Microscopic Origin of Heisenberg and Non-Heisenberg Exchange Interactions in Ferromagnetic bcc Fe.

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-neighbor 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. By making a comparison to other magnetic transition metals, we put the results of bcc Fe into context and argue that iron has a unique behavior when it comes to magnetic exchange interactions.

First-principles Dzyaloshinskii-Moriya interaction in a non-collinear framework.

We have derived an expression of the Dzyaloshinskii-Moriya interaction (DMI), where all the three components of the DMI vector can be calculated independently, for a general, non-collinear magnetic configuration. The formalism is implemented in a real space-linear muffin-tin orbital-atomic sphere approximation (RS-LMTO-ASA) method. We have chosen the Cr triangular trimer on Au(111) and Mn triangular trimers on Ag(111) and Au(111) surfaces as numerical examples. The results show that the DMI (module and direction) is drastically different between collinear and non-collinear states. Based on the relation between the spin and charge currents flowing in the system and their coupling to the non-collinear magnetic configuration of the triangular trimer, we demonstrate that the DMI interaction can be significant, even in the absence of spin-orbit coupling. This is shown to emanate from the non-collinear magnetic structure, that can induce significant spin and charge currents even with spin-orbit coupling is ignored.

The Bethe-Slater curve revisited; new insights from electronic structure theory.

The Bethe-Slater (BS) curve describes the relation between the exchange coupling and interatomic distance. Based on a simple argument of orbital overlaps, it successfully predicts the transition from antiferromagnetism to ferromagnetism, when traversing the 3d series. In a previous article [Phys. Rev. Lett. 116, 217202 (2016)] we reported that the dominant nearestneighbour (NN) interaction for 3d metals in the bcc structure indeed follows the BS curve, but the trends through the series showed a richer underlying physics than was initially assumed. The orbital decomposition of the inter-site exchange couplings revealed that various orbitals contribute to the exchange interactions in a highly non-trivial and sometimes competitive way. In this communication we perform a deeper analysis by comparing 3d metals in the bcc and fcc structures. We find that there is no coupling between the E g orbitals of one atom and T 2g orbitals of its NNs, for both cubic phases. We demonstrate that these couplings are forbidden by symmetry and formulate a general rule allowing to predict when a similar situation is going to happen. In γ-Fe, as in α-Fe, we find a strong competition in the symmetry-resolved orbital contributions and analyse the differences between the high-spin and low-spin solutions.

Erratum: The Bethe-Slater curve revisited; new insights from electronic structure theory.

A correction to this article has been published and is linked from the HTML version of this paper. The error has been fixed in the paper.

Noncollinear magnetism of Mn nanowires on Fe(1 1 0).

Magnetic properties of Mn linear nanochains on a bcc Fe(1 1 0) surface have been studied using the first-principles real space-linear muffin-tin orbital atomic sphere approximation (RS-LMTO-ASA) method. We have considered up to nine Mn atoms deposited on bcc Fe(1 1 0). Our ab initio calculations reveal the competition between the antiferromagnetic Mn-Mn and Mn-Fe couplings, presenting a behavior which is very different from Mn nanowires on Fe(0 0 1), as shown in a previous publication. Due to this competition and non-negligible Dzyaloshinskii-Moriya interaction, noncollinear magnetic structures are stabilized as ground states for the Mn nanochains on Fe(1 1 0).

Magnetic properties of Fe(x)Co(1-x) nanochains on Pt(1 1 1) surfaces.

The magnetic properties of FexCo1-x nanochains on Pt(1 1 1) were studied using the first-principles real-space linear muffin-tin orbital-atomic sphere approximation (RS-LMTO-ASA) method within the density functional theory. The relative amounts of Fe and Co atoms in a chosen nanochain were varied and several possible arrangements of the atomic species were taken into account. The results of the exchange interaction demonstrates ferromagnetic coupling for the nanowires. Our calculations of Fe and Co average magnetic moments reveal a large enhancement of both spin and orbital moments compared to Fe-Co films deposited on a Pt(1 1 1) surface. The trend for the orbital moments with respect to stoichiometry differs from all previous higher-dimensional Fe-Co alloys on Pt(1 1 1) studies.

Hyperfine and magnetic properties of Fe-Cu clusters and Fe precipitates embedded in a Cu matrix.

Using the first-principles real-space linear muffin-tin orbital method within the atomic sphere approximation (RS-LMTO-ASA) we study hyperfine and local magnetic properties of substituted pure Fe and Fe-Cu clusters in an fcc Cu matrix. Spin and orbital contributions to magnetic moments, hyperfine fields and the Mössbauer isomer shifts at the Fe sites in Fe precipitates and Fe-Cu alloy clusters of sizes up to 60 Fe atoms embedded in the Cu matrix are calculated and the influence of the local environment on these properties is discussed.