When a Yb³⁺ ion (4f¹³) is situated in a crystalline electric field of low symmetry, a Kramers doublet becomes the ground state of the J=7/2 multiplet. Magnetic properties of such systems can be usually described in terms of a magnetic dipole moment carried by the Kramers doublet. Here we show that the tetragonal compound Yb₂Pt₂Pb, which orders antiferromagnetically at T_N=2.1 K [1], exhibits a very unusual ordered state in a magnetic field, whose order parameter is likely to be a high-rank magnetic multipole moment [2].

Fig. 1. (a) Magnetic phase diagram of Yb₂Pt₂Pb for H || [110]. 
(b) Field variation of the magnetization of Yb₂Pt₂Pb for H || [110] measured at 80 mK.

Fig. 2. Proposed magnetic structures of Yb₂Pt₂Pb for H || [110]. (a) Phase I. Each Yb sublattice has a collinear structure. Thick arrows indicate the Yb magnetic moment. (b) Phase II’. Sublattice B (solid circles) remains in a collinear state, whereas sublattice A (open circles) exhibits a pseudo-spin flop. Dashed arrows denote the pseudo spins whereas double arrows indicate the multipole moments. (c) Phase III. Sublattice B remains in a collinear state, whereas sublattice A becomes parmagnetic.

The Yb lattice in Yb₂Pt₂Pb can be viewed as being composed of orthogonal dimers aligned along [110] or [1-10] directions [1]; we can define two sublattices of Yb ions: sublattice A of [110] dimers and sublattice B of [1-10] dimers. In the preceding experiment, Ochiai et al. [3] have shown that the Yb moment has a strong Ising anisotropy along the dimer axis. When a magnetic field H is applied parallel to [110], the antiferromagnetic moments on the sublattice B are decoupled from H because their Ising axes are perpendicular to H. Accordingly, only the moments on sublattice A respond to H and the phase diagram is given in Fig. 1a, where three different ordered phases I, II’ and III exist. The magnetic structures of phases I and III are shown in Figs. 2a and 2c, respectively. In phase I, both sublattices A and B are essentially in a collinear structure. In phase III, magnetic moments on sublattice B remain in a collinear structure but those on sublattice A become paramagnetic. Ochiai et al. [3] pointed out that the highly anisotropic magnetic properties can be understood by assuming the ground state doublet of Yb³⁺ ion to be predominantly composed of states ⎮±7/2〉 with the local quantization axis parallel to either [110] or [1-10].

There is another phase, phase II’, in the phase diagram [3]. The exact nature of phase II’, however, has not been clear in the preceding experiments. We have examined the low temperature magnetization of Yb₂Pt₂Pb and found that the Yb magnetic moment increases almost linearly in phase II’ and saturates without discontinuity; quite unexpectedly, the II’-III transition is of second order. This behavior of phase II’ is apparently incompatible with the Ising anisotropy of the Yb moment. We propose that a high-rank magnetic multipole moment is the order parameter in phase II’. For simplicity, let us assume the wave functions of the Kramers doublet to be ⎮±7/2〉. In a pseudo-spin representation, the z component is the magnetic dipole J_z. On the other hand, the x and y components are rank-7 magnetic multipoles (octacosahectapoles). It can then be shown that a pseudo-spin flop occurs in a magnetic field along the Ising axis, if an interaction between the multipole moments is sufficiently strong (Fig.2 b) [2]. In this situation, the magnetic moment along [110] linearly increases with H and continuously saturates, as observed by experiment.

References

• [1] M. S. Kim, M. C. Bennett, and M. C. Aronson, Phys. Rev. B 77, 144425 (2008).
• [2] Y. Shimura, T. Sakakibara, K. Iwasawa, K. Sugiyama, and Y. Onuki, J. Phys. Soc. Jpn. 81, 103601 (2012).
• [3] A. Ochiai, S. Matsuda, Y. Ikeda, Y. Shimizu, S. Toyoshima, H. Aoki, and K. Katoh, J. Phys. Soc. Jpn. 80, 123705 (2011).

Authors

• Y. Shimura, T. Sakakibara, K. Iwasawa^a, K. Sugiyama^a, and Y. Onuki^a
• ^aOsaka University