Photo-electrochemical (PEC) water splitting of hematite photoanodes suffers from low performance and efficiency. One way to increase the performance is to increase the electrochemically active surface area available for the oxygen evolution reaction. In this study, we use high ion flux, low energy helium plasma exposure to nanostructure sputtered iron thin films. Subsequent annealing in air at 645C leads to the formation of PEC active hematite (a-Fe2O3) phase in these films. The surface area, as derived from electrochemical impedance spectroscopy (EIS), was seen to increase 10e40 times with plasma exposure. The photocurrent density increased by 2e5 times for the plasma exposed films as compared to the unexposed films. However, the less nanostructured film showed a higher photocurrent density. These findings were explained by detailed chemical and structural characterization in combination with electrochemical characterization and attributed to the presence of secondary elements in the film as well as to the presence of secondary iron oxide phases apart from hematite. This work demonstrates the complex effect of plasma exposure on both film morphology and chemical composition of PEC thin films and provides further understanding on how this technique can be used for nanostructuring of other functional films.
A nonlinear magnetoresistance—called unidirectional spin-Hall magnetoresistance—is recently experimentally discovered in metallic bilayers consisting of a heavy metal and a ferromagnetic metal. To study the fundamental mechanism of unidirectional spin-Hall magnetoresistance (USMR), both ferromagnetic and heavy metallic layer thickness dependence of the USMR are presented in a Pt/Co/AlOx trilayer at room temperature. To avoid ambiguities, second harmonic Hall measurements are used for separating spin-Hall and thermal contributions to the non-linear magnetoresistance. The experimental results are fitted by using a drift-diffusion theory, with parameters extracted from an analysis of longitudinal resistivity of the Co layer within the framework of the Fuchs-Sondheimer model. A good agreement with the theory is found, demonstrating that the USMR is governed by both the spin-Hall effect in the heavy metallic layer and the metallic diffusion process in the ferromagnetic layer.
Thin films of Fe have been epitaxially sputtered on GaAs substrates with native oxide removal prior to the deposition carried out by an Ar ion milling. Films grown at substrate temperatures above 100 C show well-defined fourfold anisotropies. The onset of epitaxial growth is accompanied by an increase in the surface roughness with growth occurring in a distinct island-like pattern. The Fe layers show significantly reduced moments, which decrease with increasing temperature. Antiferromagnetic coupling between Fe layers with Cr spacers was measured in a multilayer with a Cr thickness of 2.7 nm, around the second antiferromagnetic peak.The magnetic properties of the films are discussed in the context of multilayer storage applications.
Three-dimensional (3D) nanomagnetic devices are attracting significant interest due to their potential for computing, sensing, and biological applications. However, their implementation faces great challenges regarding fabrication and characterization of 3D nanostructures. Here, we show a 3D nanomagnetic system created by 3D nanoprinting and physical vapor deposition, which acts as a conduit for domain walls. Domains formed at the substrate level are injected into a 3D nanowire, where they are controllably trapped using vectorial magnetic fields. A dark-field magneto-optical method for parallel, independent measurement of different regions in individual 3D nanostructures is also demonstrated. This work will facilitate the advanced study and exploitation of 3D nanomagnetic systems.
We present the results of a numerical study into mode conversion in an InP waveguide covered by an out-of-plane magnetized CoFe strip through the magneto-optical Kerr effect. We find that when the magnetisation direction in the strip is periodically switched along its length mode conversion is enhanced by a factor of 5 compared to a uniform magnetisation. We investigate the optical loss of ultrathin magnetic film claddings with perpendicular magnetic anisotropy and find that losses can be reduced by over a factor of two. The device envisioned could function as a mode converter that can be switched on and off by toggling the magnetic state. The non-reciprocal effects inherent in magneto-optics offer possibilities for optical isolator or circulator devices.
We show that scanning electron microscopy with polarization analysis (SEMPA) that is sensitive to both in-plane magnetization components can be used to image the out-of-plane magnetized multi-domain state in multilayered chiral spin textures. By depositing a thin layer of Fe on top of the multilayer, we image the underlying out-of-plane domain state through the mapping of its stray fields in the Fe. We also demonstrate that SEMPA can be used to image the domain wall chirality in these systems after milling away the capping layer and imaging the topmost magnetic layer directly.
