Curved Domain Walls Research Articles

Dynamics of magnetic domains and walls

General equations are proposed to describe the simultaneous rotations of the magnetization vectors and the displacements of curved domain walls in one pair of magnetostatically coupled magnetic films separated by a variable distance. Leakage-field energy is written in the ‘‘transmission-line’’ approximation. The effects of dissipation and the constraint of flux continuity across a domain wall are handled by d’Alembert’s virtual work principle. The result is a set of coupled equations of the following kinds: (1) dynamic torque balance at each point inside a domain, (2) wall-domain constraint due to flux continuity, (3) boundary condition on domain magnetization which depends on instantaneous wall positions, and (4) wall velocity. Within certain limitations these equations apply to the core of an inductive magnetic recording head.

Temperature dependence of domain structure in natural magnetite and its significance for multi-domain TRM models

Abstract Magnetic domain structures of natural magnetite grains were observed as a function of temperature with the Bitter method. The domain walls were completely rearranged during heating from 20 to 90°C. Parallel 180° domain walls at 20°C changed to complicated curved domain walls of the stress-controlled type when heated in zero field to 90°C. These changes in domain structure could be explained by the faster decrease of the magnetocrystalline anisotropy energy with increasing temperature compared with the slower decrease in the magnetoelastic energy term. Temperature-dependent domain wall changes in magnetite were postulated previously by measurements of partial thermoremanent magnetization. A synthesis of microscopic domain observations, macroscopic magnetization measurements and multidomain theories is attempted. Published data on the acquisition and decay of partial thermal remanent magnetization are interpreted in terms of the continuous rearrangement of domain structure with changing temperature.

The domain structure of synthetic stoichiometric TM10–TM75 and Al-, Mg-, Mn- and V-doped TM62 titanomagnetites

The existence of domain structure has been questioned for titanomagnetites of typical oceanic basalt composition owing to the unusual temperature dependence of their susceptibility, resembling that of spin glasses. In order to make a direct test of domain structure, a series of stoichiometric titanomagnetites between magnetite (TM0) and 75% ulvöspinel content (TM75) as well as a titanomagnetite of typical oceanic basalt composition have been synthesised using the double-sintering technique at 1300°C, in controlled atmospheres. The purity, stoichiometry and homogeneity of these materials were tested by optical, X-ray and microprobe studies as well as by magnetic measurements. Domain structures were observed using the Bitter-pattern technique after ionic polishing to produce stress-free surface of the bulk material. The optimum time required for ionic polishing was found to increase with the ulvöspinel content and to be correlated with the magnetostrictive constant θ. Magnetite showed a domain configuration which is also typical for nickel (mostly lamella-shaped domains, pine-tree-shaped closure domains, high domain wall mobility in small external fields, straight domain walls). The tendency to form lamella-shaped domains is present up to TM75 (which has a Curie temperature of only 40°C), but with an increasing tendency to form curved domain walls and to have fewer and also differently shaped closure domains. This is demonstrated in a series of photographs. The results constitute unequivocal evidence for the existence of a domain structure in the classical sense in a broad range of stoichiometric pure and doped (Al, Mg, Mn, V) titanomagnetites.

Domain structure and magnetization processes in permalloy propagation elements

A review of domain structures and magnetization processes in permalloy overlays is given, together with some new results. The simplest domain structure for a given element consists of a loop of magnetic flux, but in elements with irregular geometry the circulating flux is not constant. More complex structures arise when an element contains internal closure domains. In-plane anisotropy in permalloy affects the distribution of closure domains but with decreasing bar width the influence of anisotropy is reduced. Reversible wall motion in weak fields gives way to hysteresis effects when the applied field exceeds a certain level, H s. In particular magnetization buckling may occur. Some details of buckling in asymmetric chevrons and half-discs are given and compared with the behaviour in an I-bar. The proximity of a bubble medium containing stripe domains is shown to reduce considerably the applied fields needed for buckling in overlay components. Following saturation, changes in the demagnetized state are usually apparent. On a simple level, the spin structure and polarity of Bloch walls is altered. More noticeably the wall pattern itself can change when closure domains are created or annihilated in pairs. The significance of these fluctuations for bubble propagation is assessed by considering the intrinsic stray field profile of a Bloch wall segment. A simple wall model is employed. It is demonstrated that a curved domain wall provides a reasonable basis for modelling the field of a magnetized bar up to saturation. Calculated values of H s agree qualitatively with experiment. The external field of the bar is rather insensitive to the exact distribution of free-pole density. Together with the observed complexities of domain behabiour this reaffirms the validity of the continuum approach to modelling.

Pinning of curved domain walls by randomly distributed lattice defects

The coercive field of randomly distributed defects is derived for a rigid domain wall and for the model of a one- or two-dimensionally curved wall. The validity of these various pinning models depends on the defect density, the interaction force and on the area and the rigidity of the domain wall

Magnetostatic Energy of Two-Domain Parallelepipeds with Straight and Curved Domain Walls

Recent experimental investigations into the domain structure of ferromagnetic single-crystal platelets of high purity and perfection have yielded significant results.1,2 Thus, it was shown1 that over a limited portion of domain-wall excursion no hysteresis losses are incurred and that the magnetization of the platelet over this region is proportional to the applied field. Since the wall energy is shown to be negligible, the problem reduces to magnetostatic and external field energy considerations. We have therefore calculated the magnetostatic energy of a general rectangular parallelepiped as a function of the position and radius of curvature of a 180° domain wall dividing the platelet into two homogeneously magnetized domains. From this the demagnetizing factors, the magnetizing curve and the susceptibility of the platelet were obtained. The demagnetizing factors are compared with those of the general ellipsoid3 and limiting formulas are derived. The calculation shows the importance of the demagnetizing fields for the reversible portion of the magnetizing curve and introduces for the first time the demagnetizing energy of curved domain walls.

Curvature of domain walls

An experiment was performed whereby domain walls were forced to bulge under the influence of an applied easy-axis field <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</tex> . The region where the domain wall is bent appears to be approximately circular. To relate the radius of such a curved domain wall to theory, a model was chosen that takes into account magnetostatic, anisotropy, and exchange energy. The assumption was made that anisotropy and exchange energy, as well as the magnetostatic contribution due to the local magnetization distribution of a domain wall, may be summarized in a wall energy term. The energy of the entire system has been calculated under the constraint that the domain wall should be circular and that it is inscribed tangentially into a triangle. Minimizing the total energy with respect to the radius of curvature <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</tex> , the result can be expressed approximately by <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A \propto (H - H_{c})^{-1}</tex> where H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> is the coercive force. This result fits the model of a membrane under pressure.

Curvature of domain walls

An experiment was performed whereby domain walls were forced to bulge under the influence of an applied easy-axis field H . The region where the domain wall is bent appears to be approximately circular. To relate the radius of such a curved domain wall to theory, a model was chosen that takes into account magnetostatic, anisotropy, and exchange energy. The assumption was made that anisotropy and exchange energy, as well as the magnetostatic contribution due to the local magnetization distribution of a domain wall, may be summarized in a wall energy term. The energy of the entire system has been calculated under the constraint that the domain wall should be circular and that it is inscribed tangentially into a triangle. Minimizing the total energy with respect to the radius of curvature A , the result can be expressed approximately by A \propto (H - H_{c})^{-1} where H c is the coercive force. This result fits the model of a membrane under pressure.