Reversible magnetization of a thin superconducting film with radiation defects

The thermodynamic potential of a system of Peierls vortices in a thin superconducting film, containing radiation defects, in a perpendicular external magnetic field is calculated. The equilibrium temperature dependences of the densities of free vortices and vortices trapped by defects are found in the mean-field approximation for various magnitudes of the external field. It is shown that the equilibrium magnetization of a thin superconducting film exhibits the same features that were observed experimentally in the reversible magnetization of high-temperature superconductors. An asymptotic expression is obtained for the difference of the magnetizations of perfect and irradiated films. According to this expression, the difference depends on the pinning energy of a vortex on a defect and the density of defects.     

Magnetization of the ferromagnetic-superconductor structures

The magnetization of a structure consisting of a thin superconducting film lying on a thin ferromagnetic substrate with uniaxial anisotropy is considered. It is shown that if a ferromagnet is in a multidomain state, then due to the presence of a superconducting film, the period of its domain structures decreases, which is caused by the increase of the magnetostatic energy of the system owing to Meissner currents. In a certain range of the constant of uniaxial anisotropy, under the action of a superconducting film, a domain structure may transform from a strip structure to the structure with closure domains. It is found that due to the nonuniform magnetic field of a multidomain ferromagnet, Abrikosov vortices may exist in a thin film only at certain parameters of the magnetic field.     

Rotation of the pinning direction in the exchange bias training effect in polycrystalline NiFe/FeMn bilayers

For polycrystalline NiFe/FeMn bilayers, we have observed and quantified the rotation of the pinning direction in the exchange bias training and recovery effects. During consecutive hysteresis loops, the rotation of the pinning direction strongly depends on the magnetization reversal mechanism of the ferromagnet layer. The interfacial uncompensated magnetic moment of antiferromagnetic grains may be irreversibly switched and rotated when the magnetization reversal process of the ferromagnet layer is accompanied by domain wall motion and domain rotation, respectively.     

Probing the discrete motion of vortices with rf excitations

In this work we present experimental results on the rectification of vortices in a superconductor/ferromagnet system under a high frequency drive. The two-dimensional pinning landscape, induced by the stray fields of the ferromagnetic template, has no intrinsic asymmetry. Nevertheless, an asymmetric potential is artificially induced by an applied dc bias. The experimental results unambiguously show a biased, discrete motion of the vortices in the periodic potential at frequencies above 10 MHz. This synchronized motion is very sensitive to the external applied field. Increasing temperature leads to a reduction of the pinning potential, which in turn results in a lower ac power needed to drive the vortex lattice.     

Ordered states and structural transitions in a system of Abrikosov vortices with periodic pinning

A system of Abrikosov vortices in a quasi-two-dimensional HTSC plate is considered for various periodic lattices of pinning centers. The magnetization and equilibrium configurations of the vortex density for various values of external magnetic field and temperature are calculated using the Monte Carlo method. It is found that the interaction of the vortex system with the periodic lattice of pinning centers leads to the formation of various ordered vortex states through which the vortex system passes upon an increase or a decrease in the magnetic field. It is shown that ordered vortex states, as well as magnetic field screening processes, are responsible for the emergence of clearly manifested peaks on the magnetization curves. Extended pinning centers and the effect of multiple trapping of vortices on the behavior of magnetization are considered. Melting and crystallization of the vortex system under the periodic pinning conditions are investigated. It is found that the vortex system can crystallize upon heating in the case of periodic pinning.     

