A Heterogeneous Spin States in Volborthite with a distorted Kagome Lattice

The spin-1/2 antiferromagnetic Heisenberg model on a kagome lattice, a two dimensional network of corner-sharing equilateral triangles, is a theoretical paradigm to look for exotic spin liquid without symmetry breaking. Materials in real world, however, always deviate from the ideal model due, for example, to anisotropy, longer range interactions, lattice distortion, or disorder, which often lead to different kinds of symmetry breaking. This is by itself a very interesting issue, allowing us to understand novel mechanisms of various quantum phase transitions.

Vorlborthite Cu₃V₂O₇(OH)₂�E2H₂O has distorted kagome layers formed by isosceles triangles, and hence two Cu sites, Cu1 and Cu2. It shows a sequence of magnetization steps, indicating field-induced phase transitions [1]. We have performed ⁵¹V NMR experiments on a high quality powder sample at various magnetic fields [2-4]. The phase diagram obtained from our work is shown in Fig. 1(a). At low fields below 4.5 T, a magnetic transition near 1 K is evidenced by broadening of the NMR line and a peak in nuclear relaxation rates 1/T₁ and 1/T₂. However, the ordered phase (phase I) is anomalous with non-uniform magnitude of ordered moment and dense low energy excitations [2].



Fig. 1. (a) The phase diagram of volborthite obtained from the onset of ⁵¹V NMR line broadening as a function of temperature (squares) or magnetic field (triangles), the peak in 1/T₁ (circles), and the magnetization steps (stars). The lines are guide to the eyes. The transition between phases II and III are broadened probably due to anisotropy of g-value in a powder sample. (b) The NMR spectrum in phase II decomposed into contributions from the fast (V_f) and slowly (V_s) decaying V sites. (c) The NMR spectrum in phase III again decomposed into the V_f and V_s sites. The large shift at the V_s site indicates ferromagnetic alignment of a part of the Cu spins, which are strongly coupled to the V_s sites.

A second ordered phase (phase II) appears above 4.5 T, where the first magnetization step occurs. A remarkable feature of phase II is the existence of two types of V sites, V_f and V_s sites. Although their NMR spectra overlap as shown in Fig. 1(b), they are clearly distinguished by different spin-echo decay rates 1/T₂, the V_f (V_s) site showing fast (slow) decay, and distinct line shapes. This indicates spontaneous emergence of two types of Cu sites with distinct dynamics, which form a heterogeneous superstructure.

In phase III two distinct V sites still exist and now their spectra are clearly separated (Fig. 1c). A large internal field at the V_s site indicates a large magnetization for a part of the Cu spins, which are strongly coupled to the V_s site and provides a natural explanation for the second magnetization step, which occurs between phase II and III.



Fig. 2. Possible magnetic structures in volborthite projected onto the a-b plane. (a) Superstructure along the k₁ direction provides two inequivalent V sites, V_f and V_s, and three inequivalent Cu sites, Cu1(��), Cu1(��), and Cu2. (b) If the coupling tensors are largely isotropic and have similar magnitudes, different relaxation behavior at the V_f and V_s sites should be ascribed to the distinct spin states at the Cu1(��), and Cu1(��) sites.

Based on these observations, we propose the spin structures of phase II and III (Fig. 2). The two types of V sites naturally suggest two types of Cu1 sites, one with modulated moments and large fluctuations and the other with a fixed magnitude of moment and less fluctuations. They form a spontaneous superstructure. The second magnetization step is then associated with the ferromagnetic saturation of the latter. This scenario is partially consistent with theories for the anisotropic kagome antiferromagnet in the limit of strong interaction within 1D Cu2 chains coupled by weak and frustrated interaction through Cu1 sites.


References
[1] H. Yoshida, Y. Okamoto, T. Tayama, T. Sakakibara, M. Yokunaga, A. Matsuo, Y. Narumi, K. Kindo, M. Yoshida, M. Takigawa, and Z. Hiroi, J. Phys. Soc. Jpn. 78, 043704 (2009).
[2] M. Yoshida, M. Takigawa, H. Yoshida, Y. Okamoto, and Z. Hiroi, Phys. Rev. Lett. 103 (2009) 077207.
[3] M. Yoshida, M. Takigawa, H. Yoshida, Y. Okamoto, and Z. Hiroi, Phys. Rev. B 84, 020410(R) (2011).
[4] M. Yoshida, M. Takigawa, S. Kr?mer, S. Mukhopadhyay, M. Horvati?, C. Berthier, H. Yoshida, Y. Okamoto, and Z. Hiroi, J. Phys. Soc. Jpn. 81, 024703 (2012).