Phase domain structures in cylindrical magnets under conditions of a first-order magnetic phase transition

The magnetic and resonance properties of cylindrical magnets at first-order phase transition from paramagnetic to ferromagnetic state were theoretically studied. It has been shown that in the external magnetic field directed perpendicularly to the rotation axis, formation of a specific domain structure of paramagnetic and ferromagnetic layers can be energetically favorable. The parameters of cylindrical phase domains as well as their dependences on temperature, magnetic field and material characteristics have been calculated. Peculiarities of the magnetic resonance spectra appearing as a result of the phase domain formation have been considered. Dependence of the resonance field of the system of ferromagnetic domains on magnetization and temperature has been obtained.     

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.     

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.     

Spontaneous phase transitions in ferrite garnet films

Spontaneous phase transitions in ferrite garnet films have been studied. It has been shown that, with variations in the temperature, domain walls undergo phase transitions which cause spontaneous phase transitions in the lattice of cylindrical magnetic domains. The phase transition in a domain wall causes a spin-reorientation phase transition over the whole sample near the magnetic compensation point. The character of the phase transition in the domain wall determines the mechanism of the spin-reorientation phase transition.     

Stable spiral domains in ferrite-garnet films

Stable spiral domain structures—spiral domains stabilized by a bubble lattice and lattices of spiral domains—in epitaxial ferrite-garnet films have been experimentally investigated. The thermodynamic approach based on the concept of magnetostatic pressure is applied to explain the behavior of a spiral domain structure with a change in temperature or magnetic field. It is shown that phase transitions in spiral domains are related to phase transitions in the bubble lattice.     

Ordering classification of columnar lattices formed in magnetic fluid subjected to perpendicular fields

When the thin film of high-quality magnetic fluid is subjected to a perpendicular magnetic field, a separation of particles from the liquid matrix will occur, leading to a phase transition with a phase that is concentrated in particles separating from a dilute phase. The concentrated phase makes up the cylindrical columns that can form two-dimensional lattices. We have explored the field-induced lattices with optical microscopy, digital imaging and computer-video techniques in this study, to classify the ordering property in terms of bond-orientation order.     

Phase transitions in uniaxial ferromagnetic film covered by superconducting layers

The phase diagram and the single-domain uniform state for a uniaxial ferromagnetic film with the superconducting layers covering one or both sides of a ferromagnet are investigated. The superconductor is supposed to be a second-order one and the interaction between the magnetic sub-system and with the conductivity electrons in a superconductor is purely electromagnetic and the vortices in a superconductor are pinned. The critical thickness of the magnetic film for which the uniform state becomes absolutely stable is calculated when the external magnetic field is supposed to be in-plane of the film. It is shown that the critical thickness of the film from the magnetic material with the quality factor Q>1 monotonically decreases as the magnetic field increases in the range from zero value to the value of the transition field where the collinear phase transforms into the angular (canted) phase. Further the critical thickness increases with the increase of the field. The quasi-single-domain magnetic film states were considered when the film thickness was close to the critical one. It is shown that for a thin isolated magnetic film the domain period exponentially increases with the decrease of the film thickness. Such dependence, however for the film with double-side superconducting cover and close to the transition into the single domain state becomes logarithmic and for the film covered by superconductor only on the one side varies as the power series. The single-domain state existence and the asymptotic behaviour of the domain structure is explained by the features of the asymptotic behaviour of the domain walls within the system. As for isolated magnetic film and for a film with the superconductor cover layers the transition from the collinear phase to the inhomogeneous state is the second-order phase transition and the transition from the uniform angular phase to the inhomogeneous phase is the first-order transition.     

Formation of phase domain structures in thin films under conditions of a first-order magnetic phase transition

This paper reports on the results of a theoretical investigation into the magnetic and resonance properties of thin films in the range of the transition from a paramagnetic state to a ferromagnetic state in the case where the magnetic transition is a first-order phase transformation. It is demonstrated that, in an external magnetic field directed perpendicular to the film plane, the formation of a specific domain structure consisting of domains of the coexisting paramagnetic and ferromagnetic phases can appear to be energetically favorable. The parameters of the equilibrium system of stripe phase domains and their dependences on the temperature, the magnetic field, and the characteristics of the material are calculated. The specific features of the magnetic resonance spectra under the conditions of formed stripe phase domains are considered. A relationship is derived for the dependence of the resonance field of the system of ferromagnetic domains on the magnetization and temperature. It is shown that the alternating external field can fulfill an orientation function in the formation of stripe phase domains.     

