Magneto-optical Response of 5-SL MnBi$_2$Te$_4$ in Spin-Flip States

Abstract

Magneto-optical effects like Kerr and Faraday rotations provide a direct probe of topological order in thin films of the magnetic topological insulator MnBi$_2$Te$_4$ (MBT). Motivated by recent experimental studies of spin-flip/flop transitions in MBT thin films, we investigate the interplay between interlayer spin configurations, topological order, and magneto-optical response in five septuple-layer (5-SL) MBT using first-principles calculations and a simplified coupled-Dirac-cone model. Our results reveal that, despite possessing a non-zero out-of-plane magnetization, 5-SL MBT thin films can be either ${\cal C}=+1$ topological insulators or ${\cal C}=0$ topologically trivial insulators depending on the relative spin orientations of the top and bottom SLs. We evaluate the Faraday and Kerr rotation angles using tight-binding models derived from \textit{ab-initio} calculations and by comparing our results with those of a simplified coupled Dirac-cone model clarify the macroscopic mechanisms underlying the magneto-optical response of spin-flip states. These theoretical findings highlight the tunability of topological and magneto-optical properties in MBT thin films and provide microscopic insight into the emergence of complex topological order in layered antiferromagnetic materials.

Figures (7)

• Figure 1: (left) Schematic of a 5-SL MnBi$_{2}$Te$_{4}$ in the AFM ground state configuration. (right) Alternate spin-flip configurations with the same net magnetic moment of $5\mu_B$. Energy difference per unit cell (in meV) compared to the AFM ground state and band gaps (in meV) are given at the bottom of degenerate cases in magenta and black colors, respectively.
• Figure 2: (a) Band structure of a 5-SL MnBi$_{2}$Te$_{4}$ in the AFM ground state (GS) configuration. (b) Band structure of degenerate spin-flip alignments having 1.1 meV higher energy than the GS.
• Figure 3: (a) Topological nature of different spin flip alignments. Blue columns represent ${|\cal C}|=+1$ and red columns show ${\cal C}=0$ cases, depending on the spin alignment of the top-most and bottom-most SLs. (b) Quasi-1D left and right side-wall edge states of 110 surface, shown for the two representative ${|\cal C}|=+1$ and ${\cal C}=0$ cases, respectively.
• Figure 4: Frequency-dependent optical conductivity (in units of $e^2/h$) for the two representative spin-flipped 5-SL MnBi$_2$Te$_4$ cases. (a,c) transverse (Hall) conductivity ($\sigma_{xy}$) and (b,d) longitudinal conductivity ($\sigma_{xx}$) for the representative ${\cal C}=+1$ and ${\cal C}=0$. In each case, real and imaginary part is shown in blue and red colors, respectively. The TSS gap is shown as black dotted line.
• Figure 5: Magneto-optical response of two representative spin-flipped 5-SL MnBi$_2$Te$_4$ cases. (a,c) Faraday rotation angle, and (b,d) Kerr rotation angle (in radian (rad)) against optical frequency ($\omega$) for the representative ${\cal C}=+1$ and ${\cal C}=0$ cases.