Inhomogeneous Magnetic Systems Research Articles

Chiral Instability of the Homogeneous State of a Ferromagnetic Film on a Magnetic Substrate

The conditions of formation of chiral magnetization distributions in the systems ferromagnet/superconductor and ferromagnet/paramagnet are theoretically determined. The formation of chiral states is caused by the magnetostatic interaction in inhomogeneous magnetic systems. The estimates performed demonstrate that the predicted effects can be experimentally observed.

Direct imaging of cross-sectional magnetization reversal in an exchange-biased CoFeB/IrMn bilayer

The exchange coupling between ferromagnetic (FM) and antiferromagnetic materials has been intensely studied for fundamental physics and technological applications in various devices. However, the experimental reported magnitudes of exchange coupling are often smaller than that predicted theoretically, and for which the formation of springlike spin structure in the FM layer has been suggested as the cause. However, investigating the spin structure around the interface of exchange-coupled systems is challenging. Here we report the direct imaging of the cross-sectional magnetization reversal and spin structure at the interface of a model exchange-biased CoFeB/IrMn bilayer by a Lorentz transmission electron microscope with electron holography techniques. Through imaging of in situ magnetization reversal and spin structure at the remanent state, the springlike spin structure (either Bloch-wall-like or N\'eel-wall-like) in the CoFeB layer has been deduced within subnanometer region of the interface. This result puts a strong constraint on the theories of exchange coupling in inhomogeneous magnetic systems.

Erratum: Realization of the thermal equilibrium in inhomogeneous magnetic systems by the Landau-Lifshitz-Gilbert equation with stochastic noise, and its dynamical aspects [Phys. Rev. B 91 , 134411 (2015)

Received 25 December 2017DOI:https://doi.org/10.1103/PhysRevB.97.019904©2018 American Physical Society

Применение обобщенной модели аномальной холловской проводимости для неоднородных магнитных нанокомпозитных систем в области фазовых превращений под давлением

Применение обобщенной модели аномальной холловской проводимости для неоднородных магнитных нанокомпозитных систем в области фазовых превращений под давлением

Realization of the thermal equilibrium in inhomogeneous magnetic systems by the Landau-Lifshitz-Gilbert equation with stochastic noise, and its dynamical aspects

It is crucially important to investigate the effects of temperature on magnetic properties such as critical phenomena, nucleation, pinning, domain wall motion, and coercivity. The Landau-Lifshitz-Gilbert (LLG) equation has been applied extensively to study dynamics of magnetic properties. Approaches of Langevin noises have been developed to introduce the temperature effect into the LLG equation. To have the thermal equilibrium state (canonical distribution) as the steady state, the system parameters must satisfy some condition known as the fluctuation-dissipation relation. In inhomogeneous magnetic systems in which spin magnitudes are different at sites, the condition requires that the ratio between the amplitude of the random noise and the damping parameter depend on the magnitude of the magnetic moment at each site. Focused on inhomogeneous magnetic systems, we systematically showed agreement between the stationary state of the stochastic LLG equation and the corresponding equilibrium state obtained by Monte Carlo simulations in various magnetic systems including dipole-dipole interactions. We demonstrated how violations of the condition result in deviations from the true equilibrium state. We also studied the characteristic features of the dynamics depending on the choice of the parameter set. All the parameter sets satisfying the condition realize the same stationary state (equilibrium state). In contrast, different choices of parameter set cause seriously different relaxation processes. We show two relaxation types, i.e., magnetization reversals with uniform rotation and with nucleation.

Hybrid models of hysteresis for mixed hysteretic loops in heterogeneous magnetic materials

The mixed hysteresis behavior of counter-clockwise and clockwise loops has recently attracted the attention of the magnetics community, due to several experimental findings in inhomogeneous and hetero-structure magnetic systems. Various hybrid models are proposed here to address this behavior based on the superposition of standard hysteresis models and their newly developed clockwise variants. A special attention is also devoted to Bouc-Wen model, a typical clockwise often used by applied mechanics community, and to its relevance for mixed hysteresis. These clockwise and hybrid models have been implemented in an open-access academic software and their performance is illustrated by examples of hysteretic loops, first order reversal curves and diagrams simulated in this framework.

