2D ferromagnetic models with symmetry-breaking interactions: self-consistent harmonic approximation

Spirin, D.V.; Fridman, Yu. A.

doi:10.1016/s0921-4526(02)01697-6

Cited by 7 publications

(11 citation statements)

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“…Adding the transverse field h breaks the O(2) symmetry explicitly and causes a gap. Obviously, a similar gap could be induced by an anisotropy in the XY-plane as in the work of Spirin and Fridman [18]. Following the same procedure mentioned before, we obtain, from (9),…”

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Field‐induced effects in the S = 1 two‐dimensional Heisenberg antiferromagnet

Gouvêa

Pires

2005

Physica Status Solidi (b)

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PACS 75.10.Jm, 75.40.Cx We use the self-consistent harmonic approximation to study the spin 1 S = Heisenberg antiferromagnet on a two-dimensional lattice in a uniform applied magnetic field. The magnetic field destroys the (3) O symmetry and an XY-like behavior, with a Berezinskii -Kosterlitz -Thouless (BKT) transition, is expected. We obtain the field dependence of the transition temperature for fields varying in a wide range. There has been experimental evidence that, for low dimensional spin systems, a gap can be induced by the applied magnetic field. We also investigate the behavior of this field-induced gap.Low dimensional quantum spin systems have provided a sophisticated source of interesting phenomena revealing some novel magnetic properties. A striking example of a system exhibiting unique behavior is given by the one-dimensional (1D) integer-spin Heisenberg antiferromagnet (AF) in which the longrange order is destroyed by the zero-point quantum fluctuations. The main feature of the magnetic excitation spectrum is the well known Haldane energy gap [1]. However, the behavior of that system in applied magnetic fields is also remarkable because the field removes the zero-point fluctuations restoring a gapless spectrum. The result is a quantum phase transition at a critical field c H , to a Nèel-like state with long-range order.From the theoretical point of view, the magnetization process of a 1D AF with spin 1 S = is well understood [2], and experimental studies [3] of real quasi-1D compounds have confirmed most of the theoretical predictions. During the last decade, magnetic fields of very high intensity have become available and several properties have been observed, such as the closing of the energy gap in 1 S = onedimensional AF [4], and observation of magnetization plateaux in frustated magnets [5,6]. Dender et al. dependence but were not able to give a satisfactory explanation for the field dependence of the energy gaps in all three directions claiming that inclusion of interchain interaction would be necessary for a quantitative comparison. In a recent work, Zhao et al. [9] investigated the physical effects of the DM interaction in Cu benzoate and have given a complete quantitative account for the field dependence of the gap along the three principal axes without resorting to additional interactions.

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confidence: 74%

“…Spirin and Fridman [18] applied the SCHA to study a 2D classical anisotropic ferromagnetic model similar to the one described by (2). In their case, the uni-axial anisotropy lies in the XY-plane and breaks the (2) O symmetry of that plane.…”

Section: Original Papermentioning

confidence: 99%

Field‐induced effects in the S = 1 two‐dimensional Heisenberg antiferromagnet

Gouvêa

Pires

2005

Physica Status Solidi (b)

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“…Було показано, що дане наближення добре описує перехідні властивості цього моделю для концентрацій p  0,5. В роботі [41] з використанням даного набли-ження був досліджений Гайзенберґів феромагнетний модель з од-новісною площинною анізотропією і було знайдено, що при достат-ВПЛИВ АНГАРМОНІЗМУ ТА ЕЛЕКТРОН-ФОНОННОЇ ВЗАЄМОДІЇ НА СПЕКТЕР 403 ньо великій анізотропії відбувається фазовий перехід від феромаг-нетної до парамагнетної фази.…”

Section: методи опису впливу ангармонізму на спектер частот коливань unclassified

Influence of an Anharmonicity and Electron–Phonon Interaction on a Frequency Spectrum of Crystals with the Hexagonal Close-Packed Lattice

2011

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В огляді розглянуто основні методи опису енергетичного спектру електро-нів та спектру частот коливань атомів кристалічної ґратниці. Зроблено огляд основних метод дослідження впливу ефектів ангармонізму на фізич-ні властивості матеріялів та спектер частот коливань кристалічної ґратни-ці. Описано самоузгоджене гармонічне наближення, що базується на мето-ді двочасових Ґрінових функцій. В рамках цього наближення записано рі-внання руху для Ґрінових функцій «зміщення-зміщення», яке схоже на рівнання руху в гармонічному наближенні, але силові постійні будуть пе-ренормованими і визначаться термодинамічним усередненням других по-хідних потенціялу, а не їх рівноважним значенням. Досліджено вплив ефектів ангармонізму та електронної підсистеми на спектер частот криста-лічної ґратниці гексагонального щільнопакованого кристалу Ti 0,93 Al 0,07 .In a given review, the basic methods for description of the energy spectrum of electrons and the frequency spectrum of atomic vibrations of the crystal lattice are considered. The basic methods for investigation of influence of the anharmonicity effects on the physical properties of materials and a frequency spectrum of vibrations of the crystal lattice are reviewed. The self-consistent harmonic approximation, which is based on the method of double-time Green's functions, are described. Within the scope of this approximation, the equation of motion for the 'displacements-displacements' Green's functions, which is similar to the equation of motion in the harmonic approximation, is derived, but the force constants are renormalized and are determined by the thermodynamical averaging of second derivatives of potential rather than their equilibrium values. Appearances of the anharmonicity effects in the vibrational spectrum of the Ti 0.93 Al 0.07 hexagonal close-packed crystal lattice Успехи физ. мет. / Usp. Fiz. Met. 2011, т. 12, сс. 389-450 Îòòèñêè äîñòóïíû íåïîñðåäñòâåííî îò èçäàòåëÿ Ôîòîêîïèðîâàíèå ðàçðåøåíî òîëüêî â ñîîòâåòñòâèè ñ ëèöåíçèåé 2011 ÈÌÔ (Èíñòèòóò ìåòàëëîôèçèêè èì. Ã. Â. Êóðäþìîâà ÍÀÍ Óêðàèíû) Íàïå÷àòàíî â Óêðàèíå.

