Wang Huai-Yu

Thermodynamic properties of Heisenberg magnetic systems

In this paper, we present a comprehensive investigation of the effects of the transverse correlation function (TCF) on the thermodynamic properties of Heisenberg antiferromagnetic (AFM) and ferromagnetic (FM) systems with cubic lattices. The TCF of an FM system is positive and increases with temperature, while that of an AFM system is negative and decreases with temperature. The TCF lowers internal energy, entropy and specific heat. It always raises the free energy of an FM system but raises that of an AFM system only above a specific temperature when the spin quantum number is S ≥ 1. Comparisons between the effects of the TCFs on the FM and AFM systems are made where possible.

Effect of Transverse Correlation Function on the Thermodynamic Quantities of Ferromagnetic Systems

The effect of transverse correlation between spins on the thermodynamic properties of ferromagnetic systems is investigated in details. Qualitatively, at finite temperature the transverse correlation reflects the short-range interaction between spins, so that lowers the internal energy and consequently raises the free energy. It also means the introduction of some ordering, and hence lowers the entropy. It is depressed by the field which forces the spins to turn to the field direction, so that it decreases with the field when temperature is fixed. The low-temperature expansion of the energy shows that the inclusion of the transverse correlation at least partly considers the interaction between spin waves.

Theoretical Investigation of Exchange Bias in Compensated Cases

The exchange bias (EB) of the ferromagnetic (FM)/antiferromagnetic (AFM) bilayers in a compensated case is studied by use of the many-body Greens function method of quantum statistical theory. The so-called compensated case is that there is no net magnetization on the AFM side of the interface. Our conclusion is that the EB in this case is primarily from the asymmetry of the interfacial exchange coupling strengths between the FM and the two sublattices of the AFM. The effects of the layer thickness, temperature and the interfacial coupling strength on the exchange bias HE are investigated. The dependence of HE on the FM layer thickness and temperature is qualitatively in agreement with experimental results. HE is nearly inversely proportional to FM thickness. When temperature varies, both HE and HC decrease with temperature increasing. The anisotropy of the FM layer only slightly influence HC, but does not influence HE.

Theoretical study of mutual control mechanism between magnetization and polarization in multiferroic materials

The mutual control mechanism between magnetization and polarization in multiferroic materials is studied. The system contains a ferromagnetic sublattice and a ferroelectric sublattice. To describe the magneto–electric coupling, we propose a linear coupling Hamiltonian between ferromagnetism and ferroelectricity without microscopic derivation. This coupling enables one to retrieve the hysteresis loops measured experimentally. The thermodynamic properties of the system are calculated, such as the temperature dependences of the magnetization, polarization, internal energy and free energy. The ferromagnetic and ferroelectric hysteresis loops driven by either a magnetic or an electric field are calculated, and the magnetic spin and pseudo-spin are always flipped synchronously under the external magnetic and electric field. Our theoretical results are in agreement with the experiments.

Effects of interplay between metal subwavelength slits on extraordinary optical transmission

In this paper we study the extraordinary optical transmission of one-dimensional multi-slits in an ideal metal film. The transmissivity is calculated as a function of various structural parameters. The transmissivity oscillates, with the period being just the light wavelength, as a function of the spacing between slits. As the number of slits increases, the transmissivity varies in one of three ways. It can increase, attenuate, or remain basically unchanged, depending on the spacing between slits. Each way is in an oscillatory manner. The slit interaction responsible for the oscillating transmission strength that depends on slit spacing is the subject of more detailed investigation. The interaction most intuitively manifests as a current distribution in the metal surface between slits. We find that this current is attenuated in an oscillating fashion from the slit corners to the center of the region between two adjacent slits, and we present a mathematical expression for its waveform.

Quantum Statistical Calculation of Exchange Bias

The phenomenon of exchange bias of ferromagnetic (FM) films, which are coupled with an antiferromagnetic (AFM) film, is studied by Heisenberg model by use of the many-body Greens function method of quantum statistical theory for the uncompensated case. Exchange bias HE and coercivity Hc are calculated as functions of the FM film thickness L, temperature, the strength of the exchange interaction across the interface between FM and AFM and the anisotropy of the FM. Hc decreases with increasing L when the FM film is beyond some thickness. The dependence of the exchange bias HE on the FM film thickness and on temperature is also qualitatively in agreement with experiments.

Investigation of ultra-thin ferromagnetic films with a simple cubic lattice

Using Greens function method, we investigate ferromagnetic films with a simple cubic lattice containing up to ten monolayers. The Hamiltonian includes the Heisenberg exchange term, surface anisotropy (SA) and dipole interaction (DI). We calculate the magnetization as a function of temperature and film thickness and we analyse the behaviour of spin canting. The result is in agreement with experiments. We calculate phase diagrams of SA versus DI to show the conditions under which spontaneous magnetization can occur. As a special case, we discuss the Heisenberg model without SA and DI.

Numerical Confirmation of Multi-Reflections of Light Inside a Subwavelength Metal Slit Structure

The propagation behavior of light passing through a subwavelength metal slit structure is usually modeled by a Fabry-Perot (FP) resonant cavity based on the feature of transmission spectra. However, this mechanism belongs to a conjecture and it should be proven. We present a direct evidence from the numerical simulations of the amplitude distribution of the magnetic field by employing the time-domain simulation method. The light propagation behavior clearly shows a multi-reflection process inside a subwavelength slit as soon as it enters the slit. An analytical formula for calculating the field distribution involving the multi-reflection process is presented, and the theoretical calculations agree with the numerically simulated results. Our results provide explicit evidence that the FP model is reasonable to the description of the propagation process of light inside a subwavelength slit structure.

Statistical Average of Spin Operators for Calculation of Three-Component Magnetization (II): Solution of Equation

In this paper, the solution of Chebyshev equation with its argument being greater than 1 is obtained. The initial value of the derivative of the solution is the expression of magnetization, which is valid for any spin quantum number S. The Chebyshev equation is transformed from an ordinary differential equation obtained when we dealt with Heisenberg model, in order to calculate all three components of magnetization, by many-body Greens function under random phase approximation. The Chebyshev functions with argument being greater than 1 are discussed. This paper shows that the Chebyshev polynomials with their argument being greater than 1 have their physical application.

Statistical Average of Spin Operators for Calculation of Three-Component Magnetization

When one wants to calculate all the three components of magnetization of Heisenberg model under random phase approximation, at least one of the components should be the solution of an ordinary differential equation. In this paper such an equation is established. It is argued that the general expressions of magnetization for any spin quantum number S suggested before are the solution of the ordinary differential equation.