Spin stiffness in frustrated antiferromagnets

Southern, B. W.; Young, A. P.

doi:10.1103/physrevb.48.13170

Cited by 41 publications

(65 citation statements)

References 10 publications

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“…Similar behavior was seen in the spin correlation length, for which it was argued that a crossover takes place from the BKT behavior to another T dependence and the correlation length does not diverge except for T = 0. 22,23 Our data are consistent with such analyses as shown in Fig. 2(d).…”

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confidence: 92%

Nonequilibrium Relaxation Study of the Anisotropic Antiferromagnetic Heisenberg Model on the Triangular Lattice

Misawa

Motome

2010

J. Phys. Soc. Jpn.

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Effect of exchange anisotropy on the relaxation time of spin and vector chirality is studied for the antiferromagnetic classical Heisenberg model on the triangular lattice by using the nonequilibrium relaxation Monte Carlo method. We identify the Berezinskii-KosterlitzThouless (BKT) transition and the chiral transition in a wide range of the anisotropy, even for very small anisotropy of ∼ 0.01%. As the anisotropy decreases, both the critical temperatures steeply decrease, while the BKT critical region becomes divergently wide. We elucidate a sharp "V shape" of the phase diagram around the isotropic Heisenberg point, which suggests that the isotropic case is exceptionally singular and the associated Z2 vortex transition will be isolated from the BKT and chiral transitions. We discuss the relevance of our results to peculiar behavior of the spin relaxation time observed experimentally in triangular antiferromagnets.KEYWORDS: geometrical frustration, triangular lattice, Heisenberg model, nonequilibrium relaxation, BKT transition, chiral transition, Z2 vortex transitionAntiferromagnet on the two-dimensional triangular lattice has been intensively studied as one of the most fundamental models for the geometrically frustrated systems.1 For the isotropic Heisenberg model with nearestneighbor interactions, it is believed that the ground state of the system exhibits a three-sublattice 120• long-range order, 2 whereas the magnetic ordering is no longer retained against thermal fluctuations.3 Nevertheless, an interesting possibility was proposed by Kawamura and Miyashita, 4, 5 that is, an unconventional topological transition at a finite temperature (T ) -Z 2 vortex transition. From the symmetry point of view, the Z 2 vortex transition is different from the conventional BerezinskiiKosterlitz-Thouless (BKT) transition which occurs in the presence of anisotropy. 6,7 The relation between these two topological transitions, however, is not fully understood yet. In particular, it is still unclear how the system behaves in the region of vanishing anisotropy.Experimentally, several materials with triangular layered structure have been studied, and recently, the Z 2 vortex attracts renewed interests for understanding of their peculiar properties. One of the peculiar properties is anomalous enhancement of the spin relaxation time. Critical divergence of the relaxation time is observed in an anomalously wide range of T in many compounds, such as ACrO 2 (A=Li,H,Na), [8][9][10][11] Li 7 RuO 6 , 12and NiGa 2 S 4 . 13, 14 The critical behaviors are often argued to be a fingerprint of the Z 2 vortex transition. The Z 2 vortex, however, is a topological object specific to spin-rotational-invariant systems, and hence, it is not trivial whether its influence is observed in real compounds in which anisotropy exists.In this letter, to shed light on the origin of the anomalous critical behavior and its relation to the Z 2 vortex transition, we directly calculate the relaxation time in the antiferromagnetic Heisenberg model with classical spins ...

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confidence: 92%

Nonequilibrium Relaxation Study of the Anisotropic Antiferromagnetic Heisenberg Model on the Triangular Lattice

Misawa

Motome

2010

J. Phys. Soc. Jpn.

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“…It has been established firstly by Kawamura and Miyashita [72] that the existence of vortices is important at finite temperature in two dimensions. This has been largely confirmed by subsequent works studying the temperature dependence of thermodynamical quantities such as the correlation length, the spin-stiffness, etc [73,74,75,76,77,78]. Actually, although this has not been directly established, they certainly also play an important role for the critical physics of the STA in three dimensions.…”

Section: B the Heisenberg Casementioning

confidence: 79%

“…(76) and derives an RG equation for U k (ζ) from Eq. (74). This corresponds to the so-called Local Potential Approximation (LPA) which has been intensively explored in the past [33,170,171,172].…”

Section: Derivative Expansionmentioning

confidence: 99%

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Nonperturbative renormalization-group approach to frustrated magnets

