scholarly journals Effect of Anisotropy on the Critical Behaviour of Three- Dimensional Heisenberg Ferromagnets

1976 ◽  
Vol 31 (1) ◽  
pp. 34-40 ◽  
Author(s):  
R. Shanker ◽  
R. A. Singh
Keyword(s):  
Three Dimensional ◽  
Experimental Investigations ◽  
Isotropic Case ◽  
Zero Field ◽  
Critical Temperatures ◽  
Cubic Lattice ◽  
Simple Cubic ◽  
Simple Cubic Lattice ◽  
Anisotropic System ◽  
Critical Temperature Tc

The anisotropic nearest-neighbour Heisenberg model for the simple cubic lattice has been investigated by interpolating the anisotropy between the Ising and isotropic Heisenberg limits via general spin high-temperature series expansions of the zero-field suspectibility. This is done by estimating the critical temperature (Tc(3)) and the susceptibility exponent γ from the analysis of the series by the Ratio and Pade approximants methods. It is noted that Tc(3) varies with anisotropy while γ is almost the same for the anisotropic system, and a jump in it occurs for the isotropic case in agreement with the universality hypothesis. The effect of anisotropy on the susceptibility is also shown. Further, it is seen that estimates of γ for the two extreme limits agree well with those of previous theoretical as well as experimental investigations. In addition, critical temperatures have been summarised in a relation, and expressions for the magnetisation have been derived.

CRITICAL TEMPERATURES AND MEAN-FIELD CRITICAL COEFFICIENTS FOR THE HEISENBERG MODEL BASED ON CVM

1992 ◽  
Vol 06 (13) ◽  
pp. 2363-2374
Author(s):  
GIICHI TANAKA ◽  
MINORU KIMURA
Keyword(s):  
Heisenberg Model ◽  
Mean Field ◽  
Three Dimensional ◽  
Cluster Variation Method ◽  
Variation Method ◽  
Critical Temperatures ◽  
Cubic Lattice ◽  
Simple Cubic ◽  
Simple Cubic Lattice ◽  
Cluster Variation

Critical temperatures T c and mean-field critical coefficients [Formula: see text] for susceptibilities are calculated by a cluster-variation method (CVM) for a three-dimensional Heisenberg model on a simple cubic lattice. Both the full CVM based on a 4-spin cluster and the SCVM are applied and the same values for T c and [Formula: see text] are obtained by three different approximation in the SCVM. The results are compared with those obtained by the same approach for the three-dimensional Ising model on the simple cubic lattice.

scholarly journals Spin Waves and Skyrmions in Magneto-Ferroelectric Superlattices: Theory and Simulation†

Proceedings ◽  
2019 ◽  
Vol 46 (1) ◽  
pp. 3
Author(s):  
Hung Diep ◽  
Ildus Sharafullin
Keyword(s):  
Spin Waves ◽  
Wave Length ◽  
Magnetic Films ◽  
Zero Field ◽  
Ferroelectric Films ◽  
Spin Configuration ◽  
Dm Interaction ◽  
Cubic Lattice ◽  
Simple Cubic ◽  
Simple Cubic Lattice

We present in this paper the effects of Dzyaloshinskii–Moriya (DM) magnetoelectric coupling between ferroelectric and magnetic layers in a superlattice formed by alternate magnetic and ferroelectric films. Magnetic films are films of simple cubic lattice with Heisenberg spins interacting with each other via an exchange J and a DM interaction with the ferroelectric interface. Electrical polarizations of ± 1 are assigned at simple cubic lattice sites in the ferroelectric films. We determine the ground-state (GS) spin configuration in the magnetic film. In zero field, the GS is periodically non-collinear (helical structure) and in an applied field H perpendicular to the layers, it shows the existence of skyrmions at the interface. Using the Green’s function method we study the spin waves (SW) excited in a monolayer and also in a bilayer sandwiched between ferroelectric films, in zero field. We show that the DM interaction strongly affects the long-wave length SW mode. We calculate also the magnetization at low temperatures. We use next Monte Carlo simulations to calculate various physical quantities at finite temperatures such as the critical temperature, the layer magnetization and the layer polarization, as functions of the magneto-electric DM coupling and the applied magnetic field. Phase transition to the disordered phase is studied.

scholarly journals Skyrmions and Spin Waves in Magneto–Ferroelectric Superlattices

Entropy ◽  
2020 ◽  
Vol 22 (8) ◽  
pp. 862
Author(s):  
Ildus F. Sharafullin ◽  
Hung T. Diep
Keyword(s):  
Magnetic Field ◽  
Phase Transition ◽  
Triangular Lattice ◽  
Applied Field ◽  
Zero Field ◽  
Ferroelectric Films ◽  
Dm Interaction ◽  
Cubic Lattice ◽  
Simple Cubic ◽  
Simple Cubic Lattice

