Uniaxial Thin Films Research Articles

Time-Dependent Landau-Ginzburg Modelling of Magnetic Inhomogeneities and Spiral Domain Structures in Thin Films

ABSTRACTA Landau-Ginzburg model for a uniaxial ferromagnetic thin film is presented which includes inhomogeneities due to nearest neighbor exchange interactions. The role of external magnetic fields is studied in the determination of exact symmetries of the equation of state. Spiral domain structures allowed by symmetry considerations as exact solutions at the critical and tricritical points have recently been found experimentally in epitaxially grown single-crystal garnet ferrite films. These experiments are discussed from the point of view of our model.

The Influence of Next‐Nearest‐Neighbour Exchange Coupling on the Spin‐Wave Resonance Spectrum in Uniaxial Ferromagnetic Thin Films

AbstractThe spin‐wave resonance spectrum is calculated for a uniaxial ferromagnetic thin film with both' nearest‐neighbour and next‐nearest‐neighbour exchange coupling. The profiles of the resonance modes, the positions of the absorption lines, and their intensities are analysed for various values of the nnn coupling parameter. It is found that the spectrum is strongly affected by the nnn coupling, especially by the coupling of antiferromagnetic type.

Spin‐Wave Spectrum in Uniaxial Ferromagnetic Thin Films with Nearest‐Neighbour and Next‐Nearest‐Neighbour Exchange Couplings

AbstractThe standing spin‐wave spectrum is analysed for the uniaxial ferromagnetic thin film with nearest‐neighbour and next‐nearest‐neighbour exchange interactions. The boundary conditions are described in terms of the uniaxial surface anisotropy. It is found that the nnn exchange interactions give rise to new types of bulk and surface spin‐wave modes. The properties of the new modes are discussed in their dependence on both, nnn coupling and surface anisotropy parameters.

A one-dimensional analysis of magnetization ripple in uniaxial thin films with perpendicular anisotropy

Micromagnetic ripple theory is developed for uniaxial thin films with the easy axis of the magnetization perpendicular to the film plane. Assuming a one-dimensional variation of the magnetization, which is connected to variation of local anisotropy, in the direction of the film thickness, a general equation describing the out-of-plane ripple is deduced from the calculus of variation. Some features of the magnetization dispersion are discussed. The results of the theory show that the wavelength of the periodic oscillation of the magnetization is very short in comparison with the film thickness, and that the root-mean-square (rms) value of the out-of-plane ripple is dependent on the local anisotropy variation.

Characterization of a very thin uniaxial film on a nonabsorbing substrate by multiple wavelength ellipsometry: Palmitic acid on water*

At compact monolayer coverage the anisotropic rodlike molecules of palmitic acid, aligned parallel to each other and perpendicular to the monolayer film, are insensitive to wavelength dispersion relative to a water substrate. The relative absence of dispersion of the monolayer film makes it possible to obtain sufficient data to characterize the three unknowns of palmitic acid: the real refractive indices parallel and perpendicular to the plane of the film and the film thickness. Other nonabsorbing thin-film–substrate systems should lend themselves to similar analysis (where the dispersion of the film is relatively less than that of the substrate); particularly since automated, wavelength-tracking ellipsometers are coming into greater use.

New method to determine the domain wall energy in thin uniaxial films with perpendicular easy axis and large saturation magnetization

The surface energy density, γ, of domain walls in thin uniaxial films with perpendicular easy axis is usually found either by measurements of the domain pattern period of the stripe domain pattern or by determination of the bubble collapse field and diameter. However, when the saturation magnetization is large, the widths of stripe domains and bubbles become smaller than the minimum optical resolution, and optical observation becomes impossible. The method proposed in this paper is based on measurements of the susceptibility S = d ( M/M s)/d( H a/4π M s) of the stripe pattern at M = 0. Optical observations are avoided. The only additional important quantities are the saturation magnetization M s and the film thickness. The method has been successfully applied to MnBi films ( M s = 625 G). The determination of γ in this material yields γ = (15 ± 1) erg/cm 2.

Ellipsometry of anisotropic thin films

The reflection properties of a uniaxial thin film on an isotropic substrate have been calculated. The optic axis of the film is assumed to be parallel to the film surface. The reflection properties are summarized in terms of a reflection matrix suitable for use in the Jones calculus. A method is given for relating the reflection properties of this film-covered surface to the null settings of the polarizer and analyzer of a conventional ellipsometer. Results of calculations for a few specific cases are discussed.

