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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., Comment: 8 pages, 7 figures

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., arXiv admin note: text overlap with arXiv:1709.03764

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.

A skyrmion racetrack design is proposed that allows for thermally stable skyrmions to code information and dynamical pinning sites that move with the applied current. This concept solves the problem of intrinsic distributions of pinning times and pinning currents of skyrmions at static geometrical or magnetic pinning sites. The dynamical pinning sites are realized by a skyrmion carrying wire, where the skyrmion repulsion is used in order to keep the skyrmions at equal distances. The information is coded by an additional layer where the presence and absence of a skyrmion is used to code the information. The lowest energy barrier for a data loss is calculated to be DE = 55 kBT300 which is sufficient for long time thermal stability.

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 $\eta$ = $\Delta/I_c = 0.19 k_BT_{300}~/\mu$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 ${10^{ - 9}}$.

It is assumed that heat-assisted magnetic recording (HAMR) is the recording technique of the future. For pure hard magnetic grains in high density media with an average diameter of $5$nm and a height of $10$nm the switching probability is not sufficiently high for the use in bit-patterned media. Using a bilayer structure with 50$\%$ hard magnetic material with low Curie temperature and 50$\%$ soft magnetic material with high Curie temperature to obtain more than 99.2$\%$ switching probability, leads to very large jitter. We propose an optimized material composition to reach a switching probability of $P_{\mathrm{switch}}>99.2\%$ and simultaneously achieve the narrow transition jitter of pure hard magnetic material. Simulations with a continuous laser spot were performed with the atomistic simulation program VAMPIRE for a single cylindrical recording grain with a diameter of 5nm and a height of 10nm. Different configurations of soft magnetic material and different amounts of hard and soft magnetic material were tested and discussed. Within our analysis, a composition with 20$\%$ soft magnetic and $80\%$ hard magnetic material reaches the best results with a switching probability $P_{\mathrm{switch}}>99.2\%$, an off-track jitter parameter $\sigma_{\mathrm{off},80/20}=14.2$K and a down-track jitter parameter $\sigma_{\mathrm{down},80/20}=0.49$nm., Comment: 7 pages, 10 figures

High storage density and high data rate are two of the most desired properties of modern hard disk drives. Heat-assisted magnetic recording (HAMR) is believed to achieve both. Recording media, consisting of exchange coupled grains with a high and a low $T_{\mathrm{C}}$ part, were shown to have low DC noise, but increased AC noise, compared to hard magnetic single phase grains, like FePt [1]. In this work we extensively investigate the influence of an FeRh interlayer on the magnetic noise in exchange coupled grains. We find an optimal grain design that reduces the jitter in down-track direction by up to 30 % and in off-track direction by up to 50 %, depending on the head velocity, compared to the same structures without FeRh. Further, the mechanisms causing this jitter reduction are demonstrated. Additionally, we show that for ultrashort heat pulses and low write temperatures the switching time distribution of the analyzed grain structure is reduced by a factor of four, compared to the same structure without FeRh layer. This feature could be interesting for HAMR with a pulsed laser spot and could resume the discussion about this HAMR technique.

We propose a three-dimensional micromagnetic model that dynamically solves the Landau-Lifshitz-Gilbert equation coupled to the full spin-diffusion equation. In contrast to previous methods, we solve for the magnetization dynamics and the electric potential in a self-consistent fashion. This treatment allows for an accurate description of magnetization dependent resistance changes. Moreover, the presented algorithm describes both spin accumulation due to smooth magnetization transitions and due to material interfaces as in multilayer structures. The model and its finite-element implementation are validated by current driven motion of a magnetic vortex structure. In a second experiment, the resistivity of a magnetic multilayer structure in dependence of the tilting angle of the magnetization in the different layers is investigated. Both examples show good agreement with reference simulations and experiments respectively.

We report two effects that lead to a reduction of the switching field distribution in exchange spring media. The first effect relies on a subtle mechanism of the interplay between exchange coupling between soft and hard layers and anisotropy that allows significant reduction of the switching field distribution in exchange spring media. This effect reduces the switching field distribution by about 30% compared to single-phase media. A second effect is that due to the improved thermal stability of exchange spring media over single-phase media, thermal fluctuation leads to reduced fundamental transition jitter. The influence of this overall improved switching field distribution on the transition jitter in granular recording and the bit error rate in bit-patterned magnetic recording is discussed. The transition jitter in granular recording for a distribution of K1 values of 3% in the hard layer, taking into account thermal fluctuations during recording, is estimated to be a = 0.78 nm, which is similar to the best reported calculated jitter in optimized heat-assisted recording media.

