Nonlinear magnetic susceptibility in the Kitaev model

We study the nonlinear spin susceptibility in the Kitaev model [1]. The model has been serving as a paradigmatic model for studying a quantum spin liquid and extensive experimental efforts are currently undertaken. While the Jackeli-Khaliullin mechanism [2] predicts the ferromagnetic Kitaev model, recent theoretical studies suggest that the antiferromagnetic Kitaev model may stabilize distinct spin liquids in a magnetic field. Since the determination of the sign of the Kitaev coupling can be experimentally problematic, we propose a convenient complementary experimental signature to distinguish the two cases. Here, in the gapped spin liquid phase, we derive an analytical expression in perturbation theory and find that the nonlinear spin susceptibility exhibits a characteristic sign change at finite temperature in the ferromagnetic Kitaev model. We also present results based on numerical simulations (exact diagonalization and quantum Monte Carlo simulations), with which we show that the characteristic sign change also appears in the gapless spin liquid phase with a ferromagnetic coupling [3].

[1] Kitaev, Ann. Phys. 321, 2 (2006)
[2] Jackeli and Khaliullin, Phys. Rev. Lett. 102, 017205 (2009)
[3] Kamiya, Yoshitake, Nasu, Kato, and Motome, in preparation.