Emergence of skyrmionium in a two-dimensional ${\mathrm{CrGe}(\mathrm{Se},\mathrm{Te})}_3$ Janus monolayer

Utilization of van der Waals magnetic materials as the host of topologically protected skyrmionic and other complex spin textures has been drawing increasing attention. Here, using first-principles-based calculations, we predict a new stable magnetic ${\mathrm{CrGe}(\mathrm{Se},\mathrm{Te})}_3$ Janus monolayer with a strong Dzyaloshinskii-Moriya interaction (DMI), due to the breaking of inversion symmetry. Consequently, nanometric skyrmions (that carry a topological charge of $\pm 1$) and skyrmionium states (with a zero topological charge) can spontaneously form in the absence of magnetic field. We further unveil a subtle competition between DMI and frustration as key for stabilizing skyrmioniums.

Figure 1

(a) The top and side views of $\mathrm{Cr}\mathrm{Ge}{(\mathrm{Se},\mathrm{Te})}_3$ monolayer. (b) The calculated phonon dispersion of such Janus monolayer.

Figure 2

The evolution of the spin texture of the $\mathrm{Cr}\mathrm{Ge}{(\mathrm{Se},\mathrm{Te})}_3$ monolayer with increasing temperature: (a) 0.1 K, (b) 6.1 K, (c) 10.2 K, and (d) 20.3 K. The skyrmion and skyrmionium is highlighted with cyan and green circle, respectively. The red color denotes magnetic moments pointing up, while the blue color represents spins pointing into the opposite direction.

Figure 3

(a) Frustration strength $J_2/J_1$ dependence of relaxed skyrmioniums with DMI, with $c$ corresponding to the original ratio. (b) Total energy difference with respect to FM state for ideal parallel stripes, skyrmion, and skyrmionium, as a function of the frustration strength $J_2/J_1$.

Figure 4

Magnetic field versus temperature phase diagram of the studied $\mathrm{Cr}\mathrm{Ge}{(\mathrm{Se},\mathrm{Te})}_3$ Janus monolayer. The phase boundaries are determined by heat capacity, magnetic susceptibility, local spin chirality, as well as snapshots. The eight phases depicted are as follows: fragmented labyrinth domain, skyrmion and skyrmionium mixed phase (I), labyrinth domain (II), fragmented labyrinth domain and skyrmion mixed phase (III), isolated skyrmion and skyrmionium mixed phase (IV), isolated skyrmion (V), hybrid skyrmion phase (VI, for which some skyrmions merge together but others remain isolated), saturated ferromagnetic state (VII), and paramagnetic state (VIII). Representative spin textures are shown for phase III ($B=0.8$ T, $\text{T}=7.69$ K), phase IV ($B=1.8$ T, $T=4.14$ K), phase V ($B=2.4$ T, $T=4.14$ K), and phase VI ($B=2.4$ T, $T=13.3$ K).