Christoph Vogler

3D print of polymer bonded rare-earth magnets, and 3D magnetic field scanning with an end-user 3D printer

3D print is a recently developed technique, for single-unit production, and for structures that have been impossible to build previously. The current work presents a method to 3D print polymer bonded isotropic hard magnets with a low-cost, end-user 3D printer. Commercially available isotropic NdFeB powder inside a PA11 matrix is characterized, and prepared for the printing process. An example of a printed magnet with a complex shape that was designed to generate a specific stray field is presented, and compared with finite element simulation solving the macroscopic Maxwell equations. For magnetic characterization, and comparing 3D printed structures with injection molded parts, hysteresis measurements are performed. To measure the stray field outside the magnet, the printer is upgraded to a 3D magnetic flux density measurement system. To skip an elaborate adjusting of the sensor, a simulation is used to calibrate the angles, sensitivity, and the offset of the sensor. With this setup, a measurement resolut...

Heat-assisted magnetic recording of bit-patterned media beyond 10 Tb/in2

The limits of areal storage density that is achievable with heat-assisted magnetic recording are unknown. We addressed this central question and investigated the areal density of bit-patterned media. We analyzed the detailed switching behavior of a recording bit under various external conditions, allowing us to compute the bit error rate of a write process (shingled and conventional) for various grain spacings, write head positions, and write temperatures. Hence, we were able to optimize the areal density yielding values beyond 10 Tb/in2. Our model is based on the Landau-Lifshitz-Bloch equation and uses hard magnetic recording grains with a 5-nm diameter and 10-nm height. It assumes a realistic distribution of the Curie temperature of the underlying material, grain size, as well as grain and head position.

Magnetoelastic resonance sensor for remote strain measurements

A low cost passive wireless strain sensor is proposed. The basis of the sensor is formed by two softmagnetic magnetostrictive ribbons. The first magnetostrictive ribbon transforms mechanical stress into a stress dependent magnetic field. The second ribbon senses this field by magnetoacoustic oscillations. The resonance frequency directly depends on the applied mechanical stress. For the proposed sensor, a gauge factor Gf, which is defined as the relative change of the resonance frequency divided by the strain ɛ, of Gf = 380 is obtained. This is significantly higher than the gauge factor of standard metal foil strain gages.

Calculation of coercivity of magnetic nanostructures at finite temperatures

We report a finite temperature micromagnetic method (FTM) that allows for the calculation of the coercive field of arbitrary shaped magnetic nanostructures at time scales of nanoseconds to years. Instead of directly solving the Landau-Lifshitz-Gilbert equation, the coercive field is obtained without any free parameter by solving a non linear equation, which arises from the transition state theory. The method is applicable to magnetic structures where coercivity is determined by one thermally activated reversal or nucleation process. The method shows excellent agreement with experimentally obtained coercive fields of magnetic nanostructures and provides a deeper understanding of the mechanism of coercivity.

Thermal switching field distribution of a single domain particle for field-dependent attempt frequency

We present an analytical derivation of the switching field distribution (SFD) at finite temperature for a single domain particle from the Neel-Brown model in the presence of a linearly swept magnetic field. By considering the field dependence of the attempt frequency f0 in the rate equation, we find enhancement of coercivity compared to models using constant f0. The contribution of thermal fluctuations to the standard deviation of the switching field HC derived here reaches values of 10% HC. Considering this contribution, which has been neglected in previous work, is important for the correct interpretation of measurements of switching field distributions.

Landau-Lifshitz-Bloch equation for exchange-coupled grains

Heat assisted recording is a promising technique to further increase the storage density in hard disks. Multilayer recording grains with graded Curie temperature is discussed to further assist the write process. Describing the correct magnetization dynamics of these grains, from room temperature to far above the Curie point, during a write process is required for the calculation of bit error rates. We present a coarse grained approach based on the Landau-Lifshitz-Bloch (LLB) equation to model exchange coupled grains with low computational effort. The required temperature dependent material properties such as the zero-field equilibrium magnetization as well as the parallel and normal susceptibilities are obtained by atomistic Landau-Lifshitz-Gilbert (LLG) simulations. Each grain is described with one magnetization vector. In order to mimic the atomistic exchange interaction between the grains a special treatment of the exchange field in the coarse grained approach is presented.

A three-dimensional spin-diffusion model for micromagnetics.

We solve a time-dependent three-dimensional spin-diffusion model coupled to the Landau-Lifshitz-Gilbert equation numerically. The presented model is validated by comparison to two established spin-torque models: The model of Slonzewski that describes spin-torque in multi-layer structures in the presence of a fixed layer and the model of Zhang and Li that describes current driven domain-wall motion. It is shown that both models are incorporated by the spin-diffusion description, i.e., the nonlocal effects of the Slonzewski model are captured as well as the spin-accumulation due to magnetization gradients as described by the model of Zhang and Li. Moreover, the presented method is able to resolve the time dependency of the spin-accumulation.

A self-consistent spin-diffusion model for micromagnetics.

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.

Areal density optimizations for heat-assisted magnetic recording of high-density media

Heat-assisted magnetic recording (HAMR) is hoped to be the future recording technique for high-density storage devices. Nevertheless, there exist several realization strategies. With a coarse-grained Landau-Lifshitz-Bloch model, we investigate in detail the benefits and disadvantages of a 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 TC and a soft magnetic one with low TC, respectively. To describe the whole write process as realistically 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 pul...

Fundamental limits in heat-assisted magnetic recording and methods to overcome it with exchange spring structures

The switching probability of magnetic elements for heat-assisted recording with pulsed laser heating was investigated. It was found that FePt elements with a diameter of 5 nm and a height of 10 nm show, at a field of 0.5 T, thermally written-in errors of 12%, which is significantly too large for bit-patterned magnetic recording. Thermally written-in errors can be decreased if larger-head fields are applied. However, larger fields lead to an increase in the fundamental thermal jitter. This leads to a dilemma between thermally written-in errors and fundamental thermal jitter. This dilemma can be partly relaxed by increasing the thickness of the FePt film up to 30 nm. For realistic head fields, it is found that the fundamental thermal jitter is in the same order of magnitude of the fundamental thermal jitter in conventional recording, which is about 0.5–0.8 nm. Composite structures consisting of high Curie top layer and FePt as a hard magnetic storage layer can reduce the thermally written-in errors to be sm...