Magnetic properties of 2D nano-islands I: Ising spin model

An Ising spin effective field theory (EFT) is developed as a framework for a detailed analysis of the magnetic properties of two-dimensional (2D) nano-islands on a nonmagnetic substrate with an out of plane magnetization. The Hamiltonian with nearest neighbor exchange interactions and single-atom magnetic anisotropy defines the ground state. The calculation yields the single site spin correlations, the magnetizations, and the isothermal susceptibilities for the core and periphery domains, and the island core phase diagrams. The choice of a spin S=1 for the atoms permits the analysis of the effects of spin fluctuations via the single site spin correlations. In particular we investigate the effects due to the different anisotropies and reduced dimensionalities for the core and periphery domains. The present model calculations are developed for different 2D nano-islands lattices. Detailed theoretical results are presented for the square and hexagonal lattices, with numerical applications for the 2D Co nano-islands on Pt. The derived transition temperature for the hexagonal lattice nano-islands is in good agreement with the experimental data for Co nano-islands on Pt. Though both the core and the periphery domains have the same order-disorder transition temperature, the magnetization of each domain attains this transition differently. The temperature behavior of the spin correlations is also fundamentally different for the periphery and core sites, which entails distinctly different isothermal susceptibilities, and yields statistically averaged nano-islands susceptibilities that do not correspond to a second order phase transition. The experimental susceptibility results for 2D Co nano-islands on Pt can be interpreted within our EFT Ising model without reference to a transition from a blocking state of the particle to a superparamagnetic behavior. The results for the different lattices are formally comparable, and demonstrate the robustness and general character of the model.     

On the theory of ferromagnetism of hexagonal diborides

The electronic structure and the magnetic properties of the MnB₂ and CrB₂ compounds with hexagonal AlB₂-type lattices were studied. The problem was treated in terms of the generalized Hubbard model with an infinite electron-electron repulsion energy in the same atom. Equations for spin magnetic susceptibility were derived and used to determine the conditions of ferromagnetic instability and construct the phase diagram of the existence of ferromagnetic ordering.     

Suppression of the domain structure in uniaxial ferromagnetic films with a superconducting coating

Specific models of domain walls are used to investigate conditions for the single-domain state and quasi-single-domain states in structures with magnetic materials having a quality factor higher than one. It is shown that the critical thickness of the magnetic film in a tangentially magnetized system decreases monotonically as the magnetizing field increases from zero to the transition from the collinear to the homogeneous angular phase and then increases monotonically with increasing external field. In a thin isolated magnetic film, the size of the domains increases exponentially with decreasing thickness. This dependence is logarithmic near the transition to the single-domain state for a film coated on two sides and obeys a power law for a film coated on one side. The establishment of a single-domain state and characteristic features in the asymptotic behavior of the domain structure in magnetic films with and without coatings can be attributed to differences in the asymptotic behavior of the field of a single domain wall. Fiz. Tverd. Tela (St. Petersburg) 40, 1068–1074 (June 1998)     

Theory of cylindrical magnetic domains of submicron size

By successively taking account of the domain boundary thickness and the contribution of the magnetic field energy to the boundary energy, an expression is obtained for the total energy of a cylindrical magnetic domain in the case when the domain size is comparable to its boundary thickness. The boundary of the stability region is determined for the cylindrical magnetic domain with respect to the field as a function of the domain boundary thickness. Analysis of the results obtained permits making a deduction about the degree of influence of the boundary-layer thickness on the static properties of the cylindrical magnetic domain.Translated from lzvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 61–67, February, 1984.In conclusion the author is grateful to Yu. I. Gorobets for interest in the research and for valuable discussion.     

