RKKY signatures as a probe of band properties and photoinduced topological phase transitions in MnBi$_2$Te$_4$ films

TL;DR

The paper develops a magnetic probe based on RKKY interactions to diagnose band properties and photoinduced phase transitions in MnBi$_2$Te$_4$ films. By modeling two coupled surface Dirac cones and computing the RKKY interaction via real-space Green’s functions, the authors show that intrinsic magnetism and septuple-layer parity imprint distinct signatures on the spin textures, oscillations, and spin-frustrated terms. They identify robust markers of even- versus odd-SL films, including Fermi-energy kinks, single- versus double-period oscillations, and the presence of spin-frustrated terms, as well as polarization-chirality–dependent topological transitions under off-resonant CPL. Collectively, these results position RKKY interactions as a powerful, non-transport diagnostic tool that complements electrical measurements for exploring intrinsic magnetism–driven surface states and light-driven phase transitions in MnBi$_2$Te$_4$.

Abstract

We present a systematic study of the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction in MnBi$_2$Te$_4$ films under both dark and illuminated conditions. In the dark, the intrinsic magnetism of MnBi$_2$Te$_4$ is shown to yield a stronger anisotropic RKKY spin model compared to nonmagnetic topological insulators, providing a clear signature for differentiating these systems. Furthermore, key band properties -- such as energy gap, band degeneracy/splitting, and topological deformations of the Fermi surface -- imprint distinct signatures on the RKKY interaction, enabling clear discrimination between even- and odd-septuple-layer (SL) films. This discrimination manifests in multiple ways: through the Fermi-energy dependence or spatial oscillations of the interaction for impurities on the same surface, or via the presence versus absence of spin-frustrated terms for those on different surfaces. Under off-resonant circularly polarized light, we track photoinduced topological phase transitions and identify two characteristic signatures at the phase boundary: a sign reversal in spin-frustrated terms and a dip in collinear RKKY components. These serve as fingerprints for circular-polarization-chirality-dependent topological transitions in even- and odd-SL films, respectively. Overall, this work establishes RKKY interactions as a sensitive magnetic probe for revealing both distinctive band properties and light-driven phase transitions in MnBi$_2$Te$_4$ films, thereby complementing conventional electrical measurements while providing new insights into the influence of intrinsic magnetism on the surface-state band structure.

Figures (10)

• Figure 1: $k_x$-axis dispersion for (a) even-SL ($\lambda = -$) and (b) odd-SL ($\lambda = +$) MnBi$_2$Te$_4$ films at different Zeeman coupling strengths ($m = 0$, $0.025$ eV). Other parameters are $\Delta = 0.02$ eV and $v = 2.95\ \mathrm{eV \cdot \r{A}}$.
• Figure 2: Fermi surfaces of (a,b) even-SL ($\lambda=-$) and (c,d) odd-SL ($\lambda=+$) MnBi$_2$Te$_4$ thin films for different Zeeman coupling strengths $m = 0, 0.025$ eV. The Fermi energy is set to $\epsilon_F = 0.04$ eV in (a,c) and $0.06$ eV in (b,d). Other parameters are identical to those in Fig. \ref{['fig1']}. Labels $k_F$ and $k_{F_\pm}$ in (b,d) denote the Fermi wave numbers for the even- and odd-SL films, respectively.
• Figure 3: Evolution of the $k_x$-axis dispersion for even-SL ($\lambda=-$) MnBi$_2$Te$_4$ films at different light parameter $k_a$: (a) $k_a=0$, (b) $k_a<k_0$ (where $k_{0}=\sqrt[4]{\hbar^2 \omega^2\left(m^{2}+\Delta ^{2}\right)}/v$; here $k_a=0.03~{\rm \AA^{-1}}$), (c) $k_a=k_0$, and (d) $k_a>k_0$ ($k_a=0.1~{\rm \AA^{-1}}$). Results are shown for right-handed ($\eta=+$) CPL; identical dispersion is obtained for left-handed ($\eta=-$) polarization.
• Figure 4: $k_x$-axis dispersion for odd-SL ($\lambda=+$) MnBi$_2$Te$_4$ films at different light parameter $k_a$ (where $k_{1}=\sqrt{\hbar \omega(m-\Delta)}/v$ and $k_2 = \sqrt{\hbar \omega (m + \Delta)}/v$): (a,g) $k_a=0$, (b,h) $k_a<k_1$ ($k_a=0.01~{\rm \AA^{-1}}$), (c,i) $k_a=k_1$, (d,j) $k_1<k_a<k_2$ ($k_a=0.05~{\rm \AA^{-1}}$), (e,k) $k_a=k_2$, and (f,l) $k_a>k_2$ ($k_a=0.1~{\rm \AA^{-1}}$). The top row (a-f) and bottom row (g-l) correspond to right- ($\eta=+$) and left-handed ($\eta=-$) CPL, respectively.
• Figure 5: Chern number vs. light parameter $k_a$ for (a) even-SL ($\lambda = -$) and (b) odd-SL ($\lambda = +$) MnBi$_2$Te$_4$ films under both right- ($\eta=+$) and left-handed ($\eta=-$) CPL. Parameters: $m=0.025$ eV; others as in Fig. \ref{['fig1']}.