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 × 10 ⁶ 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.