Quantum phase transition in the three-dimensional anisotropic frustrated Heisenberg antiferromagnetic model

Viana, J. Roberto; Sousa, J. Ricardo de; Continentino, M. A.

doi:10.1103/physrevb.77.172412

Cited by 25 publications

(32 citation statements)

References 28 publications

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“…We have also treated the model (1) by using a finite cluster with N = 2 spins (EFT-2), which was previously developed in [16,27] to study the two-(λ = 0) and three-(λ = 1) dimensional limits. On the other hand, using EFT-2 we obtain not the phase diagram in the λ-α plane for all values of interlayer parameter (λ), only the particular limits (λ = 0, 1).…”

Section: Effective-field Theorymentioning

confidence: 99%

The quantum spin-1/2J₁–J₂antiferromagnet on a stacked square lattice: a study of effective-field theory in a finite cluster

Nunes

Sousa

Viana

et al. 2010

J. Phys.: Condens. Matter

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The ground state phase diagram of the quantum spin-1/2 Heisenberg antiferromagnet in the presence of nearest-neighbor (J(1)) and next-nearest-neighbor (J(2)) interactions (J(1)-J(2) model) on a stacked square lattice, where we introduce an interlayer coupling through nearest-neighbor bonds of strength J(), is studied within the framework of the differential operator technique. The Hamiltonian is solved by effective-field theory in a cluster with N=4 spins (EFT-4). We obtain the sublattice magnetization m(A) for the ordered phases: antiferromagnetic (AF) and collinear (CAF-collinear antiferromagnetic). We propose a functional for the free energy Ψ(μ)(m(μ)) (μ=A, B) to obtain the phase diagram in the λ-α plane, where λ=J()/J(1) and α=J(2)/J(1). Depending on the values of λ and α, we found different ordered states (AF and CAF) and a disordered state (quantum paramagnetic (QP)). For an intermediate region α(1c)(λ) < α < α(2c)(λ) we observe a QP phase that disappears for λ below some critical value λ(1)≈0.67. For α < α(1c)(λ) and α > α(2c)(λ), and below λ(1), we have the AF and CAF semi-classically ordered states, respectively. At α=α(1c)(λ) a second-order transition between the AF and QP states occurs and at α=α(2c)(λ) a first-order transition between the AF and CAF phases takes place. The boundaries between these ordered phases merge at the critical end point CEP≡(λ(1), α(c)), where α(c)≈0.56. Above this CEP there is again a direct first-order transition between the AF and CAF phases, with a behavior described by the point α(c) independent of λ ≥ λ(1).

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Section: Effective-field Theorymentioning

confidence: 99%

The quantum spin-1/2J₁–J₂antiferromagnet on a stacked square lattice: a study of effective-field theory in a finite cluster

Nunes

Sousa

Viana

et al. 2010

J. Phys.: Condens. Matter

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“…In this case different approaches, such as, spin-wave theories [46][47][48]51], variational cluster approach [52], differential operator technique [50] or a spherically symmetric Green function method [49], come to different conclusions with respect to the existence of a disordered ground-state phase. The underlying semi-classical physics of these approaches is different.…”

Section: Introductionmentioning

confidence: 99%

“…The underlying semi-classical physics of these approaches is different. Spin-wave theories [46][47][48]51], differential operator technique [50], and the variational cluster approach [52] include explicit symmetry breaking. Spin-wave theory uses the z-axis aligned classical states as a starting point for the calculation, whereas differential operator technique and the variational cluster approach use Weiss fields to test the presence of the antiferromagnetic order.…”

Section: Introductionmentioning

confidence: 99%

Ground-state ordering of theJ1−J2model on the simple cubic and body-centered cubic lattices

2016

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The J 1 -J 2 Heisenberg model is a "canonical" model in the field of quantum magnetism in order to study the interplay between frustration and quantum fluctuations as well as quantum phase transitions driven by frustration. Here we apply the Coupled Cluster Method (CCM) to study the spin-half J 1 -J 2 model with antiferromagnetic nearest-neighbor bonds J 1 > 0 and next-nearestneighbor bonds J 2 > 0 for the simple cubic (SC) and body-centered cubic (BCC) lattices. In particular, we wish to study the ground-state ordering of these systems as a function of the frustration parameter p = z 2 J 2 /z 1 J 1 , where z 1 (z 2 ) is the number of nearest (next-nearest) neighbors.We wish to determine the positions of the phase transitions using the CCM and we aim to resolve the nature of the phase transition points. We consider the ground-state energy, order parameters, spin-spin correlation functions as well as the spin stiffness in order to determine the ground-state phase diagrams of these models. We find a direct first-order phase transition at a value of p = 0.528 from a state of nearest-neighbor Néel order to next-nearest-neighbor Néel order for the BCC lattice.For the SC lattice the situation is more subtle. CCM results for the energy, the order parameter, the spin-spin correlation functions and the spin stiffness indicate that there is no direct first-order transition between ground-state phases with magnetic long-range order, rather it is more likely that

