Magnetic dilution in the triangular lattice antiferromagnet NaYb$_{1-x}$Lu$_{x}$O$_2$

TL;DR

This study investigates magnetic dilution in NaYbO$_2$, a triangular-lattice antiferromagnet and candidate quantum spin liquid, by substituting nonmagnetic Lu$^{3+}$ to introduce disorder. Using ac susceptibility, heat capacity, and μSR across a dilution range up to 15% (and up to 50% for bulk probes), the authors show that the zero-field quantum-disordered ground state is remarkably robust to dilution, while the field-induced up-up-down order is rapidly suppressed; the low-energy excitations evolve from a $T^2$-like to a linear-$T$ behavior with dilution. μSR reveals persistent, correlated spin fluctuations with a dynamic, homogeneous relaxation that scales with longitudinal field as $P(H,t)=P(t/H^\\gamma)$ with $\gamma\approx0.6$, consistent with a slow, entangled spin network that remains intact up to the percolation threshold. Collectively, these results support models of a Heisenberg triangular-lattice antiferromagnet in the presence of disorder, emphasizing robust entanglement and constrained low-energy dynamics even when magnetic bonds are disrupted. The findings provide experimental benchmarks for understanding quantum disorder on triangular lattices and the resilience of entangled spin networks under dilution.

Abstract

The delafossite-like compound NaYbO$_2$ hosts a triangular lattice of Yb$^{3+}$ moments and is a promising candidate for the realization of a quantum spin liquid ground state -- an exotic, quantum-disordered magnetic phase featuring long-range entanglement of spins. Tuning this system away from this quantum-disordered regime toward classical order or spin freezing is a powerful approach to shed light on the nature of the parent ground state. Here we leverage the substitution of nonmagnetic Lu$^{3+}$ onto the Yb$^{3+}$ sites to study the effects of magnetic disorder in NaYbO$_2$ using low-temperature ac susceptibility, heat capacity, and muon spin relaxation ($μ$SR) measurements. Our $μ$SR measurements reveal resilient, correlated magnetic fluctuations that persist to at least 15\% dilution, precluding conventional spin freezing and magnetic inhomogeneity. Heat capacity and magnetic susceptibility resolve a rapid suppression of the field-induced ``up-up-down'' magnetic order upon dilution and a crossover in the power-law behavior of the low-temperature magnetic excitations associated with the zero-field quantum disordered ground state. Taken together, these results support the notion of a robust network of entangled moments in NaYbO$_2$, and provides experimental validation of several models of a Heisenberg triangular lattice antiferromagnet in the presence of disorder.

Figures (10)

• Figure 1: (a) Laboratory X-ray diffraction patterns collected on samples of NaYb$_{1-x}$Lu$_x$O$_2$. (b) Lattice parameters extracted from Rietveld refinement of profile fits to the diffraction data, with the exception of NaLuO$_2$ which was adapted from Ref. zhang_observation_2024. The dotted line is provided as a guide to the eye following Vegard's Law. All datasets were collected at room temperature.
• Figure 2: (a) Temperature dependence of the real part of the magnetic susceptibility $\chi'(T)$ for NaYb$_{1-x}$Lu$_x$O$_2$ at $H=20$ Oe. (b) Curie-Weiss fits to the inverse susceptibility and (c) resulting $\theta_\mathrm{CW}$ values as a function of Lu content.
• Figure 3: (a) Magnetic contribution to the zero-field heat capacity at low temperature for each composition. (b) Integrated zero-field entropy release in units of $R\ln(2)$. Dashed lines mark the expected entropy release for each composition. (c-g) Field-dependence of the total heat capacity for select compositions. A black arrow marks the $\lambda$-anomaly associated with the field-induced two-$\mathbf{q}$ magnetic order in the $H=5~\mathrm{T}$ data. Insets: Low-temperature fits to the zero-field magnetic contribution to the heat capacity using the model $C_p(T) = aT^2+bT$. Shaded regions represent the individual contributions from the quadratic and linear terms in the model fit. (h) Integrated magnetic entropy release for the $\lambda$-anomaly at $H=5$ T. Inset: Magnetic entropy release at $H=5$ T as a function of composition.
• Figure 4: (a) Zero field depolarization at temperatures of 195 K ($x = 0.05$) and 130 K ($x = 0.15$). Curves are offset for clarity. (b) Select depolarization data in zero magnetic field for $x = 0.05$ (filled circles) and 0.15 (open circles). Curves are offset for clarity. (c) Select depolarization data in applied longitudinal magnetic fields at $T = 0.3~K$ for $x = 0.05$ (filled circles) and 0.15 (open circles). The solid lines in each panel (a-c) are fits to Eq. \ref{['eq:polarization']}. (d) Values for the depolarization rate versus temperature in zero magnetic field as extracted from fits to Eq. \ref{['eq:polarization']}. Inset: expanded view of the low-temperature variation of $\lambda$. (e) Longitudinal magnetic field scaling data for $x = 0.05$ and (f) $x = 0.15$.
• Figure S1: (a--e) Energy-dispersive spectra for Lu-substituted samples. (f) Comparison of measured vs. nominal Lu stoichiometry $x$. Error bars represent one standard deviation.