• Title/Summary/Keyword: Heisenberg model

Search Result 6, Processing Time 0.019 seconds

QUASILINEAR SCHRÖDINGER EQUATIONS FOR THE HEISENBERG FERROMAGNETIC SPIN CHAIN

  • Yongkuan Cheng;Yaotian Shen
    • Bulletin of the Korean Mathematical Society
    • /
    • v.61 no.2
    • /
    • pp.541-556
    • /
    • 2024
  • In this paper, we consider a model problem arising from a classical planar Heisenberg ferromagnetic spin chain $-{\Delta}u+V(x)u-{\frac{u}{\sqrt{1-u^2}}}{\Delta}{\sqrt{1-u^2}}={\lambda}{\mid}u{\mid}^{p-2}u$, x ∈ ℝN, where 2 ≤ p < 2*, N ≥ 3. By the Ekeland variational principle, the cut off technique, the change of variables and the L estimate, we study the existence of positive solutions. Here, we construct the L estimate of the solution in an entirely different way. Particularly, all the constants in the expression of this estimate are so well known.

The critical behaviors of resistivity in nickel films

  • Sik, Gil-Woo;Rhee Ilsu
    • Journal of Korean Vacuum Science & Technology
    • /
    • v.1 no.1
    • /
    • pp.13-18
    • /
    • 1997
  • The critical phenomena in nickel films have been studied by observing the resistivity behavior with temperatures near the Curie point. We observed the thickness dependence of the Curie point in nickel films, that is, the thinner the film is, the lower the Curie point is. This is as expected. Using the heat capacity data, we also found the amplitude ratios of bulk and film systems to be 1.222 and 1.197(average0, respectively. These values are cose to the theoretical prediction of 1.46 given by the Heisenberg, S=$\infty$ Model.

Magnetic Properties of Fe-Ni-N/Cu Multilayered Films by DC Magnetron Sputtering Method

  • Kim, Jung-Gi;Kim, Hyun-Joong;Jang, Ji-Young;Han, Kyung-Hunn
    • Journal of Magnetics
    • /
    • v.9 no.3
    • /
    • pp.79-82
    • /
    • 2004
  • The structure and magnetic properties of Fe-Ni-N/Cu multilayered films, prepared by the DC magnetron sputter, as a function of different thicknesses of Fe-Ni-N ($t_{FeNiN}$) and Cu ($t_Cu$) layers have been studied by the methods of x-ray diffraction and measurement of magnetic moment. It has been found that the enhancement of (200) orientation in Fe-Ni-N layers is observed at the ratio of layer thickness with about $t_{FeNiN}/t_{Cu}$ $\underline{\simeq}$ 3.75. The reduction of magnetization due to the formation of interdiffusion near the interface is explained by means of the dead layer model. The temperature dependence of magnetization exhibits the feature of Blochs $T^{\frac{2}{3}}$ law. The layer thickness dependence of Curie temperature has been discussed by critical temperature theory of Heisenberg model.

Electron Microscopy and Magnetic Properties of Tetra(n-butyl) ammonium salts of $[Ni(dmbit)_2]^1- (dmbit^2-:C_7H_2S_5$:2-thiobenzo[d]-1,3-dithiole-5,6-dithiolate;$dmbbip^{2-}:C_{12}H_{16}S_4$:1,2-bis(isopropylthio)benzene-4,5-dithiolat

  • No, Dong Yeon;Gang, Mi Jeong;Lee, Ha Jin;Kim, Jong Hyeon;Choe, Jin Ho
    • Bulletin of the Korean Chemical Society
    • /
    • v.17 no.1
    • /
    • pp.46-50
    • /
    • 1996
  • Monoanionic nickel(Ⅲ) complexes, [Ni(dmbit)2]1- and [Ni(dmbbip)2]1- where dmbit2- and dmbbip2- denote 2-thiobenzo[d]-1,3-dithiole-5,6-dithiolate and 1,2-bis(isopropylthio)benzen-4,5-dithiolate, respectively, have been synthesized by the iodine oxidation of dianionic complexes. In the scanning electron microscopic(SEM) images, these complexes show the well-grown two-dimensional layered structures which are clearly comparable to the dianionic ones with three-dimensional structures. Magnetic susceptibilities of nickel(Ⅲ)complexes are fitted well with the two-dimensional Heisenberg antiferromagnet model of S=1/2 system resulting in the spin-exchange parameters (|J|/k) of 11.4 K and 0.45 K, respectively. The weaker magnetic interaction in [Ni(dmbbip)2]1- is resulted from the bulky isopropyl groups on the periphery of dmbbip ligand. EPR measurements for [Ni(dmbit)2]1- give the signal with axial symmetry and the anisotropic g-values for low-spin nickel(Ⅲ) (g//=2.158, g =2.030,gav=2.074 at 300 K; g//=2.162, g =2.038, gav=2.080 at 77 K). It is therefore concluded that nickel(Ⅱ) is oxidized to nickel(Ⅲ), rather than dmbit2- and dmbbip2- ligands are, by the iodine oxidation. The paramagnetic Ni(Ⅲ) would be located in the axial symmetry(D4h) with the electronic configuration of (dxz2dyz2dz22dxy1dx2-y20).