We recently described the use of Ti(0) microfibers as an anodization substrate for the preparation of TiO2 nanotubes arrays as porous photoanodes. Here, we report the use of these fibers as a scaffold to build porous photoanodes based on a WO3/BiVO4 heterojunction. The obtained photoelectrodes show promising results under visible light irradiation for water oxidation both in a typical liquid-phase photoelectrochemical setup and in a gas phase reactor (developed in-house) based on a polymeric electrolyte membrane.
The magnetic reversal of epitaxial Fe/Cr/Fe trilayer samples grown on GaAs is studied. In wedged samples both long and short period coupling oscillations associated with Ruderman–Kittel–Kasuya–Yosida (RKKY) coupling in Cr are seen in the easy axis saturation fields. By using vector vibrating sample magnetometry and both longitudinal and transverse magnetooptical Kerr effect magnetometry we are able to determine the exact reversal path of both the magnetic layers. Changes in the reversal behavior are seen with sub-monolayer changes of the thickness of the Cr interlayer. The two main reversal paths are described in terms of whether the reversal is dominated by bilinear RKKY coupling, which leads to an antiparallel state at remanence or by biquadratic coupling which leads to a 90 degree alignment of layers at remanence. The changing reversal behaviour is discussed with respect to the possibility of using such systems for multilayer memory applications and, in particular, the limits on the required accuracy of the sample growth.
High flux, lowenergy He plasma exposure is proven to nanostructure iron thin films over their entire thickness to a highly open structure with large surface area. Froma large set of plasma exposure parameters, the ion flux, the surface temperature, and the plasma exposure time are found to be the most relevant parameters to processmechanically stable, nanostructured Fe thin films on brittle glass substrates. The nanostructure stays stable during oxidation. Different surface morphologies are found, depending on the location where the plasma plume interacts with the thin film. This method paves the way to a new direction in top down nanostructuring of thin films, which can be adopted for many functional materials in diverse applications that require a high ratio of active to projected surface area..
The Rashba effect leads to a chiral precession of the spins of moving electrons, while the Dzyaloshinskii-Moriya interaction (DMI) generates preference towards a chiral profile of local spins. We predict that the exchange interaction between these two spin systems results in a “chiral” magnetoresistance depending on the chirality of the local spin texture. We observe this magnetoresistance by measuring the domain wall (DW) resistance in a uniquely designed Pt/Co/Pt zigzag wire and by changing the chirality of the DW with applying an in-plane magnetic field. A chiralitydependent DW resistance is found, and a quantitative analysis shows a good agreement with a theory based on the Rashba model. Moreover, the DW resistance measurement allows us to independently determine the strength of the Rashba effect and the DMI simultaneously, and the result implies a possible correlation between the Rashba effect, the DMI, and the symmetric Heisenberg exchange.
The Ruderman–Kittel–Kasuya–Yosida (RKKY) coupling between two magnetic layers leads to many important technological applications. Here, the interaction between changing antiferromagnetic RKKY coupling and domain structure is studied in a sample consisting of two 5 nm thick CoFeB layers separated by a wedge of Cu up to 4 nm thick. Magnetic reversal occurs via the propagation of a zigzag domain wall front along the wedge. The modification of domain patterns created in the reversal of a coupled layers in the presence of antiferromagnetic RKKY coupling and coupling gradients is demonstrated. Firstly, the coupling leads to a smaller amplitude of the zigzag wall, which is aligned perpendicular to the easy axis, followed by elongation of the walls at higher coupling strength. The antiferromagnetic RKKY coupling, while not strong enough to cause antiparallel alignment of the layers, is argued to lead to coupling between the spins in the domain walls in the two layers, lowering their energy and driving the reversal behavior of the film.
Magnetic kink solitons are used as a probe to experimentally measure the layer-by-layer coercivity and interlayer coupling strength of an antiferromagnetically coupled perpendicularly magnetized Co multilayer. The magnetic response is well described by a nearest neighbor Ising macrospin model. By controlling the position of one, two or three solitons in the stack using globally applied magnetic fields, we successfully probe the switching of individual buried layers under different neighboring configurations, allowing us to access individual layerʼs characteristic parameters. We found the coercivity to increase dramatically up the multilayer, while the interlayer coupling strength decreased slightly. We corroborate these findings with scanning transmission electron microscopy images where a degrading quality of the multilayer is observed. This method provides a very powerful tool to characterize the quality of individual layers in complex multilayers, without the need for depth-sensitive magnetic characterization equipment.
