arXiv subjects

Riccardo Hertel

Publications and source records attributed to Riccardo Hertel.

33 records · Page 2Linked to original sources

arXiv2020

Three-Dimensional Chiral Magnetization Structures in FeGe Nanospheres

Skyrmions, spin spirals, and other chiral magnetization structures developing in materials with intrinsic Dzyaloshinsky-Moriya Interaction display unique properties that have been the subject of intense research in thin-film geometries. Here we study the formation of three-dimensional chiral magnetization structures in FeGe nanospheres by means of micromagnetic finite-element simulations. In spite of the deep sub-micron particle size, we find a surprisingly large number of distinct equilibrium states, namely, helical, meron, skyrmion, chiral-bobber and quasi-saturation state. The distribution of these states is summarized in a phase diagram displaying the ground state as a function of the external field and particle radius. This unusual multiplicity of possible magnetization states in individual nanoparticles could be a useful feature for multi-state memory devices. We also show that the magneto-dipolar interaction is almost negligible in these systems, which suggests that the particles could be arranged at high density without experiencing unwanted coupling.

cond-mat.mes-hall↗

arXiv2020

Electric Field Control of Three-Dimensional Vortex States in Core-Shell Ferroelectric Nanoparticles

In the framework of the Landau-Ginzburg-Devonshire approach coupled with electrostatic equations, we performed finite element modeling of the polarization behavior in a ferroelectric barium titanate core covered with a tunable paraelectric strontium titanate shell placed in a polymer or liquid medium. A stable two-dimensional vortex is formed in the core after a zero-field relaxation of an initial random or poly-domain distribution of the polarization, where the vortex axis is directed along one of the core crystallographic axes. Subsequently, sinusoidal pulses of a homogeneous electric field with variable period, strength, and direction are applied. The field-induced changes of the vortex structure consist in the appearance of an axial kernel in the form of a prolate nanodomain, the kernel growth, an increasing orientation of the polarization along the field, and the onset of a single-domain state. We introduced the term "kernel" to name the prolate nanodomain developed near the vortex axis and polarized perpendicular to the vortex plane. In ferromagnetism, this region is generally known as the vortex core. The vortex states with a kernel possess a manifold degeneracy, appearing from three equiprobable directions of vortex axis, clockwise and counterclockwise directions of polarization rotation along the vortex axis, and two polarization directions in the kernel. This multitude of the vortex states in a single core are promising for applications of core-shell nanoparticles and their ensembles as multi-bit memory and related logic units. The rotation of a vortex kernel over a sphere, possible for the core-shell nanoparticles in a soft matter medium with controllable viscosity, may be used to imitate qubit features.

cond-mat.mes-hall↗

arXiv2019

Large-scale magnetostatic field calculation in finite element micromagnetics with H2-matrices

Magnetostatic field calculations in micromagnetic simulations can be numerically expensive, particularly in the case of large-scale finite element simulations. The established finite element / boundary element method (FEM/BEM) by Fredkin & Koehler involves a densely populated matrix with unacceptable numerical costs for problems involving a large number of degrees of freedom $N$. By using hierarchical matrices of $\mathcal{H}^2$ type, we show that the memory requirements for the FEM/BEM method can be reduced dramatically, effectively converting the quadratic complexity $\mathcal{O}(N^2)$ of the problem to a linear one $\mathcal{O}(N)$. We obtain matrix size reductions of nearly $99\%$ in test cases with more than $10^6$ degrees of freedom, and we test the computed magnetostatic energy values by means of comparison with analytic values. The efficiency of the $\mathcal{H}^2$-matrix compression opens the way to large-scale magnetostatic field calculations in micromagnetic modeling, all while preserving the accuracy of the established FEM/BEM formalism.

math.NA↗

arXiv2018

Proposal for a micromagnetic standard problem for materials with Dzyaloshinskii-Moriya interaction

Understanding the role of the Dzyaloshinskii-Moriya interaction (DMI) for the formation of helimagnetic order, as well as the emergence of skyrmions in magnetic systems that lack inversion symmetry, has found increasing interest due to the significant potential for novel spin based technologies. Candidate materials to host skyrmions include those belonging to the B20 group such as FeGe, known for stabilising Bloch-like skyrmions, interfacial systems such as cobalt multilayers or Pd/Fe bilayers on top of Ir(111), known for stabilising Néel-like skyrmions, and, recently, alloys with a crystallographic symmetry where anti-skyrmions are stabilised. Micromagnetic simulations have become a standard approach to aid the design and optimisation of spintronic and magnetic nanodevices and are also applied to the modelling of device applications which make use of skyrmions. Several public domain micromagnetic simulation packages such as OOMMF, MuMax3 and Fidimag already offer implementations of different DMI terms. It is therefore highly desirable to propose a so-called micromagnetic standard problem that would allow one to benchmark and test the different software packages in a similar way as is done for ferromagnetic materials without DMI. Here, we provide a sequence of well-defined and increasingly complex computational problems for magnetic materials with DMI. Our test problems include 1D, 2D and 3D domains, spin wave dynamics in the presence of DMI, and validation of the analytical and numerical solutions including uniform magnetisation, edge tilting, spin waves and skyrmion formation. This set of problems can be used by developers and users of new micromagnetic simulation codes for testing and validation and hence establishing scientific credibility.

