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Sosin, S. S.; Prozorova, L. A.; Smirnov, Alex I.; Golov, A. I.; Berkutov, I. B.; Petrenko, O. A.; Zhitomirsky, M. E.

doi:10.1103/physrevb.71.094413

Cited by 96 publications

(66 citation statements)

References 23 publications

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“…Since there is a sum over all lattice sites in Eq. (30), the outcome of this equation is the same for the 1-k and 4-k states. Consequently, including the crystal electric field in the s-MFT Hamiltonian does not differentiate between 1-k and 4-k states, free-energywise.…”

Section: With Crystal Electric Fieldmentioning

confidence: 64%

“…(30) and solving the resulting s-MFT self-consistent equation where S i were spin-7/2 quantum mechanical operators and B m n coefficients in Eq. (29), were chosen in accordance with the experimental values for Gd 2 Ti 2 O 7 from Ref.…”

Section: With Crystal Electric Fieldmentioning

confidence: 99%

“…1b) is believed to exist in Gd 2 Ti 2 O 7 [20] for temperature 0.7 K < ∼ T < ∼ T c ∼ 1 K in which the POS is a superposition of spin density waves with wave vectors k = { 1 2 1 2 1 2 } [20][21][22][23][24][25][26]. While this compound has been the subject of a number of investigations [20][21][22][27][28][29][30][31][32][33][34][35][36], the mechanism responsible for the selection of 4-k order has not been identified. Further, after fifteen years of research arXiv:1310.5146v1 [cond-mat.str-el]…”

mentioning

confidence: 99%

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Fluctuation-Driven Selection at Criticality in a Frustrated Magnetic System: The Case of Multiple-kPartial Order on the Pyrochlore Lattice

et al. 2015

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We study the problem of partially ordered phases with periodically arranged disordered (paramagnetic) sites on the pyrochlore lattice, a network of corner-sharing tetrahedra. The periodicity of these phases is characterized by one or more wave vectors k = { 1 2 1 2 1 2 }. Starting from a general microscopic Hamiltonian including anisotropic nearest-neighbor exchange, long-range dipolar interactions and second-and third-nearest neighbor exchange, we identify using standard mean-field theory (s-MFT) an extended range of interaction parameters that support partially ordered phases. We demonstrate that thermal fluctuations ignored in s-MFT are responsible for the selection of one particular partially ordered phase, e.g. the "4-k" phase over the "1-k" phase. We suggest that the transition into the 4-k phase is continuous with its critical properties controlled by the cubic fixed point of a Ginzburg-Landau theory with a 4-component vector order-parameter. By combining an extension of the Thouless-Anderson-Palmer method originally used to study fluctuations in spin glasses with parallel-tempering Monte-Carlo simulations, we establish the phase diagram for different types of partially ordered phases. Our results elucidate the long-standing puzzle concerning the origin of the 4-k partially ordered phase observed in the Gd2Ti2O7 dipolar pyrochlore antiferromagnet below its paramagnetic phase transition temperature. Highly frustrated magnetism is one of the paradigms of modern condensed matter physics [1]. In frustrated magnets, the combination of lattice geometry and competing interactions often leads to degenerate classical states. The degeneracies are generally accidental as they are not protected by the symmetries of the spin Hamiltonian. Yet, the degenerate states may be related by transformations that form an emergent symmetry group. Near a continuous phase transition, these approximate symmetries provide "organizing principles" in determining the critical properties by distinguishing relevant perturbations from irrelevant ones. In the most interesting case, the leading degeneracy-lifting perturbations, which may be relevant or irrelevant in the renormalization group sense, are thermal or quantum fluctuations -a phenomenon called order-by-disorder (ObD) [2][3][4][5]. The competition among diverse degeneracy-lifting effects can result in a modulated long-range ordered state at nonzero wave vector k, which may or may not be commensurate with the lattice [6][7][8][9][10][11][12]. In some cases, a number of superposed symmetryrelated k modes within the first Brillouin zone form a socalled multiple-k order [6,7,13,14]. A particular interesting form of such modulated magnetism is a partially ordered state (POS) with periodically arranged "paramagnetic" sites [15][16][17][18]. These fluctuating magnetic moments decimate a fraction of the energy-costly frustrated bonds while retaining an extensive entropy, hence lowering the free energy.In this Letter, we study the convergence of the aforementioned phenomena (emergent symmet...

