H. Shima

Eigenfrequencies of vortex state excitations in magnetic submicron-size disks

We have theoretically and numerically studied the dynamic properties of the vortex magnetic state in soft submicron ferromagnetic dots with variable thickness and diameter. To describe the vortex translation mode eigenfrequencies, we applied the equation of motion for the vortex collective coordinates. We calculated the vortex restoring force with an explicit account of the magnetostatic interaction on the bases of the “rigid” vortex and two-vortices “side charges free” models. The latter model well explains the results of our micromagnetic numerical calculations. The translation mode eigenfrequency is inversely proportional to the vortex static initial susceptibility and lies in GHz range for submicron in-plane dot sizes.

Field evolution of magnetic vortex state in ferromagnetic disks

The evolution of a magnetic “vortex” state in submicron ferromagnetic disks has been studied as functions of disk diameter and thickness. The vortex core displacement in the applied magnetic field was calculated by minimizing the total magnetic energy consisting of the magnetostatic, exchange, and Zeeman energies. A simple analytical expression for the initial magnetic susceptibility is deduced. The initial susceptibility increases with increasing disk diameter and decreasing thickness. The calculations agree well with the experimental data obtained for the 60 nm thick permalloy disk arrays with a variable diameter from 0.2 to 0.8 μm.

Shape effect on magnetization reversal in chains of interacting ferromagnetic elements

The magnetization reversal in the chains of submicron square- and disk-shaped Permalloy dots with lateral size of 800 nm, thickness of 50 nm and variable inter dot distance was investigated by using the magneto-optical Kerr effect technique, magnetic force microscopy and micromagnetic modeling. We have found that the particle shape strongly affects the characteristic switching fields of well-separated dots, and has almost no influence on strength of inter dot interaction in chains of magnetostatically coupled elements.

Temperature dependence of magnetocrystalline anisotropy constants in the single variant state of L10-type FePt bulk single crystal

The temperature dependence of magnetocrystalline anisotropy constants and the saturation magnetization in a single variant state have been investigated for L10-type Fe60Pt40 bulk single crystal prepared under compressive stress. The uniaxial magnetocrystalline anisotropy constant Ku evaluated from the magnetization curve is 6.9×107ergcm−3 at 5K. The values of the second- and fourth-order magnetocrystalline anisotropy constants K1 and K2 at 5K determined by the Sucksmith–Thompson method are 7.4 and 0.13×107ergcm−3, respectively. Both the values of Ku and K1 decrease with increasing temperature T, while K2 is almost independent of T. The difference between the power law of the Callen and Callen model is described by the dimensionality and the thermal variation of the axial ratio c∕a due to the thermal expansion.

In-plane and out-of-plane uniaxial anisotropies in rectangular arrays of circular dots studied by ferromagnetic resonance

Ferromagnetic resonance at 9.2 GHz (X band) was used to characterize the uniaxial magnetic anisotropies in rectangular arrays of submicron circular Ni dots. The in-plane anisotropy, originated from interdot interactions in the rectangular lattice, and the perpendicular anisotropy, due to individual dot shape and magnetostriction, were explored. For in-plane dependencies of the resonance field (Hr), the main resonance mode angular dependence was well described by the standard Kittel formula. As the interdot distances decreased from 800 to 50 nm, the in-plane uniaxial anisotropy field changed from 5 to 130 Oe, in reasonable agreement with calculations. Simultaneously, the position of perpendicular Hr increased from 6.38 to 6.83 kOe, also following Kittel’s formula.

Pinning of magnetic vortices in microfabricated permalloy dot arrays

Temperature dependent magnetic properties of vortices trapped in a lithographically patterned Permalloy disk were examined. A large residual magnetization at 5 K was observed in hysteresis curves unlike theoretical prediction. The residual magnetization, coercive field, and initial susceptibility were found to be dependent on temperature. Escaping from the pinning potential was facilitated by the increase of temperature, and the pinning temperature Tpin was 9.6 K. The vortex is effectively pinned at the pinning potential when T<Tpin. This physical picture is well supported by the temperature variations of ac susceptibility for the biased dc field. The energy barrier is probably originated from defects such as the edge and surface roughnesses, and irregular grain boundaries in the disk.

Large magnetocrystalline anisotropy energy of L10-type Co100−xPtx bulk single crystals prepared under compressive stress

L10-type Co100−xPtx single crystals in a single variant state were prepared by ordering under a compressive stress in order to determine accurately the uniaxial magnetocrystalline anisotropy constant KU. Both the lattice constants a and c increase with increasing Pt concentration, whereas the axial ratio c∕a becomes minimum at x=50. The value of KU directly determined at 298K exhibits a maximum value of 4.5×107ergcm−3 for 50at.% Pt. The second- and fourth-order anisotropy constants K1 and K2 determined by the Sucksmith–Thompson method become 4.1 and 0.6×107ergcm−3, respectively. The value of K1+K2 corresponding to the magnetocrystalline energy difference between the c and a axes becomes maximum at x=50.

Magnetization reversal in magnetostatically coupled dot arrays.

The submicron permalloy dots with variable diameter and interdot distance were microfabricated into a rectangular lattice by means of e-beam lithography and lift-off techniques. The hysteresis loops exhibit characteristic magnetization reversal accompanied by “nucleation” and “annihilation” of magnetic vortices inside the dots. The magnetic response of the samples with well-separated elements is isotropic in the plane. The arrays with a small interdot distance show magnetic anisotropy with the easy axis along the shortest period in the array. This anisotropy is originated from the interdot magnetostatic interaction. In the closely packed (when interdot distance is smaller than dot radius) arrays so that d/R<1, the magnetostatic interaction decreases the vortex nucleation and annihilation fields, and increases the initial susceptibility.

Magnetostatic interdot coupling in arrays of circular ferromagnetic dots

The effect of interdot magnetostatic coupling on magnetization reversal due to nucleation, displacement and annihilation of magnetic vortices in arrays of circular permalloy dots has been studied experimentally. The magnetostatic coupling leads to decrease in both the vortex nucleation and annihilation fields, and an increase in susceptibility. The experimental data is interpreted using micromagnetic numerical calculations.