Demagnetizing factors of the rectangular rod and cylinder magnetized uniformly along the long axis are found to be expressed by the simple and approximate expressions 1/(2n+1) and 1/[2(2n/(π)1/2) +1], respectively, where n is the dimensional ratio. The error which is the difference of the value evaluated by 1/(2n+1) from the value evaluated by the exact expression of the demagnetizing factor is less than 5.48% for the rectangular rod with n<70. The error of the value evaluated by the expression 1/[2(2n/(π)1/2) +1] for the cylinder is also found to be less than 4.25% for n<100.

The magnetization curling mode for an infinite cylinder with a uniaxial magnetocrystalline anisotropy is considered. The angular dependence of the nucleation field HN and the coercive force Hc are estimated as a function of the radius, the magnetocrystalline anisotropy, and the inclination of the axis to the applied field. It is assumed that only curling and rotation in unison occur, and that the discontinuous jump by the curling mode brings the magnetization to the lower energy state given by Stoner–Wohlfarth. With this assumption, the rotational hysteresis loss Wr and integral Rh are evaluated both for an aligned and for a random assembly of infinite cylinders.

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In order to see the variation of the magnetization state in a finite cylinder, it is assumed that the magnetization changes its direction by the magnetization curling mode in which θ is given by θ=λ(z/L)2+ν, where θ is the deviation of the magnetization in the cylinder from the z axis which is the axis of the cylinder, L is half of the cylinder length, and λ and ν are the coefficients which specify the magnetization state. Finding λ and ν which minimize the total energy ε of the cylinder, we obtain the hysteresis loops and the coercive force. The coercive force obtained in this work agrees well with the experimental results for a cylinder 2.5 μm long and a diameter from about 50 to about 130 nm. It is also found that the configurations can be stable in which the magnetizations are not along the z axis, and the hysteresis loops are not rectangular, even though an applied field is along the z axis.

Articles you may be interested inReduction of grain size and intergrain interaction in Fe Pt ∕ Pt ∕ Cr trilayer thin films for perpendicular magnetic recording J. Appl. Phys. 99, 08E709 (2006); 10.1063/1.2171941BaM/Pt multilayered films with fine grains and large perpendicular magnetic anisotropy for high density recording media Co ferrite films with excellent perpendicular magnetic anisotropy and high coercivity deposited at low temperatureThe magnetization-curling mode in a columnar-structure film with perpendicular magnetization is studied on the assumption that the film is a two-dimensional array of cylinders. The angular dependence of the nucleation field H N is calculated by the Ritz method and compared with that for the coherent-rotation mode. It is found that the magnetization rotates in the curling mode for a large reduced radius S and in the coherent-rotation mode for a small S. The angular dependence of H N is different from that in an infinite cylinder. If S is large, the magnetization rotates in the curling mode for any value of 0 , where 0 is the angle between the applied field and the cylinder axis. When S is medium, the magnetization rotates in the coherent-rotation mode for a small 0 and in the curling mode for a large 0 .