Torsion-induced Dzyaloshinskii-Moriya interaction in helical magnets

TL;DR

This work identifies torsion-induced Dzyaloshinskii–Moriya interaction (tiDMI) as a magneto-mechanical coupling mechanism in helically ordered magnets with inversion symmetry, arising from angular-momentum transfer to the lattice during boundary reflections. Using the $s$-$d$ exchange model, it derives the tiDMI energy density coupling $\varepsilon_{\text{tiDMI}}= D_1 q \partial_z (\nabla\times\mathbf{u})_z$ and computes the microscopic constant $D_1$, along with the twist rate $\tau$ of a helimagnetic rod, showing $D_1 = \frac{\hbar^2 N}{32 m} \left( \frac{J}{\varepsilon_F} \right)^2$ and $\tau = -\frac{\langle T_z \rangle}{C}$. The analysis demonstrates that tiDMI does not drive spontaneous torsion or stabilize helimagnetic order in typical ferromagnets due to its small magnitude, but it can lift chiral degeneracy under externally imposed torsion, enabling magnetochiral states in experiments such as a holmium rod probed by neutron diffraction. The paper concludes with experimental proposals and a quantitative condition, $4 D_1 S |q| \Delta\varphi_{\text{ext}} > k_B T$, for observing chirality selection driven by tiDMI.

Abstract

It has been shown that in magnets possessing an inversion center in the absence of deformations, a torsion-induced Dzyaloshinsky-Moriya interaction (tiDMI) can arise. A microscopic mechanism for this interaction is described, involving the transfer of angular momentum to the lattice upon electron reflection from the magnet's boundary. An estimate of the tiDMI constant is provided. It is demonstrated that tiDMI can lift the chiral degeneracy in helimagnets, and a way for experimentally observing this effect is proposed.

Figures (2)

• Figure 1: Schematic illustration of (a,c) helical magnetization distributions $\mathbf{M}$ and (b,d) torsional deformation of a magnetic rod induced by the torque $\langle T_z \rangle$ associated with the corresponding $\mathbf{M}$. Blue arrows correspond to the case $q > 0$ (panel a) and $\langle T_z \rangle > 0$ (panel b), while red arrows correspond to $q < 0$ (panel c) and $\langle T_z \rangle < 0$ (panel d). In each case, one end of the rod is free ($z = 0$) and the other is rigidly fixed ($z = L$).
• Figure 2: Schematic illustration of magnetization distributions $\mathbf{M}$ in a helimagnetic rod maintained at $T < T_N$: (a) uniform $\mathbf{M}$ stabilized when $H > H_c$; (b) right-handed (blue arrows, $q > 0$) and left-handed (red arrows, $q < 0$) magnetic helices forming at $H < H_c$ and occupying equal volumes. Schematic illustration of chiral symmetry breaking induced by an external torque $T_z^{\text{ext}}$ that twists the rod under conditions $T < T_N$ and $H < H_c$: (c) enhanced volume fraction of the right-handed helix for $T_z^{\text{ext}} > 0$; (d) enhanced volume fraction of the left-handed helix for $T_z^{\text{ext}} < 0$. The component of $\mathbf{M}$ parallel to $\mathbf{H}$ in panels b--d is neglected.