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Section: With Crystal Electric Fieldmentioning

confidence: 64%

Section: With Crystal Electric Fieldmentioning

confidence: 99%

mentioning

confidence: 99%

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Fluctuation-Driven Selection at Criticality in a Frustrated Magnetic System: The Case of Multiple-kPartial Order on the Pyrochlore Lattice

et al. 2015

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“…Indeed, experiments on the pyrochlore magnet Gd2Ti2O7 found substantial drops of temperature around the saturation field during adiabatic demagnetization [3]. These results suggest applications for efficient lowtemperature magnetic refrigeration.…”

mentioning

confidence: 83%

Magnetocaloric effect in two-dimensional spin-1/2 antiferromagnets

Honecker

Wessel

2006

Physica B: Condensed Matter

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The magnetocaloric effect is studied at the transition to saturation in the antiferromagnetic spin-1/2 Heisenberg model on the simplest two-dimensional lattices, namely the square and the triangular lattice. Numerical results are presented for the entropy which are consistent with identical universal properties. However, the absolute values of the entropy are bigger on the geometrically frustrated triangular lattice than on the non-frustrated square lattice, indicating that frustration improves the magnetocaloric properties. Recent theoretical investigations predict an enhanced magnetocaloric effect in geometrically frustrated spin systems at low temperatures [1,2]. Indeed, experiments on the pyrochlore magnet Gd2Ti2O7 found substantial drops of temperature around the saturation field during adiabatic demagnetization [3]. These results suggest applications for efficient lowtemperature magnetic refrigeration.Investigations of quantum spin systems on twodimensional lattices have revealed a plethora of semiclassically ordered and unusual quantum ground states (see [4,5] for recent reviews). Rich behavior is also found in a magnetic field, including plateaux in the zero-temperature magnetization curve and fieldinduced quantum phase transitions (compare [5,6] and references therein).However, the magneto-thermodynamics on such lattices has received suprisingly little attention. As a first step we study the quantum phase transition at the saturation field on the square and triangular lattice. The Hamiltonian for a Heisenberg antiferromagnet in an external magnetic field h reads * Corresponding Author. Tel: +49-531-391 5190, fax: +49-531-391 5833Email address: a.honecker@tu-bs.de (A. Honecker).The Si are spin s = 1/2 operators at site i, J > 0 is the exchange constant, and i, j are nearest neighbor pairs on the given lattice. The magnetocaloric properties are determined by the entropy S(h, T ) at temperature T . One approach is to compute S(h, T ) from the eigenvalues of the Hamiltonian (1) [2] which are obtained by exact diagonalization (ED) on a finite lattice with N sites. Complete spectra are obtained for N ≤ 21 while for bigger N we use a truncation procedure valid at low energies [7]. Another approach is to obtain the entropy from a stochastic evaluation of the partition function using an extended ensemble quantum Monte Carlo (QMC) method, based on a flat-histogram formulation [8]. The latter method is restricted to unfrustrated lattices, and we employ it for the square lattice. Fig. 1 shows the entropy per site S/N as a function of temperature at the saturation field, given by hsat. = 4J and 9J/2 for the square and triangular lattice, respectively (see e.g. [6]). This corresponds to a quantum critical point in dimension d = 2 with a dynamical critical exponent z = 2. According to a scaling theory for the low-temperature physics at such a quantum critical point [9], the entropy should follow a power law