2004

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This article is devoted to the study of the critical properties of classical XY and Heisenberg frustrated magnets in three dimensions. We first analyze the experimental and numerical situations. We show that the unusual behaviors encountered in these systems, typically nonuniversal scaling, are hardly compatible with the hypothesis of a second order phase transition. Moreover, the fact that the scaling laws are significantly violated and that the anomalous dimension is negative in many cases provides strong indications that the transitions in frustrated magnets are most probably of very weak first order. We then review the various perturbative and early nonperturbative approaches used to investigate these systems. We argue that none of them provides a completely satisfactory description of the three-dimensional critical behavior. We then recall the principles of the nonperturbative approach -the effective average action method -that we have used to investigate the physics of frustrated magnets. First, we recall the treatment of the unfrustrated -O(N ) -case with this method. This allows to introduce its technical aspects. Then, we show how this method unables to clarify most of the problems encountered in the previous theoretical descriptions of frustrated magnets. Firstly, we get an explanation of the long-standing mismatch between different perturbative approaches which consists in a nonperturbative mechanism of annihilation of fixed points between two and three dimensions. Secondly, we get a coherent picture of the physics of frustrated magnets in qualitative and (semi-) quantitative agreement with the numerical and experimental results. The central feature that emerges from our approach is the existence of scaling behaviors without fixed or pseudo-fixed point and that relies on a slowing-down of the renormalization group flow in a whole region in the coupling constants space. This phenomenon allows to explain the occurence of generic weak first order behaviors and to understand the absence of universality in the critical behavior of frustrated magnets.

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“…[17] and below). The LGW model is therefore unable to find the O(4) behaviour which has been nevertheless observed numerically in d = 2 [20] . This raises serious doubts on the perturbative analysis of the LGW model away from d = 4.…”

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confidence: 89%

Frustrated Heisenberg Magnets: A Nonperturbative Approach

2000

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Frustrated magnets are a notorious example where the usual perturbative methods are in conflict. Using a nonperturbative Wilson-like approach, we get a coherent picture of the physics of Heisenberg frustrated magnets everywhere between d = 2 and d = 4. We recover all known perturbative results in a single framework and find the transition to be weakly first order in d = 3. We compute effective exponents in good agreement with numerical and experimental data.PACS No: 75.10.Hk, 11.10.Hi, 11.15.Tk Understanding the effect of competing interactions in three dimensional classical spin systems is one of the great challenges of condensed matter physics. However, after twenty five years of investigations, the nature of the universality class for the phase transition of the simplest frustrated model, the antiferromagnetic Heisenberg model on a triangular lattice (AFHT model), is still a strongly debated question [1] . Due to frustration, the ground state of the AFHT model is given by a canted configuration -the famous 120 • structure -that implies a matrix-like order parameter [2] and thus, the possibility of a new universality class. Experiments performed on materials supposed to belong to the AFHT universality class display indeed exponents different from those of the standard O(N ) universality class: for VCl These results however call for several comments. First, the exponents violate the scaling relations, at least by two standard deviations. Second, they differ significantly from those obtained by Monte Carlo (MC) simulations performed either directly on the AFHT model (ν ≃ 0.59(1), γ ≃ 1.17(2), β ≃ 0.29(1), α ≃ 0.24(2)), and on models supposed to belong to the same universality class: AFHT with rigid constraints (ν = 0.504(10), γ = 1.074(29), β = 0.221(9), α = 0.488(30)), dihedral (i.e. V 3,2 Stiefel) models (ν ≃ 0.51(1), γ ≃ 1.13(2), β ≃ 0.193(4), α ≃ 0.47(3)). See Ref.[9] for a review, and references therein. Finally, the anomalous dimensions η obtained by means of scaling relations is found to be negative in experiments as well as in MC simulations, a result forbidden by first principles for second order phase transitions [10] . All these results are hardly compatible with the assumption of universality. It has been proposed that the exponents are, in fact, effective exponents characterizing a very weakly first order transition, the so-called "almost second order phase transition [11][12][13] ".From the theoretical point of view the situation is also very unsatisfactory since one does not have a coherent picture of the expected critical behaviour of the AFHT model between two and four dimensions. On the one hand, the weak coupling expansion performed on the suitable Landau-Ginzburg-Wilson (LGW) model in the vicinity of d = 4 leads to a first order phase transition due to the lack of a stable fixed point [14][15][16] . On the other hand, the low temperature expansion performed around two dimensions on the Non-Linear Sigma (NLσ) model predicts a second order phase transition of the standard O(4)/O(3) universal...

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Spin stiffness in frustrated antiferromagnets

Cited by 41 publications

References 10 publications

Nonequilibrium Relaxation Study of the Anisotropic Antiferromagnetic Heisenberg Model on the Triangular Lattice

Nonequilibrium Relaxation Study of the Anisotropic Antiferromagnetic Heisenberg Model on the Triangular Lattice

Nonperturbative renormalization-group approach to frustrated magnets

Frustrated Heisenberg Magnets: A Nonperturbative Approach

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