Heat-assisted-magnetic recording (HAMR) is hoped to be the future recording technique for high density storage devices. Nevertheless, there exist several realizations strategies. With a coarse-grained Landau-Lifshitz-Bloch (LLB) model we investigate in detail benefits and disadvantages of continuous and pulsed laser spot recording of shingled and conventional bit-patterned media. Additionally we compare single phase grains and bits having a bilayer structure with graded Curie temperature, consisting of a hard magnetic layer with high $T_{\mathrm{C}}$ and a soft magnetic one with low $T_{\mathrm{C}}$, respectively. To describe the whole write process as realistic as possible a distribution of the grain sizes and Curie temperatures, a displacement jitter of the head and the bit positions are considered. For all these cases we calculate bit error rates of various grain patterns, temperatures and write head positions to optimize the achievable areal storage density. Within our analysis shingled HAMR with a continuous laser pulse moving over the medium reaches the best results, and thus having the highest potential to become the next generation storage device.

Magnetische Prozesse umfassen einen gro��en Bereich von Zeitskalen, welcher von Jahrzehnten, in denen sich typischerweise die thermische Stabilit��t von magnetischen Speicherk��rnern in Festplatten befindet, bis zu wenigen Pikosekunden, in welchen ultraschnelle Ummagnetisierungsprozesse ablaufen, reicht. Ziel der vorliegenden Arbeit ist es, das Verhalten magnetischer Nanostrukturen zu beschreiben. Im Speziellen wird der Einfluss der Temperatur sowohl auf deren Langzeitstabilit��t als auch auf ihre Dynamik w��hrend sehr kurzer Zeiten untersucht. Festplatten bestehen aus zahlreichen magnetischen K��rnern mit Gr����en im Nanometerbereich. Um Information bin��r auf eine Festplatte codieren zu k��nnen, muss die Magnetisierung jedes Korns entsprechend ausgerichtet werden. Aufgrund von thermischen Fluktuationen kann sich der magnetische Zustand nach gen��gend langen Zeiten willk��rlich ��ndern. Da jedoch sehr lange Wartezeiten zwischen aufeinanderfolgenden Ummagnetisierungsprozessen liegen, ist eine Absch��tzung der Stabilit��t der gespeicherten Information durch direkte Aufintegration der stochastischen Landau-Lifshitz-Gilbert (LLG) Gleichung, welche die grundlegende Bewegungsgleichung der magnetischen Momente in Rahmen des Mikromagnetismus beschreibt, praktisch nicht realisierbar. Die vorliegende Arbeit adaptiert die statistische Methode des Forward Flux Samplings (FFS) f��r den Mikromagnetismus. FFS erlaubt es die Raten von seltenen Ereignissen effizient zu berechnen, ohne dabei die langen Wartezeiten zwischen den ��berg��ngen simulieren zu m��ssen. Daher ist es m��glich thermische Stabilit��ten von Jahren mit Simulationen im Nanosekundenbereich vorherzusagen. Zur Veranschaulichung wird die Stabilit��t eines Korns mit abgestufter Anisotropiekonstante mit den entsprechenden Stabilit��ten von K��rnern mit homogenem Material und unterschiedlichen Eigenschaften verglichen. Im zweiten Teil der vorliegenden Arbeit wird hitzeunterst��tzes magnetisches Schreiben von Daten behandelt. Bei dieser erst k��rzlich entwickelten Technik erhitzt ein Laserpuls lokal und im Bruchteil einer Nanosekunde die K��rner einer Festplatte nahe an oder ��ber die Curie-Temperatur. Bei der Curie-Temperatur verschwindet die makroskopische Magnetisierung eines ferromagnetischen Teilchens und es wird paramagnetisch. Unter diesen Voraussetzungen verliert die mikromagnetische Annahme einer konstanten Magnetisierungsl��nge ihre G��ltigkeit, wodurch das System direkt mit dem Heisenberg Modell beschrieben werden muss. Die stochastische Landau-Lifshitz-Bloch (LLB) Gleichung erweitert den Mikromagnetismus in der Weise, dass es nun auch zu einer longitudinalen Relaxation der Magnetisierung kommen kann, wodurch die Magnetisierungsdynamik auch bei hohen Temperaturen weiterhin korrekt repr��sentiert werden kann. In dieser Arbeit wird ein grobk��rniges Modell, welches auf der LLB Gleichung basiert, entwickelt, um magnetische K��rner mit m��glichst wenig Rechenaufwand zu beschreiben. Spezielles Augenmerk wird dabei auf die korrekte Behandlung der Austauschwechselwirkung zwischen Lagen mit unterschiedlichen Materialien eines Korns gelegt. Mit diesem Modell k��nnen somit magnetische K��rner f��r den Einsatz im hitzeunterst��tzten magnetischen Schreiben schnell und zuverl��ssig optimiert werden., Magnetic processes cover a large range of time scales varying from decades, which is typically the thermal stability of magnetic recording grains, to picoseconds where ultrafast reversal processes take place. This work describes the behavior of magnetic nanostructures in the whole time range. In particular, it investigates the influence of temperature on both, the long-term stability and responses during very short time intervals. Hard disk drives (HDDs) consist of various magnetic grains on the scale of nanometers. In order to encode binary information on a HDD the magnetization of each grain has to be aligned. Due to thermal fluctuations such a magnetic particle can randomly change its state after some time. Since there exist long waiting times between two magnetization reversals, it is infeasible to predict the stability of the stored information, by directly integrating the stochastic Landau-Lifshitz-Gilbert (LLG) equation, which represents the equation of motion of magnetic moments in the context of micromagnetism. This work adapts the statistical method of forward flux sampling (FFS) to micromagnetism. FFS allows to efficiently calculate the rate constants of rare events, without the necessity of simulating the system during the long waiting times between the transitions. Thus, it is possible to predict thermal stabilities of years with simulations in the nanosecond regime, without any free parameters. As an example, the stability of one graded media grain is compared with those of single phase grains with different properties. The second part of this work addresses the modelling of heat-assisted recording. This is a recently developed technique, where a laser pulse locally heats the grains of a HDD near to or above the Curie temperature in a fraction of a nanosecond. At the Curie temperature the macroscopic magnetization of a ferromagnetic particle vanishes and it becomes paramagnetic. Under these conditions the micromagnetic assumption of a constant magnetization length fails and the magnetic system has to be described directly by the Heisenberg model. The stochastic Landau-Lifshitz-Bloch (LLB) equation extends micromagnetism, because it also considers the longitudinal relaxation of the magnetization, and thus correctly describes the magnetization dynamics at high temperatures. In this work a coarse-grained model based on the LLB equation is developed to describe whole magnetic grains with little computational effort. Special emphasis is put on the correct treatment of the exchange coupling between different material layers in a grain. With this model it is possible to optimize magnetic grains for heat-assisted recording fast and reliably.