The special features of ferromagnetism in ordered Heusler alloys

The electronic structure and magnetic properties of the Cu₂MnA, Ni₂MnA, Pd₂MnA, Co₂MnA, and Fe₂FeA compounds with cubic lattices, where A is a nontransition element anion (A=Al, In, Ge, As, Sn, Si, or Sb), are studied. An analysis is performed in terms of the generalized Hubbard model with an infinite electronic repulsion energy within the same atom. Equations for determining the spin magnetic susceptibility of the compounds are obtained. These equations are used to determine the conditions of ferromagnetic instability and to construct the phase diagram for the existence of ferromagnetic ordering.     

Study of the kinetics of domain structures in thin ferromagnetic films by the Wang-Landau method

The features of a phase transition between the strict striped domain structure in thin ferromagnetic films with transverse anisotropy and the so-called tetragonal phase, where domains can be twisted and broken into parts, have been analyzed. It has been shown that the phase transition should be thermodynamically treated as a Kosterlitz-Thouless transition, where ends of domains serve as vortices. It has been demonstrated with the Wang-Landau numerical algorithm that the kinetics of this phase transition is strongly slowed down owing to the existence of a large number of metastable states; in this property, the system is partially similar to spin glasses.     

Coarsening of antiferromagnetic domains in multilayers: the key role of magnetocrystalline anisotropy

The domain structure of an antiferromagnetic superlattice is studied. Synchrotron M?ssbauer and polarized neutron reflectometric maps show micrometer-size primary domain formation as the external field decreases from saturation to remanence. A secondary domain state consisting mainly of at least 1 order of magnitude larger domains is created when a small field along the layer magnetizations induces a bulk-spin-flop transition. The domain-size distribution is reproducibly dependent on the magnetic prehistory. The condition for domain coarsening is shown to be the equilibrium of the external field energy with the anisotropy energy.     

Phase ordering induced by defects in chaotic bistable media

The phase ordering dynamics of coupled chaotic bistable maps on lattices with defects is investigated. The statistical properties of the system are characterized by means of the average normalized size of spatial domains of equivalent spin variables that define the phases. It is found that spatial defects can induce the formation of domains in bistable spatiotemporal systems. The minimum distance between defects acts as parameter for a transition from a homogeneous state to a heterogeneous regime where two phases coexist The critical exponent of this transition also exhibits a transition when the coupling is increased, indicating the presence of a new class of domain where both phases coexist forming a chessboard pattern.     

W(110)基底上的铁纳米岛初始自发磁化态的微磁学模拟

用微磁学模拟研究W(110)基底上铁纳米岛的初始自发磁化态的磁畴结构,确定了不规则形状、椭圆形和矩形岛中不同磁畴态之间的各向异性常数的临界点,得到了纳米岛的磁化态作为各向异性常数和厚度函数的完整相图,相图中存在一较宽的过渡区,把双畴态与涡旋态和菱形态分开,过渡区两侧的边界是不确定的.计算结果表明,初始自发磁化态的磁畴结构主要由各向异性及岛的厚度决定,而且岛的边沿形状对涡旋态和菱形态的磁畴结构有重要影响.准确的铁纳米岛的各向异性常数仍有待于进一步确定. 关键词： 初始自发磁化磁畴结构 铁纳米岛 微磁学模拟 各向异性     

Studies of the domain structure of anisotropic sintered SmCo5 permanent magnets

In this work, investigations of the magnetic microstructure of anisotropic sintered SmCo₅ permanent magnets with high coercivity have been made using the colloid-scanning electron microscopy (SEM) technique and magnetic force microscopy (MFM). The magnets were produced by powder metallurgy (sintering) process and consisted of oriented grains with an average size of about 20 μm. They were studied in the thermally demagnetized state. Owing to the application of digital image recording, enhancement and analysis, high-quality images of the magnetic microstructure were obtained and analyzed not only qualitatively but also quantitatively. Improvements over previous results were achieved. The grains show the presence of magnetic domains, as expected. At the surface perpendicular to the alignment axis, the coarse domain structure in the form of a maze pattern with surface reverse spikes is observed. The main (maze) domains had typical widths 3–5 μm. The reverse spike domains were imaged as circles typically 1–2 μm in diameter or as elongated regions up to about 6 μm in length. Interestingly, in addition to the coarse maze domains and reverse spikes near the surface, a fine surface domain structure is revealed with MFM. The fine scale domains are found to be magnetized perpendicular to the surface and their occurrence is attributed to further reduction of the magnetostatic energy at the cost of a larger domain wall energy. On the surface parallel to the alignment axis, the main domains within individual grains are imaged as stripe domains with domain walls running approximately parallel to the alignment axis, while reverse spike domains are displayed in the form of triangular domains and occur near some grain boundaries, pores or precipitations. The magnetic alignment of grains was found to be good, but certainly not perfect. In most cases the domain structures within grains were independent of their neighbors, but in some cases (not so rare) observations indicated the existence of significant magnetostatic coupling between neighboring grains. The main and surface domain widths were determined by digital means using the stereologic method of Bodenberger and Hubert. Moreover, the domain wall energy and other intrinsic parameters for the studied magnets were determined.     

