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Register a new userMicroscopic origin of Heisenberg and non-Heisenberg exchange interactions in ferromagnetic bcc Fe
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By means of first principles calculations we investigate the nature of exchange coupling in ferromagnetic bcc Fe on a microscopic level. Analyzing the basic electronic structure reveals a drastic difference between the $3d$ orbitals of $E_g$ and $T_{2g}$ symmetries. The latter ones define the shape of the Fermi surface, while the former ones form weakly-interacting impurity levels. We demonstrate that, as a result of this, in Fe the $T_{2g}$ orbitals participate in exchange interactions, which are only weakly dependent on the configuration of the spin moments and thus can be classified as Heisenberg-like. These couplings are shown to be driven by Fermi surface nesting. In contrast, for the $E_g$ states the Heisenberg picture breaks down, since the corresponding contribution to the exchange interactions is shown to strongly depend on the reference state they are extracted from. Our analysis of the nearest-neighbour coupling indicates that the interactions among $E_g$ states are mainly proportional to the corresponding hopping integral and thus can be attributed to be of double-exchange origin.
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We show for a simple non-collinear configuration of the atomistic spins (in particular, where one spin is rotated by a finite angle in a ferromagnetic background) that the pairwise energy variation computed in terms of multiple scattering formalism cannot be fully mapped onto a bilinear Heisen- berg spin model even in the lack of spin-orbit coupling. The non-Heisenberg terms induced by the spin-polarized host appear in leading orders in the expansion of the infinitesimal angle variations. However, an Eg-T2g symmetry analysis based on the orbital decomposition of the exchange param- eters in bcc Fe leads to the conclusion that the nearest neighbor exchange parameters related to the T2g orbitals are essentially Heisenberg-like: they do not depend on the spin configuration, and can in this case be mapped onto a Heisenberg spin model even in extreme non-collinear cases.
The superexchange intertacion in transition-metal oxides, proposed initially by Anderson in 1950, is treated using contemporary tight-binding theory and existing parameters. We find also a direct exchange for nearest-neighbor metal ions, larger by a factor of order five than the superexchange. This direct exchange arises from Vddm coupling, rather than overlap of atomic charge densities, a small overlap exchange contribution which we also estimate. For FeO and CoO there is also an important negative contribution, related to Stoner ferromagnetism, from the partially filled minority-spin band which broadens when ionic spins are aligned. The corresponding J1 and J2 parameters are calculated for MnO, FeO, CoO, and NiO. They give good accounts of the Neel and the Curie-Weiss temperatures, show appropriate trends, and give a reasonable account of their volume dependences. For MnO the predicted value for the magnetic susceptibility at the Neel temperature and the crystal distortion arising from the antiferromagnetic transition were reasonably well given. Application to CuO2 planes in the cuprates gives J=1220oK, compared to an experimental 1500oK, and for LiCrO2 gives J1=4 50oK compared to an experimental 230oK.
One year after their initial discovery, two schools of thought have crystallized regarding the electronic structure and magnetic properties of ferropnictide systems. One postulates that these are itinerant weakly correlated metallic systems that become magnetic by virtue of spin-Peierls type transition due to near-nesting between the hole and the electron Fermi surface pockets. The other argues these materials are strongly or at least moderately correlated, the electrons are considerably localized and close to a Mott-Hubbard transition, with the local magnetic moments interacting via short-range superexchange. In this paper we argue that neither picture is fully correct. The systems are moderately correlated, but with correlations driven by Hunds rule coupling rather than by the on-site Hubbard repulsion. The iron moments are largely local, driven by Hunds intra-atomic exchange. Superexchange is not operative and the interactions between the Fe moments are considerably long-range and driven mostly by one-electron energies of all occupied states.
We present results of the analysis of Brillouin Light Scattering (BLS) measurements of spin waves performed on ultrathin single and multirepeat CoFeB layers with adjacent heavy metal layers. From a detailed study of the spin-wave dispersion relation, we independently extract the Heisenberg exchange interaction (also referred to as symmetric exchange interaction), the Dzyaloshinskii-Moriya interaction (DMI, also referred to as antisymmetric exchange interaction), and the anisotropy field. We find a large DMI in CoFeB thin films adjacent to a Pt layer and nearly vanishing DMI for CoFeB films adjacent to a W layer. Furthermore, the residual influence of the dipolar interaction on the dispersion relation and on the evaluation of the Heisenberg exchange parameter is demonstrated. In addition, an experimental analysis of the DMI on the spin-wave lifetime is presented. All these parameters play a crucial role in designing skyrmionic or spin-orbitronic devices.
Microscopic origin of the ferromagnetic (FM) exchange coupling in CrCl$_3$ and CrI$_3$, their common aspects and differences, are investigated on the basis of density functional theory combined with realistic modeling approach for the analysis of interatomic exchange interactions. We perform a comparative study based on the pseudopotential and linear muffin-tin orbital methods by treating the effects of electron exchange and correlation in GGA and LSDA, respectively. The results of ordinary band structure calculations are used in order to construct the minimal tight-binding type models describing the behavior of the magnetic Cr $3d$ and ligand $p$ bands in the basis of localized Wannier functions, and evaluate the effective exchange coupling ($J_{rm eff}$) between two Cr sublattices employing four different technique: (i) Second-order Greens function perturbation theory for infinitesimal spin rotations of the LSDA (GGA) potential at the Cr sites; (ii) Enforcement of the magnetic force theorem in order to treat both Cr and ligand spins on a localized footing; (iii) Constrained total-energy calculations with an external field, treated in the framework of self-consistent linear response theory. We argue that the ligand states play crucial role in the ferromagnetism of Cr trihalides, though their contribution to $J_{rm eff}$ strongly depends on additional assumptions, which are traced back to fundamentals of adiabatic spin dynamics. Particularly, by neglecting ligand spins in the Greens function method, $J_{rm eff}$ can easily become antiferromagnetic, while by treating them as localized, one can severely overestimate the FM coupling. The best considered approach is based on the constraint method, where the ligand states are allowed to relax in response to each instantaneous reorientation of the Cr spins, controlled by the external field.
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