Heisenberg antiferromagnet with anisotropic exchange on the kagomé lattice: Description of the magnetic properties of volborthite

Abstract

We study the properties of the Heisenberg antiferromagnet with spatially anisotropic nearest-neighbor exchange couplings on the kagomé net, i.e., with coupling J in one lattice direction and couplings JЈ along the other two directions. For J / JЈ տ 1, this model is believed to describe the magnetic properties of the mineral volborthite. In the classical limit, it exhibits two kinds of ground state: a ferrimagnetic state for J / JЈ Ͻ 1/2 and a large manifold of canted spin states for J / JЈ Ͼ 1 / 2. To include quantum effects self-consistently, we investigate the Sp͑N͒ symmetric generalization of the original SU͑2͒ symmetric model in the large-N limit. In addition to the dependence on the anisotropy, the Sp͑N͒ symmetric model depends on a parameter that measures the importance of quantum effects. Our numerical calculations reveal that, in the -J / JЈ plane, the system shows a rich phase diagram containing a ferrimagnetic phase, an incommensurate phase, and a decoupled chain phase, the latter two with short-and long-range order. We corroborate these results by showing that the boundaries between the various phases and several other features of the Sp͑N͒ phase diagram can be determined by analytical calculations. Finally, the application of a block-spin perturbation expansion to the trimerized version of the original spin-1 / 2 model leads us to suggest that in the limit of strong anisotropy, J / JЈ ӷ 1, the ground state of the original model is a collinearly ordered antiferromagnet, which is separated from the incommensurate state by a quantum phase transition.

Spatially anisotropic Heisenberg kagome antiferromagnet

“…37, on the other hand, used a large-N expansion applied to the Sp͑N͒-symmetric generalization of the model. In the limit JЈ Ӷ J, they found that the chains are completely decoupled, and the interstitial spins show some ͑short-range͒ spin-spin correlation that is compatible with a spiral ordering pattern.…”

“…Examples include large-N expansions of the Sp͑N͒-symmetric generalization of the model, 36,37 a blockspin perturbation approach to the trimerized kagome lattice, 37 spin. 37,38 Our approach is complementary to these studies in that it offers a fairly controlled analysis of the quasi-onedimensional limit using powerful field-theoretical methods [39][40][41] that have originally been developed for the investigation of quantum critical systems in one dimension. Recently, the quasi-one-dimensional version of the kagome antiferromagnet in a strong magnetic field, assuming that the intermediate spins are fully polarized, has been studied using similar techniques.…”

Pair correlations, short-range order, and dispersive excitations in the quasi-kagome quantum magnet volborthite

“…The subsets of this model which have been treated semiclassically or quantum mechanically are J 1 = J 1 > 0, J 2 = 0, and D z = 0, the isotropic kagome DM model (IKDM) 7,8,18 and J 1 = J 1 > 0, J 2 = 0, and D z = 0, the anisotropic kagome (AK) model. 5,6 In addition, recent L(S)DA + U calculations have suggested a model where −J 1 /J 1 ∼ 1.2-2, −J 2 /J 1 = 1.1-1.6, and J 1 = 8.6 meV. This model, which we call the coupled chain (CC) model, has only been treated classically so far.…”

Quantum spin liquid and magnetic order in a two-dimensional nonsymmorphic lattice: Considering the distorted kagome lattice of volborthite

“…12 Over the years, Volborthite has also inspired several theoretical studies. [13][14][15][16][17] In this work, we investigate possible quantum spin liquid and magnetically ordered phases on the distorted Kagome lattice, in view of the spatially anisotropic spin exchange model proposed earlier by the density functional theory (DFT) computations. 18 The distorted Kagome lattice corresponding to the so-called J − J − J 1 − J 2 model represents the nonsymmorphic layer space group, p2gg, that possesses glide symmetry, the combination of reflection and a fractional translation.…”