Possible Kitaev Quantum Spin Liquid State in 2D Materials with $S=3/2$

Quantum spin liquids (QSLs) form an extremely unusual magnetic state in which the spins are highly correlated and fluctuate coherently down to the lowest temperatures, but without symmetry breaking and without the formation of any static long-range-ordered magnetism. Such intriguing phenomena are not only of great fundamental relevance in themselves, but also hold promise for quantum computing and quantum information. Among different types of QSLs, the exactly solvable Kitaev model is attracting much attention, with most proposed candidate materials, e.g., ${\mathrm{RuCl}}_3$ and ${\mathrm{Na}}_2{\mathrm{IrO}}_3$, having an effective $S=1/2$ spin value. Here, via extensive first-principles-based simulations, we report the investigation of the Kitaev physics and possible Kitaev QSL state in epitaxially strained Cr-based monolayers, such as ${\mathrm{CrSiTe}}_3$, that rather possess a $S=3/2$ spin value. Our study thus extends the playground of Kitaev physics and QSLs to $3d$ transition metal compounds.

Figure 1

Schematization of crystal structure and the Kitaev basis of ${\mathrm{CrSiTe}}_3$ monolayer. The black parallelogram marks the unit cell of the honeycomb lattice of ${\mathrm{CrSiTe}}_3$ monolayer. The $\{XYZ\}$ basis of the Kitaev model is indicated by red, green, and blue arrows, which is determined by Löwdin orthogonalization [17] of the hard axes of the nearest neighbor Cr-Cr interactions. The $X$, $Y$, and $Z$ directions are found to be very close to the $\mathrm{Cr}─\mathrm{Te}$ bonds [18].

Figure 2

Magnetic coefficients and fidelity of ${\mathrm{CrSiTe}}_3$ monolayer. Panel (a) display the evolution of magnetic coefficients as a function of compressive strain. Panel (b) further shows the evolution of $J$, $J+K$, and $K$ for a specific strain region. The horizontal dashed line indicates the zero in energy, while the vertical lines mark the critical strains at which $J$ or $J+K$ becomes zero. Panel (c) shows the quantity of fidelity $g$ as a function of strain for different sizes of supercells.

Figure 3

Patterns of magnetic dipole moments at different strains in ${\mathrm{CrSiTe}}_3$ monolayer. (a) Spin patterns at $\eta =-2.25\%$, at which $J+K$ changes its sign. The solid and dashed rectangle marks the FM and zigzag AFM domains, respectively. Vortices and antivortices are indicated by the red and blue dots, respectively. The values represented by the dots are the vortex number, which is defined as $n=(1/2\pi ){\sum }_{i=1}^6\mathrm{\Delta }{\theta }_i$, where the rotation from $i=1–6$ is done in an anticlockwise fashion. (b),(c) Energetically degenerate states at $\eta =-2.30\%$. (d) Spin textures at $\eta =-2.41\%$, at which $J$ changes its sign. The solid and dashed ellipses mark ferromagnetic and antiferromagnetic pairs, respectively. Note that our MC simulations are followed by a conjugate gradient algorithm, indicating that the spin patterns shown here are at global or local minima [31].

Figure 4

Temperature evolution of specific heat and entropy of ${\mathrm{CrSiTe}}_3$ monolayer at different strains. Panels (a)–(c) display the specific heat in units of meV K, while panels (d)–(f) show entropy in units of $N{k}_B\ln 4$ as a function of temperature. The $2\times 3$ honeycomb lattice is used with $N=12$.