磁瓶飞行时间谱仪用复合磁场系统设计

Based on the primary requirement for the magnetic field system in magnetic-bottle time-of-flight spectrometer, an appropriate combined inhomogeneous magnetic field system is designed. The inhomogeneous higher magnetic field part, with the highest field of 1.2 Ｔ, is produced by the combination of a permanent magnet and a pole piece with optimized shape. The magnet, known as NdFeB magnet, is one of rare earth permanent magnets in N52. The guiding uniform magnetic field of 1.0×10-3 T is provided by solenoid, with length of 3 m and radius of 3 cm. The pitch between the pole piece and the near end of used solenoid is determined to be 5 cm, which can satisfy the actual engineering needs．

Refraction indices of spatially nonuniform magnetic systems and nanostructures from the first principles

An equilibrium two-time temperature Green’s function (TTGF)-based, quantum statistical mechanical approach has been used to derive from the first principles an explicit expression for the tensor of “local” refraction indices of spatially nonuniform systems in weak external electromagnetic (EM) fields in the linear approximation with regard to the field magnitudes. Written in terms of the TTGF-based, first-principle tensorial dielectric and magnetic susceptibilities, the obtained formula for the local tensor of refraction indices (TRI) is applicable to any system, including individual nanoscale objects, such as quantum dots and wires, magnetic nanostructures, composite materials, or spatially nonuniform, bulk magnetic materials. An explicit expression for the space-time Fourier transform (STFT) of the dielectric susceptibility tensor used in TRI is derived in terms of STFTs of the charge density—charge density TTGFs, while the corresponding STFT of the magnetic susceptibility tensor also includes STFTs of the microcurrent—microcurrent TTGFs. The STFTs of the equilibrium TTGFs featuring in the susceptibilities, and thus necessary to calculate TRI, can be obtained by equilibrium quantum statistical mechanical means, modeling and simulations, or from experimental data. Two TRI regimes of significant interest for applications that can be realized in spatially inhomogeneous magnetic systems have been identified.

Neutron studies in inhomogeneous magnetic systems

Many substitutional compounds display intrinsic magnetic inhomogeneities associated with the heterogeneous distribution of the magnetic or nonmagnetic ions leading to a complex scenario of magnetic interactions. In particular, in some Ce compounds with strongly correlated electron properties such as the CeNi 1 - x Cu x system, the existence of a cluster-glass state is detected at temperatures above the long-range ferromagnetic order. In this work, we present neutron diffraction studies down to very low temperature ( 50 mK ) performed on E6 at HMI and D20 and D11 at the ILL. These studies confirm the existence of a ferromagnetic structure at very low temperature with a reduced Ce magnetic moment and the existence of a low- q contribution associated with the presence of magnetic clusters. These measurements support the uniqueness of neutron studies in ascertaining the nature of magnetic order, even in nonconventional inhomogeneous situations with competing magnetic interactions.

Theory of spin transfer phenomena in magnetic metals and semiconductors

We propose a general theory of the spin-transfer effects that occur when current flows through inhomogeneous magnetic systems. Our theory does not rest on an appeal to conservation of total spin, can assess whether or not current-induced magnetization precession and switching in a particular geometry will occur coherently, and can estimate the efficacy of spin-transfer when spin–orbit interactions are present. We illustrate our theory by applying it to a toy-model twodimensional-electron-gas ferromagnet with Rashba spin–orbit interactions.

