Dynamical spin-orbital correlations versus random singlets in ${\mathrm{Ba}}_3{\mathrm{CuSb}}_2{\mathrm{O}}_9$ investigated by magnetization and electron spin resonance

High-field magnetization and high-frequency electron spin resonance (ESR) are employed to differentiate magnetism between an orthorhombic and a hexagonal majority phase of ${\mathrm{Ba}}_3{\mathrm{CuSb}}_2{\mathrm{O}}_9$. For the orthorhombic sample, an ESR signal changes its temperature dependence at $T_S\sim 200$ K, suggesting a static Jahn-Teller (JT) ordering. A magnetization curve follows a power-law behavior $M\sim H^{{\alpha }_m}$ with the exponent ${\alpha }_m=0.72\pm 0.06$ for $8<H<26$ T and ${\alpha }_m=1.06\pm 0.04$ for $H>26$ T. The ESR linewidth exhibits a critical-like divergence, $\Delta H_{pp}\left(T\right)\propto T^{-\alpha }$ with the exponents of $\alpha =0.22\pm 0.07$ and $0.32\pm 0.04$. The sublinear magnetization and the critical ESR line broadening are taken as evidence of a random singlet state. For the hexagonal sample, both $\Delta H_{pp}\left(T\right)$ and $g$ factor are described by the same thermally activated process with the energy barrier of 300 K. This evidences intrinsic coupling of spins to orbital degrees of freedom and thereby gives support for a dynamic spin-orbital entangled state. Our results demonstrate that magnetism in the spin-orbital coupled compound ${\mathrm{Ba}}_3{\mathrm{CuSb}}_2{\mathrm{O}}_9$ is dictated by a spatiotemporal structure of the JT distortions.

Figure 1

Magnetization curve $M\left(H\right)$ of the orthorhombic (94%) polycrystalline sample ${\mathrm{Ba}}_3{\mathrm{CuSb}}_2{\mathrm{O}}_9$ measured at $T=1.5$ K. The open black circles are the raw $M\left(H\right)$. The thick dashed line is a defect contribution $M_{\mathrm{imp}}\left(H\right)$, which is evaluated from a fit to Eq. (1). The green open circles represent the remaining intrinsic magnetization $M_{\mathrm{int}}\left(H\right)$ obtained by subtracting the defect part $M_{\mathrm{imp}}\left(H\right)$ from the raw data. The thick red line is a fit of $M\left(H\right)$ to a sum of Eq. (1) and a power law in the field range of $H=0$–26 T. The inset plots $M_{\mathrm{int}}\left(H\right)$ on a log-log scale. $M_{\mathrm{int}}\left(H\right)$ follows a power-law behavior, $M_{\mathrm{int}}\left(H\right)\sim H^{\alpha }$ with the exponent $\alpha =0.72\pm 0.06$ for $8<H<26$ T and $\alpha =1.06\pm 0.04$ for $H>26$ T.

Figure 2

Derivative of the ESR absorption spectra for the orthorhombic (94%) crystal (a) and the hexagonal (80%) crystal (b) of ${\mathrm{Ba}}_3{\mathrm{CuSb}}_2{\mathrm{O}}_9$ measured at $\nu =240$ GHz for $H\parallel c$ in the temperature range of $T=4$–290 K. The spectra are vertically shifted for clarity.

Figure 3

Representative fit of the ESR spectrum to Lorentzian profiles for the orthorhombic (94%) crystal at $T=259$ K (a) and at $T=4$ K (b) as well as for the hexagonal (80%) crystal at $T=260$ K (c) and $T=6$ K (d). The open circles represent the experimental data. The red thick lines are a theoretical fit of the ESR spectrum to two Lorentzian profiles (green and blue lines).

Figure 4

Temperature dependence of the peak-to-peak linewidths, $\Delta H_{pp}\left(T\right)$ (a) and the $g$ values of the orthorhombic (94%) crystal for $H\parallel c$. The solid lines are fits to a power law $\Delta H_{pp}\left(T\right)\propto T^{-\alpha }$ and the dashed lines are guides to the eye. The inset plots $\Delta H_{pp}\left(T\right)$ vs temperature on a log-log scale. The shaded regions denote the low-temperature deviation from a power-law behavior and the high-temperature hexagonal phase for $T>T_S$.

Figure 5

Temperature dependence of the peak-to-peak linewidths $\Delta H_{pp}\left(T\right)$ (a) and the $g$ values (b) of the hexagonal sample for $H\parallel c$. The solid lines at low temperatures are fits to a power law. The open triangles represent $\Delta H_{pp}^h\left(T\right)$ intrinsic to the hexagonal phase, which is obtained by subtracting the power-law contribution. The inset of (a) plots $\Delta H_{pp}\left(T\right)$ vs temperature on a log-log scale. The inset of (b) plots $H_{\mathrm{res}}$ vs frequency measured at $T=5$ K. (c) Temperature dependence of $\Delta H_{pp}^h\left(T\right)$ and the $g$ value. The solid line is a fit to Eq. (2) as described in the text.