The Magnetization plateau and commensurate - incommensurate transition
in the 2D triangular antiferromagnet Cs₂CuBr₄

The quasi-two dimensional antiferromagnet Cs₂CuBr₄, where the magnetic Cu²⁺ ions with S = 1/2 form a distorted triangular lattice in the bc-plane, has attracted keen attention, since a plateau was observed in the magnetization curve at one-third of the saturation magnetization when the magnetic field was applied along the b- or c-axes [1]. Recent neutron diffraction experiments suggested a cycloidal incommensurate spin ordering propagating along the b-axis with T_N = 1.4 K at zero field. In order to obtain microscopic insight into the spin structure and the spin dynamics in Cs₂CuBr₄, we have performed ¹³³Cs NMR experiments in the temperature range down to 0.4 K under the magnetic field up to 15.9 T. A single crystal of Cs₂CuBr₄ (2mm~3mm~4mm) was used.


Figures 1 [A] and [B] show the NMR spectra obtained for the magnetic fields applied along the b- and a-axis, respectively. Note that the spectrum [A]-(b) was measured in the 1/3-plateau phase, which occurs for the field range 14.0 - 15.5 T for H // b [1], while the others were obtained outside the plateau. In all cases, we observed two distinct ¹³³Cs resonance lines, which correspond to inequivalet sites (sites A and B) in the unit cell, although we have been yet unable to assign each line to a specific cesium site.




Fig. 1. The NMR spectra of ¹³³Cs nuclei in Cs₂CuBr₄ for the magnetic field along the [A] b- and [B] a-axis. Only the spectrum [A](b) obtained in the plateau phase shows discrete reaonance lines, while others exhibit continuous spectra. The proposed spin structure is shown for each spectrum.


The spectra in Fig. 1 [A](a) and [A](c) for H // b outside the plateau show a characteristic double-horn type line shape with a continuum of finite intensity between two peaks. Generally, such line shape is a signature of an incommensurate structure, in which the magnetic hyperfine fields at nuclei have a sinusoidal modulation yielding a continuum. The peaks of the spectra correspond to the extrema of the modulation. The fact that the spectra are asymmetric is explained if the field is in the cycloidal spin plane. Since the spins should be more densely populated along the field direction (Fig. 1[A](a)), we expect a distortion from purely sinusoical hyperfine field modulation, resulting in an asymmtric line shape.


Such a continuum is absent for the spectrum in the plateau region shown in Fig. 1[A](b). The spectrum consists only of two nearly symmetric discrete peaks with the intensity ratio approximately 1:2 for both A and B-sites. This result provides strong evidence that collinear up-up-down commensurate spin structure is realized in the 1/3-plateau phase.


In contrast, the spectra for the B-sites obtained for H // a (Fig. 1[B]), where the magnetization plateau was not observed, show symmetric double-horn type structure for all fields, indicating persistence of the incommensurate structure for the entire field range. The symmetric line shape suggests cone-type spin structure shown in Fig. 1[B], where the modulation of the hyperfine field is purely sinusoidal. It should be noted that, even though the cycloidal spin component is perpendicular to the field, anisotropic hyperfine interaction generally produces parallel component of the hyperfine field. The A-sites, on the other hand, show a sharp single peak, presumably because the anisotropy of the hyperfine interaction is not large enough.


The spin-lattice relaxation rates (1/T₁) measured at 14.5 T inside (H // b) and outside (H // a) the plateau phase are plotted against T/T_N (T_N: the Neel temperature) in Fig. 2. The relaxation rates decreases much more steeply for H // b than for H // a, indicating different low lying excitation spectra for commensurate and incommensurate phases. In particular, the slow decrease for H // a at low temperatures is presumably due to gapless phase flctuations in the incommensurate structure.




Fig. 2. Temperature dependence of the spin-lattice relaxation rate at 14.5 T inside (H // b) and outside (H // a) the plateau phase.





References
[1] H. Tanaka et al. Phys. Rev. B 67, 104431 (2003).