Experimental determination of the nonextensive entropic parameterq

We show how to extract the $q$ parameter from experimental data, considering an inhomogeneous magnetic system composed by many Maxwell-Boltzmann homogeneous parts, which after integration over the whole system recover the Tsallis non-extensivity. Analyzing the cluster distribution of La$_{0.7}$Sr$_{0.3}$MnO$_{3}$ manganite, obtained through scanning tunnelling spectroscopy, we measure the $q$ parameter and predict the bulk magnetization with good accuracy. The connection between the Griffiths phase and non-extensivity is also considered. We conclude that the entropic parameter embodies information about the dynamics, the key role to describe complex systems.

Physical meaning and measurement of the entropic parameter q in an inhomogeneous magnetic systems

In this paper we present a thorough analysis of two systems magnetically inhomogeneous: the manganite La$_{0.7}$Sr$_{0.3}$MnO$_3$/MgO and the amorphous alloy Cu$_{90}$Co$_{10}$. In both cases, the non-extensive statistics yield a faithful description of the magnetic behavior of the systems. In the model proposed here, the inhomogeneous magnetic system is composed by many Maxwell-Boltzmann homogeneous bits and the entropic parameter $q$ is related to the moments of the distribution of the inhomogeneous quantity. From the analysis of Scanning Tunnelling Spectroscopy (STS) images, the $q$ parameter can be directly measured.

Continuous spin-reorientation phase transition in the surface region of an inhomogeneous magnetic film

A continuous spin-reorientation transition from a uniform magnetic state with the in-plane orientation of the moments of all atomic layers to a nonuniform canted state in the surface region is considered. This transition was discovered in experiments on the divergence of magnetic susceptibility in a perpendicular magnetic field at a temperature of about 240 K, which is lower than the Curie point of gadolinium, equal to 292.5 K. These experiments were carried out on an ultrathin iron magnetic film deposited on the (0001) surface of a thin gadolinium film. It is shown that, in the vicinity of the spin-reorientation transition, the thermodynamic potential has a form characteristic of the Landau theory of second-order phase transitions. The orientation angle of the moment of the surface atomic layer with respect to the plane of the film, which is chosen as an order parameter, exhibits anomalous behavior and increases with temperature. Expressions are derived for the magnetic susceptibility of each atomic layer. It is shown that, in the vicinity of the transition, the irregular part of the magnetic susceptibility of each atomic layer exhibits behavior characteristic of the susceptibility in the Landau theory: it is less by a factor of two in the low-symmetry phase and diverges at the transition point. The regular part of the magnetic susceptibility of each atomic layer makes an additional contribution to the asymmetry of the total susceptibility in the vicinity of the transition point; this result follows from the fact that the inhomogeneous magnetic system considered is semi-infinite.

Influence of a uniform current on collective magnetization dynamics in a ferromagnetic metal

We discuss the influence of a uniform current $\stackrel{\ensuremath{\rightarrow}}{j}$ on the magnetization dynamics of a ferromagnetic metal. We find that the magnon energy $\ensuremath{\epsilon}(\stackrel{\ensuremath{\rightarrow}}{q})$ has a current-induced contribution proportional to $\stackrel{\ensuremath{\rightarrow}}{q}\ensuremath{\cdot}\mathcal{J}\ensuremath{\rightarrow},$ where $\mathcal{J}\ensuremath{\rightarrow}$ is the spin current, and predict that collective dynamics will be more strongly damped at finite $\stackrel{\ensuremath{\rightarrow}}{j}.$ We obtain similar results for models with and without local moment participation in the magnetic order. For transition metal ferromagnets, we estimate that the uniform magnetic state will be destabilized for $j\ensuremath{\gtrsim}{10}^{9}{\mathrm{A}\mathrm{}\mathrm{cm}}^{\ensuremath{-}2}.$ We discuss the relationship of this effect to the spin-torque effects that alter magnetization dynamics in inhomogeneous magnetic systems.

