Self-consistent spin-wave theory of layered Heisenberg magnets

Irkhin, V. Yu.; Катанин, А. А.; Katsnelson, M. I.

doi:10.1103/physrevb.60.1082

Cited by 114 publications

(96 citation statements)

References 43 publications

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“…[17][18][19] To apply this approach, we subdivide the lattice into sublattices A and B and use the DysonMaleev representation for spin operators on each sublattice,…”

Section: Spin-wave Calculationmentioning

confidence: 99%

Spin stiffness of the anisotropic Heisenberg model on the square lattice and a possible mechanism for pinning of the electronic liquid crystal direction in underdopedYBa2Cu3O6.45
Pardini
¹
,
Singh
²
,
Катанин
³

et al. 2008
Phys. Rev. B
16
13
22
2
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Using series expansions and spin-wave theory, we calculate the spin-stiffness anisotropy sx / sy in Heisenberg models on the square lattice with spatially anisotropic couplings J x , J y . We find that for the weakly anisotropic spin-half model ͑J x Ϸ J y ͒, sx / sy deviates substantially from the naive estimate sx / sy Ϸ J x / J y . We argue that this deviation can be responsible for pinning the electronic liquid crystal direction, an effect recently discovered in YBCO. For completeness, we also study the spin stiffness for arbitrary anisotropy J x / J y for spin-half and spin-one models. In the limit of J y / J x → 0, when the model reduces to weakly coupled chains, the two show dramatically different behavior. In the spin-one model, the stiffness along the chains goes to zero, implying the onset of Haldane-gap phase, whereas for the spin-half model, the stiffness along the chains increases monotonically from a value of 0.18J x for J y / J x = 1 toward 0.25J x for J y / J x → 0. In the latter case, spin-wave theory breaks down qualitatively, presumably due to the onset of topological terms with strong anisotropy. This work is motivated by the recent discovery 1,2 of the electronic liquid crystal in underdoped cuprate superconductor YBa 2 Cu 3 O 6.45 . The electronic liquid crystal manifests itself in a strong anisotropy in the low-energy inelastic neutron scattering. The liquid crystal picture implies a spontaneous violation of the directional symmetry: the "crystal" can be oriented either along the ͑1,0͒ or along the ͑0,1͒ axes in the square lattice. The YBa 2 Cu 3 O 6.45 compound has a tetragonal lattice with tiny in-plane lattice anisotropy a ‫ء‬ / b ‫ء‬ Ϸ 0.99. This tiny anisotropy is sufficient to pin the orientation of the electronic liquid crystal along the a ‫ء‬ axis. As a result, the low-energy neutron scattering 1,2 demonstrates a quasi-one-dimensional ͑1D͒ structure along a ‫ء‬ .To understand the pinning mechanism of the electronic crystal, in the present work, we study the anisotropic Heisenberg model. We calculate the in-plane anisotropy of the spin stiffness and demonstrate that this is strongly enhanced by quantum fluctuations. We argue that the enhancement is sufficient to provide a pinning mechanism for the initially spontaneous orientation of the electronic liquid crystal and suggest a specific mechanism for the pinning. The anisotropic Heisenberg model has previously attracted a lot of theoretical interests. 3-9 However, most theoretical studies have focused on the regime of strong anisotropy, where the system reduces to one of weakly coupled spin chains, and the most significant issue there is the dimensional crossover and the onset of long-range antiferromagnetic order. To the best of our knowledge, the anisotropy of spin stiffness has not been studied before. This is an important theoretical problem in itself and therefore, we extend our study to the case of arbitrary strong anisotropy. We consider both the spin-half and spin-one models where in the limit of strong anisotropy, we come to t...