In magnetic multilayer systems, a large spin-orbit coupling at the interface between heavy metals and ferromagnets can lead to intriguing phenomena such as the perpendicular magnetic anisotropy, the spin Hall effect, the Rashba effect, and especially the interfacial Dzyaloshinskii–Moriya (IDM) interaction. This interfacial nature of IDM interaction has been recently revisited because of its scientific and technological potential. Here we demonstrate an experimental technique to straightforwardly observe the IDM interaction, namely Brillouin light scattering. The non-reciprocal spin wave dispersions, systematically measured by Brillouin light scattering, allow not only the determination of the IDM energy densities beyond the regime of perpendicular magnetization but also the revelation of the inverse proportionality with the thickness of the magnetic layer, which is a clear signature of the interfacial nature. Altogether, our experimental and theoretical approaches involving double time Green’s function methods open up possibilities for exploring magnetic hybrid structures for engineering the IDM interaction.
We analyze the impact of growth conditions on the asymmetric magnetic bubble expansion under an in-plane field in ultrathin Pt/Co/Pt films. Specifically, using sputter deposition, we vary the Ar pressure during the growth of the top Pt layer. This induces a large change in the interfacial structure as evidenced by a factor three change in the effective perpendicular magnetic anisotropy. Strikingly, a discrepancy between the current theory for domain-wall propagation based on a simple domain-wall energy density and our experimental results is found. This calls for further theoretical development of domain-wall creep under in-plane fields and varying structural asymmetry.
Thin films of Co and Co/Cu/Co trilayers with wedged Cu interlayers were grown epitaxially on Cu buffer layers on hydrogen passivated Si(001) wafers. We find that single Co layers have a well-defined four-fold anisotropy but with smaller in-plane anisotropies than observed in Co grown on Cu crystals. Ruderman–Kittel–Kasuya–Yosida (RKKY) interlayer coupling is observed in one Co/Cu/Co sample which is the smoothest of the films as measured by atomic force microscopy. Some of the films also form a dot-like structure on the surface. Intermixing at elevated temperatures between the Cu buffer and Si limits the ability to form flat surfaces to promote RKKY coupling.
We demonstrate ratchet soliton propagation in individual patterned antiferromagnetically coupled superlattice elements down to 3 lm diameter using magneto-optical Kerr effect measurements. The bulk switching and soliton propagation fields are investigated as a function of the element size. It is found that on the length scale investigated here we do not see significant variation in ratchet behavior depending on the element size. The margin for soliton propagation and additional features related to downscaling are discussed.
The propagation of a kink soliton through a perpendicularly magnetized antiferromagnetically coupled multilayer stack has been imaged by scanning laser Kerr microscopy. The soliton behavior allows layer-by-layer reversal leading to clear evidence of changes of switching behavior of different layers in the stack. We find that the density of domain nucleation sites is dependent on the confguration of the neighboring layers as well as height up the stack. By growing a series of single layer and coupled trilayer samples, we are able to explain the trends in nucleation seen in the soliton stack in terms of pinhole and orange peel coupling, in agreement with STEM (Scanning transmission electron microscope) imaging.
Focused-electron-beam-induced deposition (FEBID) is employed to create freestanding magnetic nanostructures. By growing Fe nanopillars on top of a perpendicular magnetic domain wall (DW) conduit, pinning of the DWs is observed due to the stray fields emanating from the nanopillar. Furthermore, a different DW pinning behavior is observed between the up and down magnetic states of the pillar, allowing to deduce the switching fields of the pillar in a novel way. The implications of these results are two-fold: not only can 3-dimensional nano-objects be used to control DW motion in applications, it is also proposed that DW motion is a unique tool to probe the magnetic properties of nano-objects.
Spintronic devices have in general demonstrated thefeasibility of non-volatile memory storage and simple Boolean logic operations. Modern microprocessors have one further frequently used digital operation: bit-wise operations on multiple bits simultaneously. Such operations are important for binary multiplication and division and in efficient microprocessor architectures such as Reduced Instruction Set Computing (RISC). In this letter we show a 4-stage vertical serial shift register made from RKKY coupled ultrathin (0.9 nm) perpendicularly magnetised layers into which a 3-bit data word is injected. The entire 4 stage shift register occupies a total length (thickness) of only 16 nm. We show how under the action of an externally applied magnetic field bits can be shifted together as a word and then manipulated individually, including being brought together to perform logic operations. This is one of the highest level demonstrations of logic operation ever performed on data in the magneticstate and brings closer the possibility of ultrahigh density all-magnetic microprocessors.