Effect of conduction electrons on the law of approach to saturation of a metallic ferromagnet with surface pinning of the magnetic moment

The effect of conduction electrons on the magnetization curve of a metallic ferromagnet with surface pinning of the magnetic moment is investigated theoretically. The electronic contribution is due to the rearrangement of the discrete spectrum of charge carriers trapped by the nonuniform magnetic induction of such a ferromagnet, and it is a kind of diamagnetic effect that appreciably decreases the volume-averaged magnetization of the ferromagnet. A powerlaw dependence H ^−3/4 on the external magnetic field H is obtained according to the law of magnetization approach to saturation. This dependence is due to the contribution of the conduction electrons. Fiz. Tverd. Tela (St. Petersburg) 41, 647–653 (April 1999)     

Inverse crystallization of a system of Abrikosov vortices with periodic pinning

A system of vortices in a quasi-two-dimensional HTSC plate with periodic pinning is considered. The magnetization curves are calculated by the Monte Carlo method for different values of an external magnetic field and different temperatures. It is shown that the vortex system with periodic pinning may crystallize with an increase in temperature.     

Modeling of irreversible switching and viscosity phenomena in perpendicular thin films

We have developed a simple numerical model for simulating domains as well as remanence and viscosity curves in the slow dynamics regime, for thin films characterized by perpendicular magnetization and irregular domain configurations due to strong disorder. The physical system is represented as constituted of identical switching units, described by proper switching field distributions and energy barrier laws for pinning and nucleation processes. The model also includes an effective field which accounts for magnetic forces proportional to magnetization, on average. Simulations of DCD curves show that when the reversal of magnetization is governed by pinning, the coercive field depends on the physical size of the film area on which the external field is applied. In the case of viscosity phenomena described by a linear energy barrier law associated with a single predominant reversal process (pinning or nucleation), universal viscosity curves can be generated by properly transforming the DCD curve of the system. We also demonstrate that a reduction of the maximum viscosity coefficient can coexist with a reduction of the energy barrier heights.     

Interaction and pinning of plane vortices in a three-dimensional Josephson medium and possible distances between two isolated vortices

Within a continuous vortex model, exact expressions are obtained for the Josephson and magnetic energies of plane (laminar) vortices, as well as for the energy and force of pinning by cells in a three-dimensional Josephson medium. If the porosity of the medium is taken into account, the Josephson and magnetic energies of the vortex differ from those for the continuum case. The contributions to the pinning energy from the Josephson and magnetic energies have opposite signs. An algorithm for numerically solving a system of difference equations is proposed in order to find the shape and the energy of the vortex in its stable and unstable states. The continuous vortex model is shown to fail in predicting correct values of the Josephson and magnetic energy of the vortex, as well as of the pinning energy components. Expressions for the least possible distances between two isolated vortices are obtained for a small pinning parameter. Analytical results are in close agreement with computer simulation. An algorithm for numerically solving a system of difference equations is proposed in order to find the least possible distances between two isolated vortices when the pinning parameter I is not small. The minimal value of I at which the center-to-center distance N of the vortices equals three cells is 1.428; for N=2, I _min=1.947. At I>2.907, the vortices can be centered in adjacent cells.     

Pinning of planar vortices and magnetic field penetration in a three-dimensional Josephson medium

The behavior of planar (laminar) vortices in a three-dimensional, ordered Josephson medium as a function of the parameter I, which is proportional to the critical junction current and the cell size, is investigated with allowance for pinning due to the cellular structure of the medium. The minimum possible distances between two isolated vortices are calculated. A system of vortices formed in a sample in a monotonically increasing external magnetic field is analyzed. The minimum distance from the outermost vortex to the nearest neighbor is proportional to I ^−1.1. For I⩽1.3 each vortex contains a single flux quantum Φ₀, and the distance between them does not decrease in closer proximity to the boundary but remains approximately constant, implying that the magnetic field does not depend on the coordinate in the region penetrated by vortices. These facts contradict the generally accepted Bean model. The sample magnetization curve has a form typical of type II superconductors. Allowance for pinning raises the critical field H _c and induces a sudden jump in the curve at H=H _c. Zh. Tekh. Fiz. 67, 38–46 (September 1997)     

