Spontaneous Chiral-Spin Ordering in Spin-Orbit Coupled Honeycomb Magnets

Extent of frustration in the classical Kitaev-$Γ$ model via bond anisotropy

“…Thus the degeneracy related to this symmetry in all the magnetic orders shown in this study is lifted in the presence of any one or more of these terms. This explains several results of previous studies including how a FM Γ lifts the (ZZ + 12) z degeneracy and selects the ZZ z over the 12 z configurations [26,29,30,54,66]. Similarly the magnetic field pointing in the Ẑ direction lifts the ZZ + 12 and 6 + 18 degeneracies near the Kitaev region and selects the ZZ and 6-site orders respectively [38,67].…”

“…While the KSL and various ordered phases are uncovered, there still remains regions of the phase space which are not well understood, with the most peculiar region being that of ferromagnetic (FM) Kitaev and antiferromagnetic (AFM) Γ interactions (KΓ model). Several numerical simulations of the KΓ model have reported quantum disordered phases [25][26][27][28][29][30][31][32], but the phase diagram is still controversial [33]. The classical KΓ model in a small phase space near the pure Kitaev [34][35][36][37][38][39] or pure Γ region was also studied [19,30,[40][41][42][43].…”

“…Several numerical simulations of the KΓ model have reported quantum disordered phases [25][26][27][28][29][30][31][32], but the phase diagram is still controversial [33]. The classical KΓ model in a small phase space near the pure Kitaev [34][35][36][37][38][39] or pure Γ region was also studied [19,30,[40][41][42][43]. They revealed the macroscopic degeneracy at the pure Kitaev and Γ limits, and the large unit cells (LUCs) that cannot be captured by small clusters used in, for example, ED on the 24-site cluster [44,45].…”

“…In parallel, the effects of exchange anisotropy on the spin frustration have been also explored to find possible QSLs and to understand its connection to KSL [46][47][48][49]. They suggest that the strong zbond region hosts large regions of disordered phases but it is not clear whether they correspond to isolated dimer limit [47,48] or spin liquid states such as the Γ spin liquid (ΓSL) [30,43] or multi-node gapless QSLs [49]. These numerical studies may also suffer from finite size effects and thus an investigation of the classical KΓ model whereby the bond strength is tuned would offer an insight to the ground states of the anisotropic KΓ quantum model.…”

Strain-induced phase diagram of the $S = \frac32$ Kitaev material $\rm{CrSiTe_3}$

“…This leads to a prototypical JKΓΓ model, which serves as a versatile playground to explore exotic phases and collective phenomena. These include a multi-node QSL in the vicinity of the Kitaev limit [18], a gapless QSL proposed in the honeycomb Γ model [19][20][21], and a chiral-spin ordering favored by a tiny Γ interaction in the dominated Γ region [22].…”