Engineering Altermagnetism via Layer Shifts and Spin Order in Bilayer MnPS$_3$

Abstract

Altermagnetic materials combine compensated magnetic order with momentum-dependent spin splitting, offering a fundamentally new route for spintronic functionality beyond conventional ferromagnets and antiferromagnets. While most studies have focused on three-dimensional compounds, the emergence of altermagnetism in few-layer two-dimensional materials remains largely unexplored. Here, we demonstrate that bilayer MnPS$_3$, a prototypical 2D van der Waals magnet, can host stacking-induced altermagnetic phases. Using density-functional theory and spin-Laue symmetry analysis, we show that interlayer spin alignment and lateral displacement act as coupled symmetry control parameters that switch the system between Type II (collinear AFM) and Type III (altermagnetic) phases. Our systematic exploration reveals how specific stacking geometries enable momentum-dependent spin polarization without net magnetization, even in the absence of spin-orbit coupling. These results establish stacking engineering as a powerful, purely structural route for designing tunable altermagnetic states in 2D magnets, opening pathways toward symmetry-driven spintronic and magnetoelectronic devices.

Figures (6)

• Figure 1: Atomic and magnetic configurations of MnPS$_3$ monolayers and bilayers. Top: Crystal structures of the MnPS$_3$ monolayer, AA and AA$^\prime$ bilayers. The two distinct sulfur planes (upper and lower) are highlighted in the monolayer structure to clarify how their relative alignment defines the AA and AA$^\prime$ stacking geometries. In the AA$^\prime$ geometry, the upper layer is inverted along the out-of-plane axis ($z \rightarrow -z$). Bottom left and right: Local Mn coordination environments in AA and AA$^\prime$ bilayers, respectively. Bottom center: Interlayer magnetic configurations derived from the antiferromagnetic monolayer. The bilayer can adopt either parallel AFM ($\uparrow\downarrow / \uparrow\downarrow$) or antiparallel AFM ($\uparrow\downarrow / \downarrow\uparrow$), each leading to distinct symmetry and magnetic phase behavior.
• Figure 2: Relative energy maps for bilayer MnPS$_3$ under lateral displacement in the parallel ($\uparrow\downarrow / \uparrow\downarrow$) magnetic configuration. Left: AA stacking series. Right: AA$^\prime$ stacking series. Color scale indicates the relative energy (in meV) for each in-plane displacement, referenced to the lowest-energy configuration found within that stacking series (AA or AA$^\prime$). The global energy minimum of the AA series is 7.67 meV lower than that of the AA$^\prime$ series.
• Figure 3: Calculated space group symmetry maps for bilayer MnPS$_3$ under lateral displacement. Left: AA stacking series. Right: AA$^\prime$ stacking series. Color coding indicates the space group symmetry of the bilayer for each relative in-plane displacement vector $\mathbf{t}$ applied to the second layer (L$_2$).
• Figure 4: Spin-resolved electronic band structures of AA-stacked bilayer MnPS$_3$ for four in-plane displacements of the top layer: (a) $(0,1/3)$, (b) $(1/3,1/3)$, (c) $(1/3,2/3)$, and (d) $(1/2,0)$, given in fractional lattice coordinates. Top row shows the parallel ($\uparrow\downarrow/\uparrow\downarrow$) and bottom row the antiparallel ($\uparrow\downarrow/\downarrow\uparrow$) interlayer spin configuration. Red and blue indicate spin-up and spin-down bands, with the Fermi energy set at $E_F = 0$.
• Figure 5: Spin-resolved electronic band structures of AA$^\prime$-stacked bilayer MnPS$_3$ for different in-plane displacements of the top layer. Panel layout mirrors Fig. \ref{['fig:bandsAA']}: Top row shows the parallel ($\uparrow\downarrow/\uparrow\downarrow$) and bottom row the antiparallel ($\uparrow\downarrow/\downarrow\uparrow$) interlayer spin configuration. Red and blue denote spin-up and spin-down bands, with the Fermi energy set to $E_F = 0$.