Reliably predicting bit-error rates in realistic heat-assisted magnetic recording simulations is a challenging task. Integrating the Landau-Lifshitz-Bloch (LLB) equation can reduce the computational effort to determine the magnetization dynamics in the vicinity of the Curie temperature. If one aims that these dynamics coincide with trajectories calculated from the atomistic Landau-Lifshitz-Gilbert equation, one has to carefully model required temperature dependent material functions such as the zero-field equilibrium magnetization as well as the parallel and normal susceptibilities. We present an extensive study on how these functions depend on grain size and exchange interactions. We show that, if the size or the exchange constant of a reference grain is modified, the material functions can be scaled, according to the changed Curie temperature, yielding negligible errors. This is shown to be valid for volume changes of up to $\pm 40$ % and variations of the exchange constant of up to $\pm10$ %. Besides the temperature dependent material curves, computed switching probabilities also agree well with probabilities separately determined for each system. Our study suggest that there is no need to recalculate the required LLB input functions for each particle. Within the presented limits it is sufficient to scale them to the Curie temperature of the altered system.
We derive the Landau-Lifshitz-Bloch (LLB) equation for a two-component magnetic system valid up to the Curie temperature. As an example, we consider disordered GdFeCo ferrimagnet where the ultrafast optically induced magnetization switching under the action of heat alone has been recently reported. The two-component LLB equation contains the longitudinal relaxation terms responding to the exchange fields from the proper and the neighboring sublattices. We show that the sign of the longitudinal relaxation rate at high temperatures can change depending on the dynamical magnetization value and a …
A phenomenological equation called Landau-Lifshitz-Baryakhtar (LLBar) equation, which could be viewed as the combination of Landau-Lifshitz (LL) equation and an extra "exchange damping" term, was derived by Baryakhtar using Onsager's relations. We interpret the origin of this "exchange damping" as nonlocal damping by linking it to the spin current pumping. The LLBar equation is investigated numerically and analytically for the spin wave decay and domain wall motion. Our results show that the lifetime and propagation length of short-wavelength magnons in the presence of nonlocal damping could b…
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 suscep…
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 pro…
A hierarchical multiscale approach to model the magnetization dynamics of ferromagnetic ran- dom alloys is presented. First-principles calculations of the Heisenberg exchange integrals are linked to atomistic spin models based upon the stochastic Landau-Lifshitz-Gilbert (LLG) equation to calculate temperature-dependent parameters (e.g., effective exchange interactions, damping param- eters). These parameters are subsequently used in the Landau-Lifshitz-Bloch (LLB) model for multi-sublattice magnets to calculate numerically and analytically the ultrafast demagnetization times. The developed mul…
Heat assisted magnetic recording (HAMR) technology represents the most promising candidate to replace the current perpendicular recording paradigm to achieve higher storage densities. To better understand HAMR dynamics in granular media we need to describe accurately the magnetisation dynamics up to temperatures close to the Curie point. To this end we propose a multiscale approach based on the micromagnetic Landau-Lifshitz-Bloch (LLB) equation of motion parametrised using atomistic calculations. The LLB formalism describes the magnetisation dynamics at finite temperature and allows to efficie…
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_{\mathr…
The magnetic characteristics of polycrystalline exchange-biased antiferromagnet/ferromagnet-bilayers are determined by a complex interplay of parameters, describing structural and magnetic properties of the material system, including in particular the grain volume distribution of the antiferromagnet. An ideal characterization of such systems would be a non-destructive determination of the relevant parameters for each individual grain. This is in most cases not feasible, since typical characterization methods do average over larger areas. Here, we show that it is however possible to determine a…
Angular resolved measurements of the exchange bias field and the coercive field are a powerful tool to distinguish between different competing magnetic anisotropies in polycrystalline exchange bias layer systems. No simple analytical model is as yet available, which considers time dependent effects like enhanced coercivity arising from the grain size distribution of the antiferromagnet. In this work we expand an existing model class describing polycrystalline exchange bias systems by a rotatable magnetic anisotropy term to describe grain size correlated effects. Additionally, we performed angu…
In this paper we perform the detailed numerical analysis of remagnetization processes in nanocomposite magnetic materials consisting of magnetically hard grains (i.e. grains made of a material with a high magnetocrystalline anisotropy) embedded into a magnetically soft phase. Such materials are widely used for the production of permanent magnets, because they combine the high remanence with the large coercivity. We perform simulations of nanocomposites with Sr-ferrite as the hard phase and Fe or Ni as the soft phase, concentrating our efforts on analyzing the effects of ({\it i}) the imperfect…
