Ground state of magnetic dipoles on a two-dimensional lattice: structural phases in complex plasmas

We study analytically and by molecular dynamics simulations the ground state configuration of a system of magnetic dipoles fixed on a two-dimensional lattice. We find different phases, in close agreement with previous results. Building on this result and on the minimum energy requirement we determine the equilibrium lattice configuration, the magnetic order (ferromagnetic versus antiferromagnetic), and the magnetic polarization direction of a system of charged mesoscopic particles with magnetic dipole moments, in the domain where the strong electrostatic coupling leads to a crystalline ground state. Orders of magnitudes of the parameters of the system relevant to possible future dusty plasma experiments are discussed.     

Experiment and numerical simulation of interactions among magnetic dipoles induced in feeble magnetic substances under high magnetic fields

Using a two-dimensional closed vessel filled with an aqueous solution, we present triangle-lattice alignments with some spacing formed by interactions among magnetic dipoles induced in feeble magnetic substances under high magnetic fields. We conducted an experiment and a numerical simulation using Au particles with a 1 mm diameter dispersed in a _MnCl2${\mathrm{MnCl}}_2$ aqueous solution and compared their configurations quantitatively using a three-body distribution function. We confirmed that the numerical simulation demonstrates the formation of triangle-lattice alignments in a two-dimensional plane as obtained in the experiment and also verified that the interaction among induced magnetic dipoles is a significant force that governs the structure formed by feeble magnetic substances under high magnetic fields. On the basis of the results obtained in the experiment and the numerical simulation, it is clear that the distance among particles and the interaction force depend on the number of particle at a steady state and they are closely correlative with each other. The distance among particles can be estimated from the correlative relation.     

Phase transitions in a two-dimensional dipole ferrimagnet

The magnetic configurations of the system of magnetic dipoles that have different values and are arranged in a staggered order on a square lattice are studied. A numerical simulation is used to study the phase transitions in the system when the mismatch between the dipoles changes. The restructuring of the magnetic configuration of the system induced by a change in the mismatch is shown to proceed via sequential second-order phase transitions between collinear and noncollinear phases. The numerical simulation results are supported by analytical calculations performed with trial functions.     

Extremely small domain in the lattice of magnetic dipoles

Lattices of magnetic dipoles with 1–4 rows are investigated. Numerical analysis reveals the smallest stationary domains formed in the lattices, necessary conditions for the formation and destruction of such domains are obtained, and the change in the magnetic moment of the lattices during domain formation is considered. It is shown that the action of an external field on one of the dipoles forming a domain is sufficient for its breaking. The lattices in which the orientational phase transition appears upon perturbation of several dipoles and propagates over the entire system are revealed.     

Dipole-induced vortex ratchets in superconducting films with arrays of micromagnets

We investigate the transport properties of superconducting films with periodic arrays of in-plane magnetized micromagnets. Two different magnetic textures are studied: a square array of magnetic bars and a close-packed array of triangular microrings. As confirmed by magnetic force microscopy imaging, the magnetic state of both systems can be adjusted to produce arrays of almost pointlike magnetic dipoles. By carrying out transport measurements with ac drive, we observed experimentally a recently predicted ratchet effect induced by the interaction between superconducting vortices and the magnetic dipoles. Moreover, we find that these magnetic textures produce vortex-antivortex patterns, which have a crucial role in the transport properties of this hybrid system.     

Vortex structures in planar lattices of magnetic dipoles in the presence of exchange coupling

Vortex equilibrium states of planar square lattices of magnetic dipoles in the presence of the exchange interaction have been studied. It has been shown that the vortex equilibrium configurations differ in the position of the vortex center and, correspondingly, in the magnitude and direction of the total magnetic moment of the system. In the case of the position of the vortex center in the center of the array, the total magnetic moment of the system is zero. The vortex center moves in the direction perpendicular to the field under the action of the external planar magnetic field on the system. Thus, the transitions between different equilibrium vortex configurations are implemented and the magnetic moment of the system of dipoles is controlled.     

Magnetic ordering in a random system of point Ising dipoles

An exact expression for the random magnetic field distribution function is obtained for a simple model of a random system of Ising magnetic dipoles. The magnetic phase diagram for such a system is deter-mined within the framework of the random mean field theory. The magnetic characteristics of individual phases of this system are described.     

Response of a magnetic nanoparticle lattice to a magnetic field pulse near the stability boundary

The dynamic response of a system being near the stable equilibrium boundary to an external magnetic field pulse is studied for 2D lattices of magnetic nanoparticles with cubic crystallographic anisotropy. The conditions under which magnetic moment oscillations from individual dipoles propagate to the entire system are revealed. This effect results in the lattice response are significantly larger in the external pulse duration and with an amplitude rather weakly depending on initial conditions and external field parameters, the processes during which the pulse results in reorientation of only individual lattice dipoles.     

Equilibrium configurations and transitions between them in annular magnetic nanodipole systems

The equilibrium states of annular systems of magnetic dipoles have been studied by computer simulation. The bistability conditions under which the total magnetic moment of one of equilibrium configurations is zero, while the magnetic moment of another equilibrium configuration lies in the ring plane and is close to the sum of the magnetic moments of dipoles in the system, have been determined. The realization of other equilibrium configurations has also been demonstrated. We analyze transitions between equilibrium configurations by acting on the system by longitudinal and circular static fields, as well as transitions from the configuration with the maximal magnetic moment of the system to the configuration with zero total magnetic moment after the relaxation of oscillatory regimes excited by a varying field.     