One of the key challenges for future electronic memory and logic devices is finding viable ways of moving from today’s two-dimensional structures, which hold data in an x–y mesh of cells, to three-dimensional structures in which data are stored in an x–y–z lattice of cells. This could allow a many-fold increase in performance. A suggested solution is the shift register — a digital building block that passes data from cell to cell along a chain. In conventional digital microelectronics, two-dimensional shift registers are routinely constructed from a number of connected transistors. However, for three-dimensional devices the added process complexity and space needed for such transistors would largely cancel out the benefits of moving into the third dimension. ‘Physical’ shift registers, in which an intrinsic physical phenomenon is used to move data near-atomic distances, without requiring conventional transistors, are therefore much preferred. Here we demonstrate a way of implementing a spintronic unidirectional vertical shift register between perpendicularly magnetized ferromagnets of subnanometre thickness, similar to the layers used in non-volatile magnetic random-access memory. By carefully controlling the thickness of each magnetic layer and the exchange coupling between the layers, we form a ratchet that allows information in the form of a sharp magnetic kink soliton to be unidirectionally pumped (or ‘shifted’) from one magnetic layer to another. This simple and efficient shift-register concept suggests a route to the creation of three-dimensional microchips for memory and logic applications.
Perpendicularly magnetized materials have attracted significant interest owing to their high anisotropy, which gives rise to extremely narrow, nanosized domain walls. As a result, the recently studied current-induced domain wall motion (CIDWM) in these materials promises to enable a new class of data, memory and logic devices. Here we propose the spin Hall effect as an alternative mechanism for CIDWM. We are able to carefully tune the net spin Hall current in depinning experiments on Pt/Co/Pt nanowires, offering unique control over CIDWM. Furthermore, we determine that the depinning efficiency is intimately related to the internal structure of the domain wall, which we control by the application of small fields along the nanowire. This manifestation of CIDWM offers an attractive degree of freedom for manipulating domain wall motion by charge currents, and sheds light on the existence of contradicting reports on CIDWM in perpendicularly magnetized materials.
We present magnetic domain states in a material configuration with high (perpendicular) magnetic anisotropy and particularly low magnetic pinning. This material, a B-doped Co/Pt multilayer configuration, exhibits a strong magnetic contrast in x-ray transmission experiments, making it apt for dynamic imaging with modern synchrotron techniques, providing high spatial and high temporal resolution simultaneously. By analyzing the static spin structures in nanodisks at variable external fields, we show that CoB/Pt multilayers exhibit low enough domain wall pinning to manipulate the domain pattern with weak stimuli and in particular to move domains and domain walls. We demonstrate in a proof-of-principle experiment using pump-probe x-ray holographic imaging that moderate magnetic fields can induce elastic and deterministic and hence repeatable small variations of the domain configuration in CoB/Pt multilayers, which is the key to perform high-resolution imaging of the domain wall motion to gain insight to the details of the local magnetization dynamics.
We control the nucleation and propagation of topological magnetic solitons in synthetic ferrimagnetic (CoFeB/Ru)N superlattices (N = 6). This is achieved by carefully tuning the anisotropy and thickness of one of the edge layers, making it different from the other layers of the superlattice. Sharp solitons can be nucleated at one edge of the system, then unidirectionally propagated using external magnetic fields. Experimental results are modeled with macrospin simulations. We present a numerical phase diagram which maps the general behavior for the nucleation and propagation of solitons in ferrimagnets.
PhD Thesis; Another spin in the wall - Domain wall dynamics in perpendicularly magnetized devices.
Read the summary/asbtract in the book.