We present in this paper the effects of Dzyaloshinskii–Moriya (DM) magneto–electric coupling between ferroelectric and magnetic interface atomic layers in a superlattice formed by alternate magnetic and ferroelectric films. We consider two cases: magnetic and ferroelectric films have the simple cubic lattice and the triangular lattice. In the two cases, magnetic films have Heisenberg spins interacting with each other via an exchange J and a DM interaction with the ferroelectric interface. The electrical polarizations of ±1 are assumed for the ferroelectric films. We determine the ground-state (GS) spin configuration in the magnetic film and study the phase transition in each case. In the simple cubic lattice case, in zero field, the GS is periodically non collinear (helical structure) and in an applied field H perpendicular to the layers, it shows the existence of skyrmions at the interface. Using the Green’s function method we study the spin waves (SW) excited in a monolayer and also in a bilayer sandwiched between ferroelectric films, in zero field. We show that the DM interaction strongly affects the long-wave length SW mode. We calculate also the magnetization at low temperatures. We use next Monte Carlo simulations to calculate various physical quantities at finite temperatures such as the critical temperature, the layer magnetization and the layer polarization, as functions of the magneto–electric DM coupling and the applied magnetic field. Phase transition to the disordered phase is studied. In the case of the triangular lattice, we show the formation of skyrmions even in zero field and a skyrmion crystal in an applied field when the interface coupling between the ferroelectric film and the ferromagnetic film is rather strong. The skyrmion crystal is stable in a large region of the external magnetic field. The phase transition is studied.

Resistance calculation of the decorated centered cubic networks: Applications of the Green's function

2014 ◽  
Vol 28 (32) ◽  
pp. 1450252 ◽  
Author(s):  
M. Q. Owaidat ◽  
J. H. Asad ◽  
J. M. Khalifeh
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Function Method ◽  
Three Dimensional ◽  
Numerical Results ◽  
Effective Resistance ◽  
Cubic Lattice ◽  
Cubic Lattices ◽  
Simple Cubic ◽  
Simple Cubic Lattice

The effective resistance between any pair of vertices (sites) on the three-dimensional decorated centered cubic lattices is determined by using lattice Green's function method. Numerical results are presented for infinite decorated centered cubic networks. A mapping between the resistance of the edge-centered cubic lattice and that of the simple cubic lattice is shown.

Lower bound approximation to the free energy of an Ising model on a simple cubic lattice

1981 ◽  
Vol 59 (10) ◽  
pp. 1291-1295 ◽  
Author(s):  
Chin-Kun Hu ◽  
Wen-Den Chen ◽  
Yu-Ming Shih ◽  
Dong-Chung Jou ◽  
C. K. Pan ◽  
...  
Keyword(s):  
Free Energy ◽  
Ising Model ◽  
Lower Bound ◽  
Variational Method ◽  
Critical Point ◽  
Zero Field ◽  
Free Energies ◽  
Cubic Lattice ◽  
Simple Cubic ◽  
Simple Cubic Lattice

We apply a modified Kadanoff's variational method to calculate the lower bound zero-field free energies and their derivatives for an Ising model on the simple cubic lattice. We find a critical point at Kc = 0.2393769 with precision ±10−7.

Waves in three-dimensional simple cubic lattice

2006 ◽  
Vol 30 (4) ◽  
pp. 909-919 ◽  
Author(s):  
Xiao-yun Wang ◽  
Wen-shan Duan ◽  
Mai-mai Lin ◽  
Gui-xin Wan
Keyword(s):  
Three Dimensional ◽  
Cubic Lattice ◽  
Simple Cubic ◽  
Simple Cubic Lattice

Statistical mechanics and the partition of numbers II. The form of crystal surfaces

1952 ◽  
Vol 48 (4) ◽  
pp. 683-697 ◽  
Author(s):  
H. N. V. Temperley
Keyword(s):  
Surface Energy ◽  
Statistical Mechanics ◽  
Three Dimensional ◽  
Crystal Surfaces ◽  
Cubic Crystal ◽  
Cubic Lattice ◽  
Simple Cubic ◽  
Simple Cubic Lattice ◽  
First Approximation ◽  
Equilibrium Profile

AbstractThe classical theory of partition of numbers is applied to the problem of determining the equilibrium profile of a simple cubic crystal. It is concluded that it may be thermo-dynamically profitable for the surface to be ‘saw-toothed’ rather than flat, the extra entropy associated with such an arrangement compensating for the additional surface energy. For both a two- and a three-dimensional ‘saw-tooth’ the extra entropy varies, to a first approximation, in the same way as the surface energy, i.e. is proportional to or respectively, where N is the number of molecules in a ‘tooth’. For the simple cubic lattice, the entropy associated with the formation of a tooth containing N atoms is estimated to be 3.3 It is also possible to estimate the variation of the ‘equilibrium roughness’ of a crystal with temperature, if its surface energy is known.

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