Epitaxial strain has emerged as a powerful tool to tune magnetic and ferroelectric properties in functional materials such as in multiferroic perovskite oxides. Here, we use first-principles calculations to explore the evolution of magnetic interactions in the antiferromagnetic (AFM) multiferroic ${\mathrm{BiFeO}}_3$ (BFO), one of the most promising multiferroics for future technology. The epitaxial strain in BFO(001) oriented film is varied between ${\varepsilon }_{xx,yy}\in [-2\%,+2\%]$. We find that both strengths of the exchange interaction and Dzyaloshinskii-Moriya interaction decrease linearly from compressive to tensile strain whereas the uniaxial magnetocrystalline anisotropy follows a parabolic behavior which lifts the energy degeneracy of the (111) easy plane of bulk BFO. From the trends of the magnetic interactions we can explain the destruction of cycloidal order in compressive strain as observed in experiments due to the increasing anisotropy energy. For tensile strain, we predict that the ground state remains unchanged as a function of strain. By using the domain wall energy, we envision the region where isolated chiral magnetic textures might occur as a function of strain, i.e., where the collinear AFM and the spin spiral energies are equal. This transition between $-1.5$ and $-0.5\%$ of strain should allow topologically stable magnetic states such as antiferromagnetic skyrmions and/or merons to occur. Hence, our paper should trigger experimental and theoretical investigations in this range of strain.

中文翻译：

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通过外延应变设计 BiFeO3 中的磁畴壁能量：从第一原理评估多铁性斯格明子稳定性的途径

外延应变已成为调节功能材料（例如多铁钙钛矿氧化物）的磁性和铁电性能的强大工具。在这里，我们使用第一性原理计算来探索反铁磁（AFM）多铁性中磁相互作用的演化${\mathrm{铁酸铋}}_3$（BFO），未来技术中最有前途的多铁性材料之一。BFO（001）取向膜中的外延应变介于${\epsilon }_{XX,yy}\epsilon [-2\%,+2\%]$。我们发现交换相互作用和 Dzyaloshinskii-Moriya 相互作用的强度从压缩应变到拉伸应变线性下降，而单轴磁晶各向异性遵循抛物线行为，提高了块体 BFO 的 (111) 易平面的能量简并性。根据磁相互作用的趋势，我们可以解释实验中观察到的由于各向异性能量增加而导致的压缩应变摆线序的破坏。对于拉伸应变，我们预测基态作为应变的函数保持不变。通过使用磁畴壁能量，我们设想了作为应变函数可能出现孤立手性磁织构的区域，即共线 AFM 和自旋螺旋能量相等的区域。之间的这种过渡$-1.5$和$-0.5\%$应变应允许出现拓扑稳定的磁态，例如反铁磁斯格明子和/或半子。因此，我们的论文应该引发这个应变范围的实验和理论研究。