Breathing pyrochlore magnets with an alternating array of small and large tetrahedra have recently attracted attention because of their potential realization of exotic magnetic states. One promising candidate is the S = 3/2 chromium spinel oxide, LiInCr₄O₈, characterized by the small breathing factor J’/J~0.1, where J and J’ are the exchange interactions on the small and large tetrahedra, respectively (inset of Fig. 1) [1]. In this system, the spin-lattice coupling (SLC) as well as the breathing factor govern its magnetic properties, as represented by a tetramer-singlet formation [1] and a field-induced transition to a 1/2-magnetization plateau phase [2]. Another intriguing system is the sulfide, CuInCr₄S₈, where the antiferromagnetic (AFM) J and the ferromagnetic (FM) J’ coexist [3]. As shown in Fig. 1, the previously reported M-H curves at 1.4 K (orange and cyan lines for up and down sweeps, respectively) show a metamagnetic behavior with a large hysteresis loop at around H_c1 = 20~40 T, while M reaches only 45 % of the saturation magnetization of ~3.06 μB/Cr at 73 T [3].

Fig. 1. M-H curves of CuInCr₄S₈ measured at ~5 K in a single-turn coil megagauss generator up to 150 T (red and blue curves for up and down sweeps, respectively). Derivatives dM/dH are shown in the upper panel. The previously reported M-H curve measured at 1.4 K up to 73 T are also shown (orange and cyan curves for up and down sweeps, respectively) [3]. 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. Inset shows the schematic of the breathing pyrochlore lattice.

In this work, we performed magnetization measurements on a polycrystalline powder sample of CuInCr₄S₈ by using a single-turn coil system. The observed M-H curve and its derivative dM/dH at 5 K up to 150 T are shown in Fig. 1 (red and blue lines for up and down sweeps, respectively) [4]. Remarkably, a wide 1/2-plateau emerges from H_c2 ~ 65 T to H_c3 ~ 112 T as in Cr spinel oxides. Besides, two inherent features are observed: A slight change in the slope of the M-H curve at H_c2’ ~ 85 T and a shoulder like shape at H_c4 ~ 135 T. Both are accompanied by a hysteresis, suggesting first-order transitions. The saturation is estimated to H_sat ~ 180 T under the assumption that M increases linearly above 150 T, where M already reaches ~2.7 μ_B/Cr.

For interpreting the observed magnetization process, we constructed an effective spin model mapped onto the fcc lattice, which is derived from the microscopic spin model on the breathing pyrochlore lattice with the SLC as proposed in Ref. [5]. Figure 2 summarizes the calculated M-H curves for given values of the SLC parameter b and the corresponding spin structures. In spite of the simplification in our model, the calculation well reproduces the main feature of the M-H curve of CuInCr₄S₈, including a relatively wide intermediate (canted 2:1:1) phase as well as the 1/2-plateau phase with collinear 3:1 spin configuration.

Fig. 2. Calculated magnetization curves as a function of magnetic field h for b/(1 + J_FN/J) = 0 to 0.25 in steps of 0.05. The spin structures corresponding to the curve for b/(1 + J_FN/J) = 0.10 (thick green line) are shown in the upper part of the figure.

It is noteworthy that the M-H curves of LiGaCr₄S₈ and LiInCr₄S₈, where the FM interaction J’ is expected to be strong, do not exhibit the 1/2-plateau [3]. Bearing this in mind, the exotic magnetic behaviors on CuInCr₄S₈ can be attributed to the relatively dominant AFM interactions J+J_FN compared to the FM J’, which is achieved only by the moderate breathing distortion in the Cr spinel sulfide. On the other hand, the origins of the hysteretic behaviors on CuInCr₄S₈ at H_c2’ and H_c4 remain unsolved at the moment. They might originate from the interplay between the SLC and the further neighbor interactions J_FN, or the thermal and quantum effects, which are not considered in the present theory. The macroscopic spin structures beyond four sites within small tetrahedra should also be clarified, which is crucial to prove the novelty of the magnetic properties in CuInCr₄S₈. Further experimental investigations such as magnetostriction, ESR, and magnetocaloric effect measurements in high magnetic fields are ongoing to elucidate the essence of the successive phase transitions.

References

• [1] Y. Okamoto, G. J. Nilsen, J. P. Attfield, and Z. Hiroi, Phys. Rev. Lett. 110, 097203 (2013).
• [2] M. Gen, D. Nakamura, Y. Okamoto, and S. Takeyama, J. Magn. Magn. Mater. 473, 387 (2019).
• [3] Y. Okamoto, M. Mori, N. Katayama, A. Miyake, M. Tokunaga, A. Matsuo, K. Kindo, and K. Takenaka, J. Phys. Soc. Jpn. 87, 034709 (2018).
• [4] M. Gen, Y. Okamoto, M. Mori, K. Takenaka, and Y. Kohama, Phys. Rev. B 101, 054434 (2020).
• [5] K. Aoyama and H. Kawamura, Phys. Rev. B 99, 144406 (2019).

Authors

• M. Gen, Y. Okamoto^a, M. Mori^a, K. Takenaka^a, and Y. Kohama
• ^aNagoya University