We report the temperature dependence of the resistivity, the anisotropic magnetoresistance and the Hall effect of iron microwires grown by focused-electron-beam-induced deposition. By modifying the growth conditions in a controllable way, we study wires with iron compositions varying from 45% to 70%, which present different electrical conduction mechanisms, with resistivity values differing over three orders of magnitude. The magnetoresistance depends highly on the composition, and it can be understood by a subtle interplay between the anisotropic magnetoresistance and intergrain magnetoresistance due to their complex microstructure, consisting of an iron–carbon–oxygen amorphous matrix. A giant value for the anomalous Hall effect is found, which we explain by a large contribution of the skew scattering mechanism. The present results emphasize the correlation between the exotic microstructure of the microwires, and their magnetotransport properties.
We report experimentally obtained magnetic domain wall (DW) velocities of current-assisted field-driven DW creep in perpendicularly magnetized Pt/Co/Pt. We have intentionally introduced an asymmetry in the stacks by using different thicknesses of the two Pt layers sandwiching the Co layer. Thereby, it is tested whether conflicting current-induced domain wall motion (CI-DWM) results may be intrinsically related to the basic layout and growth. We sketch a scenario which could be at the basis of contradicting reports in literature where the direction of CI-DWM conflicts with spin-torque-transfer theory, allowing the sign of the current-induced effect on DW motion to be tuned.
We experimentally study the tunability of the Ruderman-Kittel-Kasuya-Yosida (RKKY) interlayer exchange coupling (IEC) in Pt/CoFeB/Pt/Ru/Pt/CoFeB/Pt stacks with perpendicular magnetic anisotropy (PMA). The perpendicular magnetization of a single Pt/Co60Fe20B20/Pt (at. %) shows full remanence and square hysteresis loops for a CoFeB thickness range of 0.60–1.0 nm. By inserting a Pt layer between the Ru and CoFeB, the PMA of the ultrathin CoFeB layers is stabilized and the IEC can be tuned. In particular, we show that the IEC versus Pt thickness exhibits a simple exponential decay with a decay length of 0.16 nm.
We report on the change in the structural and magnetic properties of magnetically soft ternary Co80xFexB20 alloys as a function of composition, thickness, and annealing temperature. Compositions high in cobalt show a significant change in coercivity after annealing. This is explained using the random anisotropy model by relating the magnetic exchange length to the grain size of the crystallites. The presented results are a systematic study explaining trends seen in the transition from soft to hard magnetic behavior, providing insight into why the soft CoFeB alloys have been so successful recently in spintronic devices.
We theoretically and experimentally analyze the pinning of a magnetic domain wall (DW) at engineered anisotropy variations in Pt/Co/Pt strips with perpendicular magnetic anisotropy. An analytical model is derived showing that a step in the anisotropy acts as an energy barrier for the DW. Quantitative measurements are performed showing that the anisotropy can be controlled by focused ion beam irradiation with Ga ions. This tool is used to experimentally study the field-induced switching of nanostrips which are locally irradiated. The boundary of the irradiated area indeed acts as a pinning barrier for the domain wall and the pinning strength increases with the anisotropy difference. Varying the thickness of the Co layer provides an additional way to tune the anisotropy, and it is shown that a thinner Co layer gives a higher starting anisotropy thereby allowing tunable DW pinning in a wider range of fields. Finally, we demonstrate that not only the anisotropy itself, but also the width of the anisotropy barrier can be tuned on the length scale of the domain wall.
In experiments on current-driven domain wall (DW) motion in nanostrips with perpendicular magnetic anisotropy (PMA), the initial DW preparation is usually not well controlled. We demonstrate precise control of DW injection using Ga and novel He focused ion beam (FIB) irradiation to locally reduce the anisotropy in part of a Pt/Co/Pt strip. DWs experience pinning at the boundary of the irradiated area. This DW pinning is more pronounced at the He irradiation boundary compared to Ga. This is attributed to a better He beam resolution, causing an anisotropy gradient over a much smaller length scale and hence, a steeper energy barrier for the DW. The results indicate that He FIB is a useful tool for anisotropy engineering of magnetic devices in the nanometer range.
It is now commonly accepted that materials exhibiting high perpendicular magnetic anisotropy are excellent candidates for devices based on current-induced domain-wall DW motion. A major hindrance of these materials however, is that they exhibit strong DW pinning. Here we report a significant increase in the field-driven DW velocity in Pt(4 nm)/Co68B32(0.6 nm)/Pt(2 nm) layers patterned into 900 nm wide strips. We compare the DW velocity between Co and Co68B32 films and discuss the observed effects using the morphology of the films investigated by high-resolution transmission electron microscopy.
