Quantum phase diagram of the $S=1/2$ triangular-lattice antiferromagnet Ba$_3$CoSb$_2$O$_9$

TL;DR

This study uses NMR spectroscopy to map the magnetic phases of the spin-1/2 triangular-lattice antiferromagnet Ba$_3$CoSb$_2$O$_9$, revealing complex phase transitions and spin configurations consistent with semi-classical modeling.

Contribution

First detailed microscopic NMR investigation of Ba$_3$CoSb$_2$O$_9$'s magnetic phases, confirming theoretical predictions and highlighting the role of quantum effects and interlayer coupling.

Findings

Identification of the up-up-down spin configuration and 1/3 magnetization plateau.

Observation of a phase transition near 3/5 of saturation magnetization.

Good agreement between experimental data and semi-classical energy density model.

Abstract

The magnetic phases of the ideal spin-1/2 triangular-lattice antiferromagnet Ba$_3$CoSb$_2$O$_9$ are identified and studied using $^{135,137}$Ba nuclear magnetic resonance (NMR) spectroscopy in magnetic fields ranging to 30T, oriented parallel and near perpendicular to the crystallographic $ab$-plane. For both directions, the saturation field is approximately 33T. Notably, the NMR spectra provide microscopic evidence for the stabilization of an up-up-down spin configuration for in-plane fields, giving rise to an one-third magnetization plateau ($M_\text{sat}/3$), as well as for a higher field phase transition near to $\sim (3/5)M_\text{sat}$ for both field orientations. Phase transitions are signaled by the evolution of the NMR spectra, and in some cases through spin-lattice relaxation measurements. The results are compared with expectations obtained from a semi-classical energy density modeling, in which quantum effects are incorporated by effective interactions extracted from the spin-wave analysis of the two-dimensional model. The interlayer coupling also plays a significant role in the outcome. Good agreement between the model and the experimental results is achieved, except for the case of fields approaching the saturation value applied along the c-axis.