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

TL;DR

The study probes dilute Ru doping in β-Li$_{2}$Ru$_{x}$Ir$_{1-x}$O$_{3}$ (with $x \lesssim 10\%$) to test the persistence of Kitaev exchange under disorder. Using magnetometry, resonant elastic X-ray scattering at the Ir $L_3$ edge, ac-heat capacity, and μSR, the authors map a evolution from incommensurate antiferromagnetism to an anisotropic spin glass, with transitions occurring around intermediate dopings. The spin glass preserves the directional Kitaev anisotropy, indicating that Kitaev interactions survive dilution and that disorder selects a glassy state by relieving frustration. This anisotropic Kitaev spin glass represents a proximate phase to the Kitaev quantum spin liquid and provides a new platform to study the interplay of $J$, $K$, and $Γ$ in Kitaev materials. The findings suggest magnetic disorder can access Kitaev-like glassy states and guide future spectroscopic and field-tuned experiments to probe exotic excitations near the QSL regime.

Abstract

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.

Figures (6)

• Figure 1: (a) Crystal structure of $\beta-$Li$_{2}$IrO$_{3}$. Li ions are omitted for visibility. Ir-O octahedra form a twisted honeycomb structure (right). (b) Phase diagram for $\beta-$Li$_{2}$IrO$_{3}$ as a function of pressure and applied field, from majumder_breakdown_2018shen_interplay_2021ruiz2017correlated. (c) Phase diagram of the $JK\Gamma$ model, with schematics of different spin configuration. The black arrow shows the effect of applied magnetic field, which moves the system from the incommensurate state to the zigzag state. Reproduced from chaloupkaKitaevHeisenbergModelHoneycomb2010arau_generic_2014.
• Figure 2: (a) Field-cooled and zero-field cooled magnetic susceptibility for the ultra-low doping regime, $x\sim0.5\%,1\%$, with inset showing $\Delta\chi_{FC}-\chi_{ZFC}$. A suppression of $T_N$ and $T_\eta$ and an increase in the total moment is seen, as expected with the doping of a $S=1$ ion. (b) Magnetization as a function of applied field for the ultra-low doping regime shows a decrease in $H^*$ with increased doping. (c-d) In the low doping regime, $T_N$ and $T_\eta$ are further suppressed. A large increase in both the magnitude of the susceptibility and the FC-ZFC splitting is seen for $x\sim5\%$. This may be explained by the spin-flop transition appearing for $x\sim5\%$, indicating that moments are aligning to the applied field even for very small $H$. (e) The $ac$-heat capacity for the ultra-low and low doping regimes shows a pronounced feature at $T_N$, which becomes broader for higher dopings.
• Figure 3: (a) Diagram depicting the scattering geometry for REXS experiments. A vertical scattering geometry was used, such that the incident beam $k_{in}$ is polarized along $\sigma_{in}$ perpendicular to the scattering plane. (b-d) Peak profiles as a function of temperature for characteristic magnetic Bragg reflections seen in $x\sim0.5\%,\,1\%,\,2\%$ samples. Variations in alignment restricted which peaks were accessible, so different peaks were studied for each sample. Intensity is normalized to the peak intensity of the lowest measured temperature. (e) Mapping of the magnetic Bragg reflections $(h,0,l)$ seen in REXS experiments for different samples. Black circles indicate lattice reflections, while orange, yellow, and red circles correspond to signals seen for different dopants. (f) Self-normalized temperature dependence of the magnetic peak intensity. $T_N$ found in scattering are consistent with those derived from magnetometry.
• Figure 4: (a) Magnetic susceptibility in the mid-doping regime, with inset showing the difference between FC and ZFC susceptibility. (b) M vs. H shows an opening of a hysteresis and the absence of the kink field $H^*$. (c) The $ac$-heat capacity shows a broad feature at $T_f$, indicative of a spin glass. (d) Thermoremenant magnetization (TRM) as a function of doping after holding in a 1T field at 2K for 10min. A longer relaxation time is seen for higher dopings. (e) TRM for $x\sim10\%$ at 5K with varying hold times at 1T. A longer relaxation time is seen for longer hold times. (f,g) Characteristic timescale extracted from exponential fits of (d,e). Higher doping levels correspond to longer characteristic timescales. In the glassy (mid-doping) regime, longer hold times also lead to longer characteristic timescales.
• Figure 5: (a) Schematic representation of a typical $\mu$SR experiment. (1) Spin-polarized muons are sent into the sample chamber, with their spin angular momentum opposite to their direction of motion. (2) A muon implants itself into the material. (3) The spin of the implanted muon precesses in the local magnetic field. (4) The muon decays into a positron, which is emitted preferentially in the direction of the muon's spin. (5) The positron is detected by the front or back detectors. The normalized difference between the number of muons detected over time by these detectors is the measured asymmetry. (b) Asymmetry as a function of time after muon implantation for different dopings, collected at 2 K. Coherent oscillations are seen in the pristine and ultra-low dopings, consistent with long-range incommensurate order, while overdamped behavior characteristic of a spin glass state is seen for higher dopings. The spectra for subsequent dopings are offset vertically for clarity. (c) Asymmetry spectra for $x\sim8\%$ in zero field collected at different temperatures. (d) From fits to the curves in (c), the volume fraction of the spin glass state is extracted, showing a $T_g$ roughly consistent with the magnetometry data. (e) Asymmetry spectra for $x\sim8\%$ at 2K as a function of applied longitudinal field, showing a steady recovery of asymmetry with increasing field as expected for a static spin glass ground state.