Strongly anisotropic spin dynamics in magnetic topological insulators

The recent discovery of magnetic topological insulators has opened new avenues to explore exotic states of matter that can emerge from the interplay between topological electronic states and magnetic degrees of freedom, be it ordered or strongly fluctuating. Motivated by the effects that the dynamics of the magnetic moments can have on the topological surface states, we investigate the magnetic fluctuations across the $\left({\mathrm{MnBi}}_2{\mathrm{Te}}_4\right){\left({\mathrm{Bi}}_2{\mathrm{Te}}_3\right)}_{\mathrm{n}}$ family. Our paramagnetic electron spin resonance experiments reveal contrasting Mn spin dynamics in different compounds, which manifests in a strongly anisotropic Mn spin relaxation in ${\mathrm{MnBi}}_{\text{2}}{\mathrm{Te}}_{\text{4}}$ while being almost isotropic in ${\mathrm{MnBi}}_{\text{4}}{\mathrm{Te}}_{\text{7}}$. Our density-functional calculations explain these striking observations in terms of the sensitivity of the local electronic structure to the Mn spin orientation, and indicate that the anisotropy of the magnetic fluctuations can be controlled by the carrier density, which may directly affect the electronic topological surface states.

Figure 1

ESR measurements. (a), (b) Temperature dependence of the spectra (field derivatives of the microwave absorption) with $H\parallel c$, for ${\mathrm{MnBi}}_{\text{2}}{\mathrm{Te}}_{\text{4}}$ and ${\mathrm{MnBi}}_{\text{4}}{\mathrm{Te}}_{\text{7}}$, respectively. (c) Angular dependence of the linewidth $\mathrm{\Delta }H$ and of the resonance field $H_{\mathrm{res}}$ at $T=20$ K for ${\mathrm{MnBi}}_{\text{2}}{\mathrm{Te}}_{\text{4}}$. Solid lines are fits of $\mathrm{\Delta }H\sim [1+{cos}^2\left(\theta \right)]$ and $H_{\mathrm{res}}\sim [1+{sin}^2\left(\theta \right)]$, where $\theta$ is the angle between $H$ and the $c$ axis. (d), (e) Temperature dependence of $H_{\mathrm{res}}$ and $\mathrm{\Delta }H$ measured with two field orientations for ${\mathrm{MnBi}}_{\text{2}}{\mathrm{Te}}_{\text{4}}$ and ${\mathrm{MnBi}}_{\text{4}}{\mathrm{Te}}_{\text{7}}$, respectively. Dashed lines are fits of the Korringa dependence $\mathrm{\Delta }H\left(T\right)=\mathrm{\Delta }{H}_0+bT$ while vertical dashed lines indicate the Néel temperature $T_{\mathrm{N}}$ and a crossover characteristic temperature $T^{*}$ between two different types of temperature behavior of $H_{\mathrm{res}}$ and $\mathrm{\Delta }H$.

Figure 2

(a), (b) Band structure and density of states, respectively, of ${\mathrm{MnBi}}_{\text{2}}{\mathrm{Te}}_{\text{4}}$ in the AFM phase for out-of-plane (blue) or in-plane (red) Mn magnetic moment direction. (c), (d) Analogous results for ${\mathrm{MnBi}}_{\text{4}}{\mathrm{Te}}_{\text{7}}$.

Figure 3

(a), (b) Pictorial representation of the anisotropic spin dynamics. An out-of-plane Mn spin is accompanied by a relatively small carrier DOS (gray electron cloud) and, accordingly, has a relatively slow dynamics as compared to an in-plane Mn spin, accompanied by a larger DOS and presenting faster dynamics. (c), (d) Estimation of relaxation rate ratio as a function of the carrier density for ${\mathrm{MnBi}}_{\text{2}}{\mathrm{Te}}_{\text{4}}$ (c) and for ${\mathrm{MnBi}}_{\text{4}}{\mathrm{Te}}_{\text{7}}$ (d). The gray circles correspond to the experimental ESR data, estimating $n$ from the Hall measurements on the same samples in Refs. [1, 13], respectively.