cond-mat.other↗

arXiv2014

Numerical micromagnetism of strong inhomogeneities

The size of micromagnetic structures, such as domain walls or vortices, is comparable to the exchange length of the ferromagnet. Both, the exchange length of the stray field $l_s$ and the magnetocrystalline exchange length $l_k$ are material-dependent quantities that usually lie in the nanometer range. This emphasizes the theoretical challenges associated with the mesoscopic nature of micromagnetism: the magnetic structures are much larger than the atomic lattice constant, but at the same time much smaller than the sample size. In computer simulations, the smallest exchange length serves as an estimate for the largest cell size admissible to prevent appreciable discretization errors. This general rule is not valid in special situations where the magnetization becomes particularly inhomogeneous. When such strongly inhomogeneous structures develop, micromagnetic simulations inevitably contain systematic and numerical errors. It is suggested to combine micromagnetic theory with a Heisenberg model to resolve such problems. We analyze cases where strongly inhomogeneous structures pose limits to standard micromagnetic simulations, arising from fundamental aspects as well as from numerical drawbacks.

physics.comp-ph↗

arXiv2014

Analytic form of head-to-head domain walls in thin ferromagnetic cylinders

The one-dimensional problem of a static head-to-head domain wall structure in a thin soft-magnetic nanowire with circular cross-section is treated within the framework of micromagnetic theory. A radius-dependent analytic form of the domain wall profile is derived by decomposing the magnetostatic energy into a monopolar and a dipolar term. We present a model in which the dipolar term of the magnetostatic energy resulting from the transverse magnetization in the center of the domain wall is calculated with Osborn's formulas for homogeneously magnetized ellipsoids [Phys. Rev. 67, 351 (1945)]. The analytic results agree almost perfectly with simulation data as long as the wire diameter is sufficiently small to prevent inhomogeneities of the magnetization along the cross-section. Owing to the recently demonstrated negligible Döring mass of these walls, our results should also apply to the dynamic case, where domain walls are driven by spin-transfer toque effects and/or an axial magnetic field.

cond-mat.mes-hall↗

arXiv2013

Multiscale and multimodel simulation of Bloch point dynamics

We present simulation results on the structure and dynamics of micromagnetic point singularities with atomistic resolution. This is achieved by embedding an atomistic computational region into a standard micromagnetic algorithm. Several length scales are bridged by means of an adaptive mesh refinement and a seamless coupling between the continuum theory and a Heisenberg formulation for the atomistic region. The code operates on graphical processing units and is able to detect and track the position of strongly inhomogeneous magnetic regions. This enables us to reliably simulate the dynamics of Bloch points, which means that a fundamental class of micromagnetic switching processes can be analyzed with unprecedented accuracy. We test the code by comparing it with established results and present its functionality with the example of a simulated field-driven Bloch point motion in a soft-magnetic cylinder.

cond-mat.mes-hall↗

arXiv2013

Spectral analysis of topological defects in an artificial spin-ice lattice

Arrays of suitably patterned and arranged magnetic elements may display artificial spin-ice structures with topological defects in the magnetization, such as Dirac monopoles and Dirac strings. It is known that these defects strongly influence the quasi-static and equilibrium behavior of the spin-ice lattice. Here we study the eigenmode dynamics of such defects in a square lattice consisting of stadium-like thin film elements using micromagnetic simulations. We find that the topological defects display distinct signatures in the mode spectrum, providing a means to qualitatively and quantitatively analyze monopoles and strings which can be measured experimentally.

cond-mat.mes-hall↗

arXiv2011

Quenched Slonczewski-Windmill in Spin-Torque Vortex-Oscillators

We present a combined analytical and numerical study on double-vortex spin-torque nano-oscillators and describe a mechanism that suppresses the windmill modes. The magnetization dynamics is dominated by the gyrotropic precession of the vortex in one of the ferromagnetic layers. In the other layer the vortex gyration is strongly damped. The dominating layer for the magnetization dynamics is determined by the current polarity. Measurements on Fe/Ag/Fe nano-pillars support these findings. The results open up a new perspective for building high quality-factor spin-torque oscillators operating at selectable, well-separated frequency bands.

