Stacking-sliding and irradiation-direction invariant Floquet altermagnets in A-type antiferromagnetic bilayers

Abstract

Arranging the stacking orders of A-type antiferromagnetic (A-AFM) bilayers offers an accessible pathway to two-dimensional altermagnets, but requires strict symmetry conditions such as layer groups, sliding positions, and twisting angles. Here, we find that circularly polarized light (CPL) irradiation breaks time-reversal symmetry, enabling the development of altermagnets beyond these constraints. Based on symmetrical analysis, our revealments indicate that A-AFM bilayer building-blocks with inversion symmetry exhibit altermagnetism robust to stacking sliding and variations of illumination directions. These bilayers can be constructed from arbitrary ferromagnetic monolayers and guided by the $d$-electron counting rule. Adopting bilayer MnBi$_2$Te$_4$ as a template, out-of-plane illumination with CPL reveals an $f$-wave altermagnetic feature at sliding positions $\left\{E|\left(0,0\right)\right\}$, $\left\{E|\left(\frac{1}{3},\frac{2}{3}\right)\right\}$ and $\left\{E|\left(\frac{2}{3},\frac{1}{3}\right)\right\}$, while a $p$-wave feature is predicted at other sliding positions. Our unveilings popularize the applicability of altermagnets in A-AFM bilayers with inversion symmetry, igniting a new wave of research in this field.

Figures (4)

• Figure 1: Schematic of building Floquet altermagnets. (a) Constructing strategy of an A-AFM bilayer with $\left[\textit{C}_\mathbf{2}||\textit{P}\right]$ from a FM monolayer. The yellow and green regions represent the top and bottom parts of the FM monolayer, respectively, while the red arrows indicate the magnetic moments. (b) The sliding-invariant AFM state is Floquet-engineered into the sliding-invariant altermagnetic state regardless of illumination directions.
• Figure 2: Illustrations of BL-MBT under normal stacking with (a) side view, (b) top view and (c) first BZ zone. The green, blue, and gray spheres represent Mn, Bi, and Te atoms, respectively. The red arrows in panel (a) indicate the direction of the magnetic moments. In panel (b), the red rhombus denotes the stacking-sliding zone.
• Figure 3: BL-MBT: band structures along high-symmetry lines and spin-splitting distributions in three types of stacking sliding positions, with the light frequency and incident direction set to $\hbar\omega$ = 9.0 eV and along $z$-axis respectively. Panel (a) exhibits the spin-resolved band structures along the high-symmetry lines $M$-$\Gamma$-$K$-$M'$-$\Gamma$-$K'$-$M$ under the light intensity of 0.3 Å$^{-1}$. The red and blue curves represent spin-up and spin-down states, respectively. Panel (b) illustrates the contour distributions of spin-splitting energies across the entire BZ, with the color gradient ranging from white to red (positive values) and blue (negative values), reflecting the relationship: $E_{\mathrm {down}}-E_{\mathrm {up}}$. The occupancy number of the Wannier bands is 83. Panels (a) and (b) correspond to the normal stacking order ($\left\{E\middle|\left(0,0\right)\right\}$). Panels (c) and (d), (e) and (f) are analogous to (a) and (b), but for the stacking sliding positions $\left\{E\middle|\left(\frac{1}{2},0\right)\right\}$ and $\left\{E\middle|\left(\frac{1}{3},0\right)\right\}$ respectively.
• Figure 4: The stacking-sliding invariance of Floquet-altermagnets in BL-MBT. Subfigures (a) and (b) demonstrate the spin-splitting energies at the $\Gamma$ and $K$ points distributing across the entire sliding zone, respectively. The color gradient, ranging from yellow to red, represents the relationship: $E_{\mathrm {down}}-E_{\mathrm {up}}$, with the light incident direction oriented along the $z$ axis.