arXiv subjects

Christoph Vogler

Publications and source records attributed to Christoph Vogler.

At least 19 recordsLinked to original sources

arXiv2021

Dipolar-stabilized first and second-order antiskyrmions in ferrimagnetic multilayers

Skyrmions and antiskyrmions are topologically protected spin structures with opposite topological charge. Particularly in coexisting phases, these two types of magnetic quasi-particles may show fascinating physics and potential for spintronic devices. While skyrmions are observed in a wide range of materials, until now antiskyrmions were exclusive to materials with D2d symmetry. In this work, we show first and second-order antiskyrmions stabilized by magnetic dipole-dipole interaction in Fe/Gd-based multilayers. We modify the magnetic properties of the multilayers by Ir insertion layers. Using Lorentz transmission electron microscopy imaging, we observe coexisting antiskyrmions, Bloch skyrmions, and type-2 bubbles and determine the range of material properties and magnetic fields where the different spin objects form and dissipate. We perform micromagnetic simulations to obtain more insight into the studied system and conclude that the reduction of saturation magnetization and uniaxial anisotropy leads to the existence of this zoo of different spin objects and that they are primarily stabilized by dipolar interaction.

cond-mat.mtrl-sci↗

arXiv2020

Chiral switching and dynamic barrier reductions in artificial square ice

Collective dynamics in lithographically-defined artificial spin ices offer profound insights into emergent correlations and phase transitions of geometrically-frustrated Ising spin systems. Their temporal and spatial evolution are often simulated using kinetic Monte Carlo simulations, which rely on the precise knowledge of the switching barriers to obtain predictive results in agreement with experimental observations. In many cases, however, the barriers are derived from simplified assumptions only, and do not take into account the full physical picture of nanomagnetic switching. Here we describe how the immediate magnetic environment of a nanomagnet reversing via quasi-coherent rotation can induce clockwise and counter-clockwise switching channels with different barrier energies. This barrier splitting for chiral reversal channels can be sizeable and, as string-method micromagnetic simulations show, is relevant for artificial spin ice systems made of both exchange -- as well as magnetostatically --dominated units. Due to the barrier splitting (and further reductions due to non-uniform reversal) transition rates can be exponentially enhanced by several orders of magnitude compared to mean-field predictions, especially in the limit of rare switching events where thermal excitation is less likely. This leads to significantly faster relaxation time scales and modified spatial correlations. Our findings are thus of integral importance to achieve realistic kinetic Monte Carlo simulations of emergent correlations in artificial spin systems, magnonic crystals, or the evolution of nanomagnetic logic circuits.

cond-mat.mes-hall↗

arXiv2020

Spin-canting effects in GMR sensors with wide dynamic field range

Magnetoresistive (xMR) sensors find extensive application in science and industry, replacing Hall sensors in various low field environments. While there have been some efforts in increasing the dynamic field range of xMR sensors, Hall sensors remain to dominate high field applications due to their wide linear range. Using a perpendicular magnetized reference system and an in-plane free layer allows us to overcome this disadvantage of xMR sensors, and, furthermore, investigate spin-canting effects in interlayer exchange coupled perpendicular synthetic antiferromagnets (p-SAF). We created p-SAFs with exchange coupling fields of up to 10 kOe, based on magnetic Co/Pt multilayer systems. The p-SAFs are either designed as "single" p-SAFs, where two Co/Pt multilayers are interlayer exchange coupled via a 4 Å thick Ru spacer, or as "double" p-SAFs, where an additional Co layer is interlayer exchange coupled to the top multilayer. These p-SAFs are used for giant magnetoresistance (GMR) sensors with wide dynamic field range. By using a p-SAF as the reference system and employing an in-plane magnetic layer as the GMR's free layer, the linear range can be effectively increased limited only by the p-SAF's switching fields. Additionally, the magnetic anisotropy of the in-plane free layer is fully controlled, which allows saturation fields by design. Different configurations were investigated, ranging from free layer magnetic saturation at lower to far higher fields than the p-SAF's switching fields. We can show through micromagnetic simulations that certain GMR transfer curves are dominated by spin-canting effects in the interlayer exchange coupled reference system. Finally, our simulation results lay out the correlation of the p-SAF's design parameters and its magnetization reversal behavior.