A microscopic mechanism for rejuvenation and memory effects in spin glasses

Aging in spin glasses (and in some other systems) reveals astonishing effects of `rejuvenation and memory' upon temperature changes. In this paper, we propose microscopic mechanisms (at the scale of spin-spin interactions) which can be at the origin of such phenomena. Firstly, we recall that, in a frustrated system, the effective average interaction between two spins may take different values (possibly with opposite signs) at different temperatures. We give simple examples of such situations, which we compute exactly. Such mechanisms can explain why new ordering processes (rejuvenation) seem to take place in spin glasses when the temperature is lowered. Secondly, we emphasize the fact that inhomogeneous interactions do naturally lead to a wide distribution of relaxation times for thermally activated flips. `Memory spots' spontaneously appear, in the sense that the flipping time of some spin clusters becomes extremely long when the temperature is decreased. Such memory spots are capable of keeping the memory of previous ordering at a higher temperature while new ordering processes occur at a lower temperature. After a qualitative discussion of these mechanisms, we show in the numerical simulation of a simplified example that this may indeed work. Our conclusion is that certain chaos-like phenomena may show up spontaneously in any frustrated and inhomogeneous magnetic system, without impeding the occurrence of memory effects.

About the local Curie temperature distribution of Invar alloys

Strongly disordered ferromagnetic alloys which exhibit magnetic inhomogeneities are described in the frame of a generalized Ginzburg-Landau theory by averaging the Ginzburg-Landau energy of a subsystem with a definite Curie temperature over the Curie temperature of all subsystems of the inhomogeneous magnetic system. It is shown that this leads to the rough scaling of a smooth phase transition. Furthermore the distribution function of the Curie temperature is derived from the experimental data of the specific heat, the volume thermal expansion coefficient and the compressibility.

Designing particular magnetic field profiles by computer

A design of specific magnetic-field profiles was performed by a power series of the general field formulas up to the 11th term. The application of this method, instead of the usual integration, was required to increase the speed of the calculation by a factor of a few hundreds and to decrease the memory capacity needed permanently for the stored data. For given magnetic parameters, the program has a self-consistent procedure to gain the prescribed homogeneity taking into account the layer distribution. The operation can be extended to the planning of strongly inhomogeneous magnetic systems as well. The elaborated method is also applicable to conventional, superconducting, multifilamentary, and high-T/sub c/ magnets.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Computer designed superconducting magnets

The designing of specific magnetic field profiles is performed by a power series of the general field formula up to 11th term. This method instead of the usual integration increased the speed of the calculation by a factor of few hundreds. At given magnet parameters the program has a self-consistent procedure to gain the prescribed homogeneity taking into account the layer distribution. The operation can be extended for the planning of strongly inhomogeneous magnetic systems too. The elaborated way is applicable to the conventional, superconducting and multifilamentary magnets as well.

Reaction field approximation for inhomogeneous ferromagnets

AbstractThe reaction field approximation method for inhomogeneous magnetic systems is extended. The Curie temperature of inhomogeneous samples is calculated on the basis of the perturbation theory. As a result the shift of the Curie temperature is obtained with respect to the value of the Curie temperature for an effective crystalline structure. A comparison of the results with those following from other methods shows that the accuracy of the presented method is the same as the cluster method and is much better than the molecular field approximation.

Surfaces and interfaces of lattice models: Mean-field theory as an area-preserving map

Mean-field theory for one-dimensionally inhomogeneous magnetic systems is formulated as an area-preserving map. The map and its associated boundary conditions are derived for nearest-neighbor Ising interactions. The corresponding continuum theory is also constructed. These mappings are two dimensional. Their phase portraits are exhibited and applied to the study of a representative set of surface and interface phenomena, including interfacial structure, surface phase transitions, wetting, prewetting, and layering. The methods developed lend themselves to easy and physical visualization of the types of solutions which the mean-field theory can have, even in rather complex situations. They also make explicit the fundamental differences between continuum mean-field theory (which is integrable) and discrete mean-field theory (which is not).