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.     

Equilibrium configurations and phase transitions in dipole lattices

Two-dimensional square and hexagonal lattices of magnetic dipoles with the number of rows 1–4 have been studied. Based on the numerical analysis, equilibrium stable domain configurations, including the minimum number of lattice dipoles, have been revealed; the conditions for the creation and destruction of domains have been determined; and their associated changes in the magnetic moment of the lattice and in the energy of the dipole interaction have been found. The conditions for the occurrence of phase transitions that change the configuration of the lattices have been investigated and the conditions for unidirectional propagation of the front of the phase transition have been established. A comparative analysis of different square and hexagonal lattices has been performed in terms of the specific features of the formed domains and the observed orientation phase transitions.     

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.     

Excitation of phase transitions in dipole lattices

Phase transitions in hexagonal lattices with three and four rows of dipoles arising as a result of the reorientation of different sets of dipoles by the external field have been studied. The conditions of the implementation of two types of symmetric phase transitions and the asymmetric transitions, when the configurations of the system to the left and to the right of the excitation region are different, have been established. Merging of two regions of the phase transitions has been considered. Unidirectional phase transitions, in which either the left or the right phase transition front propagates from the excitation region along the lattice, have been obtained in a lattice with four rows of dipoles. The variations of the total dipole moment of the system and the energy of the dipole-dipole interaction during the phase transitions have been given.     

Equilibrium states and dynamics of the dipole moment of square arrays of dipoles

The dipole lattices in the form of 3 × 3–8 × 8 dipole square arrays have been considered. It has been shown that, after turning off the external field orienting dipoles along the edges of the array, two types of equilibrium configurations of dipole moments can exist depending on the size of the system, namely, the state symmetric with respect to the diagonal of the array and the state with the total dipole moment directed along the edges of the array. It has been found that there are differences in these types of configurations with respect to the alternating-field-induced oscillation modes of the total dipole moment of the system. The dependence of the oscillation modes on the direction of linear polarization of the alternating field has been investigated.     

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.     

Magnetization reversal of elliptic Co/Si/Co nanodisks in the field of a magnetic-force microscope probe

The processes of local magnetization reversal of elliptic Co/Si/Co nanodisks under the action of a nonuniform magnetic field of a magnetic-force microscope (MFM) probe have been investigated. The specific features of the distribution of the phase MFM contrast from particles with ferromagnetic and antiferromagnetic configurations of the magnetic moments in neighboring Co layers have been discussed. It has been shown experimentally that, under the action of the probe field, there occur orientational transitions of two types: transitions from the ferromagnetic configuration to the antiferromagnetic configuration due to the reorientation of the magnetization of the upper layer and transitions in the antiferromagnetic configuration with a change in the orientation of the magnetic moment in both ferromagnetic layers. The presented results of micromagnetic simulation of the processes of transformation of the magnetization in such particles under the action of the MFM probe field explain the main regularities of the magnetization reversal processes.     

Dynamics of the lattice of magnetic nanodipoles with cubic anisotropy

The 5 × 5 square lattices of magnetic dipoles with cubic crystallographic anisotropy were investigated by the computer simulation method. The conditions for implementing the random orientation of lattice configurations, each of which are characterized by a certain response to the influence of an external magnetic pulse, as well as by the established regime of the oscillation of the total magnetic moment under the influence of an alternating field, are revealed. Regular vibration modes with a doubled frequency and quasi-periodic and chaotic modes are detected. The dependence of the system response on the parameters of the magnetic field pulse is studied.     

Structure-Induced Phase Transitions in Classic Systems of Dipoles: Unequal Kagome,Truncated Square,and Prismatic Pentagonal Lattices

Several magnetic compounds owe their properties to the particular nature of the dipole–dipole interaction. Changes induced in their structure will vary the total interaction energy in nontrivial fashions. In the present work, systems of identical particles possessing dipole moments arranged on various types of 2D structures are studied. By continuously varying a structural parameter, the state of minimum energy will favor distinct dipole configurations, giving rise to different phases. The ultimate goal is to quantitatively address the relation existing between the minimum possible energy for different systems of classic dipoles and the concomitant dipole phases that appear. The systems of dipoles considered here are studied in detail for the first time. With the exploration, new light will be shed on the existence of structural phase transitions in classical systems even at zero temperature, changes induced by the variation of a continuous parameter, and not the temperature, that resemble the ones occurring in quantum phase transitions.     

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.     

Hysteresis in small arrays of interacting magnetic nanoparticles

The out-of-plane hysteresis loops of small arrays of magnetic nanoparticles, under the influence of an external field applied perpendicular to the array and the dipolar interaction are investigated. The particles are assumed to have a perpendicular anisotropy energy that tends to align the magnetic moments to be perpendicular to the array. The magnetization is found to exhibit a plateaux-and-jumps structure as the external field is swept up and down. These jumps are associated with jumps in the energy of the system, and correspond to transition from one configuration of the moment orientation to another. The energy of different configurations of the magnetic moments for a 3×3 array in the limit of weak dipolar interaction is analyzed, as a means to understand the hysteresis loop. These jumps are more pronounced in arrays of smaller sizes and when the dipolar interaction is weak. The configuration of magnetic moments at zero external field as the field is swept up and down is found to be highly sensitive to the dipolar interaction.     