Wall contraction in Bloch wall films

The phenomenon of wall contraction characterized by a peak in the velocity-field relationship and a region of negative differential mobility is observed in uniaxial magnetic thin films of various magnetic properties by careful interrupted-pulse experiments. The observed results agree quite well with the theory for bulk samples when the extensive flux closure of thin film walls is accounted for by a suitable empirical scaling factor.

Cross-tie—Néel domain wall transition in thin magnetic films

A theoretical consideration of the hysteresis change of the domain wall structure in flat uniaxial thin magnetic films under the influence of a magnetic field parallel to the hard axis has been carried out. The theory is based on a cross-tie wall model defined in a more precise manner than that of Middelhoek. The circular Bloch line shift as a function of a magnetic field and estimates for the critical fields of both the direct “cross-tie Néel” wall transition and the inverse transition have been obtained.

1128. Point defect annealing in uniaxial permalloy thin films irradiated with 2 MeV electrons: M Roth and G Cornier, phys stat sol (a), 4 (2), Feb 1971, 519–529.

1128. Point defect annealing in uniaxial permalloy thin films irradiated with 2 MeV electrons: M Roth and G Cornier, phys stat sol (a), 4 (2), Feb 1971, 519–529.

Switching curves of magnetically coupled ferro-ferromagnetic double layer films

The switching curves are studied of a double layer film consisting of two uniaxial ferromagnetic thin films. In this coupled film system the magnetization state is investigated assuming the model of uniform rotation. The coupling between the films is described by a magnetic interface cosine coupling. Numerical results are given for the case of ferromagnetic films with different magnetic parameters coupled together by a ferromagnetic interface cosine coupling.

Point defect annealing in uniaxial permalloy thin films irradiated with 2 MeV electrons

Polycrystalline Ni82-Fe18 films on amorphous quartz substrates have been irradiated with 2 MeV electrons between room temperature and 300 °C. The annealing of the defects thus created has been studied by the variations of the induced anisotropy (i.e. the directional atom pair ordering) produced by this annealing. The experimental results show that the main disappearing process of the point defects is their absorption in the grain boundaries and surfaces, in contrast to the bulk material where the defect clustering seems to be the determinating phenomenon. However divacancy formation, vacancy-interstitial recombination, and small clustering must also be taken into account in thin films below 250 °C. Des couches minces polycristallines de Ni82-Fe18 sur support amorphe ont été irradiées entre la température ambiante et 300 °C avec des électrons de 2 MeV. La guérison des défauts ainsi créés a été étudiée par ses effets sur l'anisotropie magnétique induite, c'est-à-dire par les variations de l'ordre directionnel des paires d'atomes qu'elle produit. On constate que le mode principal de disparition des défauts est la diffusion vers la frontière des grains et non pas la formation d'agglomérats comme dans le matériau massif. Toutefois, il est nécessaire, pour expliquer les résultats expérimentaux obtenus en dessous de 250 °C, de tenir compte de la formation de bilacnes et de petits agglomérats de lacunes et de la recombinaison de lacunes et d'interstitiels.

Quasistatic rotation of the magnetization of thin films

The direction of the mean magnetization during magnetization rotation in uniaxial thin films with a reverse field which increased quasistatically has been investigated. The analysis of the observations shows that several effects happen during the magnetization rotation: reversible influence of nonlinear torques in the free ripple region, blocking, irreversible torques, deblocking, stabilization by the intrinsic demagnetizing field, locking, and partial rotation. At the critical astroid of the single-domain theory, the films do not show any critical effect during the magnetization rotation. The critical effects are given by blocking and locking. These film properties are determined by the structure constant S. Even in the nonblocked-ripple region, the mean magnetization deviates from the direction expected, according to the single-domain theory or the linear-ripple theory. This indicates the existence of nonlinear torques. After passing the blocking curve, the intrinsic demagnetizing field contributes dominantly to the nonlinear torque. This field is responsible for the stabilization of the magnetization.

