Critical thickness of antiferromagnetic layer in exchange biasing bilayer system

The exchange bias between the ferromagnetic (FM) and antiferromagnetic (AFM) bilayer was investigated within the framework of the classical Heisenberg model. The dependence of the exchange bias on the AFM layer thickness was also calculated by using the Landau-Lifshitz-Gilbert equation. The triple-Q (3Q), AF-I and T1 spin structures are obtained in the disordered γ-phase, ordered L1₀-, and L1₂-type lattices, respectively. The exchange bias is caused by the formation of the interfacial domain wall in the AFM layer, and the critical thickness d_c of AFM layer is dominated by the varied spin structures. Under the condition where the magnetic anisotropy energy is fixed to equivalent values in different alloys, the critical thickness d_c^3Q of the disordered γ-phase layer with the 3Q spin structure is thinner than that d_c^AF-I of the ordered L1₀-type layer with the AF-I spin structure. Also, the critical thickness d_c^T1 is thinner than d_c ^AF-I in ordered L1₂- and L1₀-type alloys. The relation among the critical thicknesses is dominated by the formation of a magnetic domain wall in the AFM layer. Consequently, the relation of the critical thickness can be represented as √3d_c^3Q = √2d_c^T1 = d_c^AF-I.