Optimization of spontaneous exchange bias in Mn-rich Heusler alloys

At low temperature, spontaneous (zero-field-cooled, SEB) and traditional (field-cooled) exchange bias effects may be induced in a series of NiMn-based Heusler alloys, and the exchange bias is commonly sensitive to alloying elements and compositions, while the mechanisms especially for SEB are still elusive. Therefore, the SEB in Mn-rich Heusler alloys with coexistence of ferromagnetic and antiferromagnetic exchange interactions is numerically studied by performing a modified Monte Carlo simulation. The intrinsic magnetocrystalline anisotropies (K_AF), exchange interactions (J_FM-AF and J_AF-AF), and occupation probabilities (x_FM) are directly tuned to establish their dependencies of zero-field-cooled/field-cooled thermomagnetic curves and zero-field-cooled magnetization hysteresis loops. The results indicate that the freezing temperature is monotonically enhanced with increasing K_AF and varies nonmonotonically with other parameters, and at 5 K, the irreversibility arising from antiferromagnetic components becomes high enough to trigger SEB even though no spin glass state exists. The SEB is nonmonotonic with K_AF, J_FM-AF, J_AF-AF, and x_FM, and its maximum value will be obtained at K_AF = 4.5 × 10⁶ J m^-3, J_FM-AF = 5 meV, J_AF-AF = -5 meV, or x_FM = 0.3. On the contrary, the coercivity is also nonmonotonic with K_AF and J_FM-AF while monotonic with J_AF-AF and x_FM. The values of the SEB field are nearly one order of magnitude smaller than those of coercivity, consistent with experimental data. The magnetic relaxation properties are calculated to propose two factors, i.e., ferromagnetic-like domain between ferromagnetic and antiferromagnetic components and decay rate, to determine the final SEB. This work demonstrates the mechanisms to optimize SEB in Mn-rich Heusler alloys, and physically the results obtained are also suitable for other material systems with spontaneous ferromagnet/antiferromagnet phase separations.