We present a theoretical investigation of the magnetocrystalline anisotropy (MA) in R2Fe14B (R is a rare-earth element) magnets in consideration of the non-collinearity effect (NCE) between the R and Fe magnetization directions. In particular, the temperature dependence of the MA of Dy2Fe14B magnets is detailed in terms of the nth-order MA constant (MAC) Kn(T) at a temperature T. The features of this constant are as follows: K1(T) has a broad plateau in the low-temperature range and K2(T) persistently survives in the high-temperature range. The present theory explains these features in terms of the NCE on the MA by using numerical calculations for the entire temperature range, and further, by using a high-temperature expansion. The high-temperature expansion for Kn(T) is expressed in the form of Kn(T) = κ1(T) [1 + δ(T)][−δ(T)]n−1, where κ1(T) is the part without the NCE and δ(T) is a correction factor for the NCE introduced in this study. We also provide a convenient expression to evaluate Kn(T), which can be determined only by a second-order crystalline electric field coefficient and an effective exchange field.
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