Disorder-Induced Mimicry of a Spin Liquid in ${\mathrm{YbMgGaO}}_4$

We suggest that a randomization of the pseudodipolar interaction in the spin-orbit-generated low-energy Hamiltonian of ${\mathrm{YbMgGaO}}_4$ due to an inhomogeneous charge environment from a natural mixing of ${\mathrm{Mg}}^{2+}$ and ${\mathrm{Ga}}^{3+}$ can give rise to orientational spin disorder and mimic a spin-liquid-like state. In the absence of such quenched disorder, $1/S$ and density matrix renormalization group calculations both show robust ordered states for the physically relevant phases of the model. Our scenario is consistent with the available experimental data, and further experiments are proposed to support it.

Figure 1

(a) Axes, primitive vectors, and a sketch of the 120° and stripe states. (b) $1-\mathrm{\Delta }$ vs $J_2$ phase diagram of the $XXZ$ model (1). The $⟨S⟩$ color map and boundaries (solid lines) are by the SWT; the dotted line is the classical phase boundary. The shaded white area is the spin-liquid region by the DMRG; see the text. The dashed line with the shaded region is the same for the model with ${\mathcal{H}}_{\mathrm{pd}}$ with $|J_{\pm \pm }|=0.06$; see Fig. 2. The error bars mark ${\mathrm{YbMgGaO}}_4$ parameters from Ref. [47]. (c) The DMRG scan of (1) vs $J_2$ for $\mathrm{\Delta }=0.5$ with up to 2000 states.

Figure 2

(a) DMRG results for $⟨S⟩$ vs $J_2$ with $|J_{\pm \pm }|=0.06J_1$. Dotted and dashed lines denote classical and DMRG phase boundaries, respectively. The error bar is the same as in Fig. 1. The solid black line is the SWT result for $\mathrm{\Delta }=0.5$. (b) A long-cylinder DMRG scan for $\mathrm{\Delta }=0.5$ and $J_{\pm \pm }=-0.06J_1$.

Figure 3

Energy barrier between the stripe states of different orientations in the $XXZ$ $J_1\text{−}{J}_2$ model vs $J_2$ for various $\mathrm{\Delta }$ and $S=1/2$. Upper inset: Quantum energy correction vs angle $\theta$. Lower inset: A sketch of the degenerate classical ground states with $\theta =0(\pi )$ corresponding to two stripe orientations.

Figure 4

(a) Positive and negative $J_{\pm \pm }$ bonds in a typical disorder realization. (b) Two stripe domains (dashed boxes) for random $|J_{\pm \pm }|=0.2J_1$, $⟨S⟩$ up to 0.33. (c) $\mathcal{S}(\mathbf{q})$ [66] for random $|J_{\pm \pm }|=0.1(0.05)J_1$. (d) Averaged $\mathcal{S}(\mathbf{q})$ from (c); see the text.