Switchable axionic magnetoelectric effect via spin-flop transition in topological antiferromagnets

Abstract

The MnBi$_2$Te$_4$ material family has emerged as a key platform for exploring magnetic topological phases, most notably exemplified by the experimental realization of the axion insulator state. While spin dynamics are known to significantly influence the axion state, a profound understanding of their interplay remains elusive. In this work, we employ an antiferromagnetic spin-chain model to demonstrate that an external magnetic field induces extrinsic perpendicular magnetic anisotropy. We find that an in-plane field stabilizes the antiferromagnetic order, whereas an out-of-plane field destabilizes it and triggers spin-flop transitions. Remarkably, near the surface spin-flop transition in even-layer MnBi$_2$Te$_4$ films, the axion insulator state undergoes a sharp switching behavior accompanied by distinct magnetoelectric responses. Furthermore, we propose that this switchable axionic magnetoelectric effect can be utilized to convert alternating magnetic field signals into measurable square-wave magneto-optical outputs, thereby realizing an axionic analog of a zero-crossing detector. Our findings could open a pathway toward potential applications of axion insulators in next-generation spintronic devices.

Figures (4)

• Figure 1: (a, b) Schematics of the field-induced perpendicular magnetic anisotropy. (a) In the absence of an external field, the magnetic energy landscape is isotropic with respect to the Néel vector orientation. (b) Under an applied magnetic field, two energy minima emerge where the Néel vector aligns perpendicular to the field direction. (c) Illustration of spin configurations, Berry curvatures of surface states, and out-of-plane magnetoelectric coefficient for even-SL AFM TIs (i) before and (ii) after the spin-flop transition induced by an external field.
• Figure 2: (a) Magnetic anisotropy energy versus Néel vector orientation under in-plane magnetic fields ($B_x$), considering only the linear Zeeman coupling: without the uniaxial anisotropy (solid lines) and with out-of-plane anisotropy (dashed lines, $D_z=0.02$ meV). (b) Magnetic energy, including both linear and higher-order coupling between the Néel vector and magnetic field, plotted as a function of higher-order coupling strength at fixed $B_x=0.5$ T: without (solid lines) and with out-of-plane uniaxial anisotropy (dashed lines). (c) Out-of-plane component ($L_z$) of the Néel vector as a function of in-plane field ($B_x$) for different interlayer exchange couplings ($J$). Insets: Schematics of spin configurations under different $B_x$ with $J$ = 0.2 meV. (d) In-plane component ($L_x$) of the Néel vector as a function of out-of-plane field $B_z$ for different out-of-plane anisotropic strengths. Insets: Schematics of spin configurations under different $B_z$ with $D_z$ = 0.02 meV.
• Figure 3: (a) Evolution of spin configurations in each SL and the difference between the $z$-component magnetic moments of top and bottom surfaces versus out-plane magnetic field $B_z$ in a six-SL MnBi$_2$Te$_4$ film, obtained from atomistic spin simulations. Surface spin-flop (SSF) and bulk spin-flop (BSF) transitions occur at $B_z=3.00$ T and $3.45$ T, respectively. (b) The out-of-plane magnetoelectric coupling coefficient $\alpha_{zz}$ and corresponding surface Berry curvature configurations as a function of out-of-plane magnetic field $B_z$. (c) Layer resolved magnetoelectric coupling coefficient $\alpha_{zz}$ in the (upper panel) AFM state and (lower panel) SSF state. (d) Thickness dependence of $\alpha_{zz}$, illustrating the finite-size effect. Detailed parameters in atomistic spin simulations and numerical calculations are provided in the SM SM.
• Figure 4: (a,b) Schematic of an axionic zero-crossing detector constructed from an even-SL MnBi$_2$Te$_4$ film, which transforms alternating input magnetic signals to square-wave outputs (a) and experimental setup (b), where a static out-of-plane magnetic field is applied to position the MnBi$_2$Te$_4$ film at its SSF transition point and an alternating out-of-plane magnetic field is further applied as the input signal. The output signal is obtained from the magneto-optical Kerr rotation angle induced by an out-of-plane electric field for an incident linearly polarized THz light. (c,d) The time-varying input alternating magnetic field (c) and the obtained square-wave-like output (d) from the corresponding Kerr angles under $48.4$-THz light. Detailed parameters in numerical calculations are provided in the SM SM.