We present an analytical derivation of the switching field distribution for a single domain particle from the N\'eel-Brown model in the presence of a linearly swept magnetic field and influenced by thermal fluctuations. We show that the switching field distribution corresponds to a probability density function and can be obtained by solving a master equation for the not-switching probability together with the transition rate for the magnetization according to the Arrhenius-N\'eel Law. By calculating the first and second moments of the probability density function we succeed in modeling rate-dependent coercivity and the standard deviation of the coercive field. Complementary to the analytical approach, we also present a Monte Carlo simulation for the switching of a macrospin, which allows us to account for the field dependence of the attempt frequency. The results show excellent agreement with results from a Langevin dynamics simulation and therefore point out the importance to include the relevant dependencies in the attempt frequency. However, we conclude that the N\'eel-Brown model fails to predict switching fields correctly for common field rates and material parameters used in magnetic recording from the loss of normalization of the probability density function. Investigating the transition regime between thermally assisted and dynamic switching will be of future interest regarding the development of new magnetic recording technologies.

We present an analytical derivation of the switching field distribution for a single domain particle from the N��el-Brown model in the presence of a linearly swept magnetic field and influenced by thermal fluctuations. We show that the switching field distribution corresponds to a probability density function and can be obtained by solving a master equation for the not-switching probability together with the transition rate for the magnetization according to the Arrhenius-N��el Law. By calculating the first and second moments of the probability density function we succeed in modeling rate-dependent coercivity and the standard deviation of the coercive field. Complementary to the analytical approach, we also present a Monte Carlo simulation for the switching of a macrospin, which allows us to account for the field dependence of the attempt frequency. The results show excellent agreement with results from a Langevin dynamics simulation and therefore point out the importance to include the relevant dependencies in the attempt frequency. However, we conclude that the N��el-Brown model fails to predict switching fields correctly for common field rates and material parameters used in magnetic recording from the loss of normalization of the probability density function. Investigating the transition regime between thermally assisted and dynamic switching will be of future interest regarding the development of new magnetic recording technologies.

Magnetoelastic sensors are used in a wide field of wireless sensing applications. The sensing element is a low-cost magnetostrictive ribbon whose resonant frequency depends on the measured quantity. The accuracy of magnetoelastic sensors is limited by the fact that the resonant frequency is also affected by the earth's magnetic field. In this paper we present a technique to minimize this effect by applying an antisymmetric magnetic bias field to the ribbon. The ribbon's response to external perturbation fields was measured and compared to a conventional sensor design. Our results show that the influence of the earth's magnetic field could be reduced by 77%.

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.