Strong Dzyaloshinskii-Moriya interaction in monolayer ${\mathrm{CrI}}_3$ on metal substrates

Dzyaloshinskii-Moriya interaction (DMI) is the primary mechanism for realizing real-space chiral spin textures, which are regarded as key components for the next-generation spintronics. However, DMI arises from a perturbation term of the spin-orbit interaction and is usually weak in pristine magnetic semiconductors. To date, large DMI and the resulting skyrmions are only realized in a few materials under stringent conditions. Using first-principles calculations, we demonstrate that significant DMI occurs between nearest-neighbor Cr atoms in two-dimensional (2D) magnetic semiconductor ${\mathrm{CrI}}_3$ on Au or Cu substrates. This exceptionally strong DMI is generated by the interfacial charge transfer and weak chemical interactions between chromium halides and metal substrates, which break the spatial inversion symmetry. These findings highlight the significance of substrate effects in 2D magnets and expand the inventory of feasible materials with strong DMI.

Figure 1

The top and side views of (a) ${\mathrm{CrI}}_3$/BL h-BN, (b) ${\mathrm{CrI}}_3$/graphene, (c) ${\mathrm{CrCl}}_3$/Au(111), (d) ${\mathrm{CrI}}_3$/Au(111), and (e) ${\mathrm{CrI}}_3$/Cu(111). Here ${\mathrm{CrI}}_3$/BL h-BN ($\sqrt{3}/5$) represents a $\sqrt{3}\times \sqrt{3}$ supercell of ${\mathrm{CrI}}_3$ combined with the $5\times 5$ supercell of bilayer h-BN.

Figure 2

Average magnetic exchange parameters of five $\mathrm{Cr}{X}_3$-substrate systems. (a) The averaged exchange parameters $D$ and $\left|J\right|$ between nearest-neighbor Cr pairs; (b) the ratios $\frac{D}{\left|J\right|}$ of present in comparison with the other computational studies [59, 60, 61].

Figure 3

The charge density redistribution $\mathrm{\Delta }\rho (\vec{r}$) caused by substrates within the plane of top-layer and bottom-layer iodine atoms in (a) ${\mathrm{CrI}}_3$/BL h-BN and (b) ${\mathrm{CrI}}_3$/Cu(111).

Figure 4

Magnetic anisotropy energy (MAE) as a function of sliding distance of $\mathrm{Cr}{X}_3$ in the $x$ direction of ${\mathrm{CrI}}_3$/BL h-BN, ${\mathrm{CrCl}}_3$/Au(111), and ${\mathrm{CrI}}_3$/Au(111). The origin of the horizontal axis corresponds to the optimized structure shown in Fig. 1. ${\mathrm{CrI}}_3$ shifts along the $x$ direction by 0.2 Å per step relative to substrate. The curves are moving averages of the data points.