Non-reciprocal spin-wave excitations in Rashba-Hubbard ferromagnets

TL;DR

The paper investigates nonreciprocal spin-wave excitations in a one-orbital Rashba-Hubbard ferromagnet on a square lattice. Using static Hartree-Fock mean-field theory to access ferromagnetic states and random-phase approximation to compute spin-wave spectra, it shows that in-plane magnetization yields a linear-in-$q$ contribution to the low-energy dispersion, producing $\omega({\bf q}) \neq \omega(-{\bf q})$ and direction-dependent group velocities, while out-of-plane magnetization preserves reciprocity with a quadratic dispersion. The nonreciprocity emerges from the combined influence of Rashba SOC and on-site Coulomb interaction, effectively realizing an in-plane antisymmetric DM-like effect. These results provide microscopic insight into spin-wave asymmetry at square-lattice interfaces with broken inversion symmetry and have potential implications for spintronic/magnonic device engineering.

Abstract

We explore the nonreciprocity of spin-wave excitations in the Rashba-Hubbard ferromagnet on a square lattice. Our study reveals that the propagation of spin-wave excitations exhibit non-reciprocal behavior, i.e., spin waves traveling in opposite directions display asymmetry in energy dispersion $ω({\bf q}) \ne ω(-{\bf q)}$, which also results in an asymmetric behavior of group velocity, spin stiffness, etc. We find that this asymmetric behavior arises only when the magnetic moments are aligned inside the atomic plane, while the excitations remain symmetric for out-of-plane magnetization. The first dominating term in the low-energy dispersion is linear. However, if the magnetic moments are out-of-plane, then the first dominant term is quadratic instead. The low-energy non-quadratic behavior is examined in the intermediate-to-strong coupling regime for various strengths of Rashba spin-orbit coupling.

Figures (8)

• Figure 1: (a) The DOS in the unordered state for different SOC couplings. (b) For $\lambda = 0.4$, contributions from different band to the DOS are plotted.
• Figure 2: For the unordered state, (a) the electronic dispersion is shown for $\lambda = 0.4$ along the high-symmetry direction. (b) The electronic dispersion in the entire Brillouin zone for $\lambda = 0.0$. For $\lambda = 0.4$, the two split bands $\varepsilon_1({\bf k})$ and $\varepsilon_2({\bf k})$ are shown (c) and (d).
• Figure 3: (a) Out-of-plane magnetization $m_z$ and (b) in-plane magnetization $m_x$ as a function of RSOC for different strengths of $U$.
• Figure 4: For $U = 2W$ and $\lambda = 0.3$, the spin-wave dispersion along the high-symmetry directions when the magnetic moments are aligned (a) out-of-plane and (b) in-plane ($x$-direction). Nonreciprocity is observed along -Y $\xrightarrow{}\Gamma\xrightarrow{}$ Y. In inset, a zoomed-in view of the shifted minima is shown, where the arrow indicates the shift. Similarly, in (c) moments are aligned in $y$-direction, and the non reciprocity is observed along X $\xrightarrow{}\Gamma\xrightarrow{}$ -X direction.
• Figure 5: For out-of-plane magnetic moments, (a) the spin-wave dispersion for different RSOC strength, (b) coefficient of $q^2_{x/y}$, and (c) the constant term, as a function of RSOC and $U$.