Unconventional magnetic field response of the hyperhoneycomb Kitaev magnet $\beta -{\text{Li}}_2{\text{IrO}}_3$

Abstract

We present a unified description of the response of the hyperhoneycomb Kitaev magnet $\beta$-${\text{Li}}_2{\text{IrO}}_3$ to applied magnetic fields along the orthorhombic directions $\mathbf{a}$, $\mathbf{b}$ and $\mathbf{c}$. This description is based on the minimal nearest-neighbor $J$-$K$-$\Gamma$ model and builds on the idea that the incommensurate counter-rotating order observed experimentally at zero field can be treated as a long-distance twisting of a nearby commensurate order with six spin sublattices. The results reveal that the behavior of the system for $\mathbf{H}\parallel \mathbf{a}$, $\mathbf{H}\parallel \mathbf{b}$ and $\mathbf{H}\parallel \mathbf{c}$ share a number of qualitative features, including: i) a strong intertwining of the modulated, counter-rotating order with a set of uniform orders; ii) the disappearance of the modulated order at a critical field $H^{\ast }$, whose value is strongly anisotropic with $H_{\mathbf{b}}^{\ast }<H_{\mathbf{c}}^{\ast }\ll H_{\mathbf{a}}^{\ast }$; iii) the presence of a robust zigzag phase above $H^{\ast }$; and iv) the fulfillment of the Bragg peak intensity sum rule. It is noteworthy that the disappearance of the modulated order for $\mathbf{H}\parallel \mathbf{c}$ proceeds via a `metamagnetic' first-order transition which does not restore all broken symmetries. This implies the existence of a second finite-$T$ phase transition at higher magnetic fields. We also demonstrate that quantum fluctuations give rise to a significant reduction of the local moments for all directions of the field. The results for the total magnetization for $\mathbf{H}\parallel \mathbf{b}$ are consistent with available data and confirm a previous assertion that the system is very close to the highly-frustrated $K$-$\Gamma$ line in parameter space. Our predictions for the magnetic response for fields along $\mathbf{a}$ and $\mathbf{c}$ await experimental verification.

arXiv comment19 pages, 12 figures

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