Features of magnetization reversal in LCMO/YBCO heterostructures

The change in the magnetic domain structure due to the proximity of a superconductor has been experimentally investigated for the first time. The complex character of magnetization reversal at temperatures below critical, caused by the mutual long-range effect of a superconductor and a magnet, has been shown. In particular, it is found that even magnetization reversal of the heterostructure by an in-plane field leads to the formation of Abrikosov vortices in the superconductor, carrying a flux perpendicularly to the film plane. It is shown that this is a consequence of the transformation of narrow domain walls into wide stripes due to the interaction with scattering fields from the superconductor. In turn, after penetration of the magnetic flux into the superconductor at some depth, the scattering fields cause backward magnetization reversal of the external film edge, as a result of which vortices with oppositely directed fluxes enter the crystal and propagate in the superconductor bulk in the form of chains along twins, as in the case of magnetization by a perpendicular magnetic field. Thus, at longitudinal magnetization, the flux enters the superconducting film in the form of wide stripes with alternating perpendicular induction, which is explained by the long-range interaction of the scattering fields of the superconductor with the manganite magnetization.     

Spin-wave resonance in multilayer films (one-dimensional magnon crystals). Identification rules

The characteristic modification of the spectrum of the exchange spin waves has been revealed in ferromagnet/ferromagnet multilayer films with a thickness of N(d ₁ + d ₂) by the spin-wave resonance method. This modification is due to the first bandgap at the wavenumber k _b = π/(d ₁ + d ₂) of a magnon crystal, which is formed by one-dimensional modulation of the magnetization. It has been shown that the transformation of the multilayer film with thermal annealing to the film of a single-phase alloy is accompanied by the disappearance of this modification of the spectrum.     

Magnetization distribution in magneto-optical medium on patterned substrate

A micromagnetic calculation of magnetization in a ferromagnetic thin film with a perpendicular magnetic anisotropy fabricated on a patterned substrate is carried out. The domain wall energy of pinning of domain walls between up and down magnetized domains is shown to be determined by geometry of substrate. Estimations of regions of stability of two different domain structures in the hexagonal lattice of circle patches are given.     

Kinetics of magnetization reversal in a heterophase nanomagnet with spatially modulated anisotropy

Magnetization reversal modes in a thin-film NiFeCuMo ferromagnet (FM) with periodically varying in-plane anisotropy are studied by the magneto-optical indicator film (MOIF) technique. The uni-directional anisotropy in FM regions exchange-coupled to a FeMn antiferromagnet (AFM) film in the form of square mesh stripes is alternated by the uniaxial anisotropy in the FM regions inside this mesh. It is shown that the boundaries formed along the edges of these stripes, which separate FM regions with different anisotropy, crucially influence the kinetics of domain-structure transformation in both types of FM regions. It is established that the lateral exchange anisotropy in the ferromagnet, which is determined by the stabilization of the spin distribution in the FM layer along the FM-(FM/AFM) interface, leads to the asymmetry of the magnetization reversal in FM regions bordered with an FM/AFM structure. Anisotropy of the mobility of 180-degree “charged” and “uncharged” domain walls situated, respectively, perpendicular and parallel to the unidirectional anisotropy axis is revealed. The difference observed between the mobilities of charged and uncharged domain walls is attributed to the difference in the spin distribution in these walls with respect to the unidirectional anisotropy axis and is a key factor for the difference between the magnetization reversal kinetics in horizontal and vertical exchange-biased FM stripes. Drastic differences are revealed in the asymmetry of magnetization reversal processes in mutually perpendicular narrow stripes of FM/AFM structures. Possible mechanisms of magnetization reversal in low-dimensional FM-(FM/AFM) heterostructures are discussed with regard to the effect of domain walls localized on the edges of AFM layers.     

