Characterization of Three-Dimensional Magnetic Alignment for Magnetically Biaxial Particles

The three-dimensional magnetic alignment (3DMA) is analytically investigated for magnetically biaxial particles with the susceptibility χ₁>χ₂>χ₃ in an amplitude-modulated (AM) elliptic field B= i₁Bb₁cos ωt + i₂Bb₂sin ωt as a prototype method for 3DMA. The distribution function and the biaxial ordering matrix are numerically calculated by the Boltzmann distribution and the rotational diffusion equation. The 3DMA attains the optimum performance in the rapid rotation regime (RRR) with the infinity rotation frequency ω while the RRR is effectively available at lower rotation frequencies. The intermediate magnetization axis χ₂ is inferior to the easy and hard magnetization axes χ₁ and χ₃ in the time development and the equilibrium state of alignment. In all the methods for 3DMA, the dynamic and equilibrium behavior in the RRR are universally characterized by the reduced energy α= V(Bb₁)²(χ₃ - χ₁)/(2µ₀k_BT), the biaxial deviation of susceptibility k = (χ₂-χ₁)/(χ₃-χ₁), the field modulation factor q = (b₂/b₁)², and the reduced time t_r = | α| Dt where D is the rotational diffusion constant.