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We present a unified description of the response of the hyperhoneycomb Kitaev magnet β-Li 2 IrO 3 to applied magnetic fields along the orthorhombic directions a, b and c. This description is based on the minimal nearest-neighbor J-K-Γ 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 H a, H b and H 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 * , whose value is strongly anisotropic with H * b < H * c H * a ; iii) the presence of a robust zigzag phase above H * ; and iv) the fulfillment of the Bragg peak intensity sum rule. It is noteworthy that the disappearance of the modulated order for H 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 H b are consistent with available data and confirm a previous assertion that the system is very close to the highly-frustrated K-Γ line in parameter space. Our predictions for the magnetic response for fields along a and c await experimental verification. arXiv:1910.13925v1 [cond-mat.str-el]

We revisit the theory of magnetic Raman scattering in Mott insulators with strong spin-orbit coupling, with a major focus on Kitaev materials. We show that Kitaev materials with bond-anisotropic interactions are generally expected to show both one-and two-magnon responses. It is further shown that, in order to obtain the correct leading contributions to the Raman vertex operator R, one must take into account the precise, photon-assisted microscopic hopping processes of the electrons and that, in systems with multiple hopping paths, R contains terms beyond those appearing in the traditional Loudon-Fleury theory. Most saliently, a numerical implementation of the revised formalism to the case of the three-dimensional hyperhoneycomb Kitaev material β-Li 2 IrO 3 reveals that the non-Loudon-Fleury scattering terms actually dominate the Raman intensity. In addition, they induce a qualitative modification of the polarization dependence, including, e.g., the emergence of a sharp one-magnon peak at low energies, which is not expected in the traditional Loudon-Fleury theory. This peak is shown to arise from microscopic photon-assisted tunneling processes that are of similar type with the ones leading to the symmetric off-diagonal interaction (known to be present in many Kitaev materials), but take the form of a bond-directional magnetic dipole term in the Raman vertex. These results are expected to apply across all Kitaev materials and mark a drastic change of paradigm for the understanding of Raman scattering in materials with strong spin-orbit coupling and multiple exchange paths.

We present a theoretical study of the response of β-Li 2 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-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 counterrotating 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 three-dimensional (3D) Kitaev magnet γ-Li 2 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.

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