Electronic transport spectroscopy of carbon nanotubes in a magnetic field

We report magnetic field spectroscopy measurements in carbon nanotube quantum dots exhibiting fourfold shell structure in the energy level spectrum. The magnetic field induces a large splitting between the two orbital states of each shell, demonstrating their opposite magnetic moment and determining transitions in the spin and orbital configuration of the quantum dot ground state. We use inelastic cotunneling spectroscopy to accurately resolve the spin and orbital contributions to the magnetic moment. A small coupling is found between orbitals with opposite magnetic moment leading to anticrossing behavior at zero field.     

Magnetostatic interaction effects in an ordering hexagonal array of ferromagnetic nanoparticles

The results from investigating magnetostatic interaction effects in ordered hexagonal arrays of anisotropic single-domain ferromagnetic nanoparticles are presented. It is demonstrated theoretically and experimentally that two stable states (with quasi-uniform configurations of magnetic moments and with zero averaged magnetic moment configurations) can be easily attained in such arrays. It is shown that the structure of an ferromagnetic resonance spectrum depends strongly on the extent of magnetostatic interaction and the spatial configuration of the magnetic moments in the array.     

Universal fluctuations in orbital diamagnetism

Bohr–van Leuween theorem has attracted the notice of physicists for more than 100 years. The theorem states about the absence of magnetisation in classical systems in thermal equilibrium. In this paper, we discuss about fluctuations of magnetic moment in classical systems. In recent years, this topic has been investigated intensively and it is not free from controversy. We have considered a system consisting of a single particle moving in a plane. A magnetic field is applied perpendicular to the plane. The system is in contact with a thermal bath. We have considered three cases: (a) particle moving in a homogeneous medium, (b) particle moving in a medium with space-dependent friction and (c) particle moving in a medium with space-dependent temperature. For all the three cases, the average magnetic moment and fluctuations in magnetic moment have been calculated. Average magnetic moment saturates to a finite value in the case of free particle but goes to zero when the particle is confined by a 2D harmonic potential. Fluctuations in magnetic moment shows universal features in the presence of arbitrary friction inhomogeneity. For this case, the system reaches equilibrium asymptotically. In the case of space-dependent temperature profile, the stationary distribution is non-Gibbsian and fluctuations deviate from universal value for the bounded system only.     

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.     

Phase transitions in lattices of magnetic dipoles

Hexagonal magnetic-dipole lattices containing three to six rows are investigated. Conditions of the excitation of phase transitions that change the orientation configuration of the system are revealed on the basis of a numerical analysis. The changes in the magnetic moment of the system and in the energy of dipole-dipole interaction upon the emergence of phase transitions are found. Both symmetric phase transitions propagating identically on the two sides of the lattice away from the excitation region and asymmetric phase transitions such in which the configurations of the system to the left and to the right of the excitation region are different are considered. Conditions under which there occur unidirectional phase transitions in which either the left-or the right-hand front of the phase transition propagates along the lattice are found.     

Vibrations in Magnet/Superconductor Levitation Systems

The problem of a small magnet levitating above a very thin superconducting disc in the Meissner state is analysed. The dipole-dipole interaction model is employed to derive analytical expressions for the interaction energy, levitation force, magnetic stiffness and frequency of small vibrations about the equilibrium position in two different configurations, i.e. with the magnetic moment parallel and perpendicular to the superconductor. The results show that the frequency of small vibrations decreases with the increasing levitation height for a particular radius of the superconducting disc, which is in good agreement with the experimental results. However, the frequency increases monotonically up to saturation by increasing the radius of the disc for a particular height of the magnet. In addition, the frequency of vibrations is higher when the system is in the vertical configuration than that when the system is in the horizontal configuration.     

缺陷铁纳米环体系的磁特性研究

采用Monte Carlo方法与快速傅里叶变换微磁学方法相结合的方式,模拟含不同缺陷的铁纳米环的磁滞回线、组态、剩磁等磁特性.研究发现:缺陷的大小与位置明显影响系统的磁化过程.当缺陷较小时,系统存在双稳态特征,此性质与无缺陷系统类似;当缺陷增大时,系统过渡状态增加,双稳态特征不再明显.进一步的研究发现,缺陷系统的剩磁随缺陷半径D的增大而增大.上述结果与非对称纳米环系统的磁特性类似,并可以通过零场状态下的系统自旋组态的变化加以解释.当系统圆心与缺陷中心的间距Y增加时,剩磁与Y的关系是非线性的:剩磁先随Y的增大而增大,后随Y的增大而减小.模拟结果可用零场状态下不同Y值的组态变化进行详细解释.上述研究结果表明,缺陷可以明显影响铁纳米环的磁特性.     

Vortex–antivortex states in nanostructured superconductor–ferromagnet hybrids

The formation of vortex–antivortex states in a superconducting film with a square array of magnetic dipoles magnetized perpendicularly to the film is investigated in the framework of the time-dependent Ginzburg–Landau equations. It is shown that a possible route to obtain equilibrium states is obtained following an experimentally realizable field-cooling procedure. The states thus obtained demonstrate a rich variety of phases, depending on magnetic moment intensity and dipole array-to-superconducting film distance. For instance, in the region of the phase diagram where each dipoles is able to generate N = 2 vortex–antivortex pairs, the antivortices induced by the negative stray fields of the dipoles undergo two transitions before ultimately merging into doubly-quantized giant antivortices. For N = 4, a state consisting on a three-quanta giant vortex below each dipole and an interstitial vortex–antivortex molecule was observed. Such state is thermodynamically stable and is induced by the fourfold symmetry of the dipole array, similar to symmetry-induced vortex–antivortex molecules found in mesoscopic superconductors.     

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.