Exchange coupling between magnetic grains is essential for maintaining the stability of stored information in magnetic recording media. Using an atomistic spin model, we have investigated the coupling between neighbouring magnetic grains where magnetic impurity atoms have migrated into the non-magnetic grain boundary. We find that when the impurity density is low a biquadratic term in addition to the bilinear term is required to properly describe the inter-granular exchange coupling. The temperature dependence both terms is found to follow a power law behaviour with the biquadratic exchange co…
The compound alpha-Fe1.4Ga0.6O3 has been prepared by mechanical alloying of alpha-Fe2O3 and Ga2O3 and subsequent heating of the mechanical alloyed samples in vacuum condition. Magnetic ordering of alpha-Fe2O3 has been modified by substitution of non-magnetic Ga atoms. The ferromagnetism in alpha-Fe1.4Ga0.6O3 is more soft and enhanced in comparison to alpha-Fe2O3. Mössbauer spectroscopy also confirmed enhanced ferromagnetic order in alpha-Fe1.4Ga0.6O3. The room temperature soft ferromagnetism by Ga substitution is interesting for designing alpha-Fe2O3 based unconventional ferromagnet, which is …
Antiferromagnetic spintronic devices have the potential to outperform conventional ferromagnetic devices due to their ultrafast dynamics and high data density. A challenge in designing these devices is the control and detection of the orientation of the anti-ferromagnet. One of the most promising ways to achieve this is through the exchange bias effect. This is of particular importance in large scale multigranular devices. Due to the large system sizes, previously, only micromagnetic simulations have been possible, these have an assumed distribution of antiferromagnetic anisotropy directions. …
Rate coefficients of the Arrhenius-Neel form are calculated for thermally activated magnetic moment reversal for dual layer exchange-coupled composite (ECC) media based on the Langer formalism and are applied to study the sweep rate dependence of MH hysteresis loops as a function of the exchange coupling I between the layers. The individual grains are modelled as two exchange coupled Stoner-Wohlfarth particles from which the minimum energy paths connecting the minimum energy states are calculated using a variant of the string method and the energy barriers and attempt frequencies calculated as…
Here, we investigated the influence of grain formation on the magnetization reversal of SmCo5/Co at low temperature. A set of SmCo5/Co bi-layer samples were fabricated under identical conditions on MgO(100) and glass substrates with a Cr underlayer. Analysis of each magnetic layer by an Atomic Force Microscope (AFM) reveals that MgO(100) results small and uniform grain formation of 23 nm in contrast to 57 nm on glass, and x-ray diffraction studies show that the sample on MgO(100) has high crystallinity with SmCo5(11 0) phase. At room temperature, both samples exhibit good hard magnetic propert…
The effect of grain boundaries on magnetic exchange interactions in iron
Brno University of Technology（布尔诺理工大学）；AGH University of Krakow（克拉科夫AGH科技大学）；Central European Institute of Technology (CEITEC)（中欧技术研究所）；Normandie Université, UNIROUEN, INSA Rouen, CNRS, GPM（诺曼底大学，鲁昂大学，鲁昂国立应用科学学院，法国国家科学研究中心，GPM实验室）
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…
We study a nonlinear kinetic model of mass exchange between interacting grains. The transition rates follow the Arrhenius equation with an activation energy that depends on the grain mass. We show that the activation parameter can be absorbed in the initial conditions for the grain masses, and that the total mass is conserved. We obtain numerical solutions of the coupled, nonlinear, ordinary differential equations of mass exchange for the two-grain system, and we compare them with approximate theoretical solutions in specific neighborhoods of the phase space. Using phase plane methods, we dete…
We studied exchange bias in magnetic multilayers incorporating antiferromagent CoO doped with up to 35 atomic percent of Pt. The exchange bias increased with doping in epitaxial films, but did not significantly change in polycrystalline films at the lowest measured temperature of 5 K, and decreased at higher temperatures. We explain our results by the increased granularity of the doped antiferromagnetic films, resulting in simultaneous enhancement of the uncompensated spin density and reduction of the magnetic stability of antiferromagnetic grains.
To identify the possible mechanism of coercivity (Hc) degradation of Nd-Fe-B sintered magnets, we study the roles of the exchange field acting on the 4f electrons in Nd ions and theoretically investigate how the variation of the exchange field affects the values of the magnetic anisotropy constants K1 and K2. We find that, with decreasing exchange field strength, both values decrease as a result of the lower asphericity of the 4f electron cloud, indicating that the local anisotropy constants might become small around the grain boundaries where the exchange fields are decreased owing to the sma…
With the increasing availability of experimental and computational data concerning the properties and distribution of grain boundaries in polycrystalline materials, there is a corresponding need to efficiently and systematically express functions on the grain boundary space. A grain boundary can be described by the rotations applied to two grains on either side of a fixed boundary plane, suggesting that the grain boundary space is related to the space of rotations. This observation is used to construct an orthornormal function basis, allowing effectively arbitrary functions on the grain bounda…
The mechanism of ion bombardment induced magnetic patterning of exchange bias layer systems for creating engineered magnetic stray field landscapes is still unclear. We compare results from vectorial magneto-optic Kerr effect measurements to a recently proposed model with time dependent rotatable magnetic anisotropy. Results show massive reduction of rotational magnetic anisotropy compared to all other magnetic anisotropies. We disprove the assumption of comparable weakening of all magnetic anisotropies and show that ion bombardment mainly influences smaller grains in the antiferromagnet.
