Non-collinear antiferromagnetic states in Ru-based Heusler compounds induced by biquadratic coupling

TL;DR

This study reveals that biquadratic coupling and frustrated isotropic interactions in Ru-based Heusler compounds induce non-collinear antiferromagnetic states, with thermal stability varying between different compositions.

Contribution

It demonstrates how biquadratic coupling leads to non-collinear magnetic ground states in Ru$_{2}$Mn$Z$ compounds, expanding understanding of magnetic interactions in Heusler materials.

Findings

Non-collinear ground states are stabilized by biquadratic coupling.

Ru$_{2}$MnSi transitions from multi-q to single-q phase with temperature.

Ru$_{2}$MnSb maintains multi-q phase due to stronger biquadratic coupling.

Abstract

We investigate the magnetic properties of Ru$_{2}$Mn$Z$ ($Z$ = Sn, Sb, Ge, Si) chemically ordered full Heusler compounds for zero as well as finite temperatures. Based on first principles calculations we derive the interatomic isotropic bilinear and biquadratic couplings between Mn atoms from the paramagnetic state. We find frustrated isotropic couplings for all compounds and in case of $Z$ = Si and Sb a nearest-neighbor biquadratic coupling that favors perpendicular alignment between the Mn spins. By using an extended classical Heisenberg model in combination with spin dynamics simulations we obtain the magnetic equilibrium states. From these simulations we conclude that the biquadratic coupling, in combination with the frustrated isotropic interactions, leads to non-collinear magnetic ground states in the Ru$_{2}$MnSi and Ru$_{2}$MnSb compounds. In particular, for these alloys we find two distinct, non-collinear ground states which are energetically equivalent and can be identified as $3-q$ and $4-q$ states on a frustrated fcc lattice. Investigating the thermal stability of the non-collinear phase we find that in case of Ru$_{2}$MnSi the multiple$-q$ phase undergoes a transition to the single$-q$ phase, while in case of Ru$_{2}$MnSb the corresponding transition is not obtained due to the larger magnitude of the nearest-neighbor biquadratic coupling.