Hybrid organic–inorganic perovskites are famous for the diversity of their chemical compositions, phases, phase transitions, and associated physical properties. We use a combination of experimental and computational techniques to reveal a strong coupling between structure, magnetism, and spin splitting in a representative of the largest family of hybrid organic–inorganic perovskites: the formates. With the help of first-principles simulations, we find spin splitting in both conduction and valence bands of [NH₂NH₃]Co(HCOO)₃ induced by spin–orbit interactions, which can reach up to 14 meV. Our magnetic measurements reveal that this material exhibits canted antiferromagnetism below 15.5 K. The direction of the associated antiferromagnetic order parameter is strongly coupled with spin splitting in the centrosymmetric phase, allowing for the creation and annihilation of spin splitting through the application of a magnetic field. Furthermore, the structural phase transition to the experimentally observed polar Pna2₁ phase completely changes the aforementioned spin splitting and its coupling to magnetic degrees of freedom. This reveals that in [NH₂NH₃]Co(HCOO)₃, the structure and magnetism are strongly coupled to spin splitting and can be manipulated through electric and magnetic fields. We believe that our findings offer an important step toward a fundamental understanding and practical applications of materials with coupled properties.

中文翻译：

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有机-无机杂化钙钛矿结构和磁性与自旋分裂的耦合

有机-无机杂化钙钛矿以其化学成分、物相、相变和相关物理性质的多样性而闻名。我们结合实验和计算技术，揭示了有机-无机杂化钙钛矿最大家族的代表：甲酸盐中结构、磁性和自旋分裂之间的强耦合。借助第一性原理模拟，我们发现自旋轨道相互作用引起的[NH ₂ NH ₃ ]Co(HCOO) ₃导带和价带中的自旋分裂最高可达14 meV。我们的磁性测量表明，这种材料在 15.5 K 以下表现出倾斜的反铁磁性。相关反铁磁有序参数的方向与中心对称相中的自旋分裂密切相关，允许通过施加磁场来产生和消除自旋分裂。此外，实验观察到的极性Pna 2 ₁相的结构相变完全改变了上述自旋分裂及其与磁自由度的耦合。这表明，在[NH ₂ NH ₃ ]Co(HCOO) ₃中，结构和磁性与自旋分裂强烈耦合，并且可以通过电场和磁场来操纵。我们相信，我们的发现为对具有耦合特性的材料的基本理解和实际应用迈出了重要的一步。