Rare-Earth Triangular Lattice Spin Liquid: A Single-Crystal Study of ${\mathrm{YbMgGaO}}_4$

${\text{YbMgGaO}}_4$, a structurally perfect two-dimensional triangular lattice with an odd number of electrons per unit cell and spin-orbit entangled effective spin-$1/2$ local moments for the ${\mathrm{Yb}}^{3+}$ ions, is likely to experimentally realize the quantum spin liquid ground state. We report the first experimental characterization of single-crystal ${\text{YbMgGaO}}_4$ samples. Because of the spin-orbit entanglement, the interaction between the neighboring ${\mathrm{Yb}}^{3+}$ moments depends on the bond orientations and is highly anisotropic in the spin space. We carry out thermodynamic and the electron spin resonance measurements to confirm the anisotropic nature of the spin interaction as well as to quantitatively determine the couplings. Our result is a first step towards the theoretical understanding of the possible quantum spin liquid ground state in this system and sheds new light on the search for quantum spin liquids in strong spin-orbit coupled insulators.

Figure 1

The ${\text{YbMgGaO}}_4$ lattice structure (a) and the triangular lattice in the $ab$ plane (b) formed by the ${\mathrm{Yb}}^{3+}$ ions. The inset defines the coordinate system for the spin components.

Figure 2

(a),(b) The magnetization of the ${\text{YbMgGaO}}_4$ single crystals measured at 10, 6, 3, and 1.9 K. The dashed lines are linear fits of the experimental results for fields above 12 T at 1.9 K. The solid curves are the corresponding magnetization calculated by the molecular field approximation. (c),(d) The inverse spin susceptibilites (after subtracting the Van Vleck paramagnetism) fitted by the Curie-Weiss law (in dashed lines) for the ${\text{YbMgGaO}}_4$ single crystals.

Figure 3

The temperature dependence of the ESR linewidths (a) parallel and (b) perpendicular to the $c$ axis. The dashed lines are the corresponding constant fits to the ESR linewidth data at $T>6\mathrm{K}$. (c) The deviation $R_p$ of the experimental ESR linewidths from the theoretical ones for ${\text{YbMgGaO}}_4$. The dashed rectangle gives the optimal parameters $|J_{\pm \pm }|=0.155(9)\mathrm{K}$ and $|J_{z\pm }|=0.04(10)\mathrm{K}$.

Figure 4

(a) Angular dependence of the ESR linewidth. The dashed curve is the calculated ESR linewidth. (b) The magnetic susceptibilities of the ${\mathrm{YbMgGaO}}_4$ single crystal after subtracting the Van Vleck paramagnetism. The solid curves are the calculated susceptibilities using the high-temperature series expansion. The dashed curves are the Curie-Weiss susceptibilities.