Tuning the magnetic properties of Kitaev materials via the antiferromagnetic proximity effect: Novel phases and application to an $α$-RuCl$_3$/MnPS$_3$ bilayer

Abstract

In recent years, the increasing level of control over van der Waals (vdW) heterostructures has opened new routes to tune the properties of quantum materials. Motivated by these developments, we examine the potential consequences of interfacing a Kitaev honeycomb magnet, such as $α$-RuCl$_3$, with a nearly lattice-matched vdW antiferromagnet. By combining perturbation theory, exact diagonalization, and a classical energy-minimization method, we show that an effective staggered magnetic field originating from the vdW antiferromagnet can drive a monolayer of a Kitaev material into various novel phases, including an antichiral Kitaev spin liquid, a nonmagnetic nematic phase, and different types of skyrmion crystals. We then apply first-principle simulations to assess the prospect of concretely realizing this setup in a heterobilayer of $α$-RuCl$_3$ and the easy-axis antiferromagnet MnPS$_3$.

Figures (5)

• Figure 1: Schematics of the results of third-order perturbation theory in $h$ around the exactly-solvable Kitaev point $g=0$ for a (a) uniform and (b) staggered external magnetic field. Left: Next-nearest-neighbor Majorana hopping terms induced by the field. The blue arrows are correlated with the sign of the complex hopping amplitudes. Middle: Effect of the perturbations on the Majorana spectrum near the two inequivalent corners, $\bm{K}$ and $\bm{K}'$, of the first Brillouin zone. Right: Qualitative difference between the chiral and antichiral edges modes.
• Figure 2: (a) 24-site cluster used for our ED calculations. (b) Momentum resolution of the finite-size cluster. The inner hexagon represents the first Brillouin zone, whereas the outer hexagon connects the six equivalent $\bm{\Gamma}'$ points. (c,d) Ground-state phase diagrams of Models 1 and 2 from Table \ref{['tab:edmodels']}. Both models exhibit a robust field-induced $X$ phase which precedes polarizition for nearly all values of $g$ up to $1$. (e) Comparison between two-point correlations $C^{\alpha\alpha}$ relative to site $0$ (orange triangle) in the KSL and the purple phase above it in (c). The data were obtained for $(g, h/\abs{K_1}) = (0.075,0.175)$ and $(0.09,0.35)$, which are highlighted in (c). The value of $C^{\alpha\alpha}$ at each site is represented by a circle whose radius is proportional to $\abs{C^{\alpha\alpha}}$ and whose color reflects the sign of $C^{\alpha\alpha}$. Blue (red) circles indicate FM (AFM) correlations.
• Figure 3: Static spin structure factor $\mathcal{S} (\mathbf{k})$ obtained by applying (a) ED and (b) a classical energy-minimization method to Model 1 on the 24-site cluster shown in Fig. \ref{['fig:ed_cluster+pds']}(a). The results were obtained for the points $(g, h/\abs{K_1}) = (0.17, 0.50)$ and $(0.75,1.18)$, respectively. The yellow hexagons have the same meaning as in Fig. \ref{['fig:ed_cluster+pds']}(b).
• Figure 4: Results obtained from classical energy minimization for Model 1 at fixed $g = 0.75$. (a) Staggered magnetization per site, $m_h = - (Nh)^{-1} \sum_{i} \mathbf{h}_i \cdot \mathbf{S}_i$, as a function of $h$. Between the zigzag (ZZ) and polarized phases, the system realizes a sequence of SkXs (gray shaded region) and topologically trivial triple-$\mathbf{Q}$ phases with progressively smaller ordering wavevectors. The former are characterized by their sublattice-resolved topological charges, $(n_\mathrm{sk}^A, n_\mathrm{sk}^B)$. (b) Static structure factors per site, $\mathcal{S}(\textbf{k})/N$, for the four points highlighted in the magnetization curve. Data are shown for the discrete momenta compatible with the clusters on which the solutions were obtained. The inner yellow hexagon delineates the first Brillouin zone. (c,d) Magnetic unit cells of the $(-1,+1)$ and $(-3,+1)$ SkXs, respectively. Shaded disks highlight the location of skyrmions.
• Figure 5: (a) Structure of the bilayer $\alpha$-RuCl$_3$/MnPS$_3$. Ru:gray, Cl:green, Mn:purple, S:yellow, P:silver (b,c) Single layers of $\alpha$-RuCl$_3$ and MnPS$_3$, respectively, showing cation-cation distances. (d) Density of states for a fully ferromagnetic configuration (interlayer anti-ferromagnetic configuration is qualitatively similar).