Quantum disordered state in the $J_1\text{−}{J}_2$ square-lattice antiferromagnet ${\mathrm{Sr}}_2\mathrm{Cu}\left({\mathrm{Te}}_{0.95}{\mathrm{W}}_{0.05}\right){\mathrm{O}}_6$

The $B$-site ordered double perovskites ${\mathrm{Sr}}_2\mathrm{Cu}\left({\mathrm{Te}}_{1-x}{\mathrm{W}}_x\right){\mathrm{O}}_6$ provide an excellent arena for investigating exotic phases expected for the $J_1\text{−}{J}_2$ square-lattice Heisenberg antiferromagnet. Here, combining magnetic susceptibility and specific-heat measurements with electron spin resonance (ESR) and muon spin rotation/relaxation $\left(\mu \mathrm{SR}\right)$ techniques, we explore a spin-liquid-like state in the vicinity of the Néel critical end point $(x=0.05–0.1)$. The specific heat and the ESR and muon relaxation rates give evidence for an energy hierarchy of low-energy excitations, reminiscent of randomness-induced singlet states. In addition, the weak transverse $\mu \mathrm{SR}$ data show a fraction of frozen magnetic moments in the random-singlet background. The origin of a random-singlet-like state near the phase boundary is discussed in terms of concomitant exchange randomness and local strain generated by the ${\mathrm{W}}^{6+}\text{−}\mathrm{for}\text{−}{\mathrm{Te}}^{6+}$ substitution.

Figure 1

(a) Crystal structure of ${\mathrm{Sr}}_2\mathrm{Cu}\left({\mathrm{Te}}_{1-x}{\mathrm{W}}_x\right){\mathrm{O}}_6$ together with magnetic exchange interactions, $J_1$ and $J_2$, on a square lattice (dot lines). The green, blue, dark yellow, and red spheres denote Sr, Cu, Te/W, and O ions, respectively. (b) dc magnetic susceptibility data $\chi \left(T\right)$ of $x=0$, 0.05, and 0.1 as a function of temperature measured at ${\mu }_{0}H=0.1$ T. The solid lines represent the high-temperature extension fittings. (c) Inverse magnetic susceptibility of $x=0.05$ and 0.1 as a function of temperature. The solid lines are fittings to the Curie-Weiss law. (d) High-field magnetization data of $x=0.05$ and 0.1 measured at $T=1.5$ K together with the low-field SQUID data (symbols).

Figure 2

(a) Low-temperature dependence of the specific heat of ${\mathrm{Sr}}_2\mathrm{Cu}\left({\mathrm{Te}}_{1-x}{\mathrm{W}}_x\right){\mathrm{O}}_6$ ($x=0.05$) at selected fields ${\mu }_{0}H=$ 0, 5, and 9 T plotted in a double logarithmic scale. (b) Specific heat divided by temperature together with the nonmagnetic counterpart ${\mathrm{Sr}}_2\mathrm{Zn}\left({\mathrm{Te}}_{0.95}{\mathrm{W}}_{0.05}\right){\mathrm{O}}_6$. The magnetic specific heat divided by temperature $C_{\mathrm{mag}}/T$ (red open circles) is obtained by subtracting the nonmagnetic contribution from the raw $C/T$ data. (c) Log-log plot of $C_{\mathrm{mag}}/T$ vs temperature. The solid lines are fits of the $C_m/T$ data to a power law, and the red open symbols represent the magnetic entropy.

Figure 3

(a) Derivative of the ESR absorption spectra for the $x=0.05$ compound at selected temperatures. The ESR spectra are fitted to a sum (pink thick line) of two Lorentzian profiles (thin solid lines). (b) Log-log plot of the peak-to-peak linewidth $\mathrm{\Delta }{H}_{\text{pp}}$ vs temperature. The solid lines represent a power-law fit. (c) Log-log plot of the $g$-factors as a function of temperature. The gray shading marks a qualitative change of the ESR spectra.

Figure 4

Temperature evolution of the muon spin polarization for ${\mathrm{Sr}}_2\mathrm{Cu}\left({\mathrm{Te}}_{1-x}{\mathrm{W}}_x\right){\mathrm{O}}_6$ ($x=0.05$) at zero field (a) and at longitudinal fields (b), and for the $x=0.1$ compound at zero field (c) and at longitudinal fields (d). The solid lines are fits to Eq. (1) as explained in the main text.

Figure 5

(a) Log-log plots of the muon spin relaxation rate vs temperature for ${\mathrm{Sr}}_2\mathrm{Cu}\left({\mathrm{Te}}_{1-x}{\mathrm{W}}_x\right){\mathrm{O}}_6$ ($x=0.05$ and 0.1) measured at zero field. Linear solid lines are fits to the power law. (b) Stretching exponent of $x=0.05$ and 0.1 plotted in a double logarithmic scale. (c) Longitudinal-field dependence of the muon spin relaxation rate at $T=0.3$ and 0.07 K for $x=0.05$ and 0.1 compounds, respectively, together with their fits to Eq. (2).

Figure 6

(a) Temperature evolution of the $\mu \mathrm{SR}$ spectra for the compound ${\mathrm{Sr}}_2\mathrm{Cu}\left({\mathrm{Te}}_{1-x}{\mathrm{W}}_x\right){\mathrm{O}}_6$ ($x=0.05$) at a weak transverse field of 0.002 T. (b) Magnetic volume fraction and (c) transverse muon spin relaxation rate as a function of temperature plotted on a log-log scale.