Ferromagnetic Resonance Spectroscopy on the Kagome Magnet MgMn$_6$Sn$_6$

TL;DR

MgMn6Sn6 is a kagome ferromagnet with a nontrivial topological electronic structure. The authors perform broadband ferromagnetic resonance measurements across a wide frequency, field, and temperature range and model the data with linear spin-wave theory using SpinW to extract the intrinsic magnetocrystalline anisotropy. They find a strong easy-plane anisotropy with a large anisotropy energy density that persists toward the ordering temperature, indicating substantial orbital contributions to Mn moments and a significant role of spin-orbit coupling. These results support SOC as essential for the material's topological electronic properties and anomalous Hall effect, and they motivate first-principles calculations to connect the anisotropy to the electronic structure.

Abstract

MgMn$_6$Sn$_6$ is the itinerant ferromagnet on the kagome lattice with high ordering temperature featuring complex electronic properties due to the nontrivial topological electronic band structure, where the spin-orbit coupling (SOC) plays a crucial role. Here, we report a detailed ferromagnetic resonance (FMR) spectroscopic study of MgMn$_6$Sn$_6$ aimed to elucidate and quantify the intrinsic magnetocrystalline anisotropy that is responsible for the alignment of the Mn magnetic moments in the kagome plane. By analyzing the frequency, magnetic field, and temperature dependences of the FMR modes, we have quantified the magnetocrystalline anisotropy energy density that reaches the value of approximately $ 3.5\cdot 10^6$ erg/cm$^3$ at $T = 3$ K and reduces to about $1\cdot 10^6$ erg/cm$^3$ at $T = 300$ K. The revealed significantly strong magnetic anisotropy suggests a sizable contribution of the orbital magnetic moment to the spin magnetic moment of Mn, supporting the scenario of the essential role of SOC for the nontrivial electronic properties of MgMn$_6$Sn$_6$.

Figures (8)

• Figure 1: Crystal structure of MgMn$_6$Sn$_6$. The atoms are colored as Mg = light blue, Mn = red, Sn = dark yellow. Red arrows depict the direction of the Mn magnetic moments in the ferromagnetically ordered state. (a) The unit cell can be viewed as composed of two slabs of atoms Mn--(Mg-Sn)--Mn and Mn--Sn--Sn--Sn--Mn stacking along the $c$-axis. (b) Mn atoms in each slab form the kagome lattice with the magnetic moments ferromagnetically ordered in the $ab$-plane.
• Figure 2: Spin wave excitation spectrum of MgMn$_6$Sn$_6$ modeled with the SpinW software. (a) Energy dispersion of the 6 spin wave modes in the magnetic Brillouin zone. (b) Inelastic neutron scattering intensity (cross-section) Re S$^\perp(\hbar\omega,\mathbf{q}$) as a function of the momentum transfer $\mathbf{q}$.
• Figure 3: Magnetic field dependence of the energy of the uniform (${\bf q} = 0$) spin wave mode of MgMn$_6$Sn$_6$ for different orientations of the applied magnetic field calculated with the SpinW software.
• Figure 4: (a) Spectra at different frequencies for $\mathbf{H}\parallel\mathbf{c}$ at $T = 3$ K. The FMR signal is marked by circles, and the parasitic line is marked by crosses. (b) Spectra at different temperatures for $\mathbf{H}\perp\mathbf{c}$ at $\nu = 144$ GHz. The position of the FMR signal is traced by the dashed line, and that of the parasitic signal is marked by the vertical dotted line at the resonance field corresponding to $g = 2$ at this frequency. (c) Temperature dependence of the resonance field of the FMR signal for $\mathbf{H}\parallel\mathbf{c}$ (circles) and $\mathbf{H}\perp\mathbf{c}$ (squares), and of the parasitic signal (crosses) at $\nu = 144$ GHz. The dashed line denotes the paramagnetic resonance field with $g = 2$ at this frequency.
• Figure 5: Frequency $\nu$versus resonance field $H_{\rm res}$ dependence of the spectral lines at $T = 3$ K for $\mathbf{H}\parallel\mathbf{c}$ and $\mathbf{H}\perp\mathbf{c}$ field geometries. Circles and squares correspond to FMR signals in the two field orientations, and crosses denote $H_{\rm res}$ of the parasitic signal. Solid curves are results of the numerical modeling of the FMR branches. Dashed line denotes the paramagnetic resonance branch $\nu = (g\mu_{\rm B}\mu_{0}/h)H$ with $g = 2$.