Model for domain wall avalanches in ferromagnetic thin films

The Barkhausen jumps or avalanches in magnetic domain-walls motion between successive pinned configurations, due the competition among magnetic external driving force and substrum quenched disorder, appear in bulk materials and thin films. We introduce a model based in rules for the domain wall evolution of ferromagnetic media with exchange or short-range interactions, that include disorder and driving force effects. We simulate in 2-dimensions with Monte Carlo dynamics, calculate numerically distributions of sizes and durations of the jumps and find power-law critical behavior. The avalanche-size exponent is in excellent agreement with experimental results for thin films and is close to predictions of the other models, such as like random-field and random-bond disorder, or functional renormalization group. The model allows us to review current issues in the study of avalanches motion of the magnetic domain walls in thin films with ferromagnetic interactions and opens a new approach to describe these materials with dipolar or long-range interactions.     

Low field wall mobility in thin conducting ferromagnetic films

The factors which may determine the low field domain wall mobility in thin ferromagnetic films of nickel iron are reconsidered in the light of recent experimental and theoretical work which has been published.     

On the domain structure of thin ferromagnetic films

The energy of Bloch walls is calculated for very thin ferromagnetic films with respect to the demagnetizing energy of a Bloch wall. A model of the stability of the domain structure in thin films is proposed.Part of this paper was delivered at the conference of solid state physics in Sopoty (Poland) November 5–11th, 1956.     

Measurements of nanoscale domain wall flexing in a ferromagnetic thin film

We use the high spatial sensitivity of the anomalous Hall effect in the ferromagnetic semiconductor Ga(1-x)Mn(x)As, combined with the magneto-optical Kerr effect, to probe the nanoscale elastic flexing behavior of a single magnetic domain wall in a ferromagnetic thin film. Our technique allows position sensitive characterization of the pinning site density, which we estimate to be ～10(14) cm(-3). Analysis of single site depinning events and their temperature dependence yields estimates of pinning site forces (10 pN range) as well as the thermal deactivation energy. Our data provide evidence for a much higher intrinsic domain wall mobility for flexing than previously observed in optically probed μm scale measurements.     

Asymmetry in the dynamics of domain walls in thin exchange-coupled ferromagnetic films

The kinetics of remagnetization after magnetic field switching was studied by the magneto-optic visualization technique in the bilayer hybrid structure composed of exchange-coupled FeNi and FeMn films. It was observed that not only the static but the dynamic characteristics of remagnetization as well depend on the polarity of a field applied along the direction of easy magnetization. The rate of the process was found to be exponentially dependent on the field strength in both directions, but the rate varied by factors of 10 upon inversion of the field. It was shown that this difference is the consequence of variation of both the time of domains nucleation and the velocity of domain walls motion.     

Magnetooptic setup for investigating the dynamic properties of domain walls in thin ferromagnetic films

A magnetooptic Kerr setup is designed for investigating the dynamic properties of domain walls in thin ferromagnetic films subjected to an external magnetic field in the temperature range 20–150°C. With this setup, the method of interrupted magnetization is implemented and the magnetic (domain) structure is visualized based on the meridional Kerr effect. The domain structure is displayed on a PC monitor using a Nikon DXM 1200 high-resolution digital video camera. A dedicated software makes it possible to automatize measurements and data processing.     

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.     

Dipolar interactions in ferromagnetic thin films

We introduce a discrete model describing the motion of a zigzag domain wall in a disordered ferromagnet with in-plane magnetization, driven by an external magnetic field. The main ingredients are dipolar interactions and anisotropy. We investigate the dynamic hysteresis by analyzing the effects of external field frequency on the coercive field by Monte Carlo simulations. Our results are in good agreement with experiments on Fe/GaAs films reported in literature, and we conclude that dynamic hysteresis in this case can be explained by a single propagating domain wall model without invoking domain nucleation.     

