Kim Kyoung-Whan, Lee Kyung-Jin, Lee Hyun-Woo, Stiles M D
Center for Nanoscale Science and Technology, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA.
Maryland NanoCenter, University of Maryland, College Park, Maryland 20742, USA.
Phys Rev B. 2016 Nov;94(18). doi: 10.1103/PhysRevB.94.184402. Epub 2016 Nov 3.
We compute the magnetocrystalline anisotropy energy within two-dimensional Rashba models. For a ferromagnetic free-electron Rashba model, the magnetic anisotropy is exactly zero regardless of the strength of the Rashba coupling, unless only the lowest band is occupied. For this latter case, the model predicts in-plane anisotropy. For a more realistic Rashba model with finite band width, the magnetic anisotropy evolves from in-plane to perpendicular and back to in-plane as bands are progressively filled. This evolution agrees with first-principles calculations on the interfacial anisotropy, suggesting that the Rashba model captures energetics leading to anisotropy originating from the interface provided that the model takes account of the finite Brillouin zone. The results show that the electron density modulation by doping or an external voltage is more important for voltage-controlled magnetic anisotropy than the modulation of the Rashba parameter.
我们在二维Rashba模型中计算磁晶各向异性能量。对于铁磁自由电子Rashba模型，除非仅占据最低能带，否则无论Rashba耦合强度如何，磁各向异性都恰好为零。对于后一种情况，该模型预测面内各向异性。对于具有有限带宽的更现实的Rashba模型，随着能带逐渐填充，磁各向异性从面内演变为垂直，然后又回到面内。这种演变与关于界面各向异性的第一性原理计算结果一致，这表明只要该模型考虑了有限的布里渊区，Rashba模型就能捕捉到导致源于界面的各向异性的能量学。结果表明，对于电压控制的磁各向异性，通过掺杂或外部电压进行的电子密度调制比Rashba参数的调制更为重要。
