Double hysteresis loops in ferromagnetic crystals

Abstract

2014 A single domain with mixed magnetocrystalline and uniaxial anisotropies can show a magnetization curve composed of two asymmetric loops connected by a section over which the magnetization is reversible. The irreversible process starts at acritical field. The double loop could be a possible explanation for the mechanism of magnetization in materials with contricted loops as Perminvars. LE JOURNAL DE PHYSIQUE ET LE RADIUM TOME 20, FEVRIER-MARS 1959, Single ferromagnetic domains of cubic structure may show double hysteresis loops [1, 2]. The transition of the ordinary hysteresis loop into the double loop depens on : 1° the magnitude of the magnetic uniaxial anisotropy and its direction with respect to that of the magnetic field and to that of the crystallographics axes ; 20 the ratio of the constants of uniaxial anisotropy and magnetocrystalline anisotropy. The magnetization in the direction of the magnetic field, I, is obtained by minimising the free energy of the crystal. For a prolate spheroidal domain whose polar axis lies along the [100] direction, the values of 1 are given by the following expressions : for a magnetic field, H, in a [001] direct ion. where Ii is the magnetocrystalline constant. Ta is the spontaneous magnetization and Na, Nb are the demagnetization coefficients along the polar and equatorial axes. A rectangular magnetization loop can be derived from these relations for a positive K. The shape of this loop changes with changing value of the factor F. For F = 0.5 the loop becomes -double. In case of a negative K, the magnetization loop is ordinary and its coercive force is equal to zero for F == 0.5. When the magnetic field lies along the polar axis of the domain, the magnetization loop is rectangular for .K > 0 and its coercive force increases with increasing factor F. Two double hysteresis loops of a crystal with a positive K are illustrated in figure 1 for F 0.5 and F =1.