Magnetization process of the breathing pyrochlore magnet ${\mathrm{CuInCr}}_4{\mathrm{S}}_8$ in ultrahigh magnetic fields up to 150 T

The magnetization process of the breathing pyrochlore magnet ${\mathrm{CuInCr}}_4{\mathrm{S}}_8$ has been investigated in ultrahigh magnetic fields up to 150 T. Successive phase transitions characterized by a substantially wide 1/2-plateau from 65 T to 112 T are observed in this system, resembling those reported in chromium spinel oxides. In addition to the 1/2-plateau phase, the magnetization is found to exhibit two inherent behaviors: A slight change in the slope of the $M\text{−}H$ curve at $\sim 85$ T and a shoulderlike shape at $\sim 135$ T prior to the saturation. Both of them are accompanied by a hysteresis, suggesting first-order transitions. The theoretical calculation applicable to ${\mathrm{CuInCr}}_4{\mathrm{S}}_8$ is also shown, based on the microscopic model with the spin-lattice coupling. The calculation fairly well reproduces the main features of the experimentally observed magnetization process, including a relatively wide cant 2:1:1 phase clearly observed in the previous work [Y. Okamoto et al., J. Phys. Soc. Jpn. 87, 034709 (2018)]. The robust 1/2-plateau on ${\mathrm{CuInCr}}_4{\mathrm{S}}_8$ seems to be originated from the dominant antiferromagnetic exchange interactions and the strong spin-lattice coupling.

Figure 1

$M\text{−}H$ curves of a powder sample of ${\mathrm{CuInCr}}_4{\mathrm{S}}_8$ measured at approximately 5 K in a HSTC megagauss generator. Measurements were performed up to 134 T (pink and purple curves for up and down sweeps, respectively) and 150 T (red and blue curves for up and down sweeps, respectively). Derivatives $dM/dH$ of the $M\text{−}H$ curves up to 150 T are shown in the upper panel. The previously reported $M\text{−}H$ curve and its derivative $dM/dH$ measured at 1.4 K in a nondestructive pulsed magnet up to 73 T are also shown (orange and cyan curves for up and down sweeps, respectively) [41]. Each data is shifted vertically for clarity. The dashed lines in the upper panel indicate $dM/dH=0$ lines. Transition fields are denoted by brackets or arrows in the upper panel, and drawn by the shaded areas (first order) or dashed lines (second order) in the lower panel.

Figure 2

(a) Crystal structure of the breathing pyrochlore lattice with two kinds of NN exchange interactions, $J$ and $J^{\prime }$, in the small and large tetrahedra, respectively. Second NN $\left(J_2\right)$ and third NN interactions $(J_{3a}$ and $J_{3b}$ for two symmetrically inequivalent paths) are also shown. (b) Model transformation from the breathing pyrochlore magnet with $J>0$ and $J^{\prime }<0$ to the fcc lattice antiferromagnet. Four spins in each large tetrahedron are converted to one localized spin, as indicated by red arrows. (c) Two types of the AFM ordering which are candidates for the ground state on the fcc lattice antiferromagnet. Up and down spins are described by red and blue arrows, respectively.

Figure 3

(a) Phase diagram of Eq. (10) as a function of the spin-lattice coupling parameter $b$ and magnetic field $h$. Red solid and blue dashed lines denote first- and second-order transitions, respectively. The regions shaded in pink, yellow, blue, white, and green express a cant 2:2, cant 2:1:1, 1/2-plateau, cant 3:1, and fully polarized phase, respectively. Schematic spin configuration within a single tetrahedron and its irreducible representation of the tetrahedral symmetry group are also illustrated in each region. This phase diagram is applicable to any value of $J_{\mathrm{FN}}$. (b) Magnetization curves as a function of magnetic field $h$ for $b/(1+J_{\mathrm{FN}}/J)=0$ to 0.25 in steps of 0.05. The transition fields, $h_{\mathrm{c}1},h_{\mathrm{c}2},h_{\mathrm{c}3}$, and $h_{\mathrm{sat}}$, are indicated for the case of $b/(1+J_{\mathrm{FN}}/J)=0.10$ as example.

Figure 4

Two possible 3-up 1-down spin structures for the 1/2-plateau phase on the fcc lattice. Up and down spins are described by red and blue arrows, respectively.