Phase Diagram and Spin Dynamics in Volborthite with a Distorted Kagome Lattice

The search for exotic ground states in two-dimensional (2D) spin systems with frustrated interactions is a challenge in condensed matter physics. In particular, the spin-1/2 antiferromagnetic Heisenberg model on a kagome lattice, a 2D network of corner-sharing equilateral triangles, is believed to have spin-liquid ground state with no broken symmetry. All candidate materials known to date, however, depart from the ideal kagome model in one way or another due to disorder, structural distortion, anisotropy, or longer range interactions. Volborthite Cu₃V₂O₇(OH)₂�E2H₂O is an example, which, unlike the ideal model, has kagome-like layers formed by isosceles triangles. Consequently, it has two Cu sites and two kinds of exchange interactions (Fig. 1, inset). Nevertheless, the absence of magnetic order down to 2 K, much lower than the Curie-Weiss temperature 115 K, indicates strong effects of frustration [1]. Recently, H. Yoshida et al. have significantly improved sample quality by hydrothermal annealing, allowing us to study intrinsic properties at lower temperatures [2].




Fig. 1. (Inset) The crystal structure of Cu₃V₂O₇(OH)₂�E2H₂O. (main panel) The phase diagram proposed by the present study. The squares (triangles) represent the phase boundaries determined from the NMR spectra as function of temperature (Fig. 2) (magnetic field). The circles and asterisks indicate the peak of 1/T₁ (Fig. 3) and the onset of the hysteresis in the susceptibility [2].

We have performed ⁵¹V-NMR experiments on a high-quality powder sample of volborthite. The NMR spectrum at B = 1 T shows a sudden broadening near T = 1 K (Fig. 2) accompanied with a sharp peak in the nuclear spin-lattice relaxation rate 1/T₁ (Fig. 3), indicating a magnetic transition. Similar but weaker anomalies have been reported previously [3], which coincided with the hysteresis of the susceptibility. Since the hysteresis in our sample is suppressed below 0.3 K at 1 T, the magnetic transition has nothing to do with the spin-glass like behavior. The dynamics in the low temperature phase is quite unusual. The T-linear behavior of 1/T₁ (Fig. 3) below 0.6 K indicates highly enhanced low-energy fluctuations incompatible with the spin-wave theory. The spin-echo decay rate 1/T₂ also shows anomalous enhancement and reaches a finite value at T = 0, indicating extremely slow fluctuations. This means the power spectrum of the local spin correlation G(t) = {S(t)�ES(0)} has at least two frequency scales as illustrated in Fig. 3. Although line broadening and a peak in 1/T₁ are normally considered evidence for a magnetic order, it remains still open in our case whether the order is truly static in the sense that G(t) remains finite in the limit of t �� ��.




Fig. 2. T-dependence of the line width (FWHM) at various magnetic fields. (B' stands for the center of gravity of the spectrum.) The inset shows the NMR spectra at 11.243 MHz (B' = 1 T).




Fig. 3. T-dependence of 1/T₁ at various magnetic fields B. The asterisks represent the T-dependence of 1/T₂ at 1 T. The solid (dotted) line shows the power law dependence T^�� with �� = 1 (1.5). The inset shows a schematic illustration of G(��), the power spectrum of the local spin correlation function, with two distinct frequency scales.


We found a sudden change of the NMR spectra when the field exceeds 4.5 T, where the first magnetization step was observed [2]. The behavior of 1/T₁ also changes qualitatively (Fig. 3), indicating a second magnetic phase with distinct spin structure and dynamics at high B. The B-T phase diagram established by our work is shown in Fig. 1. We expect more phases will be identified by future work.


References
[1] Z. Hiroi, N. Kobayashi, M. Hanawa, M. Nohara, H. Takagi, Y. Kato and M. Takigawa, J. Phys. Soc. Jpn. 70 (2001) 3377.
[2] 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 (2009) 043704.
[3] F. Bert, D. Bono, P. Mendels, F. Ladieu, F. Duc, J.-C.Trombe and P. Millet, Phys. Rev. Lett. 95 (2005) 087203.