Supplementary information files for: Superconductivity assisted change of the perpendicular magnetic anisotropy in V/MgO/Fe junctions

Supplementary files for article: Superconductivity assisted change of the perpendicular magnetic anisotropy in V/MgO/Fe junctions.Controlling the perpendicular magnetic anisotropy (PMA) in thin films has received considerable attention in recent years due to its technological importance. PMA based devices usually involve heavy-metal (oxide)/ferromagnetic-metal bilayers, where, thanks to interfacial spin-orbit coupling (SOC), the in-plane (IP) stability of the magnetization is broken. Here we show that in V/MgO/Fe(001) epitaxial junctions with competing in-plane and out-of-plane (OOP) magnetic anisotropies, the SOC mediated interaction between a ferromagnet (FM) and a superconductor (SC) enhances the effective PMA below the superconducting transition. This produces a partial magnetization reorientation without any applied field for all but the largest junctions, where the IP anisotropy is more robust; for the smallest junctions there is a reduction of the field required to induce a complete OOP transition (HOOP) due to the stronger competition between the IP and OOP anisotropies. Our results suggest that the degree of effective PMA could be controlled by the junction lateral size in the presence of superconductivity and an applied electric field. We also discuss how the HOOP field could be affected by the interaction between magnetic stray fields and superconducting vortices. Our experimental findings, supported by numerical modelling of the ferromagnet-superconductor interaction, open pathways to active control of magnetic anisotropy in the emerging dissipation-free superconducting spin electronics.<br>

论文补充文件：超导辅助下V/MgO/Fe结中垂直磁各向异性的变化。由于其技术重要性，近年来薄膜中垂直磁各向异性（PMA）的调控受到了广泛关注。基于PMA的器件通常涉及重金属（氧化物）/铁磁金属双层结构，在此结构中，得益于界面自旋轨道耦合（SOC），磁化强度的面内（IP）稳定性被打破。本文表明，在具有面内与面外（OOP）磁各向异性竞争的V/MgO/Fe(001)外延结中，铁磁体（FM）与超导体（SC）之间由SOC介导的相互作用会在超导转变温度以下增强有效PMA。这导致除最大结（其IP各向异性更显著）外的所有结在无外场条件下发生部分磁化重取向；对于最小结，由于IP与OOP各向异性间的竞争更强烈，诱导完全OOP转变所需的磁场（HOOP）有所降低。我们的结果表明，在超导状态及外电场存在的情况下，有效PMA的程度可通过结的横向尺寸进行调控。我们还讨论了磁杂散场与超导涡旋之间的相互作用如何影响HOOP磁场。我们的实验结果得到了铁磁体-超导体相互作用数值模拟的支持，为新兴的无耗散超导自旋电子学中磁各向异性的主动调控开辟了途径。