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.     

Dynamic stability of a spiral domain in an ac magnetic field

The dependence of the stability of a magnetic spiral domain in a film on the parameters of the film and its domain structure and on an external magnetic field is considered within a phenomenological model. The model allows one to explain a number of experimentally observed properties of dynamic spiral domains resulting from the process of self-organization of domains and domain walls in an iron-garnet film placed in an external ac magnetic field.     

Magnetostatic energy and stripe domain structure in a ferromagnetic plate of finite width with in-plane anisotropy

The magnetostatic energy and domain structure (DS) in a long ferromagnetic plate of a finite width with in-plane anisotropy are calculated for the case of the domain magnetization vectors lying in the plane of the plate. The situation where the DS period is much shorter than the width but is considerably larger than the thickness of the plate is analyzed in detail. The equilibrium DS period and the width ratio of two adjacent domains are determined as functions of an external magnetic field parallel to the plane of the plate by minimizing the energy. The DS period is found to be proportional to the plate width and the domain wall energy and inversely proportional to the squared saturation magnetization. While the width of the favorable domains (with the magnetization parallel to the field) grows with increasing field, the unfavorable domains, rather than disappearing completely, form relatively narrow transition regions between the favorable domains, i.e., 360° domain walls.     

Magnetic structure and mechanisms of magnetic reversal of a quick-quenched ferromagnetic wire core

Mechanisms of motion of the domain top separating oppositely magnetized domains through an amorphous ferromagnetic wire core are investigated in an external magnetic field. The equilibrium parameters of the domain in the wire core are determined. It is established that the character of motion of the domain top trough the wire core depends on the mutual orientation of the external magnetic field and the domain magnetization. It is demonstrated that amorphous ferromagnetic wires based on transition metals possess the magnetic diode effect. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 64–69, February, 2008.     

Motion of domain walls under the action of spin-polarized current in a magnetic junction

The effect of spin-polarized current on a domain structure in a magnetic junction consisting of two ferromagnetic metallic layers separated by an ultrathin nonmagnetic layer is studied within a phenomenological theory. The magnetization of one ferromagnetic layer (layer 1) is assumed to be fixed, while that of the other ferromagnetic layer (layer 2) can be freely oriented both parallel and antiparallel to the magnetization of layer 1. Layer 2 can be split into domains. Charge transfer from layer 1 to layer 2 is not attended with spin scattering by the interface but results in spin injection. Due to s-d exchange interaction, injected spins tend to orient the magnetization in the domains parallel to layer 1. This causes the domain walls to move and “favorable” domains to grow. The average magnetization current injected into layer 2 and its contribution to the s-d exchange energy are found by solving the continuity equation for carriers with spins pointing up and down. From the minimum condition for the total magnetic energy of the junction, the parameters of the periodic domain structure in layer 2 are determined as functions of current through the junction and magnetic field. It is shown that the spin-polarized current can magnetize layer 2 up to saturation even in the absence of an external magnetic field. The associated current densities are on the order of 10⁵ A/cm². In the presence of the field, its effect can be compensated by such a high current. Current-induced magnetization reversal in the layer is also possible.     

Domain wall dynamics and Hall effect in eddy current loop in amorphous ferromagnetic wire with small helical anisotropy

Small helical anisotropy was induced in amorphous ferromagnetic Co_68.2Fe_4.3Si_12.5B₁₅ wire by current annealing and simultaneous application of tensile stress and torsion. Presence of helical anisotropy was confirmed by measurement and analysis of the circular magnetic flux versus axial magnetic field hysteresis loops. These measurements also showed that a single domain wall between circular domains can be created by placing the wire in a sufficiently high inhomogeneous magnetic field generated by Helmholtz coils with opposite currents. The domain wall velocity versus axial driving field was measured. The results show that the basic dynamic properties (magnitude of the wall mobility, field interval in which linear dependencies between velocity and field are observed, accelerated increase of the velocity for higher fields) are very similar to those obtained for the domain wall between circular domains driven by a constant circular field. The Hall effect was detected in the eddy current loop generated by the moving domain wall.     

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.     

