Reentrant incommensurate order and anomalous magnetic torque in the Kitaev magnet $\beta$-${\text{Li}}_2{\text{IrO}}_3$

We present a theoretical study of the response of $\beta$-${\text{Li}}_2{\text{IrO}}_3$ under external magnetic fields in the $ab$, $bc$ and $ac$ crystallographic planes. The results are based on the minimal nearest-neighbor $J$-$K$-$\mathrm{\Gamma }$ model and reveal a rich intertwining of field-induced phases and magnetic phase transitions with distinctive signatures that can be probed directly via torque magnetometry. Most saliently, we observe: i) an unusual reentrance of the incommensurate counter-rotating order for fields in the $ab$-plane, and ii) a set of abrupt torque discontinuities which are particularly large for fields rotating in the $bc$ plane, and whose characteristic shape resembles closely the ones observed in the 3D Kitaev magnet $\gamma$-${\text{Li}}_2{\text{IrO}}_3$. An experimental confirmation of these predictions will pave the way for an accurate determination of all relevant microscopic parameters of this 3D Kitaev magnet.