On the Theory of the Two-Dimensional Heisenberg Antiferromagnet with Frustration on a Square Lattice

The thermodynamics of coupled frustrated ferromagnetic chains is studied within a spin-rotationinvariant Green's function approach. We consider an isotropic Heisenberg spin-half system with a ferromagnetic in-chain coupling J1 < 0 between nearest neighbors and a frustrating antiferromagnetic next-nearest neighbor in-chain coupling J2 > 0. We focus on moderate strength of frustration J2 < |J1|/4 such that the in-chain spin-spin correlations are predominantly ferromagnetic. We consider two inter-chain couplings (ICs) J ⊥,y and J ⊥,z , corresponding to the two axis perpendicular to the chain, where ferromagnetic as well as antiferromagnetic ICs are taken into account. We discuss the influence of frustration on the ground-state properties for antiferromagnetic ICs, where the ground state is of quantum nature. The major part of our study is devoted to the finitetemperature properties. We calculate the critical temperature Tc as a function of the competing exchange couplings J2, J ⊥,y , J ⊥,z . We find that for fixed ICs Tc monotonically decreases with increasing frustration J2, where as J2 → |J1|/4 the Tc(J2)-curve drops down rapidly. To characterize the magnetic ordering below and above Tc we calculate the spin-spin correlation functions S0SR , the magnetic order parameter M , the uniform static susceptibility χ0 as well as the correlation length ξ. Moreover, we discuss the specific heat CV and the temperature dependence of the excitation spectrum ωq. As J2 → |J1|/4 some unusual frustration-induced features were found, such as an increase of the in-chain spin stiffness (in case of ferromagnetic ICs) or of the in-chain spin-wave velocity (in case of antiferromagnetic ICs) with growing temperature.

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“…9,19,20,60,[62][63][64][67][68][69][70] Therefore, we illustrate here only some basic relevant features of the method. At that we follow Refs.…”

Section: Rotation-invariant Green's Function Methods (Rgm)mentioning

confidence: 99%

Thermodynamics of frustrated ferromagnetic spin-12Heisenberg chains: Role of interchain coupling

2017

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“…Another promising approach to calculate the thermodynamics of quasi-2D magnetic systems is a spin-rotation invariant Green's function method (RGM). 12,13,14,15,16,17,18,19,20 The RGM allows a consistent description of LRO as well as of short-range order (SRO) at arbitrary temperatures in magnetic systems of arbitrary dimension. …”

mentioning

confidence: 99%

“…An advantage of this method is the possibility to treat magnetic orderdisorder transitions driven by quantum fluctuations as well as by thermal fluctuations and to provide a good description of magnetic SRO. 12,13,14,15,16,17,18,19,20 To evaluate all relevant correlation functions S mα S nβ and several thermodynamic quantities we have to calculate a set of Fourier-transformed commutator Green's functions S + qα ; S − qβ ω which are connected with the dynamic spin susceptibilities by χ +− qαβ (ω) = − S + qα ; S − qβ ω . Using the equations of motion and supposing spinrotational invariance, i.e.…”

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confidence: 99%

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Green’s function theory of quasi-two-dimensional spin-half Heisenberg ferromagnets: Stacked square versus stacked kagomé lattices

2005

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We consider the thermodynamic properties of the quasi-two-dimensional spin-half Heisenberg ferromagnet on the stacked square and the stacked kagomé lattices by using the spin-rotationinvariant Green's function method. We calculate the critical temperature TC, the uniform static susceptibility χ, the correlation lengths ξν and the magnetization M and investigate the short-range order above TC . We find that TC and M at T > 0 are smaller for the stacked kagomé lattice which we attribute to frustration effects becoming relevant at finite temperatures. Introduction: Quasi-two-dimensional magnets have attracted much attention in recent years. 1,2 According to the Mermin-Wagner theorem 3 strictly two-dimensional (2D) Heisenberg magnets do not possess magnetic longrange order (LRO) at any finite temperature. Therefore, the exchange coupling between planes is crucial for the existence of a finite critical temperature T C . Though most of the quasi-2D magnetic insulators are antiferromagnets there are also some quasi-2D ferromagnetic insulators like K 2 CuF 4 , La 2 BaCuO 5 , Cs 2 AgF 4 . 4 The calculation of thermodynamic properties for quasi-2D magnets is an important issue, 5,6,7,8,9 in particular with respect to the interpretation of experimental results. Especially in the limit of weak interlayer coupling the evaluation of T C is challenging. Recently accurate values for the critical temperature of a Heisenberg magnet on a stacked square lattice by Monte-Carlo calculations 10 and on the cubic lattice by high-temperature series expansion 11 have been presented. Another promising approach to calculate the thermodynamics of quasi-2D magnetic systems is a spin-rotation invariant Green's function method (RGM). 12,13,14,15,16,17,18,19,20 The RGM allows a consistent description of LRO as well as of short-range order (SRO) at arbitrary temperatures in magnetic systems of arbitrary dimension.

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“…As already mentioned, the calculations are performed in SSSA for the spin-spin Green's function [7,35,36,48,49,58,59].…”

Section: Spherically Symmetric Self-consistent Approachmentioning

confidence: 99%

Thermodynamic properties of the 2D frustrated Heisenberg model for the entire J1–J2 circle

Mikheyenkov

Shvartsberg

Valiulin

et al. 2016

Journal of Magnetism and Magnetic Materials

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Using the spherically symmetric self-consistent Green's function method, we consider thermodynamic properties of the S = 1/2 J 1 -J 2 Heisenberg model on the 2D square lattice. We calculate the temperature dependence of the spin-spin correlation functions c r = S z 0 S z r , the gaps in the spin excitation spectrum, the energy E and the heat capacity C V for the whole J 1 -J 2 -circle, i.e. for arbitrary ϕ, J 1 = cos(ϕ), J 2 = sin(ϕ). Due to low dimension there is no long-range order at T = 0, but the short-range holds the memory of the parent zerotemperature ordered phase (antiferromagnetic, stripe or ferromagnetic). E(ϕ) and C V (ϕ) demonstrate extrema "above" the long-range ordered phases and in the regions of rapid short-range rearranging. Tracts of c r (ϕ) lines have several nodes leading to nonmonotonic c r (T ) dependence. For any fixed ϕ the heat capacity C V (T ) always has maximum, tending to zero at T → 0, in the narrow vicinity of ϕ = 155 • it exhibits an additional frustrationinduced low-temperature maximum. We have also found the nonmonotonic behaviour of the spin gaps at ϕ = 270 • ± 0 and exponentially small antiferromagnetic gap up to (T 0.5) for ϕ 270 • . PACS codes

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On the Theory of the Two-Dimensional Heisenberg Antiferromagnet with Frustration on a Square Lattice

Cited by 35 publications

References 23 publications

Thermodynamics of frustrated ferromagnetic spin-12Heisenberg chains: Role of interchain coupling

Thermodynamics of frustrated ferromagnetic spin-12Heisenberg chains: Role of interchain coupling

Green’s function theory of quasi-two-dimensional spin-half Heisenberg ferromagnets: Stacked square versus stacked kagomé lattices

Thermodynamic properties of the 2D frustrated Heisenberg model for the entire J1–J2 circle

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