Multistage symmetry breaking in the breathing pyrochlore lattice ${\mathrm{Li}(\mathrm{Ga},\mathrm{In})\mathrm{Cr}}_4{\mathrm{O}}_8$

We present magnetic susceptibility, dielectric constant, high-frequency electron spin resonance, ${}^7\mathrm{Li}$ nuclear magnetic resonance, and zero-field muon spin relaxation measurements of ${\mathrm{LiACr}}_4{\mathrm{O}}_8$ ($\mathrm{A}=\mathrm{Ga}$, In), towards realizing a breathing pyrochlore lattice. Unlike the uniform pyrochlore ${\mathrm{ZnCr}}_2{\mathrm{O}}_4$ lattice, both the In and the Ga compounds feature two-stage symmetry breaking: a magnetostructural phase transition with subsequent antiferromagnetic ordering. We find a disparate symmetry breaking process between the In and the Ga compounds, having different degrees of bond alternation. Our data reveal that the Ga compound with moderate bond alternation shows the concomitant structural and magnetic transition at $T_S=15.2$ K, followed by the magnetic ordering at $T_m=12.9$ K. In contrast, the In compound with strong bond alternation undergoes a thermal crossover at $T^{*}\approx 20.1$ K from a tetramer singlet to a dimer singlet or a correlated paramagnet with a separate weak magnetostructural transition at $T_S=17.6$ K and the second antiferromagnetic ordering at $T_m=13.7$ K. This suggests that the magnetic phases and correlations of the breathing pyrochlore lattice can be determined from the competition between bond alternation and spin-lattice coupling, thus stabilizing long-range magnetic ordering against a nonmagnetic singlet.

Figure 1

(a) Sketch of a breathing pyrochlore lattice. The two tetrahedra alternate in size with two exchange interactions, $J$ and $J^{\prime }$. (b) Temperature dependence of the magnetic susceptibility of ${\mathrm{LiGaCr}}_4{\mathrm{O}}_8$ (open circles) and ${\mathrm{LiInCr}}_4{\mathrm{O}}_8$ (filled squares) samples measured in an external field of 1 T. (c) Inverse magnetic susceptibility plotted together with Curie-Weiss fits (solid lines).

Figure 2

Real part of the relative dielectric constant of (a) ${\mathrm{LiGaCr}}_4{\mathrm{O}}_8$ and (b) ${\mathrm{LiInCr}}_4{\mathrm{O}}_8$ measured at zero magnetic field as a function of the temperature and frequency. Shaded areas indicate two dielectric anomalies: the magnetostructural phase transition at $T_S$ and the ensuing magnetic transition at $T_m$ together with the magnetodielectric anomaly occurring at about 60 K.

Figure 3

Derivative of the ESR absorption spectra of (a) $\mathrm{A}=\mathrm{Ga}$ and (b) $\mathrm{A}=\mathrm{In}$ at various temperatures. Spectra are vertically shifted for clarity.

Figure 4

(a), (b) The peak-to-peak ESR line width $\mathrm{\Delta }{H}_{pp}\left(T\right)$ vs temperature is plotted for $\mathrm{A}=\mathrm{Ga}$ and In on a log-log scale. Solid lines are fits to a power law, $\mathrm{\Delta }{H}_{pp}\left(T\right)\propto T^{-p}$. Arrows indicate a temperature interval where $\mathrm{\Delta }{H}_{pp}\left(T\right)$ changes its exponent $p$. (c), (d) The temperature dependence of the resonance field $H_{\mathrm{res}}\left(T\right)$ for $\mathrm{A}=\mathrm{Ga}$ and In is shown with the magnetic susceptibility for comparison.

Figure 5

(a) Representative ${}^7\mathrm{Li}$ NMR fast Fourier transform spectra of ${\mathrm{LiACr}}_4{\mathrm{O}}_8$ ($\mathrm{A}=\mathrm{Ga}$ and In). The vertical scale is normalized by the peak height. (b) ${}^7\mathrm{Li}$ nuclear spin-lattice relaxation rate $1/T_1$ on a log-log scale measured at ${\mu }_{0}H=10.99$ T for $\mathrm{A}=\mathrm{Ga}$ (open circles) and at ${\mu }_{0}H=5.00$ T (filled squares) and 10.05 T for $\mathrm{A}=\mathrm{In}$ (open triangles). Inset: Plot of the recovery curves of $\mathrm{A}=\mathrm{Ga}$ vs time at $T=8$, 14, and 20 K.

Figure 6

(a) Nuclear spin-spin relaxation rate $1/T_2$ measured at ${\mu }_{0}H=10.99$ T for $\mathrm{A}=\mathrm{Ga}$ (filled circles) and ${\mu }_{0}H=10.05$ T for $\mathrm{A}=\mathrm{In}$ (filled squares). (b) ($T_1{T)}^{-1}$ vs temperature for $\mathrm{A}=\mathrm{Ga}$. The solid line is a fit to the equation ${\left(T_{1}T\right)}^{-1}\propto {(T-T_m)}^{-\alpha }$. (c) $log(1/T_1)$ vs inverse temperature measured at ${\mu }_{0}H=5.00$ T (filled squares) and ${\mu }_{0}H=10.05$ T (open triangles) for $\mathrm{A}=\mathrm{In}$. Solid lines are fits to an activation behavior and dashed lines are guides for the eye to indicate a change in a spin gap. (d) Spin gap $\mathrm{\Delta }\left(H\right)$ vs temperature.

Figure 7

(a), (c) Temperature dependence of $\mu \mathrm{SR}$ spectra taken at ISIS for ${\mathrm{LiInCr}}_4{\mathrm{O}}_8$ and ${\mathrm{LiGaCr}}_4{\mathrm{O}}_8$ at various temperatures, respectively. (b), (d) Temperature dependence of $\mu \mathrm{SR}$ spectra recorded at TRIUMF for ${\mathrm{LiInCr}}_4{\mathrm{O}}_8$ and ${\mathrm{LiGaCr}}_4{\mathrm{O}}_8$ at various temperatures, respectively. Solid black lines represent fits to the data as described in the text. Inset in (d): Oscillation signal of ${\mathrm{LiGaCr}}_4{\mathrm{O}}_8$ for the first 0.17 $\mu \mathrm{s}$.

Figure 8

(a) Temperature dependence of the initial asymmetry of ${\mathrm{LiACr}}_4{\mathrm{O}}_8$ extracted from the $\mu \mathrm{SR}$ spectra taken at ISIS. (b) Muon relaxation rate ${\lambda }_s$ of ${\mathrm{LiACr}}_4{\mathrm{O}}_8$ as a function of temperature, obtained from the $\mu \mathrm{SR}$ spectra recorded at TRIUMF. The shaded region denotes the magnetic ordering. (c) Temperature dependence of the muon-spin-precession frequency $f_{\mu }$. The solid green line is a fit to Eq. (2).