Tailoring exchange bias in reentrant spin glass by ferromagnetic cluster size engineering

Many properties of materials exhibit a heavy dependency on the domain/grain size due to the change in interface density. Here, we show that in bulk Ni2Mn1+xGa1-x alloys (0.4 < x < 0.7), the exchange bias (EB) effect appears in the reentrant spin glass region and the magnitude of exchange bias (HEB) depends on the size of the ferromagnetic (FM) cluster in the antiferromagnetic (AFM) matrix. It was found that HEB first increases and then deceases as the size of the FM cluster decreases, which shows a non-monotonical relationship with the FM cluster size, and the relationship is similar to the grain size dependence of material properties such as the mechanical strength of metals and dielectric permittivity of ferroelectric ceramics. Further phase field simulation results repeat this phenomenon and illustrate that the change in EB can be attributed to the change in density of the FM/AFM interface, which provides a regulatable extra bias field through the Dzyaloshinskii-Moriya interaction. This work provides a method to tune HEB in bulk materials and reveals the mechanism of the dependency of EB on the FM cluster size, which could guide the design of bulk exchange-bias materials.