Nernst-Ettingshausen effect in thin ferromagnetic films

A new thermomagnetic effect in a ferromagnetic film is discussed. When a temperature gradient is established along the x axis in a ferromagnetic sample, a transverse electric field arises in the same plane as the spontaneous-magnetization vector (in the case H = 0, where H is the external magnetic field). A phenomenological expression is given for the transverse electric field as a function of the square of the magnetization. Theory is given for the Nernst-Ettingshausen effect due to the spin-orbit interaction in a ferromagnetic film in the effectivemass approximation, and the Nernst-Ettingshausen constant is derived. The calculation is carried out by the density-matrix method derived by Kohn and Luttinger.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 11, pp. 28–32, November, 1969.     

Magnetic anisotropy in thin ferromagnetic films

The magnetic properties of thin ferromagnetic films are studied taking into account the magnetic anisotropy term in the Hamiltonian. In the second approximation equations are obtained for the magnetization of the monatomic layers parallel to the surface of the thin film. From these equations one obtains the Curie temperature, which depends on the thickness of the thin film and the ratio a between the anisotropy constant and the exchange energy between two neighbours. A value can be chosen for such that the thin film becomes ferromagnetic only for a thickness greater than a definite value and in this manner the theoretical results can be fitted to the experimental data. The situation in cobalt thin films is dealt with in particular.

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The author extends his thanks to the research workers of CIFA 1 as well as to Dr. L. Valenta for information on the same subject.     

Magnons in surface-rearranged ferromagnetic thin films

By a Green function approach, spin waves in a surface-rearranged ferromagnetic thin film are derived both analytically and numerically. Heisenberg exchange, bulk and surface anisotropy between nearest neighbors and external magnetic field are taken into account for an sc film with {001} surfaces. Because of the anisotropies, the dynamical matrix defined from the Green function equations is not Hermitian, so we generalize the Bogoliubov canonical transformation to derive the spin wave spectrum. The spin waves propagating inside the film result from the superposition of two sine or hyperbolic sine waves. The amplitude and polarization of spin waves are shown to be quite sensitive to the details of the surface rearrangements, whereas spin wave energies are not so sensitive to such rerrangements, except when soft modes occur in the unrearranged configuration. In that case, we show that when the surface rearrangement is taken into account, soft modes disappear in the spin wave spectrum.     

Experimental investigation of the magnetic structure of domain walls in thin ferromagnetic films

The structure of domain walls in thin magnetic films has been studied by the Lorentz method using electron microscopy. The possible existence of the coinciding and opposite directions of rotation of the magnetization vector in Néel domain walls has been proved experimentally. The domain walls separating 90° domains have been found in single-crystal magnetic films. These walls consist of domains with a considerably smaller area than 90° domains.     

Evidence of domain wall scattering in thin films of granular CoFe-AgCu

Thin films of the giant magnetoresistive granular CoFe-AgCu system prepared by rf sputtering displayed a great variety of domain-like microstructures with a net out-of-plane component of the magnetization for ferromagnetic volume concentrations above about 0.25. Therefore, magnetic percolation takes place at ferromagnetic concentrations much lower than the physical percolation threshold. The out-of-plane structure of the as-deposited samples in magnetic virgin state consisted of a distribution of both quasi-circular domains and short stripes depending on the ferromagnetic content. Furthermore, these samples present high metastability and a variety of remanent in-plane and out-of-plane microstructures can be achieved as a function of the magnetic history. Besides, the evolution of the magnetic microstructure yields strong training effects on magnetotransport properties, due to the extra contribution of the electron scattering at the domain walls. All in all, the observed behavior is the result of a subtle correlation between perpendicular anisotropy produced by residual stresses, exchange interparticle interactions due to CoFe alloyed in the matrix, and dipolar interactions. Thus, as high structural evolution occurs through annealing, the features of randomly distributed ferromagnetic particles are recovered and, the out-of-plane domain structures and the training effects disappear. Received 30 September 1999     

Loss separation for dynamic hysteresis in ferromagnetic thin films

We develop a theory for dynamic hysteresis in ferromagnetic thin films, on the basis of the phenomenological principle of loss separation. We observe that, remarkably, the theory of loss separation, originally derived for bulk metallic materials, is applicable to disordered magnetic systems under fairly general conditions regardless of the particular damping mechanism. We confirm our theory both by numerical simulations of a driven random-field Ising model, and by reexamining several experimental data reported in the literature on dynamic hysteresis in thin films. All the experiments examined and the simulations find a natural interpretation in terms of loss separation. The power losses' dependence on the driving field rate predicted by our theory fits satisfactorily all the data in the entire frequency range, thus reconciling the apparent lack of universality observed in different materials.     

