The energy of 180° domain walls of uniaxial crystals with the different magnetocrystalline anisotropy type

[Display omitted] •The strongest anisotropy in uniaxial crystals belongs to EA and EP MCA types.•The weakest anisotropy belongs to the K1 + K2 = 0 ratio in the EC and coexistence area.•The DW energy of uniaxial crystals should be calculated by five expressions. The main aim of the present work is to analyze the magnetocrystalline anisotropy (MCA) energy function of uniaxial crystals and to derive analytical expressions for the domain wall (DW) energy taking into account two MCA constants. Thus, the article presents a detailed analysis of the magnetocrystalline anisotropy energy function of uniaxial crystals taking into account two MCA constants (K1, K2). The values of the MCA energy extremes and the position of the easy magnetization directions (EMD) and hard magnetization directions (HMD) were determined. The MCA diagram was plotted in “K1”-“K2” coordinates. Six types of MCA have been found for uniaxial crystals. Two of them are simple with one maximum and one minimum of the EA(θ) function, and four are complex with two absolute and one local extreme for each. It is shown that EA(K1, K2) function has the smallest difference between the maximum and minimum values equal to |K1|/4 and the smallest angle between EMD and HMD equal to π/4 when the K1 + K2 = 0 condition is met. Analytical expressions for the 180° Bloch domain wall energy surface density (γ) were derived for uniaxial crystals with each MCA type. It is found that the γ(K1, K2) function has a minimum, equal to γ=2A|K1| when the relation K1 + K2 = 0 between MCA constants is satisfied. The derived analytical expressions are useful for a detailed spin-reorientation transition analysis. To illustrate this, examples of the application of the obtained results to MCA analyses of real crystals and DW energy calculations are given.