The origins of indirect spin exchange in crystalline thin films of Copper Octabutoxy Phthalocyanine (Cu-OBPc) are investigated using Magnetic Circular Dichroism (MCD) spectroscopy. These studies are made possible by a solution deposition technique which produces highly ordered films with macroscopic grain sizes suitable for optical studies. For temperatures lower than 2 K, the contribution of a specific state in the valence band manifold originating from the hybridized lone pair in nitrogen orbitals of the Phthalocyanine ring, bears the Brillouin-like signature of an exchange interaction with …
It has been observed that in bulk and polycrystalline thin films of collossal magnetoresistive (CMR) materials the magnetoresistance follows a different behaviour compared to single crystals or single crystalline films below the ferromagnetic transition temperature Tc. In this paper we develop a phenomenological model to explain the magnetic field dependence of resistance in granular CMR materials taking into account the spin polarised tunnelling at the grain boundaries. The model has been fitted to two systems, namely, La0.55Ho0.15Sr0.3MnO3 and La1.8Y0.5Ca0.7Mn2O7. From the fitted result we h…
On the basis of a previous theoretical approach to the plastic flow of highly refined materials, a physical explanation for diffusion bonding is essayed, which yields closed--form equations relating the bonding progress with time, temperature, applied pressure and the constants characterizing the material. Excellent agreement with experiment is attained, with no adjustable parameter. In the novel scheme, diffusion bonding is caused by the interpenetration of the two sufaces at the grain level. The process is driven by the strong tensile stress field induced in the plane of the interface by the…
We explored the magnetic behavior of a common two-phase nanomagnetic system by Monte Carlo computer simulation of a modified Heisenberg model on a 3D complex lattice with single- and cluster-spins. The effect of exchange coupling between two component magnetic phases was studied on the enhancement in Curie temperature (ECT) of the intergranular amorphous region of a common duplex-phase alloy system, with numerous nano-crystallites embedded in amorphous matrix. The dependences of ECT were investigated systematically upon the nanocrystallite size, the volume fraction and the interspace among cry…
Recent experiments showed that the robust charge-ordering in manganites can be weakened by reducing the grain size down to nanoscale. Weak ferromagnetism was evidenced in both nanoparticles and nanowires of charge-ordered manganites. To explain these observations, a phenomenological model based on surface phase separation is proposed. The relaxation of superexchange interaction on the surface layer allows formation of a ferromagnetic shell, whose thickness increases with decreasing grain size. Possible exchange bias and softening of the ferromagnetic transition in nanosized charge-ordered mang…
This work gives insights into processing and characterisation of bulk nanocrystalline FeCr materials. The investigated FeCr alloys, consisting of 30, 50 and 70 at.% ferromagnetic Fe and remaining anti-ferromagnetic Cr, are processed by arc melting and subsequent severe plastic deformation by high pressure torsion. The physical similarities between elemental Fe and Cr in combination with the nanocrystalline structure of the as-deformed alloys, necessitates advanced characterisation techniques for the as-deformed state: In-situ annealing synchrotron X-ray diffraction measurements as well as elec…
High-pressure torsion (HPT), a technique of severe plastic deformation (SPD), is shown as a promising processing method for exchange-spring magnetic materials in bulk form. Powder mixtures of Fe and SmCo$_{5}$ are consolidated and deformed by HPT exhibiting sample dimensions of several millimetres, being essential for bulky magnetic applications. The structural evolution during HPT deformation of Fe-SmCo$_{5}$ compounds at room- and elevated- temperatures of chemical compositions consisting of 87, 47, 24 and 10 wt.% Fe is studied and microstructurally analysed. Electron microscopy and synchrot…
The effect of annealing under a magnetic field on the microstructure and properties of YNixMn1-xO3 (x=0.33 and 0.5) films has been investigated. It is found that the ferromagnetic transition temperature is significantly enhanced after post annealing in the presence of an 8 T magnetic field. Characterization study shows that the microstructure is affected, obtaining larger grains of uniform size when films are annealed under a magnetic field. The improvement in the ordering temperature of all films is interpreted in terms of the grain growth caused by the magnetic-field driving force for bounda…
We employ an atomistic model using a nearest-neighbor Heisenberg Hamiltonian exchange to study computationally the dependence of the Curie temperature of L10-FePt on finite-size and surface effects in Heat-assisted Magnetic Recording (HAMR) media. We demonstrate the existence of a size threshold at 3.5nm below which the impact of finite-size effects start to permeate into the center of the grains and contribute to the reduction of the Curie temperature. We find a correlation between the Curie temperature and the percentage of atomistic bonds lost on the surface as a function of grain size, whi…
Magnetic lateral multilayers have been fabricated on weak perpendicular magnetic anisotropy amorphous Nd-Co films in order to perform a systematic study on the conditions for controlled nucleation of topological defects within their magnetic stripe domain pattern. A lateral thickness modulation of period $w$ is defined on the nanostructured samples that, in turn, induces a lateral modulation of both magnetic stripe domain periods $λ$ and average in-plane magnetization component $M_{inplane}$. Depending on lateral multilayer period and in-plane applied field, thin and thick regions switch indep…
