spin-density contributions.
• The spin-current (SC) and spin-density (SD) terms show strong angular dependence and are non-zero only in non-collinear configurations, vanishing in the collinear limit.
• The charge-current (CC) term is negligible in the co-planar state, confirming that it is primarily a SOC-induced effect, while non-collinearity drives the dominant non-relativistic contributions.
• In Mn₃Sn, the non-collinear spin texture generates a significant DM interaction that explains the observed weak ferromagnetism, even though the crystal symmetry forbids a net torque via standard symmetry arguments.
• The magnetic anisotropy due to non-collinearity is calculated to be ~3 μeV, consistent with experimental observations and comparable in magnitude to SOC-induced anisotropy.
• Non-collinearity can generate spin-currents and spin-orbit-like effects that dominate over traditional SOC effects in spintronic phenomena such as the spin Hall effect and spin relaxation mechanisms.