25 research outputs found
First-principles calculation of the parameters used by atomistic magnetic simulations
While the ground state of magnetic materials is in general well described on the basis of spin density functional theory (SDFT), the theoretical description of finite-temperature and non-equilibrium properties require an extension beyond the standard SDFT. Time-dependent SDFT (TD-SDFT), which give for example access to dynamical properties are computationally very demanding and can currently be hardly applied to complex solids. Here we focus on the alternative approach based on the combination of a parameterized phenomenological spin Hamiltonian and SDFT-based electronic structure calculations, giving access to the dynamical and finite-temperature properties for example via spin-dynamics simulations using the Landau–Lifshitz–Gilbert (LLG) equation or Monte Carlo simulations. We present an overview on the various methods to calculate the parameters of the various phenomenological Hamiltonians with an emphasis on the KKR Green function method as one of the most flexible band structure methods giving access to practically all relevant parameters. Concerning these, it is crucial to account for the spin–orbit coupling (SOC) by performing relativistic SDFT-based calculations as it plays a key role for magnetic anisotropy and chiral exchange interactions represented by the DMI parameters in the spin Hamiltonian. This concerns also the Gilbert damping parameters characterizing magnetization dissipation in the LLG equation, chiral multispin interaction parameters of the extended Heisenberg Hamiltonian, as well as spin–lattice interaction parameters describing the interplay of spin and lattice dynamics processes, for which an efficient computational scheme has been developed recently by the present authors
Spin-lattice interaction parameters from first principles: theory and implementation
A scheme is presented to calculate on a first-principles level
the spin-lattice coupling (SLC) parameters needed to perform
combined molecular-spin dynamics (MSD) simulations. By treating changes to
the spin configuration and atomic positions on the same level, closed
expressions for the atomic SLC parameters could be derived in a coherent way up
to any order. The properties of the SLC parameters are discussed considering
separately the symmetric and antisymmetric parts of the SLC tensor. The changes
due to atomic displacements of the spin-spin exchange coupling (SSC) parameters
estimated using the SLC parameters are compared with the SSC parameters
calculated for an embedded cluster with the central atom displaced,
demonstrating good agreement of these results. Moreover, this allows to study
the impact of different SLC contributions, linear and quadratic with respect to
displacements, on the properties of the modified SSC parameters. In addition,
we represent an approach to calculate the site-diagonal SLC parameters
characterizing local magnetic anisotropy induced by a lattice distortion, which
is a counterpart of the approach based on magnetic torque used for the
investigations of magneto-crystalline anisotropy (MCA) as well as for
calculations of the MCA constants. In particular, the dependence of the induced
magnetic torque on different types of atomic displacements is analyzed.Comment: 16 page
Chirality-inverted Dzyaloshinskii-Moriya interaction
The Dzyaloshinskii-Moriya interaction (DMI) is an antisymmetric exchange
interaction, which is responsible for the formation of topologically protected
spin textures in chiral magnets. Here, by measuring the dispersion relation of
the DM energy, we quantify the atomistic DMI in a model system, i.e., a Co
double layer on Ir(001). We unambiguously demonstrate the presence of a
chirality-inverted DMI, i.e., a sign change in the chirality index of DMI from
negative to positive, when comparing the interaction between nearest neighbors
to that between neighbors located at longer distances. The effect is in analogy
to the change in the character of the Heisenberg exchange interaction from,
e.g., ferromagnetic to antiferromagnetic. We show that the pattern of the
atomistic DMI in epitaxial magnetic structures can be very complex and provide
critical insights into the nature of DMI. We anticipate that the observed
effect is general and occurs in many magnetic nanostructures grown on
heavy-element metallic substrates.Comment: 4 pages, 3 figure
Atomically Resolved Chemical Reactivity of Small Fe Clusters
Small metal clusters have been investigated for decades due to their beneficial catalytic activity. It was found that edges are most reactive and the number of catalytic events increases with the cluster's size. However, a direct measurement of chemical reactivity of individual atoms within the clusters has not been reported yet. We combine the high-resolution capability of CO-terminated tips in scanning probe microscopy with their ability to probe chemical binding forces on single Fe atoms to study the chemical reactivity of atom-by-atom assembled Fe clusters from 1 to 15 atoms on the atomic scale. We find that the chemical reactivity of individual atoms within flat Fe clusters does not depend on the cluster size but on the coordination number of the investigated atom. Furthermore, we explain the atomic contrast of the investigated Fe clusters by relating the force spectra of individual atoms with atomic force microscopy images of the clusters
Calculating spin-lattice interactions in ferro- and antiferromagnets: the role of symmetry, dimension and frustration
Recently, the interplay between spin and lattice degrees of freedom has
gained a lot of attention due to its importance for various fundamental
phenomena as well as for spintronic and magnonic applications. Examples are
ultrafast angular momentum transfer between the spin and lattice subsystems
during ultrafast demagnetization, frustration driven by structural distortions
in transition metal oxides, or in acoustically driven spin-wave resonances. In
this work, we provide a systematic analysis of spin-lattice interactions for
ferro- and antiferromagnetic materials and focus on the role of lattice
symmetries and dimensions, magnetic order, and the relevance of spin-lattice
interactions for angular momentum transfer as well as magnetic frustration. For
this purpose, we use a recently developed scheme which allows an efficient
calculation of spin-lattice interaction tensors from first principles. In
addition to that, we provide a more accurate and self consistent scheme to
calculate ab initio spin lattice interactions by using embedded clusters which
allows to benchmark the performance of the scheme introduced previously
Rotationally invariant formulation of spin-lattice coupling in multi-scale modeling
In the spirit of multi-scale modeling, we develop a theoretical framework for
spin-lattice coupling that connects, on the one hand, to ab initio calculations
of spin-lattice coupling parameters and, on the other hand, to the
magneto-elastic continuum theory. The derived Hamiltonian describes a closed
system of spin and lattice degrees of freedom and explicitly conserves the
total momentum, angular momentum and energy. Using a new numerical
implementation that corrects earlier Suzuki-Trotter decompositions we perform
simulations on the basis of the resulting equations of motion to investigate
the combined magnetic and mechanical motion of a ferromagnetic nanoparticle,
thereby validating our developed method. In addition to the ferromagnetic
resonance mode of the spin system we find another low-frequency mechanical
response and a rotation of the particle according to the Einstein-de-Haas
effect. The framework developed herein will enable the use of multi-scale
modeling for investigating and understanding a broad range of
magneto-mechanical phenomena from slow to ultrafast time scales