Coupled spin dimer magnets provide a stage to embody the quantum physics of interacting lattice bosons. These magnets often exhibit a gapped singlet ground state. In an external magnetic field exceeding the energy gap, the S_z = +1 component of the spin triplet is created on the dimer. The S_z = +1 component, called a magnon, acts as a boson on the dimer lattice. The number of magnons can be tuned via the external magnetic field corresponding to the chemical potential. Magnons move to neighboring dimers and interact with one another owing to the transverse and longitudinal components of the interdimer exchange interactions, respectively. When the hopping term is dominant, magnons can undergo Bose–Einstein condensation while when the hopping term is suppressed so that the repulsive interaction due to the antiferromagnetic interdimer interaction is dominant, magnons can crystallize to form a regular array.

Fig. 1. (a) Perspective view of the crystal structure of Ba₂CoSi₂O₆Cl₂. Dotted lines denote the chemical unit cell. A magnetic Co²⁺ ion is located approximately at the center of the base of the CoO₄Cl pyramid, where the pyramids are linked via orange-colored SiO₄ tetrahedra in the ab plane. (b) Model of the exchange network for Ba₂CoSi₂O₆Cl₂. Thick solid lines represent the intradimer exchange interaction J, and thin solid, dashed and dotted lines represent the interdimer exchange interactions

Fig. 2. Magnetization curves measured at 1.3K for H || c* and H || ab using a piece of single crystal corrected for Van Vleck paramagnetism. Dashed lines are theoretical magnetization curves calculated using the anisotropy of the interdimer exchange interaction and the intradimer exchange interaction.

Here we report the crystal structure of the spin dimer magnet Ba₂CoSi₂O₆Cl₂ and show that this compound exhibits magnon crystallization in a high magnetic field owing to the strong frustration of interdimer exchange interactions, which is different from the orthogonal dimer model [1]. The crystal structure consists of CoO₄Cl pyramids with a Cl^- ion at the apex, as shown in Fig 1(a). Magnetic Co²⁺ is located approximately at the center of the base composed of O^2-, which is approximately parallel to the ab-plane. Two CoO₄Cl pyramids form a chemical dimer with their bases facing each other. The magnetic property of Co²⁺ in an octahedral environment is determined by the lowest orbital triplet ⁴T₁. This orbital triplet splits into six Kramers doublets owing to spin–orbit coupling and the low-symmetric crystal field. When the temperature T is much lower than the magnitude of the spin–orbit coupling constant, the magnetic property is determined by the lowest Kramers doublet, and the effective magnetic moment of Co²⁺ is represented by the fictitious spin-1/2 operator [2, 3].

Figure 2 shows the magnetization curves for Ba₂CoSi₂O₆Cl₂ single crystal measured at 1.3 K for H || c* and H || ab. The entire magnetization process was observed up to a magnetic field of 70 T. The saturation of the Co²⁺ spin occurs at H_s ≃57 and 41 T for H || c* and H || ab, respectively. It can be clearly seen that the magnetization processes for both field directions are stepwise with a plateau at M_s/2. The singlet ground state is stabilized in a wide field range below H_c. These magnetization processes can be explained to consider that the interdimer exchange interactions are perfectly frustrated, which corresponds to the case J^ab₁₁ + J^ab₂₂ = J^ab₁₂ + J^ab₂₁ within the exchange network shown in Fig. 1(b). In this case, the magnon cannot move onto the neighboring dimer, because the hopping amplitude is proportional to J^ab₁₁ + J^ab₂₂ - J^ab₁₂ - J^ab₂₁. Hence, the ground state is determined by the balance between the Zeeman energy and the repulsive interaction between magnons. Consequently, a stepwise magnetization process with the M_s/2 plateau occurs, as observed in Ba₂CoSi₂O₆Cl₂.

In conclusion, this compound should be described as a 2D coupled spin dimer system with XY-like exchange interactions. Ba₂CoSi₂O₆Cl₂ exhibits a stepwise magnetization process with an M_s/2 plateau, irrespective of the magnetic field directions. This finding shows that the frustration for the interdimer exchange interactions is almost perfect. The M_s/2 plateau state is almost exactly given by the alternate product of singlet and triplet dimers, which corresponds to a Wigner crystal of magnons.

References

• [1] H. Tanaka, N. Kurita, M. Okada, E. Kunihiro, Y. Shirata, K. Fujii, H. Uekusa, A. Matsuo, K. Kindo, and H. Nojiri, J. Phys. Soc. Jpn. 83, 103701 (2014).
• [2] A. Abragam and M. H. L Pryce, Proc. R. Soc. London, Ser. A 206, 173 (1951)
• [3] M. E. Lines, Phys. Rev. 131, 546 (1963)

Authors

• H. Tanaka^a, N. Kurita^a, M. Okada^a, E. Kunihiro^a, Y. Shirata^a, K. Fujii^a, H. Uekusa^a, A. Matsuo, K. Kindo, and H. Nojiri^b
• ^aTokyo Institute of Technology
• ^bTohoku University