cond-mat.mtrl-sci↗

arXiv2020

Microscopic origin of magnetization reversal in exchange-coupled ferro-/ferrimagnetic bilayers

In this study, the magnetic reversal process of exchange-coupled bilayer systems, consisting of a ferrimagnetic TbFeCo alloy layer and a ferromagnetic [Co/Ni/Pt]N multilayer, was investigated. In particular, minor loop studies, probing solely the reversal characteristics of the softer ferromagnetic layer, reveal two distinct reversal mechanisms, which depend strongly on the thickness of the ferromagnetic layer. For thick layers, irreversible switching of the macroscopic minor loop is observed. The underlying microscopic origin of this reversal process was studied in detail by high-resolution magnetic force microscopy, showing that the reversal is triggered by in-plane domain walls propagating through the ferromagnetic layer. In contrast, thin ferromagnetic layers show a hysteresis-free reversal, which is nucleation-dominated due to grain-to-grain variations in magnetic anisotropy of the Co/Ni/Pt multilayer and an inhomogeneous exchange coupling with the magnetically hard TbFeCo layer, as confirmed by micromagnetic simulations.

cond-mat.mtrl-sci↗

arXiv2020

Dependence of energy barrier reduction on collective excitations in square artificial spin ice: A comprehensive comparison of simulation techniques

We perform micromagnetic simulations to study the switching barriers in square artificial spin ice systems consisting of elongated single domain magnetic islands arranged on a square lattice. By considering a double vertex composed of one central island and six nearest neighbor islands, we calculate the energy barriers between two types of double vertices by applying the string method. We investigate by means of micromagnetic simulations the consequences of the neighboring islands, the inhomogeneities in the magnetization of the islands and the reversal mechanisms on the energy barrier by comparing three different approaches with increasing complexity. The micromagnetic models, where the string method is applied, are compared to the currently common method, the mean barrier approximation. Our investigations indicate that a proper micromagnetic modeling of the switching process leads to significantly lower energy barriers, by up to 35% compared to the mean-barrier approximation, so decreasing the expected average life time up to seven orders of magnitude. Hereby, we investigate the influence of parallel switching channels and the conceptional approach of using a mean-barrier to calculate the corresponding rates.

physics.comp-ph↗

arXiv2020

Hysteresis-free magnetization reversal of exchange-coupled bilayers with finite magnetic anisotropy

Exchange-coupled structures consisting of ferromagnetic and ferrimagnetic layers become technologically more and more important. We show experimentally the occurrence of completely reversible, hysteresis-free minor loops of [Co(0.2 nm)/Ni(0.4 nm)/Pt(0.6 nm)]$_N$ multilayers exchange-coupled to a 20 nm thick ferrimagnetic Tb$_{28}$Co$_{14}$Fe$_{58}$ layer, acting as hard magnetic pinning layer. Furthermore, we present detailed theoretical investigations by means of micromagnetic simulations and most important a purely analytical derivation for the condition of the occurrence of full reversibility in magnetization reversal. Hysteresis-free loops always occur if a domain wall is formed during the reversal of the ferromagnetic layer and generates an intrinsic hard-axis bias field that overcomes the magnetic anisotropy field of the ferromagnetic layer. The derived condition further reveals that the magnetic anisotropy and the bulk exchange of both layers, as well as the exchange coupling strength and the thickness of the ferromagnetic layer play an important role for its reversibility.

cond-mat.mtrl-sci↗

arXiv2019

Statistical analysis of read-back signals in magnetic recording on granular media

