Mesolithic Forest Hunters in Ukrainian Polessye

Zaliznyak, Leonid

doi:10.30861/9780860548508

Cited by 6 publications

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“…(41) implies thatQ is decreased compared to Q = ( 2π 3 , 2π 3 ) for the ideal triangular lattice, whilẽ Q ≈ 2π · (0.357, 0.357) is observed in experiments. 13,14 Therefore, it is likely that the shift in RbMnBr 3 is mainly due to the anisotropic corrections to the nearest-neighbor coupling, which are captured already in the simplest row model. 8,9 Nevertheless, correction of Eq.…”

Section: Discussionmentioning

confidence: 99%

“…1(c), and the one with n = 8 is relevant for the phases realized in RbMnBr 3 and KNiCl 3 . 12,13,14 In this case j q = 4j cos Q cos Q ′ +2j cos 2Q and it is easy to see that the energy of the modulated state is given by the same expression as for the frustrated square lattice, Eq. (40), but with j ′ = j and J ′ = J (as in the previous example, we use Q = q · (a1+a2) 2 and Q ′ = q · (a1−a2) 2 ).…”

Section: Generalized Row Models On Triangular Latticementioning

confidence: 97%

“…In some cases, as in KNiCl 3 , both phases are found to coexist at low temperature. 12 Perhaps, the most intriguing is the case of RbMnBr 3 , in which most experiments find the orthorhombic low-T phase, 13,14,15 and an incommensurate spiral spin structure with propagation vector Q = (1/3 + q, 1/3 + q, 1), 13,14,15,16 in place of the commensurate "triangular" antiferromagnetic order with Q = (1/3, 1/3, 1), which is characteristic of the non-distorted hexagonal materials CsMnBr 3 , CsNiCl 3 , etc. 17,18,19 In a magnetic field of about 3 T applied in the easy plane the spin structure becomes commensurate, with Q = (1/8, 1/8, 1).…”

Section: Introductionmentioning

confidence: 99%

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Heisenberg magnet with modulated exchange

Zaliznyak

2003

Phys. Rev. B

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A modification of the ground state of the classical-spin Heisenberg Hamiltonian in the presence of a weak superstructural distortion of an otherwise Bravais lattice is examined. It is shown that a slight modulation of the crystal lattice with wavevector $\bQ_c$ results in a corresponding modulation of the exchange interaction which, in the leading order, is parametrized by no more than two constants per bond, and perturbs the spin Hamiltonian by adding the ``Umklapp'' terms $\sim S^\alpha_{\bq} S^\alpha_{\bq \pm \bQ_c}$. As a result, for a general spin-spiral ground state of the non-perturbed exchange Hamiltonian, an incommensurate shift of the propagation vector, $\bQ$, and additional new magnetic Bragg peaks, at $\bQ \pm n\bQ_c$, $n = 1,2,...$, appear, and its energy is lowered as it adapts to the exchange modulation. Consequently, the lattice distortion may open a region of stability of the incommensurate spiral phase which otherwise does not win the competition with the collinear N\'{e}el state. Such is the case for the frustrated square-lattice antiferromagnet. In addition, the ``Umklapp'' terms provide a commensuration mechanism, which may lock the spin structure to the lattice modulation vector $\bQ_c$, if there is sufficient easy-axis anisotropy, or a magnetic field in an easy plane.Comment: 13 pages, submitted to PR

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Section: Discussionmentioning

confidence: 99%

Section: Generalized Row Models On Triangular Latticementioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

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Heisenberg magnet with modulated exchange

Zaliznyak

2003

Phys. Rev. B

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“…In most general case, this results in a harmonic modulation of the exchange coupling. It has either the same wavevector Q c , if it appears as a first-order correction to J ij in small parameter ǫ ∼ ǫ1,2 rij ≪ 1, or the wavevector 2Q c , if it appears only in the second order, ∼ ǫ 2 , [19]. There is also a second-order correction to the bond energy,J ij = J ij + δJ ij .…”

Section: A Zaliznyakmentioning

confidence: 99%

“…This corresponds to a bunched spiral [17,18,19]. Based on very general exchange symmetry arguments [18,19,20], in the absence of any additional symmetry breaking, the perturbing terms have to be proportional to the non-perturbed order parameter. As a result, the leading new Fourrier-components, S Q±Q c , are,…”

Section: A Zaliznyakmentioning

confidence: 99%

Spiral order induced by distortion in a frustrated square-lattice antiferromagnet

Zaliznyak

2004

Phys. Rev. B

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In a strongly frustrated square-lattice antiferromagnet with diagonal coupling J ′ , for α = J/(2J ′ ) 1, an incommensurate spiral state with propagation vectorQ = (π ± δ, π ± δ) near (π, π) competes closely with the Néel collinear antiferromagnetic ground state. For classical Heisenberg spins the energy of the spiral state can be lowered as it adapts to a distortion of the crystal lattice. As a result, a weak superstructural modulation such as exists in doped cuprates might stabilize an incommensurate spiral phase for some range of the parameter α close to 1. An interplay between small distortion of the crystal lattice and the magnetic properties of the material is currently a subject of intense research. One problem which supplies strong motivation for such studies is that of stripe order in the lightly doped high-T c cuprates La 2−x Sr x CuO 4+y (LSCO) and in related nickelates [1,2]. These phases are always associated with a weak superstructural distortion of the original "stacked square lattice" structure of the un-doped parent material. Incommensurate magnetism in these compounds is usually interpreted in terms of a segregation of the doped charges into lines which separate the antiferromagnetic domains ("stripes") characteristic of the un-doped material. Although modulation of the crystal structure which is induced by charge-stripe segregation is often too small to be observed in experiment [1], it is clear that essential result of the stripe order for the spin system of cuprates is a periodic modulation of the exchange coupling in the Heisenberg spin Hamiltonian which describes their magnetic properties [3]. So far, though, only the simplest "average" consequence of the stripe superstructure, in the form of the effective weakening of exchange coupling in the direction perpendicular to the stripes, has been considered [4]. A similar problem, of an interplay between the spin order and the cooperative Jahn-Teller distortion accompanying the charge order, arises in the context of the charge-ordered phases in doped manganites [5].Because the low-energy magnetic properties of layered LSCO cuprates are believed to be adequately described by the two-dimensional (2D) Heisenberg spin Hamiltonian, this model has recently become a focus of intense research. Special attention was devoted to the frustrated square lattice, where in addition to the nearest-neighbor exchange interaction, J > 0, there is a diagonal coupling, J ′ > 0, such that α = J 2J ′ is close to 1. It was originally motivated by the predictions that non-Néel resonating valence bond states [6,7] and quantum-critical behavior [8] associated with the T = 0 order-disorder phase transitions which may occur in this case might be important for the physics of the superconductivity in cuprates.Despite RVB spin-liquid state and quantum criticality are strongly predicated upon the quantum nature of the spins (S=1/2 in cuprates), a semiclassical spin-wave theory appears to provide a surprisingly good guidance to the behavior of the frustrated square-lattice antif...

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Mesolithic Sources of the First Indo-European Cultures in Europe Based on Archaeological Data

Залізняк¹

2016

Archaeology

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Mesolithic Forest Hunters in Ukrainian Polessye

Cited by 6 publications

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Heisenberg magnet with modulated exchange

Heisenberg magnet with modulated exchange

Spiral order induced by distortion in a frustrated square-lattice antiferromagnet

Mesolithic Sources of the First Indo-European Cultures in Europe Based on Archaeological Data

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