Reduction of demagnetizing effects under nonuniform hard-axis drive in uniaxial thin films

When subject to a nonuniform transverse field, a thin magnetic film may exhibit an effective anisotropy field of several times H k . It is shown that both using a keeper film and making the elements narrow in their easy-axis direction lowers the demagnetizing fields. A method is explained to compute the magnetization distribution with or without keeper for film elements of finite width. Numerical results for typical memory elements are given.

Astroid plotter for thin magnetic films

The rotational astroid of uniaxial thin films may be obtained from the cross-field loop <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m_{x} , h_{y}</tex> graphically or electronically by assuming Slenczewski's tangent rule. The graphical construction by means of the tangent rule is demonstrated. The derivation of the transformation to obtain the astroid electronically is given, and a comparison is made with astroids obtained graphically as well as those obtained by direct static measurements. An astroid plotter has been constructed using standard analog computer components in conjunction with a Kerr apparatus. The resulting displays give the entire rotational astroid and completely avoid wall switching and blocking phenomena. Examples are shown of applications of the astroid plotter with particular emphasis on obtaining the influence of bit geometry for all orientations of magnetization.

Mathematical models for loss measurements in thin permalloy films with ramp drives

Uniaxial thin Permalloy films are driven with a large amplitude sinusoidal H field in order to approximate a ramp drive. The H field is characterized by rise times which exceed 3 \times 10^{6} Oe/s. Two mathematical models are suggested to represent the loss measurements obtained in a domain wall motion region and in an incoherent rotation region. A normalized loss threshold is determined which characterizes the transition between the two regions. In the slow reversal or wall motion region, the normalized losses are proportional to the square root of α where H = \alpha t . In the relatively fast reversal or incoherent rotation region, the normalized losses are proportional to α. In both cases the inverse switching time is proportional to the coercive force in excess of the static value. Experimental data verify the reasonableness of the mathematical models.

High-Order Anisotropies in Uniaxial Magnetic Films

The coupling of uniaxial ferromagnets whose easy directions are not parallel is studied. It is shown that field-dependent effective high-order anisotropies may be produced, and that as the coupling is weakened increasingly high-order anisotropies will become detectable. These results are applied to uniaxial thin films with anisotropy dispersion. It is shown that treating such films as having complex uniaxial and biaxial anisotropy is somewhat oversimplified.

A New Property of Ferromagnetic‐Antiferromagnetic Coupling

AbstractThree systems exhibiting ferromagnetic‐antiferromagnetic coupling, CoCoO, NiFeNiFeMn, NiFeCr2O3, are studied using uniaxial thin films. A new property of such systems is found, i.e., a concentration of the hysteresis loops as a function of the number of cycles traced (n). This contraction follows a 1/\documentclass{article}\pagestyle{empty}\begin{document}$\sqrt n $\end{document}n law for the first 50 cycles and is related to the rotational hysteresis. This phenomenon is attributed to fluctuations in the ferromagnetic‐antiferromagnetic coupling, which modify the magnetic interactions between differently coupled regions with each reversal.

Demagnetization of Flat Uniaxial Thin Films Under Hard Direction Drive

The demagnetizing fields are derived for all points of flat uniaxial thin films under various drive fields. The derivation is accomplished by breaking up the flat film into a number of sheets in superposition and integrating their individual contributions to the demagnetizing fields. The scheme is self-consistent in that the magnetization results as a consequence of the derivation, and need not be assumed. Further, the accuracy does not depend on the position with respect to the edges, but rather on the number of sheets. The general approach to the problem is discussed briefly and the final equation for a rectangular geometry given. The discussion is concerned with one-dimensional examples, demonstrating the somewhat unexpected form of the demagnetizing fields under various hard axis drive conditions. Single bits as well as continuous films of Permalloy driven by uniform fields and multiple strip lines are treated. The effect of registration on the demagnetization is also discussed.

The effect of magnetic domain structure on Bragg reflection in transmission electron microscopy

Abstract Usual methods of observing magnetic domain walls in transmission electron microscopy all rely on the deflection caused to the electron beam by the Lorentz force. This deflection can also alter the conditions for Bragg reflection of the electrons. In buckled specimens containing bend extinction contours, the position of the contours can be altered. This effect is particularly noticeable in cobalt, where two different types of effects have been observed. In addition to revealing the position of the domain walls when the specimen is in focus, the effect provides an interesting visible demonstration of the magnetostatic potential distribution in uniaxial thin films proposed by Malek and Kamberský (1958).