Spatial distribution of Gaussian fluctuations of the molecular field and magnetization in the pyramid-like Ising nanoscopic system interacting with the substrate

We study thermodynamic properties of an Ising model of a ferromagnetic nanoscopic pyramid deposited onto a ferromagnetic bulk substrate. The influence of the interaction between the pyramid and the substrate is calculated in terms of the equilibrium reduced-state (density) operator used for description of thermodynamic properties of nanoscopic systems. The spatial distribution of the fluctuations of molecular field and magnetization in the nanoscopic pyramid is obtained in the Gaussian fluctuations approximation. Experimental consequences for the magnetic force measurements are briefly discussed.Comment: 13 pages, 10 figure

Spatial Dependence of Magnetization and Gaussian Fluctuations of Molecular Field in an Ising Nanopyramid Interacting with the Substrate

We study thermodynamic properties of an Ising model of a ferromagnetic nanoscopic pyramid deposited on a ferromagnetic bulk substrate. The influence of the interaction between the pyramid and the substrate is calculated in terms of the reduced-state (density) operator used for description of thermodynamic properties of nanoscopic systems. The spatial distribution of magnetization in the nanopyramid is obtained in the Gaussian fluctuations approximation

Generalized kinetic and evolution equations in the approach of the nonequilibrium statistical operator

The method of the nonequilibrium statistical operator developed by D. N. Zubarev is employed to analyse and derive generalized transport and kinetic equations. The degrees of freedom in solids can often be represented as a few interacting subsystems (electrons, spins, phonons, nuclear spins, etc.). Perturbation of one subsystem may produce a nonequilibrium state which is then relaxed to an equilibrium state due to the interaction between particles or with a thermal bath. The generalized kinetic equations were derived for a system weakly coupled to a thermal bath to elucidate the nature of transport and relaxation processes. It was shown that the "collision term" had the same functional form as for the generalized kinetic equations for the system with small interactions among particles. The applicability of the general formalism to physically relevant situations is investigated. It is shown that some known generalized kinetic equations (e.g. kinetic equation for magnons, Peierls equation for phonons) naturally emerges within the NSO formalism. The relaxation of a small dynamic subsystem in contact with a thermal bath is considered on the basis of the derived equations. The Schrodinger-type equation for the average amplitude describing the energy shift and damping of a particle in a thermal bath and the coupled kinetic equation describing the dynamic and statistical aspects of the motion are derived and analysed. The equations derived can help in the understanding of the origin of irreversible behavior in quantum phenomena.Comment: 21 pages, Revte

Statistical Theory of Spin Relaxation and Diffusion in Solids

A comprehensive theoretical description is given for the spin relaxation and diffusion in solids. The formulation is made in a general statistical-mechanical way. The method of the nonequilibrium statistical operator (NSO) developed by D. N. Zubarev is employed to analyze a relaxation dynamics of a spin subsystem. Perturbation of this subsystem in solids may produce a nonequilibrium state which is then relaxed to an equilibrium state due to the interaction between the particles or with a thermal bath (lattice). The generalized kinetic equations were derived previously for a system weakly coupled to a thermal bath to elucidate the nature of transport and relaxation processes. In this paper, these results are used to describe the relaxation and diffusion of nuclear spins in solids. The aim is to formulate a successive and coherent microscopic description of the nuclear magnetic relaxation and diffusion in solids. The nuclear spin-lattice relaxation is considered and the Gorter relation is derived. As an example, a theory of spin diffusion of the nuclear magnetic moment in dilute alloys (like Cu-Mn) is developed. It is shown that due to the dipolar interaction between host nuclear spins and impurity spins, a nonuniform distribution in the host nuclear spin system will occur and consequently the macroscopic relaxation time will be strongly determined by the spin diffusion. The explicit expressions for the relaxation time in certain physically relevant cases are given.Comment: 41 pages, 119 Refs. Corrected typos, added reference

Generalised Equilibrium Reduced-Density Operator

Equilibrium reduced-density operators for subsystems of the universe are derived from the generalised Schrödinger variational principle, additionally assuming that the values of von Neumann entropy for the subsystems are fixed and higher than zero. The obtained reduced-density operator may be useful for description of the properties of an arbitrary system (macroscopic, mesoscopic, nanoscopic, or microscopic) in the equilibrium mixed state

Ising Model of Thin Film with Random Surface Field

Thermodynamical properties of an Ising model of a ferromagnetic thin film deposited onto a ferromagnetic substrate of rough surface contacting the thin film were studied. The influence of the interaction between the substrate and the film as well as the effect of the substrate surface roughness were found to be describable in this model by a temperature dependent random surface field. Magnetization of the thin film was calculated for various temperatures at different assumed values of the substrate Curie temperature as well as for various surface roughness grades of the substrate and various couplings between the film and the substrate

Nonequilibrium Reduced-Density Operator for Nanoscopic Systems

Retarded forms of the nonequilibrium reduced-density operator are derived from the generalized Schrödinger variational principle of a system with both mechanical and thermal perturbations, taking into account the additional condition that the values of generalized thermodynamic coordinates are fixed at infinitely remote past. This reduced density operator may be useful in describing nonequilibrium properties of nanoscopic and mesoscopic systems, as well as ultrathin films. With the help of this reduced-density operator the generalized Green-Kubo formulae are obtained

Collective Excitations in Heisenberg Ultrathin Films with Inhomogeneous Spatial Distribution of Magnetisation

The influence of non-magnetic substrate on the collective excitation of the Heisenberg (s=1/2) ferromagnetic ultrathin films with homogeneous and inhomogeneous spatial distribution of magnetization is investigated. It has been proved that the collective excitation spectrum of ultrathin film may, to a significant degree, depend on the value of the coefficient characterizing the film coupling with its substrate

Nonequilibrium Reduced-Density Operator for Nanoscopic Systems

Retarded forms of the nonequilibrium reduced-density operator are derived from the generalized Schrödinger variational principle of a system with both mechanical and thermal perturbations, taking into account the additional condition that the values of generalized thermodynamic coordinates are fixed at infinitely remote past. This reduced density operator may be useful in describing nonequilibrium properties of nanoscopic and mesoscopic systems, as well as ultrathin films. With the help of this reduced-density operator the generalized Green-Kubo formulae are obtained

Gaussian Fluctuations of Molecular Field in Quasi-One-Dimensional Ising Model

Quasi-one-dimensional spin systems described by an Ising-like Hamiltonian with a strong space anisotropy (s=1/2) are investigated. Magnetic properties of this model are examined in the approximation including Gaussian fluctuations of molecular field. This paper reports an attempt at obtaining more accurate results for Gaussian fluctuation of molecular field by an exact formula for mean fluctuations of a spin