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“…[17][18][19] To apply this approach, we subdivide the lattice into sublattices A and B and use the DysonMaleev representation for spin operators on each sublattice,…”

Section: Spin-wave Calculationmentioning

confidence: 99%

Spin stiffness of the anisotropic Heisenberg model on the square lattice and a possible mechanism for pinning of the electronic liquid crystal direction in underdopedYBa2Cu3O6.45
Pardini
¹
,
Singh
²
,
Катанин
³

et al. 2008
Phys. Rev. B
16
13
22
2
View full text Add to dashboard Cite

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“…Finally, we estimated the Curie temperature of -doped DMS according to the self-consistent spin-wave theory of layered Heisenberg model (S 2:0) with fluctuation cor-rections [19]. This approach was successfully applied to several layered magnets and should be appropriate for the present cases.…”

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confidence: 99%

Carrier-Induced Magnetic Ordering Control in a Digital (Ga,Mn)As Structure

Hong

Wang

2005

Phys. Rev. Lett.

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With the full potential linearized augmented plane method, we theoretically investigated the carrier-induced magnetization reversal in digital (Ga,Mn)As heterostructures with varying distance between the two Mn layers along with the distribution and concentration of external carriers. The presence of external holes induces switching from the antiferromagnetic to ferromagnetic state when d(Mn-Mn)=16.96 A, whereas the addition of electrons produces no significant effect. We demonstrate a possibility to separately control T(c) and magnetic reversal in digital (Ga,MN)As alloys.

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“…Note that these expressions are of similar form as corresponding formulas for the Neél temperature T N obtained by selfconsistent spin-wave theories. 6,8,9 We compare our data for T C in Tab. I with results for the Neél temperature T N of the stacked square-lattice antiferromagnet.…”

mentioning

confidence: 99%

“…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.…”

mentioning

confidence: 99%

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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Self-consistent spin-wave theory of layered Heisenberg magnets

Cited by 114 publications

References 43 publications

Spin stiffness of the anisotropic Heisenberg model on the square lattice and a possible mechanism for pinning of the electronic liquid crystal direction in underdopedYBa2Cu3O6.45
Pardini
¹
,
Singh
²
,
Катанин
³

et al. 2008
Phys. Rev. B
16
13
22
2
View full text Add to dashboard Cite

Spin stiffness of the anisotropic Heisenberg model on the square lattice and a possible mechanism for pinning of the electronic liquid crystal direction in underdopedYBa2Cu3O6.45
Pardini
¹
,
Singh
²
,
Катанин
³

et al. 2008
Phys. Rev. B
16
13
22
2
View full text Add to dashboard Cite

Carrier-Induced Magnetic Ordering Control in a Digital (Ga,Mn)As Structure

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

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Self-consistent spin-wave theory of layered Heisenberg magnets

Cited by 114 publications

References 43 publications

Spin stiffness of the anisotropic Heisenberg model on the square lattice and a possible mechanism for pinning of the electronic liquid crystal direction in underdopedYBa2Cu3O6.45Pardini1, Singh2, Катанин3 et al. 2008Phys. Rev. B1613222View full textAdd to dashboardCite

Spin stiffness of the anisotropic Heisenberg model on the square lattice and a possible mechanism for pinning of the electronic liquid crystal direction in underdopedYBa2Cu3O6.45Pardini1, Singh2, Катанин3 et al. 2008Phys. Rev. B1613222View full textAdd to dashboardCite

Carrier-Induced Magnetic Ordering Control in a Digital (Ga,Mn)As Structure

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

Contact Info

Product

Resources

About

Spin stiffness of the anisotropic Heisenberg model on the square lattice and a possible mechanism for pinning of the electronic liquid crystal direction in underdopedYBa2Cu3O6.45
Pardini
¹
,
Singh
²
,
Катанин
³

et al. 2008
Phys. Rev. B
16
13
22
2
View full text Add to dashboard Cite

Spin stiffness of the anisotropic Heisenberg model on the square lattice and a possible mechanism for pinning of the electronic liquid crystal direction in underdopedYBa2Cu3O6.45
Pardini
¹
,
Singh
²
,
Катанин
³

et al. 2008
Phys. Rev. B
16
13
22
2
View full text Add to dashboard Cite