# Anisotropic temperature-field phase diagram of single-crystalline $\beta$-Li$_2$IrO$_3$: magnetization, specific heat, and $^7$Li NMR study

## TL;DR

This study investigates the anisotropic magnetic and thermal properties of single-crystalline $eta$-Li$_2$IrO$_3$, revealing field-dependent magnetic transitions and a crossover to a quantum paramagnetic state under specific magnetic field orientations.

## Contribution

It provides detailed experimental insights into the anisotropic phase diagram and magnetic behavior of $eta$-Li$_2$IrO$_3$, highlighting the effects of magnetic field direction on its magnetic ordering and quantum states.

## Key findings

- Magnetization anisotropy reflects ferromagnetic Kitaev interaction and off-diagonal anisotropy.
- Magnetic field along $b$ suppresses the N{é}el temperature to zero at 2.8 T.
- Field-induced crossover to a quantum paramagnetic state observed around 2.8 T.

## Abstract

Detailed magnetization, specific heat, and $^7$Li nuclear magnetic resonance (NMR) measurements on single crystals of the hyperhoneycomb Kitaev magnet $\beta$-Li$_2$IrO$_3$ are reported. At high temperatures, {\cred anisotropy of the magnetization is reflected by the different Curie-Weiss temperatures for different field directions}, in agreement with the combination of a ferromagnetic Kitaev interaction ($K$) and a negative off-diagonal anisotropy ($\Gamma$) as two leading terms in the spin Hamiltonian. At low temperatures, magnetic fields applied along $a$ or $c$ have only a weak effect on the system and reduce the N\'eel temperature from 38 K at 0 T to about 35.5 K at 14 T, with no field-induced transitions observed up to 58 T on a powder sample. In contrast, the field applied along $b$ causes a drastic reduction in the $T_N$ that vanishes around $H_c=2.8$ T giving way to a crossover toward a quantum paramagnetic state. $^7$Li NMR measurements in this field-induced state reveal a gradual line broadening and a continuous evolution of the line shift with temperature, suggesting the development of local magnetic fields. The spin-lattice relaxation rate shows a peak around the crossover temperature 40 K and follows power-law behavior below this temperature.