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“…The interest is stimulated by a search for new fundamental effects such as the magnetization plateaus, 1,2,3,4,5,6,7,8,9 the magnetization jumps, 10,11,12,13 new complicated magnetic phase diagrams, 8,14 and new types of the critical behavior 15 as well as by a possible technological application of frustrated magnets in the adiabatic demagnetization refrigerators due to their unique magnetocaloric properties. 16,17 A zerotemperature behavior of geometrically frustrated antiferromagnets in the vicinity of the saturation field H c has been recently discussed by Schulenburg and coworkers. 10,11,12,13 Above H c in the fully polarized phase, these models have a flat branch of magnons with energy (H − H c ).…”

mentioning

confidence: 99%

Exact low-temperature behavior of a kagomé antiferromagnet at high fields

2004

Self Cite

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Low-energy degrees of freedom of a spin-1/2 kagomé antiferromagnet in the vicinity of the saturation field are mapped to a hard-hexagon model on a triangular lattice. The latter model is exactly solvable. The presented mapping allows to obtain quantitative description of the magnetothermodynamics of a quantum kagomé antiferromagnet up to exponentially small corrections as well as predict the critical behavior for the transition into a magnon crystal state. Analogous mapping is presented for the sawtooth chain, which is mapped onto a model of classical hard dimers on a chain.PACS numbers: 75.50. Ee, 75.45.+j, 75.10.Jm, 75.30.Sg In the past few years there have been increased attention to the behavior of frustrated magnetic materials at high fields. The interest is stimulated by a search for new fundamental effects such as the magnetization plateaus, 1,2,3,4,5,6,7,8,9 the magnetization jumps, 10,11,12,13 new complicated magnetic phase diagrams, 8,14 and new types of the critical behavior 15 as well as by a possible technological application of frustrated magnets in the adiabatic demagnetization refrigerators due to their unique magnetocaloric properties. 16,17 A zerotemperature behavior of geometrically frustrated antiferromagnets in the vicinity of the saturation field H c has been recently discussed by Schulenburg and coworkers. 10,11,12,13 Above H c in the fully polarized phase, these models have a flat branch of magnons with energy (H − H c ). Such dispersionless excitations correspond in real space to localized spin flips, which do not interact with each other unless touched. Upon decreasing magnetic field through H c , the energy of a single excitation becomes negative and magnons condense into a closepacked crystal structure. The present work is devoted to theoretical investigation of the low-temperature thermodynamics of magnon crystals. Specifically, we consider spin-1/2 Heisenberg models on a kagomé lattice and a sawtooth (or ∆) chain, see Fig. 1. While the former lattice is one of the best known examples of geometric frustration, which is realized, e.g., in SrCr 9p Ga 12−9p O 19 , 18 the latter spin model is applicable to magnetic delafossite YCuO 2.5 . 19 We show that the thermodynamic potential in the vicinity of H c for the two quantum models can be calculated exactly up to corrections, which are exponentially small at low temperatures.We consider nearest-neighbor spin-1/2 Heisenberg models in an external fieldFor a kagomé lattice all nearest-neighbor bonds have the same strength J ij ≡ 1. The spectrum of single-magnon excitations in the fully polarized phase iswhere γ k = 1 6 δ e ik·δ is a sum over nearest-neighbor sites on a triangular Bravais lattice. At the saturation field H c = 3 the energy of excitations from the lowest dispersionless branch vanishes. The sawtooth chain exhibits a similar behavior for the special ratio of the two coupling constants J 2 = 1 2 J 1 . In the following we always assume the above choice of the parameters with J 1 ≡ 1. Above H c = 2 the sawtooth chain antiferromag...

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Magnetocaloric effect in pyrochlore antiferromagnetGd2Ti2O7

Cited by 96 publications

References 23 publications

Fluctuation-Driven Selection at Criticality in a Frustrated Magnetic System: The Case of Multiple-kPartial Order on the Pyrochlore Lattice

Fluctuation-Driven Selection at Criticality in a Frustrated Magnetic System: The Case of Multiple-kPartial Order on the Pyrochlore Lattice

Magnetocaloric effect in two-dimensional spin-1/2 antiferromagnets

Exact low-temperature behavior of a kagomé antiferromagnet at high fields

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