Anisotropic Kitaev Spin Glass in Li$_{2}$Ru$_{x}$Ir$_{1-x}$O$_{3}$

Kitaev iridates have been proposed as candidates for realizing an elusive quantum spin liquid (QSL) state, in which strong spin-orbit coupling and bond-directional exchange generate a highly frustrated and entangled ground state. However, all physical systems proposed to host this ground state, including Li$_2$IrO$3$, Na$2$IrO$3$, and RuCl$3$, develop magnetic order at low temperatures due to competing interactions. Nonetheless, theoretical modeling of experimental data has shown that Kitaev interactions are still present, motivating the application of perturbations such as pressure, magnetic field, and chemical doping to drive the system into the QSL phase. Here we study $β$-Li${2}$Ru${x}$Ir${1-x}$O${3}$ with dilute levels of Ru, $x \lesssim 10%$. Through a combination of magnetometry, resonant elastic X-ray scattering, ac-heat capacity, and muon spin relaxation/resonance, we show that weak magnetic disorder suppresses long-range antiferromagnetic order and stabilizes an anisotropic spin glass that retains key signatures of Kitaev exchange. This Kitaev spin glass shows pronounced directional anisotropy in its magnetic susceptibility and thermoremenant magnetization. These results demonstrate that dilute magnetic disorder can access an anisotropic Kitaev spin glass: a proximate phase that freezes the Kitaev frustration landscape. This could provide a new window into the degeneracy, anisotropy, and competing interactions underlying the Kitaev QSL.

💡 Research Summary

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The authors investigate how dilute substitution of Ru for Ir in the three‑dimensional honeycomb iridate β‑Li₂IrO₃ influences its magnetic ground state. By synthesizing high‑quality single crystals with Ru concentrations up to 10 % (x ≲ 0.10), they map the evolution from the incommensurate spiral antiferromagnet of the parent compound to a novel anisotropic spin‑glass phase that retains key signatures of Kitaev exchange.

Magnetization measurements (both field‑cooled/zero‑field‑cooled susceptibility and M‑H loops) reveal a systematic suppression of the Néel temperature (T_N) and the higher‑temperature anomaly (T_η) as Ru content increases. In the ultra‑low‑doping regime (x ≤ 1 %), T_N and T_η drop by only a few kelvin, while the overall susceptibility grows and the critical field H* associated with the field‑induced zigzag transition shifts to lower values, indicating that even a small amount of magnetic disorder destabilizes the spiral order. In the low‑doping regime (1 % ≤ x ≤ 5 %), the susceptibility increase becomes more pronounced, the FC‑ZFC splitting widens, and a spin‑flop transition appears near x ≈ 5 %, suggesting that the antiferromagnetic state is being replaced by a field‑aligned, glassy configuration.

When Ru exceeds ~5 %, only a single low‑temperature transition remains. The system exhibits a strong FC‑ZFC divergence, a narrow S‑shaped hysteresis without the H* kink, and a broadened, less pronounced feature in the ac‑heat capacity. Resonant elastic X‑ray scattering (REXS) at the Ir L₃ edge shows that the incommensurate magnetic propagation vector (q ≈ (0.567, 0, l)) persists with only minor, non‑systematic shifts in the h‑component for x ≤ 5 %, but disappears entirely for x ≈ 10 %, confirming the loss of long‑range order.

Muon spin relaxation (μSR) experiments provide the decisive evidence for a glassy state. In the 5 %–10 % doping range, the asymmetry spectra display a rapid initial depolarization followed by a long‑time tail with a stretched‑exponential form, indicative of a broad distribution of static internal fields and slow spin dynamics. The extracted relaxation rates and stretching exponents are consistent with a canonical spin glass, yet the persistence of Kitaev‑type anisotropy is inferred from the direction‑dependent susceptibility and the residual anisotropic response in μSR under different muon spin orientations.

The authors argue that Ru acts primarily as a magnetic S = 1 impurity that weakens the Heisenberg (J) and off‑diagonal Γ exchanges while leaving the bond‑directional Kitaev term (K) relatively intact. This selective suppression pushes the system into a regime where the highly frustrated Kitaev manifold dominates, but disorder prevents the formation of a coherent quantum spin liquid, freezing the system into an “anisotropic Kitaev spin glass.” The observed directional anisotropy—greater susceptibility along certain crystallographic axes and anisotropic muon relaxation—demonstrates that the frozen spins still respect the underlying bond‑directional exchange geometry.

Overall, the work establishes a new proximate phase of the Kitaev model: a spin‑glass that inherits the bond‑directional frustration of the Kitaev Hamiltonian. It shows that dilute magnetic disorder alone can access this phase without the need for high pressure, strong magnetic fields, or heavy charge doping. The findings broaden the experimental landscape for probing Kitaev physics, offering a platform where the degeneracy and anisotropy of the Kitaev exchange can be studied in a frozen, yet still highly frustrated, environment. This could have implications for designing anisotropic quantum memory elements or exploring disorder‑stabilized topological excitations in frustrated magnets.