Tb0.3Dy0.7Fe2合金磁畴偏转的滞回特性研究

研究了不同载荷作用下Tb_0.3Dy_0.7Fe₂合金在压磁和磁弹性效应中磁畴偏转的滞回特性. 基于Stoner-Wolhfarth模型的能量极小原理, 采用绘制自由能-磁畴偏转角度关系曲线的求解方法, 研究了压磁和磁弹性效应中载荷作用下的磁畴角度偏转和磁化过程, 计算分析了不同载荷作用下磁畴偏转的滞回特性. 研究表明, 压磁和磁弹性效应中磁畴偏转均存在明显的滞回、跃迁效应, 其中磁化强度的滞回效应来源于磁畴偏转的角度跃迁; 压磁效应中预加磁场的施加将增大磁化强度的滞回, 同时使滞回曲线向大压应力方向偏移; 磁弹性效应中磁畴偏转的滞回存在两个临界磁场强度, 不同磁场强度下合金具有不同的磁畴偏转路径和磁化滞回曲线, 临界磁场强度的大小取决于预压应力的施加. 理论分析对类磁致伸缩材料磁畴偏转模型的完善和材料器件的设计应用非常有意义.     

Modeling of the loading path dependent magnetomechanical behavior of Galfenol alloy

The magnetomechanical behavior of single-crystal Galfenol alloy was found to be strongly dependent on the loading paths. An energy-based anisotropic domain rotation model, assuming that the interaction between domains can be ignored and the probability of the magnetic moment pointing along a particular direction is related to the free energy along this direction, is used to simulate the magnetostriction versus magnetic field and stress curve and to track the magnetic domain motion trail. The main reason for loading path dependent effect is the rotation/flipping of the magnetic domains under different loading paths. The effect of loading and unloading paths on 90° magnetic domain motion was studied by choosing different loading and unloading state and paths. The results show that prior loading magnetic field can make the 90° magnetic domains flip to the directions of 45° domains because the magnetic field is the driving force to make the domains rotate, and the final loading state and the loading path both have great influence on the motion of 90° magnetic domains.     

Elastic domains in antiferromagnets on substrates

We consider periodic domain structures which appear due to the magnetoelastic interaction if the antiferromagnetic crystal is attached to an elastic substrate. The peculiar behavior of such structures in an external magnetic field is discussed. In particular, we find the magnetic field dependence of the equilibrium period and the concentrations of different domains.     

Cylindrical domain structure in metamagnets and its stability conditions

The possibility of the existence of a cylindrical magnetic domain structure near the first-order phase transition line is investigated theoretically in metamagnets, compounds with anisotropy energy substantially exceeding the exchange interaction energy. The domain structure of such compounds is related to the kinetics of the transition from the paramagnetic to the antiferromagnetic state. The static properties of isolated cylindrical magnetic domains and their equilibrium lattices are studied using an energetic approach. It is shown that for a low-temperature metamagnetic phase transition domains of the existence of a cylindrical domain structure, lattices and isolated cylindrical magnetic domains, abut, on the domain of plane-parallel domain structure existence from both sides. The features of their behavior are determined as a function of the magnitude of the external magnetic fields.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 84–88, March, 1988.The author is grateful to Yu. I. Gorobets for supporting the research and for useful remarks, and also to D. A. Yablonskii and I. M. Vitebskii for fruitful discussions.     

Magnetic domain and local atomic structures of the Fe<Subscript>0.94</Subscript>Si<Subscript>0.06</Subscript> alloy before and after thermomagnetic treatment in an alternating-current magnetic field

The changes observed in the local atomic structure of an iron alloy with 6 at % Si as a result of thermomagnetic treatment in an alternating-current magnetic field and their correlation with magnetic characteristics, such as the domain structure and magnetic properties, have been investigated using Mössbauer spectroscopy. It has been shown that the destabilization of the domain structure is caused by the destruction of uniaxial magnetic anisotropy in domains due to a disordered distribution of pairs of silicon atoms along the 〈100〉 easy magnetization axes. Annealing and cooling without an external magnetic field and in an alternating-current magnetic field lead to a change in the magnetic texture of single-crystal samples of the siliconiron alloy. When the samples are annealed in an alternating-current magnetic field, the magnitude of this effect depends on the orientation of the magnetic field with respect to the crystallographic axes of the sample.     

