Comparative study of methodologies to compute the intrinsic Gilbert damping: interrelations, validity and physical consequences

Magnetic exchange interactions at the proximity of a superconductor

Interfacing magnetism with superconductivity gives rise to a wonderful playground for intertwining key degrees of freedom: Cooper pairs, spin, charge, and spin-orbit interaction, from which emerge a wealth of exciting phenomena, fundamental in the nascent field of superconducting spinorbitronics and topological quantum technologies. Magnetic exchange interactions (MEIs), being isotropic or chiral such as the Dzyaloshinskii-Moriya interactions, are vital in establishing the magnetic behavior at these interfaces as well as in dictating not only complex transport phenomena, but also the manifestation of topologically trivial or non-trivial objects. Here, we propose a methodology enabling the extraction of the tensor of MEI from electronic structure simulations accounting for superconductivity. We apply our scheme to the case of a Mn layer deposited on Nb(110) surface and explore proximity-induced impact on the MEI. The latter are weakly modified by a realistic electron-phonon coupling. However, tuning the superconducting order parameter, we unveil potential change of the magnetic order accompanied with chirality switching, as induced by the interplay of spin-orbit interaction and Cooper pairing. Owing to its simple formulation, our methodology can be readily implemented in state-of-the-art frameworks capable of tackling superconductivity and magnetism. We thus foresee implications in the simulations and prediction of topological superconducting bits as well as of cryogenic superconducting hybrid devices involving magnetic units.

Superconductivity in Nb: Impact of Temperature, Dimensionality and Cooper-Pairing

The ability to realistically simulate the electronic structure of superconducting materials is important to understand and predict various properties emerging in both the superconducting topological and spintronics realms. We introduce a tight-binding implementation of the Bogoliubov-de Gennes method, parameterized from density functional theory, which we utilize to explore the bulk and thin films of Nb, known to host a significant superconducting gap. The latter is useful for various applications such as the exploration of trivial and topological in-gap states. Here, we focus on the simulation's aspects of superconductivity and study the impact of temperature, Cooper-pair coupling and dimensionality on the value of the superconducting pairing interactions and gaps.

Plane wave implementation of the magnetic force theorem for magnetic exchange constants: application to bulk Fe, Co and Ni

We present a plane wave implementation of the magnetic force theorem, which provides a first principles framework for extracting exchange constants parameterizing a classical Heisenberg model description of magnetic materials. It is shown that the full microscopic exchange tensor may be expressed in terms of the static Kohn-Sham susceptibility tensor and the exchange-correlation magnetic field. This formulation allows one to define arbitrary magnetic sites localized to predefined spatial regions, hence rendering the problem of finding Heisenberg parameters independent of any orbital decomposition of the problem. The susceptibility is calculated in a plane wave basis, which allows for systematic convergence with respect to unoccupied bands and spatial representation. We then apply the method to the well-studied problem of calculating adiabatic spin wave spectra for bulk Fe, Co and Ni, finding good agreement with previous calculations. In particular, we utilize the freedom of defining magnetic sites to show that the calculated Heisenberg parameters are robust towards changes in the definition of magnetic sites. This demonstrates that the magnetic sites can be regarded as well-defined and thus asserts the relevance of the Heisenberg model description despite the itinerant nature of the magnetic state.

Generalization of the Landau-Lifshitz-Gilbert equation by multi-body contributions to Gilbert damping for non-collinear magnets

We propose a systematic and sequential expansion of the Landau-Lifshitz-Gilbert equation utilizing the dependence of the Gilbert damping tensor on the angle between magnetic moments, which arises from multi-body scattering processes. The tensor consists of a damping-like term and a correction to the gyromagnetic ratio. Based on electronic structure theory, both terms are shown to depend on e.g. the scalar, anisotropic, vector-chiral and scalar-chiral products of magnetic moments:e_i⋅e_j, (n_ij⋅e_i)(n_ij⋅e_j),n_ij⋅ (e_i×e_j),(ei⋅ej)2,e_i⋅ (e_j×e_k) …, where some terms are subjected to the spin-orbit fieldn_ijin first and second order. We explore the magnitude of the different contributions using both the Alexander-Anderson model and time-dependent density functional theory in magnetic adatoms and dimers deposited on Au(111) surface.