Energy Boundaries between Single-domain Particle and Particles having Limited Number of Domains in the Sm₂Fe₁₇N₃ Magnetic Material

Abstract

The observation using magnetic force microscopy (MFM) of the Sm₂Fe₁₇N₃ (SFN) particles having 2-4μm in diameters (D), totally about 15 particles, revealed that the particles show single-domain state and/or more than 3 domain state. Magnetic and domain wall energies of the single-domain particle (SDP) and these of two and three domain particles (2DP, 3DP) were calculated using the measured saturated polarization (J_s) and the domain wall energy (γ). The results of the calculation are as follows : (1) the energy difference between the 2DP and 3DP is less than 6% in the total energies, in the range of E_SDP > E_3DP> E_2DP : (2) the 3DP becomes stable, E_2DP > E_3DP, in the particles of D>3.0μm assuming the critical diameter is 2μm. Local demagnetizing field and existence of macroscopic defects in a particle strongly influence on the nucleation of domain wall formation, and it is obvious that the 2DP has a higher static magnetic energy compared to that of the 3DP. Therefore, it can be considered that the morphological complexity of the real particles results in the increase of stability of the 3DP than that of the 2DP in the sample particles. On the other hand, the discrepancy between the calculated critical diameter of SDP (d_c≈0.18μm) and the measured one (d_c≈2μm) can be explained by the temperature dependence of relative ratio of crystal magnetic anisotropy and saturated polarization in the SFN particles, i. e. (K=K(T) / K^{R. T.}) vs. (Js= J_s(T) / J_s^{R. T.}). It is revealed that the decrease in the anisotropy is pronounced in the higher temperature region near the Curie temperature than that in the saturated polarization (K₁∝J_sⁿ (n>4)). It should be the origin of the measured large SDP size than that of theoretically calculated critical radius using K₁, and J_s at room temperature.