Calculation of hysteresis loops in face-centered cubic thin films

A total energy equation for a single-crystalline face-centered cubic thin film with its close-packed (111) plane parallel to the film plane is used to calculate in-plane and out-of-plane hysteresis loops at various values of the cubic magnetocrystalline anisotropy constant (K1). In-plane loops show that the easy and hard axes are the <112> and <110> directions, respectively, and that the coercivities, which are nearly independent of the sign of K1, are quite low over the K1 values due to the small variation of the magnetocrystalline anisotropy energy during the field sweep. The out-of-plane loops are similarly shaped to those of typical thin films, except for the appearance of a small hysteresis loop near the origin, which is attributed to an irreversible magnetization jump from one easy axis to another in the (111) plane. The magnetic parameters such as K1 are estimated by comparing the theoretical results for in-plane and out-of-plane hysteresis loops with the experimental results measured for an epitaxial Co thin film. The value of K1 is estimated to be − 1.2 × 106 erg/cm3, which is significantly higher than that of − 6×105 erg/cm3 for bulk Co, but is in good agreement with the values of − 1.3 to − 1.6 × 106 erg/cm3 reported for Co thin films.