Rectified vortex motion in an Nb film with a spacing-graded array of holes

Superconducting Nb thin films with a spacing-graded array of holes were prepared by electron beam lithography. Two films with different hole gradients were fabricated. The ac-driven vortices were investigated in Nb superconductors with a spacing-graded array of holes. The measurements revealed pronounced rectified voltage when the vortex lattice is driven by an ac injected current. The rectified voltage is mainly caused by the strength of the vortex–vortex interaction. The rectified motion of a vortex is affected by the pinning potential of the spacing-graded array and the applied magnetic field. The vortex–vortex interaction strength changes the effective pinning landscape of the vortices and an asymmetric potential is formed. Vortices depin easily from high concentration to low concentration of pinning sites. In both samples, the ac-driven vortices exhibit a variety of dynamical responses and the rectified voltage is tunable with the applied magnetic field.     

Unidirectional anisotropy in a ferromagnet-antiferromagnet system

The unidirectional anisotropy arising in a ferromagnetic film on an antiferromagnetic substrate due to the proximity effect is investigated. Consideration is given to the smooth and rough film-substrate interfaces. The conditions of the formation of a domain wall in the film and the passage of the wall into the substrate in the course of magnetization reversal are determined. The parameters of the static spin vortices formed in the vicinity of the rough interface are studied as functions of the magnetic field strength.     

Multivortex states in large pinning centers

We have studied the vortex pinning in the large centers, i.e. in the spatial regions with the characteristic size a comparable with the London lenght λ. It is shown that the type of configuration and the number of vortices in the cluster are dependent on the ration a/λ and change nonmonotonically with the temperature. The influence of such vortex clusters on the decay of magnetization and the current-voltage characteristics are discussed. The important role of the potential barrier for the penetration of vortices into the pinning center is shown. The new state of vortex cluster, “vortex polaron”, is predicted. The stability of the multivortex state is discussed.     

Effect of surface spin waves on the magnetization of thin films

The theoretical calculation of the magnetization across the thickness of the film shows that it may be either lower or higher near the surface than at the centre of the film depending on the surface anisotropy. For intermediate surface anisotropy values the plots of magnetization vs distance from the surface show several extrema. The temperature dependences of magnetization show only small departures from the usual theoretical behaviour of thin films for the cases when surface spin waves are present. The given examples are calculated for uniaxial h.c.p. Heisenberg ferromagnet.     

磁性d波超导/铁磁/磁性d波超导结中的约瑟夫森效应

通过求解磁性d波超导中的能隙和磁交换能的自洽方程, 研究磁性d波超导/铁磁/磁性d波超导结中的约瑟夫森电流. 计算结果表明: 1)临界电流随中间的铁磁层厚度呈现出两种不同周期的振荡混合, 通过增强铁磁层中的磁交换能q₀和铁磁/磁性d波超导界面处的势垒强度z₀, 短周期分量可从长周期中分离出来, 反之, 通过降低q₀和z₀, 长周期分量可从短周期中分离出来; 2)在两边磁性d波超导的磁化方向取平行时, 在取一些特定的铁磁层厚度下, 磁性d波超导中的磁交换能可增强系统的临界电流. 关键词： 磁性d波超导体 铁磁体 约瑟夫森电流     

Line vortex pinning and spacing in a three-dimensional ordered Josephson medium

A method of calculating the configuration of two line vortices interacting in a three-dimensional ordered Josephson medium and a minimal distance between them at a given pinning parameter is proposed. The axes of the vortices lie in the middle row of an infinite slab 9 or 13 cells thick with different conditions at the boundaries of the slab. Away from the centers of the vortices, the system of finite-difference equations becomes linear. Fluxoid quantization conditions in cells near the centers of the vortices serve as boundary conditions. An exact solution is approached by iterations in those phase discontinuities which cannot be considered small. This technique provides a much higher calculation accuracy and offers a wider domain of applicability than the earlier methods. Critical values I _d of the pinning parameter at which two initial vortices keep given spacing d between them are calculated. For various vortex configurations, maximal pinning forces are calculated as functions of the pinning parameter and the distance to the nearest vortices. It is shown that the pinning force decreases near parallel vortices and increases near antiparallel ones.