Magnetic field control of 90°, 180°, and 360° domain wall resistance

In the present work, we have compared the resistance of the 90°, 180°, and 360° domain walls in the presence of external magnetic field. The calculations are based on the Boltzmann transport equation within the relaxation time approximation. One-dimensional Néel-type domain walls between two domains whose magnetization differs by angle of 90°, 180°, and 360° are considered. The results indicate that the resistance of the 360° DW is more considerable than that of the 90° and 180° DWs. It is also found that the domain wall resistance can be controlled by applying transverse magnetic field. Increasing the strength of the external magnetic field enhances the domain wall resistance. In providing spintronic devices based on magnetic nanomaterials, considering and controlling the effect of domain wall on resistivity are essential.     

Dynamics of magnetic domain wall motion after nucleation: dependence on the wall energy

The dynamics of magnetic domain wall motion in the FeNi layer of a FeNi/Al2O3/Co trilayer has been investigated by a combination of x-ray magnetic circular dichroism, photoelectron emission microscopy, and a stroboscopic pump-probe technique. The nucleation of domains and subsequent expansion by domain wall motion in the FeNi layer during nanosecond-long magnetic field pulses was observed in the viscous regime up to the Walker limit field. We attribute an observed delay of domain expansion to the influence of the domain wall energy that acts against the domain expansion and that plays an important role when domains are small.     

Interaction of a shear wave with a moving domain wall in a ferromagnetic crystal with allowance for the external magnetic field

The boundary-value problem of the magnetoelastic wave interaction with a moving domain wall in a ferromagnetic crystal is solved in the nonexchange magnetostatic approximation with allowance for the external magnetic field. It is shown that the difference introduced by magnetic field between the ferromagnetic resonance frequencies of the domains does not cause any noticeably departure of the refraction characteristics of reflected and transmitted waves from those observed at zero frequency mismatch. By contrast, the magnitudes of the transmission and reflection coefficients strongly depend on the external magnetic field and on the mobility of the domain wall. The dependence of the magnitude of the reflection coefficient on the external magnetic field at a fixed angle of shear wave incidence is found to possess two ferromagnetic resonance peaks. The positions and heights of the peaks may vary depending on the mobility of the domain wall.     

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.     

Magnetic ordering in (110) Eu films in an applied magnetic field

Below its ordering temperature (T _N = 90 K), bulk bcc Eu has a helical magnetic state with propagation vectors along the three equivalent 〈100〉 directions. In contrast, epitaxial (110)Eu films exhibit a unique magnetic ordering: the domain with a magnetic helix propagating along the in-plane [001] direction vanishes on cooling, at the expense of other domains with helices propagating along [100] and [010]. This paper is devoted to the study of the stability of the magnetic domains in an external magnetic field using neutron scattering experiments and macroscopic magnetization measurements. The helix propagating along the [001] direction can be restored by the application of an external field along this direction. On the contrary, when a magnetic field is applied along an intermediate direction, specifically [10], the domain with a helix propagating along [001] is suppressed. Both effects depend on the film thickness. They are explained if one considers that, because of the low magnetic anisotropy of Eu, a helix with a propagation vector parallel to (or close to) the applied magnetic field is energetically more favourable than cycloidal structures with unchanged propagation vectors. Finally, the amplitudes of the propagation vectors and their directions (that are modified in films compared to bulk) do not vary under magnetic field.     

Finite lifetime of spiral domains in the anger state of multidomain magnetic films

The finite lifetime T _g of a dynamic spiral domain in the anger state in a multidomain film with perpendicular magnetic anisotropy is estimated theoretically in the framework of a dissipative model. The finite lifetime of spiral domains is investigated as a function of the frequency of an external ac magnetic field that varies according to a harmonic law.     

Two-step flux penetration in classic antiferromagnetic superconductor

The influence of antiferromagnetic order on the mixed state of a superconductor may result in creation of spin-flop domains along vortices. This may happen when an external magnetic field is strong enough to flip over magnetic moments in the vortex core from their ground state configuration. The formation of domain structure causes modification of the surface energy barrier, and creation of the new state in which magnetic flux density is independent of the applied field. The modified surface energy barrier has been calculated for parameters of the antiferromagnetic superconductor DyMo₆S₈. The prediction of two-step flux penetration process has been verified by precise magnetization measurements performed on the single crystal of DyMo₆S₈ at milikelvin temperatures. A characteristic plateau on the virgin curve B(H ₀) has been found and attributed to the modified surface energy barrier. The end of the plateau determines the critical field, which we call the second critical field for flux penetration. Received 16 August 2002 / Received in final form 22 October 2002 Published online 29 November 2002     

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.