We systematically study the effect of oxygen content on the magneto-transport and microstructure of Fe:O:C nanowires deposited by focused-electron-beam-induced (FEBID) deposition. The Fe/O ratio can be varied with an Fe content varying between ∼50 and 80 at.% with overall low C content (≈16 ± 3 at.%) by adding H2O during the deposition while keeping the beam parameters constant as measured by energy dispersive x-ray (EDX) spectroscopy. The room-temperature magnetic properties for deposits with an Fe content of 66–71 at.% are investigated using the magneto-optical Kerr effect (MOKE) and electric magneto-transport measurements. The nanostructure of the deposits is investigated through cross-sectional high-resolution transmission electron microscopy (HRTEM) imaging, allowing us to link the observed magneto-resistance and resistivity to the transport mechanism in the deposits. These results demonstrate that functional magnetic nanostructures can be created, paving the way for new magnetic or even spintronics devices.
For applications of domain wall DW motion in magnetic devices, it is vital to control the creation and position of the DW.We use Ga+ irradiation of Pt/Co/Pt strips to locally change the perpendicular magnetic anisotropy. This allows us to controllably inject DWs into a device at a tunable field. The observed initial linear decrease and subsequent increase in the DW injection field upon increasingirradiation dose are explained by micromagnetic simulations and an analytical one-dimensional model.
We have studied the magnetization reversal process in perpendicularly magnetized ultrathin Pt/Co100−xBx / Pt films by means of magneto-optical magnetometry and microscopy. The addition of boron enhances the effective Barkhausen volume indicating a decrease in domain-wall pinning site density and/or strength. This potentially reduces the field and critical current-density for domain-wall depinning/motion, indicating that perpendicularly magnetized Pt/Co100−xBx / Pt could be an interesting candidate for domain-wall motion studies and applications.
We study spin motive forces, that is, spin-dependent forces and voltages induced by time-dependent magnetization textures, for moving magnetic vortices and domain walls. First, we consider the voltage generated by a one-dimensional field-driven domain wall. Next, we perform detailed calculations on field-driven vortex domain walls. We find that the results for the voltage as a function of magnetic field differ between the one-dimensional and vortex domain walls. For the experimentally relevant case of a vortex domain wall, the dependence of voltage on the field around Walker breakdown depends qualitatively on the ratio of the so-called β parameter to the Gilbert damping constant and thus provides a way to determine this ratio experimentally. We also consider vortices on a magnetic disk in the presence of an ac magnetic field. In this case, the phase difference between field and voltage on the edge is determined by the β parameter, providing another experimental method to determine this quantity.
We report a correlation between the spin polarization of the tunneling electrons and the magnetic moment of amorphous CoFeB alloys. Such a correlation is surprising since the spin polarization of the tunneling electrons involves s-like electrons close to the Fermi level (EF), while the magnetic moment mainly arises due to all the d electrons below EF. We show that probing the s and d bands individually provides clear and crucial evidence for such a correlation to exist through s-d hybridization, and demonstrate the tunability of the electronic and magnetic properties of CoFeB alloys.
Time resolved magneto-optical Kerr measurements are carried out to study the precessional dynamics of ferromagneticthin films with out-of-plane anisotropy. A combined analysis of parameters, such as coercive fields, magnetic anisotropy, and Gilbert damping α, is reported. Using a macrospin approximation and the Landau–Lifshitz–Gilbert equation, the effective anisotropy and α are obtained. A large damping varying with the applied field as well as with the thickness of the ferromagnetic layer is reported. Simulations using a distribution in the effective anisotropy allow us to reproduce the field evolution of α. Moreover, its thickness dependence correlates with the spin pumping effect.
We present measurements of tunneling spin polarization (TSP) of Co72Fe20B8 alloys in Al/Al2O3/Co72Fe20B8 tunnel junctions to further unravel the role of crystallization of the CoFeB electrodes. Whereas the TSP of films of a few hundred angstrom source is rather insensitive to anneals up to 500 C, a 50 A source film shows a strong reduction of TSP. It is hypothesized that these differences are related to a rather inhomogeneous crystallization of the Co72Fe20B8. Magneto-optical Kerr-effect measurement on 300 A thick CoFeB wedges are used to relate the measured coercivity to these crystallization processes.