Temperature dependence of the magnetic susceptibility of magnetic dispersed nanosystems

The temperature dependence of the complex magnetic susceptibility of different magnetic nano-colloids and finely dispersed magnetite powder is studied. The results are explained with allowance for the magnetic moment relaxation in single-domain particles and phase transitions in a system of interacting dipoles.     

Equilibrium values and dynamics of the net magnetic moment of a system of magnetic dipoles

Equilibrium states of different systems formed by coupled spherical bodies with dipole magnetic moments have been investigated using a numerical analysis. The bistable states and the corresponding values of the net magnetic moment are determined for a number of planar and three-dimensional systems of dipoles, and the conditions providing the existence of orientational configurations of coupled dipoles involved in the bistability are analyzed. The disturbances of the magnetic moment due to the quasi-static passage of an additional dipole and the dynamic modes excited by a homogeneous alternating magnetic field and represented by periodic, quasi-periodic, and chaotic oscillations of the magnetic moment of the system are considered for several types of systems. The bifurcation diagrams of the dynamic modes are constructed, and the specific features typical of the systems under consideration are revealed.     

Problem of two magnetic dipoles with consideration of the equation of motion of their spins

The problem of two interacting magnetic dipoles with consideration of their spins is examined. The possibility of the appearance of stable-discrete states of this system (without the collapse of the dipoles) in the case of resonance is shown. Quantitative estimates of the stability of a system of macroscopic dipoles are presented.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika:, No. 7, pp. 74–78, July, 1985.The author thanks A. I. Filatov for interest in the work and the participants of the I. M. Ternov seminar for its discussion.     

Dynamic multistable states in a system of magnetic dipoles

Bistable and multistable states induced by a fluctuating magnetic field in a system of four magnetic dipoles were studied numerically. The possibility of performing switchings and cyclic transitions between the different oscillatory regimes by changing field parameters is examined, along with the possibility of creating conditions under which the system is sensitive to noise signals.     

Singularities motion equations in 2-dimensional ideal hydrodynamics of incompressible fluid

In this Letter, we have obtained motion equations for a wide class of one-dimensional singularities in 2D ideal hydrodynamics. The simplest of them, are well known as point vortices. More complicated singularities correspond to vorticity point dipoles. It has been proved that point multipoles of a higher order (quadrupoles and more) are not the exact solutions of two-dimensional ideal hydrodynamics. The motion equations for a system of interacting point vortices and point dipoles have been obtained. It is shown that these equations are Hamiltonian ones and have three motion integrals in involution. It means the complete integrability of two-particle system, which has a point vortex and a point dipole.     

Collective effects accompanying magnetization of two-dimensional lattices of nanosize magnetic particles

Collective effects arising in a two-dimensional lattice of nanosize magnetic particles as a result of the dipole interparticle interaction are investigated by Hall magnetometry. The experimental system consists of 10⁵ permalloy particles having a diameter of ∼40 nm and a height of ∼40 nm and forming a lattice with a rectangular unit cell (90 nm×180 nm). We attribute the characteristic features observed in the magnetization curves to quasi-one-dimensionality of the experimental lattice of particles and to the formation of solitons in chains of dipoles. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 6, 475–479 (25 September 1998)     

Hysteresis of the Magnetic Particle in a Dipolar Ising Model

Zero-temperature Monte Carlo simulations are used to investigate the hysteresis of a magnetic particle in a dipolar Ising model.The magnetic particle is described in a systemm of permanent dipoles,and the dipoles are located in a cubic lattice site.The effects of the shape and the size of the particle on the hysteresis loop at zero temperature are obtained.For strong exchange interactions,the shapes of magnetic hysteresis loops approach rectangle.For weak exchange interactions,the effects of the size and the shape of the particle on the loops are more remarkable than those of strong exchange interactions case.The slope of the hysteresis loop decreases with the increase of the ratio of the semi major axis to the semi minor axis of the ellipsoidal magnetic particle,and there is an increase of the slope of the hysteresis with the decrease of the size of the magnetic particle.The effects of the shape and size of the particle on the coercive force at zero temperature are also investigated.     

Melting in a two dimensional system with dipole interaction

Molecular-dynamics simulations show that the solid-liquid phase transition in a two-dimensional system of dipoles is of first order. The translational and orientational correlation function, the static form-factor and the dielectric function are calculated. We analyze also the self-diffusion coefficient. It is seen that self-diffusion takes place mainly on the cluster boundaries.     

Lamellar-like structures in ferrofluids placed in strong magnetic fields

We consider a ferrofluid system consisting of magnetic particles interacting with a magnetic dipole–dipole interaction. We study the strong magnetic field regime where all magnetic dipoles are completely polarized in the direction of the magnetic field. We introduce a lattice gas model that serves to describe space ordering phenomena in such systems. It is found that, within mean field theory, this model predicts a second order phase transition to a phase with inhomogeneous lamellar-like ordering below a certain critical temperature.