Yb Mössbauer and neutron diffraction investigation of the antiferromagnetic phase in the Kondo lattices YbP and YbN

The Kondo lattices YbP and YbN (nonstoichiometric samples) have been investigated by ¹⁷⁰Yb Mössbauer spectroscopy, in the temperature range 0.085 K to 80 K in zero magnetic field in YbN and with an applied magnetic field at T=0.045 K in YbP and YbN, and by neutron diffraction in YbN. In both compounds, the antiferromagnetic transition at T_N0.7 K is first order and occurs through a progressive growth of paramagnetic domains as the temperature increases. The measured exchange interaction is much larger than k_BT_N in both compounds and it is found to be isotropic in YbP and anisotropic in YbN. The saturated magnetic moment in both compounds is reduced by 50% with respect to the value calculated from the crystal field and exchange interactions. These properties are interpreted in terms of the competition between the Kondo effect and the RKKY exchange interaction; using a model mean field NCA calculation to describe the magnetic phase, the Kondo temperatures T_K are found to be near 5–10 K.     

Magnetic domains in non-ferromagnetic metals: The non-linear de Haas-van Alphen effect

This review is devoted to an exposition of the principles of the physics of magnetic domains in non-ferromagnetic metals and diamagnetic phase transitions, which lead to the formation of the so-called Condon domains during magnetic oscillations in a three-dimensional electron gas. One of the goals of the review is to provide a deeper insight into the nature of this instability of the electron gas in normal metals and improve the understanding of this type of non-spin magnetism. We discuss theoretical aspects of the physics underlying magnetic ordering of conduction electrons in bulk metals and in thin films, and describe the behaviour of the susceptibility, thermal expansion, specific heat, compressibility, sound velocity, magnetic induction bifurcation, the order parameter, domain formation, wetting of domain walls, nucleation and kinetics of diamagnetic phase transitions. In the vicinity of diamagnetic phase transitions the results obtained coincide with those following from the Landau theory of phase transitions. The existence of the critical sample size for the diamagnetic phase transition in thin films is considered. We place special emphasis on the problem of the order of diamagnetic phase transitions. The survey is partly motivated as complementary to the recent review by G. Solt and V. Egorov describing the experimental situation in the field. Contents PAGE 1. Introduction 386 2. Diamagnetic phase transitions and Condon domains 390 2.1. Shoenberg's and Condon's consideration of the phenomena 390 2.2. Phase diagrams for one de Haas-van Alphen cycle 395 3. Critical phenomena at second-order diamagnetic phase transitions in three-dimensional metals 397 3.1. Introduction 397 3.2. Order parameter and susceptibility 397 3.3. Specific heat jump 403 3.4. Phase diagrams 407 3.5. Finite-size effects 410 3.6. Compressibility, thermal expansion and sound velocity 414 4. Condon domains and resonance methods of their investigation 417 4.1. Introduction 417 4.2. Nuclear magnetic resonance and Condon domains 418 4.3. Muon spin resonance spectroscopy and Condon domains 420 4.4. Critical exponents at diamagnetic phase transitions in silver and beryllium 426 4.5. Helicon resonance and Condon domains 428 4.6. Critical dynamics of the diamagnetic phase transition in aluminium 430 5. First-order diamagnetic phase transitions 431 5.1. Introduction 431 5.2. Domain formation 433 5.3. Kinetics 436 5.4. Wetting 441 5.5. Nucleation 442 5.6. Order of diamagnetic phase transitions 444 5.7. Hysteresis and Condon domains 445 6. Summary 446 7. Some open issues 448 Acknowledgements 450 References 451