To understand fantastic multiferroicity of CoCr₂O₄, a Heisenberg spin model on three-dimensional spinel lattice was constructed. In the model, we considered multiple magnetic interactions including nearest-neighbor A-A, A-B, B-B couplings as well as next-nearest-neighbor interaction among B sites. Monte Carlo simulation is employed to obtain magnetoelectric quantities. Influences of exchange couplings on magnetoelectric behaviors are emphatically investigated under rotation of magnetic field. It is found that macroscopic magnetization and polarization stem mainly from contributions of B1 ions. With varying exchange couplings of A-A interaction and next-nearest-neighboring B-B interaction among B-site ions, B-site ions exhibit prominent magnetoelectric responses, while A-site ions remain unchanged. It indicates distinct differences between symmetry and magnetic interaction environment for A-site and B-site ions in spinel lattice.

We choose a confined point-contact geometry as research model. Steady-state oscillations of magnetic vortex driven by a spin-polarized current are calculated with analytical calculations based on Thiele's equation. It indicates that magnetic vortex can maintain steady oscillations in a specific current range. Current density range depends on nanocontact dimensions and dot aspect ratios. Both orbital radius and frequency of steady oscillations increases with current density. Adjustable range of oscillation frequency decreases dramatically with increasing nanoeontaet size.

With a modified analytical embedded atom method (MAEAM),structure stability and phonon spectra of fcc metals are calculated.A pair-potential function was proposed considering farther neighbor atomic interaction.A new truncated function and an enhanced smooth connection condition are used for the cutoff of pair potential.Model parameters are determined through fitting mono-vacancy migration energy,cohesion energy,three independent elastic constants and an equilibrium condition.Under same volume,we calculated binding energies of various metal structures.It shows that fcc structures of Ag,Al,Au,Cu,Ir,Ni,Pd,Pt and Rh are more stable.Energy-volume curves of these metals fit the results of Rose equation.Structure stabilities are proved with volume change.Phonon dispersions of fcc metals along[100],[110] and [111] directions agree with experiments and other calculations.

Monte Carlo method is used to study hysteresis loops of FM/AFM systems with FM core embedded in an AFM matrix in a classical Heisenberg model. Magnetocrystalline anisotropy and exchange interaction are considered. It indicates that the shape of hysteresis loops changes with reverse maximal external field. The magnetization shows a jumping transition to metastable equilibrium with an increasing of external fields along positive z axis. The jumping range is independent of reverse maximal external field. With an increasing of AFM magnetocrystalline anisotrepy, exchange bias is obvious and larger external fields are needed for magnetization saturation. With an increasing of AFM exchange interaction, new hysteresis loops may appear in positive and negative external fields.

Monte Carlo simulation is used to study the magnetic properties of magnetic monolayer films with an Ising-like model in which the exchange interaction and dipolar interaction are considered.The system shows an abnormal magnetization with an increasing of the dipolar interaction at low reduced temperatures.The magnetization is divided into two stages.The magnetization becomes difficult with increasing temperature in low external fields.The reverse process occurs in high external fields.This magnetization behavior results in an abnormal phenomenon that the magnetic entropy changes above zero at low temperatures in external fields.An accurate method is introduced to deal with the long-range interaction.