Magnetic order and spin excitations in layered Heisenberg antiferromagnets with compass-model anisotropies

Abstract

The spin-wave excitation spectrum, the magnetization, and the Néel temperature for the quasitwo-dimensional spin-1/2 antiferromagnetic Heisenberg model with compass-model interaction in the plane proposed for iridates are calculated in the random phase approximation. The spin-wave spectrum agrees well with data of Lanczos diagonalization. We find that the Néel temperature is enhanced by the compass-model interaction and is close to the experimental value for Ba2IrO4.PACS numbers: 75.40.Gb Spin-orbital physics in transition-metal oxides has been extensively studied in recent years. A number of theoretical models was proposed to describe a complicated nature of phase transitions induced by competing spin and orbital interactions as originally was considered in Ref. [1]. Whereas the isotropic spin interaction can be treated within the conventional Heisenberg model, to study the orientation-dependent orbital interaction the compass model is commonly used. The latter reveals a large degeneracy of ground states resulting in a complicated phase diagram. In particular, quantum and thermodynamic phase transitions in the two-dimensional (2D) compass model were studied in Refs. [2][3][4], where a first-order transition was found for the symmetric compass model. A generalized 2D Compass-Heisenberg (CH) model was introduced in Ref. [5], where an important role of the spin Heisenberg interaction in lifting the high degeneracy of the ground state of the compass model was stressed. In Ref.[6] a phase diagram of the CH model and excitations within Lanczos exact diagonalization for finite clusters on a square lattice were considered in detail. In particular, spin-wave excitations and column-flip excitations in nanoclusters characteristic to the compass model were analyzed.A strong relativistic spin-orbital coupling reveals a compass-model type interaction in 5d transition metals. In particular, it was shown in Ref. [7], that a strong spin-orbit coupling in such compounds as Sr 2 IrO 4 and Ba 2 IrO 4 results in an effective antiferromagnetic (AF) Heisenberg model for the pseudospins 1/2 with the compass-model anisotropy. The model can be used to explain the AF long-range order (LRO) below the Néel temperature T N = 230 K in Sr 2 IrO 4 and T N = 240 K in Ba 2 IrO 4 (see, e.g., [8]). The spin-wave spectrum measured by magnetic resonance inelastic x-ray scattering (RIXS) in Sr 2 IrO 4 shows a dispersion similar to that one in the undoped cuprate La 2 CuO 4 [9].In the present paper we calculate the spin-wave excitation spectrum and magnetization for a layered AF Heisenberg model with anisotropic compass-model interaction in the plane. To take into account the finitetemperature renormalization of the spectrum and to calculate the Néel temperature T N , we employ the equation of motion method for the Green functions (GFs) for spin S = 1/2 using the random phase approximation (RPA) [10]. The results are compared with experimental data for iridates and theoretical studies of the 2D CH model in Ref.[5] and in Refs. [11,12].We consider ...

Magnetic order in the two-dimensional compass-Heisenberg model

“…1 the Néel temperature T N as function of Γ y for two ratios of Γ x /Γ y is plotted. Our results for T N remarkably deviate from those found in RPA [8]. For Γ x /Γ y = 1.5, T N exhibits qualitatively the same dependence on Γ y , but is appreciably reduced as compared to RPA.…”

“…To obtain a closed system of self-consistency equations, we proceed as follows. As in our recent study of the model (1) by means of the RPA and linear spin-wave theory (LSWT) [8], we consider an anisotropic CM interaction, Γ x > Γ y > 0, so that the LRO phase is an easy-axis AF with the magnetization along the x axis. Accordingly, we put C y = C z = 0, where we can also consider the limiting case Γ x = Γ y .…”

“…(17) of Ref. [8] with the sublattice magnetization σ substituted by the spin S = 1/2. In the LRO phase, 0 < T ≤ T N , we have found that the ansatzr α (T ) =r α (0), wherē…”

“…[7]. Recently we have calculated the spin-wave excitation spectrum and T N for a layered CH model by means of the random phase approximation (RPA) [8] (see also Refs. [9]).…”

Magnetic order and spin excitations in the Kitaev–Heisenberg model on a honeycomb lattice

“…To take into account the finite-temperature renormalization of the spectrum and to calculate the transition temperature T c , we employ the equation of motion method for Green functions (GFs) [35] for spin S = 1/2 using the random phase approximation (RPA) [36], as we have done for the compass-Heisenberg model on the square lattice in Ref. [37].…”