The comprehensive simulation of magnetic recording, including the write and read-back process, on granular media becomes computationally expensive if the magnetization dynamics of each grain are explicitly computed. In addition, in heat-assisted magnetic recording, the writing of a single track becomes a random process since the temperature must be considered and thermal noise is involved. Further, varying grain structures of various granular media must also be taken into account to obtain correct statistics for the final read-back signal. Hence, it requires many repetitions of the write process to investigate the mean signal as well as the noise. This work presents a method that improves the statistical evaluation of the whole recording process. The idea is to avoid writing the magnetization to one of its binary states. Instead, we assign each grain its probability of occupying one of its stable states, which can be calculated in advance in terms of a switching probability phase diagram. In the read-back process, we combine the probabilities to calculate a mean signal and its variance. Afterwards, repetitions on different media lead to the final read-back signal. Using a recording example, we show that the statistical behavior of the evaluated signal-to-noise ratio can be significantly improved by applying this probability mapping method, while the computational effort remains low.

physics.app-ph↗

arXiv2019

Hybrid FFT algorithm for fast demagnetization field calculations on non-equidistant magnetic layers

In micromagnetic simulations, the demagnetization field is by far the computationally most expensive field component and often a limiting factor in large multilayer systems. We present an exact method to calculate the demagnetization field of magnetic layers with arbitrary thicknesses. In this approach we combine the widely used fast-Fourier-transform based circular convolution method with an explicit convolution using a generalized form of the Newell formulas. We implement the method both for central processors and graphics processors and find that significant speedups for irregular multilayer geometries can be achieved. Using this method we optimize the geometry of a magnetic random-access memory cell by varying a single specific layer thickness and simulate a hysteresis curve to determine the resulting switching field.

physics.comp-ph↗

arXiv2019

The superior role of the Gilbert damping on the signal-to-noise ratio in heat-assisted magnetic recording

In magnetic recording the signal-to-noise ratio (SNR) is a good indicator for the quality of written bits. However, a priori it is not clear which parameters have the strongest influence on the SNR. In this work, we investigate the role of the Gilbert damping on the SNR. Grains consisting of FePt like hard magnetic material with two different grain sizes $d_1=5\,$nm and $d_2=7\,$nm are considered and simulations of heat-assisted magnetic recording (HAMR) are performed with the atomistic simulation program VAMPIRE. The simulations display that the SNR saturates for damping constants larger or equal than 0.1. Additionally, we can show that the Gilbert damping together with the bit length have a major effect on the SNR whereas other write head and material parameters only have a minor relevance on the SNR.

physics.app-ph↗

arXiv2019

Write head design for effective curvature reduction in heat-assisted magnetic recording by topology optimization

The reduction of the transition curvature of written bits in heat-assisted magnetic recording (HAMR) is expected to play an important role for the future areal density increase of hard disk drives. Recently a write head design with flipped write and return poles was proposed. In this design a large spatial field gradient of the write head was the key to significantly reduce the transition curvature. In this work we optimized the write pole of a heat-assisted magnetic recording head in order to produce large field gradients as well as large fields in the region of the heat pulse. This is done by topology optimization. The simulations are performed with dolfin-adjoint. For the maximum field gradients of $8.1\,$mT/nm, $8.6\,$mT/nm and $11.8\,$mT/nm, locally resolved footprints of an FePt like hard magnetic recording medium are computed with a coarse-grained Landau-Lifshitz-Bloch (LLB) model and the resulting transition curvature is analysed. Additional simulations with a bilayer structure with $50\%$ hard and $50\%$ soft magnetic material are computed. The results show that for both recording media, the optimized head design does not lead to any significant improvement of the written track. Thus, we analyse the transition curvature for the optimized write heads theoretically with an effective recording time window (ERTW) model. Moreover, we check how higher field gradients influence the curvature reduction. The results show that a simple optimization of the conventional head design design is not sufficient for effective curvature reduction. Instead, new head concepts will be needed to reduce transition curvature.

physics.app-ph↗

arXiv2019

Improving the Signal-to-noise Ratio for Heat-Assisted Magnetic Recording by Optimizing a High/Low Tc bilayer structure

