Novel Phase Transitions in the Breathing Pyrochlore Lattice: ${}^7\mathrm{Li}\text{−}\mathrm{NMR}$ on ${\mathrm{LiInCr}}_4{\mathrm{O}}_8$ and ${\mathrm{LiGaCr}}_4{\mathrm{O}}_8$

We report ${}^7\mathrm{Li}\text{−}\mathrm{NMR}$ studies on ${\mathrm{LiInCr}}_4{\mathrm{O}}_8$ and ${\mathrm{LiGaCr}}_4{\mathrm{O}}_8$, in which ${\mathrm{Cr}}^{3+}$ ions with spin $3/2$ form a breathing pyrochlore lattice, a network of tetrahedra with alternating sizes. In ${\mathrm{LiInCr}}_4{\mathrm{O}}_8$ with large alternation, the nuclear relaxation rate $1/T_1$ shows an activated temperature ($T$) dependence down to 18 K, indicating a singlet ground state with a spin gap. This behavior, however, is disrupted by an antiferromagnetic transition at 13 K, which is preceded by another, most likely structural, transition at 16 K. In contrast, ${\mathrm{LiGaCr}}_4{\mathrm{O}}_8$ with a small alternation shows no spin gap but exhibits a first-order antiferromagnetic transition over a distributed $T$ range 13–20 K. Nevertheless, $1/T_1$ of the paramagnetic phase diverges toward 13 K, indicating proximity to a second-order transition. The results indicate that ${\mathrm{LiGaCr}}_4{\mathrm{O}}_8$ is located in the vicinity of a tricritical point in the phase diagram.

Figure 1

Temperature dependence of the NMR spectra for ${\mathrm{LiInCr}}_4{\mathrm{O}}_8$ obtained at 2 T. The vertical scale is normalized by the peak intensity for each spectrum. The origin of the horizontal axis $\mathrm{\Delta }f=0$ corresponds to the center of gravity of the spectrum. The inset shows the structure of a breathing pyrochlore lattice.

Figure 2

Upper panel: Temperature dependences of $1/T_1$ measured at 2 T for ${\mathrm{LiInCr}}_4{\mathrm{O}}_8$ with a fit to the activation law and the $C_p/T$ data at zero field taken from Ref. [23]. Lower panel: Temperature dependences of $1/T_1^{\text{para}}$ and $1/T_1^{\mathrm{AFM}}$ measured at 2 T for ${\mathrm{LiGaCr}}_4{\mathrm{O}}_8$. The shaded area represents the coexistence region determined by Fig. 3. The solid line is the fit to Eq. (3). The inset shows the recovery curves at different temperatures.

Figure 3

(a) Temperature dependence of the NMR spectra for ${\mathrm{LiGaCr}}_4{\mathrm{O}}_8$ obtained at 2 T. The vertical scale is normalized by the peak intensity. The origin of the horizontal axis $\mathrm{\Delta }f=0$ corresponds to the center of gravity. (b) The AFM components of the spectra below 16 K. The vertical scale is normalized by the top of the broad line for each spectrum, ignoring the sharp paramagnetic component. (c) The solid red circles (open blue triangles) show the intensity of the paramagnetic line multiplied by temperature $I_{p}T$, which represents the paramagnetic volume fraction, measured with heating (cooling). The same data are expanded in the inset. The black dots show the $C_p/T$ data at zero field reported in Ref. [23]. The red crosses show $d(I_{p}T)/dT$ obtained from the central difference of the discrete $I_{p}T$ data.

Figure 4

Schematic phase diagram for ${\mathrm{LiGaCr}}_4{\mathrm{O}}_8$. On the vertical axis, $\alpha$ represents a phenomenological tuning parameter of the Hamiltonian. The region $\mathrm{\Delta }\alpha$ shows the distribution of $\alpha$ in our sample. The dashed and solid double lines indicate first- and second-order transitions, respectively, which are separated by the tricritical point indicated by the open circle.