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 Ni₂Mn_1+xGa_1−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 (H_EB) depends on the size of the ferromagnetic (FM) cluster in the antiferromagnetic (AFM) matrix. It was found that H_EB 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 H_EB 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.

中文翻译：

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利用铁磁团簇尺寸工程调整折返旋转玻璃的交换偏向

由于界面密度的变化，材料的许多特性对畴/晶粒尺寸表现出极大的依赖性。在这里，我们表明，在块状Ni ₂ Mn _{1+ x} Ga _{1- x}合金中（0.4 < x <0.7），交换偏斜（EB）效应出现在凹角自旋玻璃区域中，并且交换偏斜的大小（H _EB）取决于反铁磁（AFM）矩阵中铁磁（FM）簇的大小。发现H _EB随FM团簇尺寸的减小先增大然后减小，这表明与FM团簇尺寸具有非单调关系，并且该关系类似于材料特性（例如金属的机械强度和介电常数）的晶粒尺寸依赖性铁电陶瓷。进一步的相场模拟结果重复了这种现象，并说明EB的变化可归因于FM / AFM界面密度的变化，这通过Dzyaloshinskii-Moriya相互作用提供了可调节的额外偏置场。这项工作提供了一种调整散装物料中H _EB的方法，并揭示了EB对FM簇尺寸的依赖性机制，这可以指导散装交换性物料的设计。