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首页> 外文期刊>Physical review >Exchange interactions and local-moment fluctuation corrections in ferromagnets at finite temperatures based on noncollinear density-functional calculations
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Exchange interactions and local-moment fluctuation corrections in ferromagnets at finite temperatures based on noncollinear density-functional calculations

机译：基于非共线密度函数计算的有限温度下铁磁体的交换相互作用和局部矩波动校正

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We explore the derivation of interatomic exchange interactions in ferromagnets within density-functional theory (DFT) and the mapping of DFT results onto a spin Hamiltonian. We delve into the problem of systems comprising atoms with strong spontaneous moments together with atoms with weak induced moments. All moments are considered as degrees of freedom, with the strong moments thermally fluctuating only in angle and the weak moments thermally fluctuating in angle and magnitude. We argue that a quadratic dependence of the energy on the weak local moments magnitude, which is a good approximation in many cases, allows for an elimination of the weak-moment degrees of freedom from the thermodynamic expressions in favor of a renormalization of the Heisenberg interactions among the strong moments. We show that the renormalization is valid at all temperatures accounting for the thermal fluctuations and resulting in temperature-independent renormalized interactions. These are shown to be the ones directly derived from total-energy DFT calculations by constraining the strong-moment directions, as is done, e.g., in spin-spiral methods. We furthermore prove that within this framework the thermodynamics of the weak-moment subsystem, and in particular all correlation functions, can be derived as polynomials of the correlation functions of the strong-moment subsystem with coefficients that depend on the spin susceptibility and that can be calculated within DFT. These conclusions are rigorous under certain physical assumptions on the measure in the magnetic phase space. We implement the scheme in the full-potential linearized augmented plane wave method using the concept of spin-spiral states, considering applicable symmetry relations and the use of the magnetic force theorem. Our analytical results are corroborated by numerical calculations employing DFT and a Monte Carlo method.
机译：我们探索密度泛函理论（DFT）内铁磁体中原子间交换相互作用的推导，并将DFT结果映射到自旋哈密顿量上。我们研究了包含具有强自发矩的原子和具有弱诱导矩的原子的系统的问题。所有力矩都被视为自由度，其中强力矩仅在角度上发生热波动，而弱力矩在角度和幅度上发生热波动。我们认为，能量对弱局部矩幅值的二次依赖性（在许多情况下是一个很好的近似值）可以消除热力学表达式中的弱矩自由度，从而有利于海森堡相互作用的重新归一化在最重要的时刻我们表明，重归一化在所有温度下均有效，这考虑了热波动并导致了与温度无关的重归一化相互作用。这些被证明是通过约束强矩方向而直接从总能量DFT计算中得出的，例如在自旋螺旋方法中所做的那样。我们进一步证明，在此框架内，弱矩子系统的热力学，尤其是所有相关函数，可以作为强矩子系统相关函数的多项式导出，其系数取决于自旋磁化率，并且可以在DFT中计算。在磁相空间中的度量的某些物理假设下，这些结论是严格的。考虑到适用的对称关系和磁力定理，我们使用自旋螺旋状态的概念以全电位线性化增强平面波方法实施该方案。我们的分析结果通过使用DFT和蒙特卡洛方法的数值计算得到了证实。

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