We optimize the recording medium for heat-assisted magnetic recording by using a high/low $T_{\mathrm{c}}$ bilayer structure to reduce AC and DC noise. Compared to a former work, small Gilbert damping $α=0.02$ is considered for the FePt like hard magnetic material. Atomistic simulations are performed for a cylindrical recording grain with diameter $d=5\,$nm and height $h=8\,$nm. Different soft magnetic material compositions are tested and the amount of hard and soft magnetic material is optimized. The results show that for a soft magnetic material with $α_{\mathrm{SM}}=0.1$ and $J_{ij,\mathrm{SM}}=7.72\times 10^{-21}\,$J/link a composition with $50\%$ hard and $50\%$ soft magnetic material leads to the best results. Additionally, we analyse how much the areal density can be improved by using the optimized bilayer structure compared to the pure hard magnetic recording material. It turns out that the optimized bilayer design allows an areal density that is $1\,$Tb/in$^2$ higher than that of the pure hard magnetic material while obtaining the same SNR.

physics.app-ph↗

arXiv2019

Systematic parameterization of heat-assisted magnetic recording switching probabilities and the consequences for the resulting SNR

The signal-to-noise ratio (SNR) of a bit series written with heat-assisted magnetic recording (HAMR) on granular media depends on a large number of different parameters. The choice of material properties is essential for the obtained switching probabilities of single grains and therefore for the written bits' quality in terms of SNR. Studies where the effects of different material compositions on transition jitter and the switching probability are evaluated were done, but it is not obvious, how significant those improvements will finally change the received SNR. To investigate that influence, we developed an analytical model of the switching probability phase diagram, which contains independent parameters for, inter alia, transition width, switching probability and curvature. Different values lead to corresponding bit patterns on granular media, where a reader model detects the resulting signal, which is finally converted to a parameter dependent SNR value. For grain diameters between 4 and 8nm, we show an increase of ~10dB for bit lengths between 4 and 12nm, an increase of ~9dB for maximum switching probabilities between 0.64 and 1.00, a decrease of ~5dB for down-track-jitter parameters between 0 and 4nm and an increase of ~1dB for reduced bit curvature. Those results are furthermore compared to the theoretical formulas for the SNR. We obtain a good agreement, even though we show slight deviations.

physics.app-ph↗

arXiv2018

GPU Accelerated Atomistic Energy Barrier Calculations of Skyrmion Annihilations

We present GPU accelerated simulations to calculate the annihilation energy of magnetic skyrmions in an atomistic spin model considering dipole-dipole, exchange, uniaxial-anisotropy and Dzyaloshinskii-Moriya interactions using the simplified string method. The skyrmion annihilation energy is directly related to its thermal stability and is a key measure for the applicability of magnetic skyrmions to storage and logic devices. We investigate annihilations mediated by Bloch points as well as annihilations via boundaries for various interaction energies. Both processes show similar behaviour, with boundary annihilations resulting in slightly smaller energy barriers than Bloch point annihilations.

physics.comp-ph↗

arXiv2018

Spin Torque Efficiency and Analytic Error Rate Estimates of Skyrmion Racetrack Memory

In this paper the thermal stability of skyrmion bubbles and the critical currents to move them over pinning sites is investigated. For the used pinning geometries and the used parameters, the unexpected behavior is reported that the energy barrier to overcome the pinning site is larger than the energy barrier of the annihilation of a skyrmion. The annihilation takes place at boundaries by current driven motion as well as due to the excitation over energy barriers, in the absence of currents, without forming Bloch points. It is reported that the pinning sites, which are required to allow thermally stable bits, significantly increase the critical current densities to move the bits in skyrmion like structures to about $j_{crit}$ = 0.62 TA/m$^2$. These currents are similar to those obtained experimentally to move stable skyrmions at room temperature. By calculating the thermal stability as well as the critical current, we can derive the spin torque efficiency $η$ = $Δ/I_c = 0.19 k_BT_{300}~/μ$A, which is in a similar range to the simulated spin torque efficiency of MRAM structures. Finally, it is shown that the stochastic depinning process of any racetrack like device requires extremely narrow depinning time distribution smaller than ~6% of the current pulse length to reach bit error rates smaller than ${10^{ - 9}}$.