X-ray detected ferromagnetic resonance in thin films

We discuss the physical content of X-ray Detected Magnetic Resonance (XDMR), i.e. a novel spectroscopy which uses XMCD to probe the resonant precession of the local magnetization in a strong microwave pump field. We focus on the simplest case of a steady-state precession of elemental moments in the non-linear regime of angular foldover. Like XMCD, XDMR is element and edge selective and could become a unique tool to investigate how precessional dynamics can locally affect the spin and orbital magnetization of p- or d-projected DOS. This should be possible only in the limit where there is no overdamping due to ultrafast orbit-lattice relaxation.     

Giant Skyrmions stabilized by dipole-dipole interactions in thin ferromagnetic films

Motivated by a recent magnetization reversal experiment on a TbFeCo thin film, we study a topological excitation in the anisotropic nonlinear sigma model together with the Zeeman and magnetic dipole-dipole interactions. Dipole-dipole interactions turn a ferromagnet into a frustrated spin system, which allows a nontrivial spin texture such as a giant Skyrmion. We derive an analytic formula for the Skyrmion radius. The radius is controllable by the external magnetic field. It is intriguing that a Skyrmion may have already been observed as a magnetic domain. A salient feature is that a single Skyrmion can be created or destroyed experimentally. An analysis is made also on Skyrmions in chiral magnets.     

Localized ferromagnetic resonance in inhomogeneous thin films

The effect of sample inhomogeneity on the ferromagnetic resonance linewidth is determined by diagonalization of a spin wave Hamiltonian for ferromagnetic thin films with inhomogeneities spanning a wide range of characteristic length scales. A model inhomogeneity is used that consists of size D grains and an anisotropy field H(p) that varies randomly from grain to grain in a film with thickness d and magnetization M(s). The resulting linewidth agrees well with the two-magnon model for small inhomogeneity, H(p)DpiM(s)d, the precession becomes localized and the spectrum approaches that of local precession on independent grains.     

Enhanced gilbert damping in thin ferromagnetic films

The precession of the magnetization of a ferromagnet is shown to transfer spins into adjacent normal metal layers. This "pumping" of spins slows down the precession corresponding to an enhanced Gilbert damping constant in the Landau-Lifshitz equation. The damping is expressed in terms of the scattering matrix of the ferromagnetic layer, which is accessible to model and first-principles calculations. Our estimates for permalloy thin films explain the trends observed in recent experiments.     

Vanishing magnetic interactions in ferromagnetic thin films

We have used element-specific hysteresis measurements, based on the x-ray magnetic circular dichroism technique, to investigate magnetic trilayer structures composed of Fe and Ni layers. Within a critical regime we have discovered a class of structures in which the exchange interaction, the mechanism responsible for the macroscopic magnetism, can become vanishingly small. The experimental observations are supported by first principles theory and are explained as arising from a cancellation of several competing magnetic interactions. Hence, we have discovered a system with a novel exchange interaction between magnetic layers in direct contact that replaces the conventional exchange interaction in ferromagnets.     

Surface spin waves in ferromagnetic thin films

Surface spin-wave modes are calculated for (100) surface of simple cubic structure. An isotropic part as well as an anisotropic part are introduced in the spin Hamiltonian. The anisotropic factor is allowed to vary on the first two surface layers. Dispersion curves are derived by a Green function formalism.The authors are indebted to Dr A. P. Legrand for his help in numerical calculations and to Dr J. Korringa for his continuous encouragement and suggestions.