Magnetic properties of nanoscale compass-Heisenberg planar clusters

Trousselet, Fabien; Oleś, Andrzej M.; Horsch, Peter

doi:10.1103/physrevb.86.134412

Cited by 37 publications

(25 citation statements)

References 53 publications

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“…• Heisenberg-compass model was introduced in the context of interacting t 2g orbital degrees of freedom and its 2D quantum incarnation was also investigated in the context of quantum computation (Trousselet et al, 2010;Trousselet et al, 2012). Another physical context in which such a hybrid model appears is the modeling of the consequences of the presence of orbital degrees of freedom in LaTiO 3 on the magnetic interactions in this material (Khaliullin, 2001).…”

Section: B Hybrid Compass Modelsmentioning

confidence: 99%

Compass models: Theory and physical motivations

2015

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Compass models are theories of matter in which the couplings between the internal spin (or other relevant field) components are inherently spatially (typically, direction) dependent. A simple illustrative example is furnished by the 90 • compass model on a square lattice in which only couplings of the form τ x i τ x j (where {τ a i }a denote Pauli operators at site i) are associated with nearest neighbor sites i and j separated along the x axis of the lattice while τ y i τ y j couplings appear for sites separated by a lattice constant along the y axis. Such compass-type interactions can appear in diverse physical systems. This includes Mott insulators with orbital degrees of freedom where interactions sensitively depend on the spatial orientation of the orbitals involved, the low energy effective theories of frustrated quantum magnets, vacancy centers and cold atomic gases. The fundamental inter-dependence between internal (spin, orbital, or other) and external (i.e., spatial) degrees of freedom which underlies compass models generally leads to very rich behaviors including the frustration of (semi-)classical ordered states on non-frustrated lattices and to enhanced quantum effects prompting, in certain cases, the appearance of zero temperature quantum spin liquids. As a consequence of these frustrations, new types of symmetries and their associated degeneracies may appear. These intermediate symmetries lie midway between the extremes of global symmetries and local gauge symmetries and lead to effective dimensional reductions. We review compass models in a unified manner, paying close attention to exact consequences of these symmetries, and to thermal and quantum fluctuations that stabilize orders via order out of disorder effects. This is complemented by a survey of numerical results.

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Section: B Hybrid Compass Modelsmentioning

confidence: 99%

Compass models: Theory and physical motivations

2015

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“…A generic model which stands for all these situations is the 2D compass model. It represents directional orbital interactions between e g or t 2g orbitals on the bonds in a 2D square or three-dimensional (3D) cubic lattice [19][20][21][22][23][24][25][26]. Its better understanding is crucial not only for spin-orbital systems but also for its realizations in optical lattices [27].…”

Section: Introductionmentioning

confidence: 99%

Variational tensor network renormalization in imaginary time: Two-dimensional quantum compass model at finite temperature

2016

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Progress in describing thermodynamic phase transitions in quantum systems is obtained by noticing that the Gibbs operator e −βH for a two-dimensional (2D) lattice system with a Hamiltonian H can be represented by a three-dimensional tensor network, the third dimension being the imaginary time (inverse temperature) β. Coarse-graining the network along β results in a 2D projected entangled-pair operator (PEPO) with a finite bond dimension D. The coarse-graining is performed by a tree tensor network of isometries. The isometries are optimized variationally -taking into account full tensor environment -to maximize the accuracy of the PEPO. The algorithm is applied to the isotropic quantum compass model on an infinite square lattice near a symmetry-breaking phase transition at finite temperature. From the linear susceptibility in the symmetric phase and the order parameter in the symmetry-broken phase the critical temperature is estimated at Tc = 0.0606(4)J, where J is the isotropic coupling constant between S = 1/2 pseudospins.

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“…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.…”

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

2015

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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 ...

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Magnetic properties of nanoscale compass-Heisenberg planar clusters

Cited by 37 publications

References 53 publications

Compass models: Theory and physical motivations

Compass models: Theory and physical motivations

Variational tensor network renormalization in imaginary time: Two-dimensional quantum compass model at finite temperature

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

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