cond-mat.mes-hall↗

arXiv2011

Spin-Transfer Torque Induced Vortex Dynamics in Fe/Ag/Fe Nanopillars

We report experimental and analytical work on spin-transfer torque induced vortex dynamics in metallic nanopillars with in-plane magnetized layers. We study nanopillars with a diameter of 150 nm, containing two Fe layers with a thickness of 15 nm and 30 nm respectively, separated by a 6 nm Ag spacer. The sample geometry is such that it allows for the formation of magnetic vortices in the Fe disks. As confirmed by micromagnetic simulations, we are able to prepare states where one magnetic layer is homogeneously magnetized while the other contains a vortex. We experimentally show that in this configuration spin-transfer torque can excite vortex dynamics and analyze their dependence on a magnetic field applied in the sample plane. The center of gyration is continuously dislocated from the disk center, and the potential changes its shape with field strength. The latter is reflected in the field dependence of the excitation frequency. In the second part we propose a novel mechanism for the excitation of the gyrotropic mode in nanopillars with a perfectly homogeneously magnetized in-plane polarizing layer. We analytically show that in this configuration the vortex can absorb energy from the spin-polarized electric current if the angular spin-transfer efficiency function is asymmetric. This effect is supported by micromagnetic simulations.

cond-mat.mes-hall↗

arXiv2010

The magnonic limit of domain wall propagation in ferromagnetic nanotubes

We report a study on the field-driven propagation of vortex-like domain walls in ferromagnetic nanotubes. This particular geometry gives rise to a special feature of the static wall configuration, which significantly influences its dynamics. Unlike domain walls in flat strips, the left-right symmetry of domain wall propagation is broken. Furthermore, the domain wall velocity is not limited by the Walker breakdown. Under sufficiently large magnetic fields, the domain wall velocity reaches the velocity of spin waves (about 1000 m/s) and is thereafter connected with a direct emission of spin waves. The moving domain wall maintains its main structure but has characteristic spin-wave tails attached. The spatial profile of this topological soliton is determined by the spin-wave dispersion.

cond-mat.mes-hall↗

arXiv2010

Imaging ferroelectric domains in multiferroics using a low-energy electron microscope in the mirror operation mode

We report on low-energy electron microscopy imaging of ferroelectric domains with submicron resolution. Periodic strips of 'up' and 'down'-polarized ferroelectric domains in bismuth ferrite -a room temperature multiferroic- serve as a model system to compare low-energy electron microscopy with the established piezoresponse force microscopy. The results confirm the possibility of full-field imaging of ferroelectric domains with short acquisition times by exploiting the sensitivity of ultraslow electrons to small variations of the electric potential near surfaces in the "mirror" operation mode.

physics.ins-det↗

arXiv2008

Oersted fields and current density profiles in spin-torque driven magnetization dynamics -- Finite element modelling of realistic geometries

The classical impact of electrical currents on magnetic nanostructures is analyzed with numerical calculations of current-density distributions and Oersted fields in typical contact geometries. For the Oersted field calculation, a hybrid finite element / boundary element method (FEM/BEM) technique is presented which can be applied to samples of arbitrary shape. Based on the FEM/BEM analysis, it is argued that reliable micromagnetic simulations on spin-tranfer-torque driven magnetization processes should include precise calculations of the Oersted field, particularly in the case of pillar contact geometries. Similarly, finite-element simulations demonstrate that numerical calculations of current-density distributions are required, e.g., in the case of magnetic strips with an indentation. Such strips are frequently used for the design of devices based on current-driven domain-wall motion. A dramatic increase of the current density is found at the apex of the notch, which is expected to strongly affect the magnetization processes in such strips.

cond-mat.other↗

arXiv2008

Ultrafast dynamics of a magnetic antivortex - Micromagnetic simulations

The antivortex is a fundamental magnetization structure which is the topological counterpart of the well-known magnetic vortex. We study here the ultrafast dynamic behavior of an isolated antivortex in a patterned Permalloy thin-film element. Using micromagnetic simulations we predict that the antivortex response to an ultrashort external field pulse is characterized by the production of a new antivortex as well as of a temporary vortex, followed by an annihilation process. These processes are complementary to the recently reported response of a vortex and, like for the vortex, lead to the reversal of the orientation of the antivortex core region. In addition to its fundamental interest, this dynamic magnetization process could be used for the generation and propagation of spin waves for novel logical circuits.

cond-mat.mtrl-sci↗

arXiv2005

Influence of domain wall interactions on nanosecond switching in magnetic tunnel junctions

We have obtained microscopic evidence of the influence of domain wall stray fields on the nanosecond magnetization switching in magnetic trilayer systems. The nucleation barrier initiating the magnetic switching of the soft magnetic Fe20Ni80 layer in magnetic tunnel junction-like FeNi/Al2O3/Co trilayers is considerably lowered by stray fields generated by domain walls present in the hard magnetic Co layer. This internal bias field can significantly increase the local switching speed of the soft layer. The effect is visualized using nanosecond time- and layer-resolved magnetic domain imaging and confirmed by micromagnetic simulations.

cond-mat.other↗