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“…15 The XY model with in-plane anisotropy was studied by Spirin and Fridman. 16 The effect of a magnetic field applied perpendicular to the xy plane was taken into account by Pires.…”

Section: 11mentioning

confidence: 99%

“…15 The XY model with in-plane anisotropy was studied by Spirin and Fridman. 16 The effect of a magnetic field applied perpendicular to the xy plane was taken into account by Pires. 14 Recently Knafo et al 17 pointed out that it would be useful if the theoretical models for XY-like models, which already consider interplane coupling, would also incorporate in-plane anisotropy. This is the aim of the present Brief Report.…”

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confidence: 99%

Phase diagram of the antiferromagneticXYmodel in two dimensions in a magnetic field

2008

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The phase diagram of the quasi-two-dimensional easy-plane antiferromagnetic model, with a magnetic field applied in the easy plane, is studied using the self-consistent harmonic approximation. We found a linear dependence of the transition temperature as a function of the field for large values of the field. Our results are in agreement with experimental data for the spin-1 honeycomb compound BaNi 2 V 2 O 3 . DOI: 10.1103/PhysRevB.78.212408 PACS number͑s͒: 75.10.Hk, 75.30.Kz, 75.40.Mg The XY model in two dimensions provides the best example of a phase transition mediated by topological defects. A variety of analytical and numerical methods have been presented in the literature in an attempt to fully understand the nature of its transition. As it is well known the model has a phase transition at a temperature T BKT called the Berezinskii-Kosterlitz-Thouless ͑BKT͒ temperature. 1,2 This phase transition is associated with the emergence of a topological order, resulting from the pairing of vortices with opposite circulation. The BKT mechanism does not involve any spontaneous symmetry breaking 3 and emergence of a spatially uniform order parameter. The low-temperature phase is associated with a quasi-long-range order for finite T, with the correlation of the order parameter decaying algebraically in space. Above the critical temperature the correlations decay exponentially. This picture is applicable to a wide variety of two-dimensional phenomena. 4 A recent experiment in a trapped atomic gas 5 not only confirms the BKT theory in a new system, but also reveals for the first time the role played by local topological defects or vortices. A very convenient technique to study the XY model is the self-consistent harmonic approximation ͑SHCA͒. The SHCA was originally proposed by Pokrovsky and Uimin 6 to study the twodimensional ͑2D͒ classical planar rotor model. Later, Minnhagen 7 pointed out that the SCHA overestimated the transition temperature because it did not take into account vortex fluctuations and he suggested a way to improve the thermodynamics of the planar rotor by replacing the exchange constant J with a "renormalized" J͑T͒. This procedure leads to a better estimate of T BKT . Menezes et al. 8 extended the SCHA to the classical XY model and Pires 9 applied it to the quantum model. The approximation consists in replacing the Hamiltonian of the system by an effective harmonic Hamiltonian with renormalized parameters. Several applications to classical systems were found to agree very well with Monte Carlo and experimental results. 10,11The SCHA was also used in the study of the 1D quantum sine-Gordon problem, where it describes correctly the phase transition of the model. The reason is that it is equivalent to a renormalization-group analysis to one loop. 12 To test the reliability of the quantum SCHA we will compare the transition temperature calculated theoretically with experimental results, for two S = 1 compounds. 13 In these cases we have an exchange anisotropy of the form A͑S i z S j z ͒. The calculati...

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2D ferromagnetic models with symmetry-breaking interactions: self-consistent harmonic approximation

Cited by 7 publications

References 12 publications

Field‐induced effects in the S = 1 two‐dimensional Heisenberg antiferromagnet

Field‐induced effects in the S = 1 two‐dimensional Heisenberg antiferromagnet

Influence of an Anharmonicity and Electron–Phonon Interaction on a Frequency Spectrum of Crystals with the Hexagonal Close-Packed Lattice

Phase diagram of the antiferromagneticXYmodel in two dimensions in a magnetic field

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