cond-mat.mtrl-sci↗

arXiv2018

Large Scale Finite-Element Simulation of Micromagnetic Thermal Noise

An efficient method for the calculation of ferromagnetic resonant modes of magnetic structures is presented. Finite-element discretization allows flexible geometries and location dependent material parameters. The resonant modes can be used for a semi-analytical calculation of the power spectral density of the thermal white-noise, which is relevant for many sensor applications. The proposed method is validated by comparing the noise spectrum of a nano-disk with time-domain simulations.

physics.comp-ph↗

arXiv2018

Curie temperature modulated structure to improve the performance in heat-assisted magnetic recording

We investigate how a temperature reduction in z-direction influences the switching probability and the noise in heat-assisted magnetic recording (HAMR) for a bit in bit-patterned media with dimensions d=5nm and h=10nm. Pure hard magnetic bits are considered and simulations with a continuous laser pulse are performed using the atomistic simulation tool VAMPIRE. The results display that the switching behavior shows a thermally induced exchange spring effect. Simultaneously, both the AC and the DC noise increase. Additionally, we illustrate how an artificial Curie temperature gradient within the material can compensate the HAMR performance loss due to the temperature gradient. Further, due to the graded Curie temperature, DC noise can be reduced compared to a structure where no temperature gradient is considered.

cond-mat.mtrl-sci↗

arXiv2018

Stochastic ferrimagnetic Landau-Lifshitz-Bloch equation for finite magnetic structures

Precise modeling of the magnetization dynamics of nanoparticles with finite size effects at fast varying temperatures is a computationally challenging task. Based on the Landau-Lifshitz-Bloch (LLB) equation we derive a coarse grained model for disordered ferrimagnets, which is both fast and accurate. First, we incorporate stochastic fluctuations to the existing ferrimagnetic LLB equation. Further, we derive a thermodynamic expression for the temperature dependent susceptibilities, which is essential to model finite size effects. Together with the zero field equilibrium magnetization the susceptibilities are used in the stochastic ferrimagnetic LLB to simulate a $5\times10$ nm$^2$ ferrimagnetic GdFeCo particle with 70 % FeCo and 30 % Gd under various external applied fields and heat pulses. The obtained trajectories agree well with those of an atomistic model, which solves the stochastic Landau-Lifshitz-Gilbert equation for each atom. Additionally, we derive an expression for the intergrain exchange field which couple the ferromagnetic sublattices of a ferrimagnet. A comparison of the magnetization dynamics obtained from this simpler model with those of the ferrimagnetic LLB equation shows a perfect agreement.

cond-mat.mtrl-sci↗

arXiv2017

Topologically Protected Vortex Structures to Realize Low-Noise Magnetic Sensors

Micromagnetic sensors play a major role towards the miniaturization in the industrial society. The adoption of new and emerging sensor technologies like anisotropic magnetoresistance (AMR), giant magnetoresistance (GMR) and tunnel magnetoresistance (TMR) sensors are mainly driven by their integrability and enhanced sensitivity. At the core of such sensors, a microstructured ferromagnetic thin film element transduces the magnetic signal. Such elements usually switch via multi-domain, C- or S-shaped magnetization states and, therefore, often exhibit an open non-linear hysteresis curve. Linearity and hysteretic effects, as well as magnetic noise are key features in the improvement of such sensors. Here, we report on the physical origin of these disturbing factors and the inherent connection of noise and hysteresis. Critical noise sources are identified by means of analytic and micromagnetic models. The dominant noise source is due to irreproducible magnetic switching of the transducer element at external fields close to the Stoner Wohlfarth switching field. Furthermore, a solution is presented to overcome these limiting factors: a disruptive sensor design is proposed and analyzed which realizes a topologically protected magnetic vortex state in the transducer element. Compared to state of the art sensors the proposed sensor layout has negligible hysteresis, a linear regime about an order of magnitude higher and lower magnetic noise making the sensor ideal candidate for applications ranging from automotive industry to biological application.

cond-mat.mes-hall↗