交换作用与磁力定理
Exchange interactions and magnetic force theorem
摘要：
我们批判性地重新审视原子间交换作用的问题，它描述了在某些平衡态附近由自旋的无限小旋转引起的总能量变化。对于小的变化，这样的相互作用可以总是与响应函数相关。然而，该关系的形式可以取决于附加的近似。特别地，通常使用的磁力定理（MFT）规定了交换相互作用与响应函数之间的线性关系，而精确理论要求这种依赖关系是逆的。我们探讨的起源和后果，这些差异的定义为广泛的一类材料：铁磁性镍，反铁磁性NiO，半金属氧化铬2，多铁性HoMnO 3，和层状磁铁CrCl 3和CrI3。虽然在大多数情况下，MFT产生相当合理的结果，并且可以在长波长和强耦合限制下严格证明，但确切的公式似乎更一致，特别是在处理交换相互作用理论中通常出现的两个重要问题时：（i）配位体状态的处理，以及（ii）选择合适的变量来描述自旋的无穷小旋转。这两个问题都可以有效地解决，采用绝热自旋动力学的想法补充交换相互作用的精确表达式。特别是，我们提出了一个简单的“向下折叠”的过程中消除的配位体自旋转移到本地化的自旋之间的相互作用参数的影响。此外，我们认为自旋矩的旋转更适合于描述低能激发，而整个磁化矩阵的旋转会引起更强的扰动的自旋系统。
英文摘要：
We critically reexamine the problem of interatomic exchange interactions, which describe the total energy change caused by infinitesimal rotations of spins near some equilibrium state. For the small variations, such interactions can be always related to the response function. However, the form of this relation can depend on additional approximations. Particularly, the commonly used magnetic force theorem (MFT) prescribes the linear relation between the exchange interactions and the response function, while the exact theory requires this dependence to be inverse. We explore the origin and consequences of these differences in the definition for the wide class of materials: ferromagnetic Ni, antiferromagnetic NiO, half-metallic CrO2, multiferroic HoMnO3, and layered magnets CrCl3 and CrI3. While in most of these cases, MFT produces quite reasonable results and can be rigorously justifies in the long wavelength and strong-coupling limits, the exact formulation appears to be more consistent, especially in dealing with two important issues, which typically arise in the theory of exchange interactions: (i) the treatment of the ligand states, and (ii) the choice of the suitable variable for the description of infinitesimal rotations of spins. Both issues can be efficiently resolved by employing the ideas of adiabatic spin dynamics supplemented with the exact expression for the exchange interactions. Particularly, we propose a simple "downfolding" procedure for the elimination of the ligand spins by transferring their effect to the interaction parameters between the localized spins. Furthermore, we argue that the rotations of spin moments are more suitable for the description of low-energy excitations, while the rotations of the whole magnetization matrix cause much stronger perturbation in the system of spins.
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