Erratum: Renormalization of the spin-wave spectrum in three-dimensional ferromagnets with dipolar interaction [Phys. Rev. B<b>74</b>, 014435 (2006)]

Syromyatnikov, A. V.

doi:10.1103/physrevb.81.139901

Cited by 8 publications

(30 citation statements)

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“…Besides the well-known Schwinger representation [11] and the Holstein-Primakoff representation [2], there are many other schemes, including the realization of su (2) algebra [3,4,12,13,14], and the realization of su q (2) and su q (n) algebra [15,16]. On the other hand, the spin wave plays an important role in magnetic problems [17,18]. The concept of spin wave has become a widely applied tool in the fields related to magnetism.…”

Section: Introductionmentioning

confidence: 99%

Intermediate-statistics spin waves

Dai

Xie²

2009

J. Stat. Mech.

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In this paper, we show that spin waves, the elementary excitation of the Heisenberg magnetic system, obey a kind of intermediate statistics with a finite maximum occupation number n. We construct an operator realization for the intermediate statistics obeyed by magnons, the quantized spin waves, and then construct a corresponding intermediate-statistics realization for the angular momentum algebra in terms of the creation and annihilation operators of the magnons. In other words, instead of the Holstein–Primakoff representation, a bosonic representation subject to a constraint on the occupation number, we present an intermediate-statistics representation with no constraints. In this realization, the maximum occupation number is naturally embodied in the commutation relation of creation and annihilation operators, while the Holstein–Primakoff representation is a bosonic operator relation with an additional putting-in-by-hand restriction on the occupation number. We deduce the intermediate-statistics distribution function for magnons from the intermediate-statistics commutation relation of the creation and annihilation operators directly, which is a modified Bose–Einstein distribution. On the basis of these results, we calculate the dispersion relations for ferromagnetic and antiferromagnetic spin waves. The relations between the intermediate statistics that magnons obey and the other two important kinds of intermediate statistics, Haldane–Wu statistics and the fractional statistics of anyons, are discussed. We also compare the spectrum of the intermediate-statistics spin wave with the exact solution of the one-dimensional s = 1/2 Heisenberg model, which is obtained by the Bethe ansatz method. For ferromagnets, we take the contributions from the interaction between magnons (the quartic contribution), the next-to-nearest-neighbor interaction, and the dipolar interaction into account for comparison with the experiment.

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Section: Introductionmentioning

confidence: 99%

Intermediate-statistics spin waves

Dai

Xie²

2009

J. Stat. Mech.

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“…Then it gives positive negligibly small correction to the bare spectrum (7). But it is significant that similar to 3D FM considered in our previous paper [11] we obtain also the spin-wave gap D in the spectrum given by Eq. (9).…”

Section: S$1mentioning

confidence: 73%

“…Thus, we obtain such gap in 3D FM in the first order of 1=S in our recent paper [11]. It was found to be proportional to o 0…”

Section: Introductionmentioning

confidence: 86%

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Spin-wave interaction in two-dimensional ferromagnets with dipolar forces

Syromyatnikov

2009

Journal of Magnetism and Magnetic Materials

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“…One obtains from Eqs. (10), (14), (15), (17), and (18) for the classical spectrum at k ≪ 1 in the leading order in…”

Section: Magnon Spectrummentioning

confidence: 99%

Breakdown of long-wavelength magnons in cubic antiferromagnets with dipolar forces at small temperature

Batalov

Syromyatnikov

2015

Phys. Rev. B

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Using 1/S expansion, we discuss the magnon spectrum of Heisenberg antiferromagnet (AF) on a simple cubic lattice with small dipolar interaction at small temperature T ≪ TN , where TN is the Neel temperature. Similar to 3D and 2D ferromagnets, quantum and thermal fluctuations renormalize greatly the bare gapless spectrum leading to a gap ∆ ∼ ω0, where ω0 is the characteristic dipolar energy. This gap is accompanied by anisotropic corrections to the free energy which make the cube edges easy directions for the staggered magnetization (dipolar anisotropy). In accordance with previous results, we find that dipolar forces split the magnon spectrum into two branches. This splitting makes possible two types of processes which lead to a considerable enhance of the damping compared to the Heisenberg AF: a magnon decay into two other magnons and a confluence of two magnons. It is found that magnons are well defined quasiparticles in quantum AF. We demonstrate however that a small fraction of long-wavelength magnons can be overdamped in AFs with S ≫ 1 and in quantum AFs with a single-ion anisotropy competing with the dipolar anisotropy. Particular materials are pointed out which can be suitable for experimental observation of this long-wavelength magnons breakdown that contradicts expectation of the quasiparticle concept.

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Erratum: Renormalization of the spin-wave spectrum in three-dimensional ferromagnets with dipolar interaction [Phys. Rev. B74, 014435 (2006)]

Abstract: Erratum: Renormalization of the spin-wave spectrum in three-dimensional ferromagnets with dipolar interaction [Phys. Rev. B 74, 014435 (2006)]

Cited by 8 publications

References 0 publications

Intermediate-statistics spin waves

Intermediate-statistics spin waves

Spin-wave interaction in two-dimensional ferromagnets with dipolar forces

Breakdown of long-wavelength magnons in cubic antiferromagnets with dipolar forces at small temperature

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