Critical properties of highly frustrated pyrochlore antiferromagnets

Reimers, J. N.; Greedan, J. E.; Björgvinsson, Már

doi:10.1103/physrevb.45.7295

Cited by 68 publications

(61 citation statements)

References 47 publications

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“…The 1/n expansion applied to (4.17) yields a continuous transition characterized by the exponents [84], One possible example of such noncoplanar criticality was studied by Reimers, Greedan and Björgvinsson for pyrochlore antiferromagnet FeF 3 both by neutrondiffraction experiment and by Monte Carlo simulation [86]. The reported exponent values were quite unusual, α = 0.6(1), β = 0.18(2), γ = 1.1(1) and ν = 0.38(2), although Mailhot and Plumer argued that the same data were also not inconsistent with a first-order transition [87].…”

Section: (F) Further Generalization Of Noncollinear Transitionsmentioning

confidence: 99%

Untitled

Kawamura¹

1998

J. Phys.: Condens. Matter

342

470

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Recent theoretical and experimental studies on the critical properties of frustrated antiferromagnets with the noncollinear spin order, including stacked-triangular antiferromagnets and helimagnets, are reviewed. Particular emphasis is put on the novel critical and multicritical behaviors exhibited by these magnets, together with an important role played by the 'chirality'. §1. Introduction Phase transitions and critical phenomena have been a central issue of statistical physics for many years. In particular, phase transitions of magnets or of 'spin systems' have attracted special interest. Thanks to extensive theoretical and experimental studies, we now have rather good understanding of the nature of phase transitions of standard ferromagnets and antiferromagnets. By the term 'standard', I mean here regular and unfrustrated magnets without quenched disorder and frustration. They include ferromagnets and unfrustrated antiferromagnets with the collinear spin order.One key notion which emerged through these studies is the notion of universality. According to the universality hypothesis, a variety of continuous (or secondorder) phase transitions can be classified into a small number of universality classes determined by a few basic properties characterizing the system under study, such as the space dimensionality d, the symmetry of the order parameter and the range of interaction. If one is interested only in the so-called universal quantities, such as critical exponents, amplitude ratios and scaled equation of state, various phase transitions should exhibit exactly the same behavior. In the case of standard bulk magnets in three spatial dimensions (d = 3), universality class is basically determined by the number of the spin components, n. Physically, the index n is related to the type of magnetic anisotropy: Namely, n = 1 (Ising), n = 2 (XY ) and n = 3 (Heisenberg) correspond to magnets with easy-axis-type anisotropy, easy-plane-type anisotropy and no anisotropy (isotropic magnets), respectively. The critical properties associated with these n-component O(n) universality classes have been extensively studied and are now rather well understood. From the renormalization-group (RG) viewpoint, these critical properties are governed by the so-called Wilson-Fisher O(n) fixed point.

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Section: (F) Further Generalization Of Noncollinear Transitionsmentioning

confidence: 99%

Untitled

Kawamura¹

1998

J. Phys.: Condens. Matter

342

470

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“…7,8 Theoretically, the most transparent way to lift the degeneracy is to include nnn interactions in the Hamiltonian. 1 Experiment and MC simulations on pyrochlores 9 show ordering with an unusual critical behavior (β ≈ 0.18) in this case. According to the spinwave results of Ref.…”

Section: Introductionmentioning

confidence: 99%

“…The diagonalizing transformation has the explicit form 9) where the summation over the repeated indices is implied andÛ is the real unitary matrix,Û −1 =Û T , i.e., U −1 nl = U ln . The columns of the matrixÛ are the three normalized eigenvectors U n = (U 1n , U 2n , U 3n ) of the interaction matrixV :…”

Section: Lattice Structure and The Hamiltonianmentioning

confidence: 99%

Classical spin liquid: Exact solution for the infinite-component antiferromagnetic model on thekagomélattice

Garanin

Canals

1999

Phys. Rev. B

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Thermodynamic quantities and correlation functions (CF's) of the classical antiferromagnet on the kagomé lattice are studied for the exactly solvable infinite-component spin-vector model, D → ∞. In this limit, the critical coupling of fluctuations dies out and the critical behavior simplifies, but the effect of would be Goldstone modes preventing ordering at any nonzero temperature is properly accounted for. In contrast to conventional two-dimensional magnets with continuous symmetry showing extended short-range order at distances smaller than the correlation length, r < ∼ ξc ∝ exp(T * /T ), correlations in the kagomé-lattice model decay already at the scale of the lattice spacing due to the strong degeneracy of the ground state characterized by a macroscopic number of strongly fluctuating local degrees of freedom. At low temperatures, spin CF's decay as S0Sr ∝ 1/r 2 in the range a0 ≪ r ≪ ξc ∝ T −1/2 , where a0 is the lattice spacing. Analytical results for the principal thermodynamic quantities in our model are in fairly good quantitative agreement with the Monte Carlo simulations for the classical Heisenberg model, D = 3. The neutron-scattering cross section has its maxima beyond the first Brillouin zone; at T → 0 it becomes nonanalytic but does not diverge at any q. PACS number(s): 75.50.Ee, 75.40.Cx

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“…One possible example of such noncoplanar criticality was supposed to be the pyrochlore antiferromagnets FeF 3 [36] and [1] (page 4733). The coefficients n ± i (3) are (the analytic expressions are in the Appendix C)…”

Section: B Nonplanar Ordering: M=3mentioning

confidence: 99%

Five-loop ϵ expansion for O(n)×O(m) spin models

Calabrese

Parruccini

2004

Nuclear Physics B

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We compute the Renormalization Group functions of a Landau-GinzburgWilson Hamiltonian with O(n)×O(m) symmetry up to five-loop in Minimal Subtraction scheme. The line n + (m, d), which limits the region of secondorder phase transition, is reconstructed in the framework of the ǫ = 4 − d expansion for generic values of m up to O(ǫ 5 ). For the physically interesting case of noncollinear but planar orderings (m = 2) we obtain n + (2, 3) = 6.1(6) by exploiting different resummation procedures. We substantiate this results re-analyzing six-loop fixed dimension series with pseudo-ǫ expansion, obtaining n + (2, 3) = 6.22(12). We also provide predictions for the critical exponents characterizing the second-order phase transition occurring for n > n + .

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Critical properties of highly frustrated pyrochlore antiferromagnets

Cited by 68 publications

References 47 publications

Untitled

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Classical spin liquid: Exact solution for the infinite-component antiferromagnetic model on thekagomélattice

Five-loop ϵ expansion for O(n)×O(m) spin models

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