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“…This model has also been investigated recently by other groups. [16][17][18][19][20][21][22][23] We calculate the spin wave dispersion relations for this model. We report classical and quantum Monte Carlo simulations and molecular field theory calculations of χ(T ) and the magnetic heat capacity C mag (T ).…”

Section: Introductionmentioning

confidence: 99%

Magnetic exchange interactions inBaMn2As2: A case study of theJ1-
Johnston
¹
,
McQueeney
²
,
Lake
³

et al. 2011
Phys. Rev. B

166

198

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BaMn2As2 is unique among BaT2As2 compounds crystallizing in the body-centered-tetragonal ThCr2Si2 structure, which contain stacked square lattices of 3d transition metal T atoms, since it has an insulating large-moment (3.9 µB/Mn) G-type (checkerboard) antiferromagnetic AF ground state. We report measurements of the anisotropic magnetic susceptibility χ versus temperature T from 300 to 1000 K of single crystals of BaMn2As2, and magnetic inelastic neutron scattering measurements at 8 K and 75 As NMR measurements from 4 to 300 K of polycrystalline samples. The Néel temperature determined from the χ(T ) measurements is TN = 618(3) K. The measurements are analyzed using the J1-J2-Jc Heisenberg model for the stacked square lattice, where J1 and J2 are respectively the nearest-neighbor (NN) and next-nearest-neighbor intraplane exchange interactions and Jc is the NN interplane interaction. Linear spin wave theory for G-type AF ordering and classical and quantum Monte Carlo simulations and molecular field theory calculations of χ(T ) and of the magnetic heat capacity Cmag(T ) are presented versus J1, J2 and Jc. We also obtain band theoretical estimates of the exchange couplings in BaMn2As2. From analyses of our χ(T ), NMR, neutron scattering, and previously published heat capacity data for BaMn2As2 on the basis of the above theories for the J1-J2-Jc Heisenberg model and our band-theoretical results, our best estimates of the exchange constants in BaMn2As2 are J1 ≈ 13 meV, J2/J1 ≈ 0.3 and Jc/J1 ≈ 0.1, which are all antiferromagnetic. From our classical Monte Carlo simulations of the G-type AF ordering transition, these exchange parameters predict TN ≈ 640 K for spin S = 5/2, in close agreement with experiment. Using spin wave theory, we also utilize these exchange constants to estimate the suppression of the ordered moment due to quantum fluctuations for comparison with the observed value and again obtain S = 5/2 for the Mn spin.

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Quantum phase transition in the three-dimensional anisotropic frustrated Heisenberg antiferromagnetic model

Cited by 25 publications

References 28 publications

The quantum spin-1/2J₁–J₂antiferromagnet on a stacked square lattice: a study of effective-field theory in a finite cluster

The quantum spin-1/2J₁–J₂antiferromagnet on a stacked square lattice: a study of effective-field theory in a finite cluster

Ground-state ordering of theJ1−J2model on the simple cubic and body-centered cubic lattices

Magnetic exchange interactions inBaMn2As2: A case study of theJ1-
Johnston
¹
,
McQueeney
²
,
Lake
³

et al. 2011
Phys. Rev. B

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Quantum phase transition in the three-dimensional anisotropic frustrated Heisenberg antiferromagnetic model

Cited by 25 publications

References 28 publications

The quantum spin-1/2J1–J2antiferromagnet on a stacked square lattice: a study of effective-field theory in a finite cluster

The quantum spin-1/2J1–J2antiferromagnet on a stacked square lattice: a study of effective-field theory in a finite cluster

Ground-state ordering of theJ1−J2model on the simple cubic and body-centered cubic lattices

Magnetic exchange interactions inBaMn2As2: A case study of theJ1-Johnston1, McQueeney2, Lake3 et al. 2011Phys. Rev. B

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The quantum spin-1/2J₁–J₂antiferromagnet on a stacked square lattice: a study of effective-field theory in a finite cluster

The quantum spin-1/2J₁–J₂antiferromagnet on a stacked square lattice: a study of effective-field theory in a finite cluster

Magnetic exchange interactions inBaMn2As2: A case study of theJ1-
Johnston
¹
,
McQueeney
²
,
Lake
³

et al. 2011
Phys. Rev. B