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Theoretical estimation of surface magnetic anisotropy on L1 0 -FePt thin films: Case of perfect and defect Surfaces.
Abstract
We carried out first-principle calculations of magnetocrystalline anisotropy of L10-FePt thin films terminated by either perfect Fe (Pt) layers or defect surfaces, including vacancies or substituted surface atoms. Inspired by the experimental strategy for determining magnetic anisotropy, we present here a theoretical model for analyzing volume and surface magnetic anisotropies for L10-FePt thin films with different surface terminations. We demonstrate that surface anisotropy does not depend solely on the film thickness, but also on the atomic environment of the surface layer. Perpendicular surface anisotropy of L10-FePt thin films reaches its maximum with full Pt termination, which decreases with increasing Pt vacancies and becomes parallel to the surface for a full Fe surface. In the case of mixed surfaces, surface anisotropy of (3Pt,1Fe) is enhanced compared to platinum-rich surface with one vacancy, and tends to be more in-plane for an iron-rich surface (3Fe,1Pt). Our results could be used to study surface anisotropy effects on L10-FePt surfaces by mean of classical magnetic models, and they are very promising for the development of high density magnetic data storage such as magnetic memory.
... This alignment of the c-axis results in a magnetization oriented in a specific direction on the plane. Such a uniaxial configuration could be called in-plane fixed magnetic anisotropy, as opposed to conventional in-plane All previous first-principles calculations of L1 0 FePt films assumed a (001) surface (atomic Fe and Pt monolayers lying in the film plane) [47][48][49][50][51][52][53][54]. The FePt films considered were up to 19 atomic monolayers thick [54]. ...
... Such a uniaxial configuration could be called in-plane fixed magnetic anisotropy, as opposed to conventional in-plane All previous first-principles calculations of L1 0 FePt films assumed a (001) surface (atomic Fe and Pt monolayers lying in the film plane) [47][48][49][50][51][52][53][54]. The FePt films considered were up to 19 atomic monolayers thick [54]. The effect of film thickness on magnetic properties was investigated, and parameters such as surface magnetic anisotropy and bulk magnetic anisotropy were determined [47]. ...
... None of the structures considered were subjected to film geometry optimization. Such a simplification can be justified by results from Hammar et al. [54], where optimization of the geometry of FePt film showed that mainly the positions of only three outer atomic monolayers change, and the change in the distance between these layers is only about 1 -2% and does not significantly affect the magnetic properties. All structure representations were prepared using VESTA code [56]. ...
Ultrathin L1$_0$ films with different $c$-axis orientations relative to the film plane are promising candidates for data storage materials. In this work, within the framework of density functional theory, we calculated the magnetic properties of ultrathin L1$_0$ (111) and (010) films with thicknesses ranging from 4 to 16 atomic monolayers (from about 0.8 to 3.5~nm). The highest average magnetic moments are observed for the thinnest films considered, and with increasing film thickness, the values converge towards the magnetic moment for bulk. The observed increase comes mainly from enhanced moments in the two atomic monolayers closest to the surface of the films. The easy axis of magnetization of (111) films prefers an alignment close to the tetragonal axis, an example of tilted magnetic anisotropy. The 6-monolayer (111) film (about 1.3~nm thick) inclines the easy axis of magnetization of about 45{\deg} to the film plane, which can find use in applications. The (010) films show an in-plane easy magnetization axis in a unique L1$_0$ tetragonal direction. This is an unusual type of in-plane anisotropy, as the particular direction preference is very strong. The computational results encourage further experimental studies of L1$_0$ systems with tilted and in-plane fixed magnetic anisotropy.
... Layered systems are particularly interesting for their ability to tune effective material parameters such as MAE. Among such systems, iron-based layered systems are of considerable interest [16][17][18][19]. An intriguing and important topic from the point of view of applications is the influence of the crystallographic structure of Fe, its thickness, and the presence of other layers above and below the Fe layer on magnetic parameters such as the MAE of the studied system. ...
Iron-based layered systems are of great interest because of their ability to tune effective material parameters such as magnetic anisotropy energy (MAE). The influence of the crystallographic structure of Fe, its thickness, and the presence of other layers above and below the Fe layer on magnetic parameters, such as the MAE of the studied system, is an intriguing and important topic from an application point of view. Here, we present a density functional theory (DFT) study of the magnetic anisotropy of nine-monolayer Fe, FeCo, and FeCo films with B, C, and N dopants placed in octahedral interstitial positions. The theoretical study is based on calculations using the full-potential local-orbital code FPLO and the generalized gradient approximation. The chemical disorder in the FeCo layers was modeled using the virtual crystal approximation. The structures of the layers were subjected to optimization of the geometry of the interlayer spacings and the neighborhood of the dopant sites. We determined the local magnetic moments and the excess charge at each layer position. We also identified the influence of dopant atoms on the magnetic properties of FeCo layers, such as magnetization and magnetic anisotropy.
... This can be understood as when the bit size is reduced to increase the storage density, materials with high magnetic anisotropy is required to stabilize the thermal fluctuations due to superparamagnetism [6][7][8][9]. In this context, L1 0 ordered FePt emerges as a promising material among all other anisotropic materials due to its extremely high magneto crystalline anisotropy (K u ~ 7 × 10 7 erg cm − 3 ), saturation magnetization (M s ~ 1100 emu cm − 3 ) and chemical stability towards oxidation [10][11][12][13]. Due to its high anisotropy, it permits the reduction in bit size down to 4 nm that is very close to value required for achieving the areal density of about 8 Tbit/inch 2 [14]. ...
In the present work, enhanced L10 ordering kinetics with improved crystallographic texturing in [001] direction and high magnetic coercivity of about 6 kOe is observed in L10 ordered Fe(1-x)CuxPt films, after successive isochronal vacuum annealing of multilayer structure [(Fe(1-x)/Cux)/Pt]x10. Synchrotron grazing incidence x-ray diffraction (GIXRD) measurements, performed using area detector confirms the onset of L10 ordering at 200 °C and presence of high degree of ordering at 300 °C. In-plane and out-of-plane GIXRD measurements validates texturing of magnetic easy axis [001] in out of film plane direction. Enormous increase in magnetic coercivity is observed from MOKE measurements in L10 ordered state. Lower ordering temperature with enhance (001) texturing and high magnetic coercivity is desirable for potential device applications of FePt. Effect of Cu and annealing temperature on structural and magnetic properties is investigated systematically in Fe(1-x)CuxPt films. Structural investigation discloses that lattice distortion in L10 ordered state caused by Cu addition and high interfacial energy associated with initial multilayer structure drives faster interdiffusion. Both of these aspects collectively work for FCC to FCT transformation, hence results in enhanced kinetics and texturing effects of L10 FePt.
Ultrathin L1 0 FePt films with different c-axis orientations relative to the film plane are promising candidates for data storage materials. In this work, within the framework of density functional theory, we calculated the magnetic properties of ultrathin L1 0 FePt (111) and (010) films with thicknesses ranging from 4 to 16 atomic monolayers (from about 0.8 to 3.5 nm). The highest average magnetic moments are observed for the thinnest films considered and, with increasing film thickness, the values converge towards the magnetic moment for bulk. The observed increase comes mainly from enhanced moments in the two atomic monolayers closest to the surface of the films. The easy axis of magnetization of (111) films prefers an alignment close to the tetragonal axis-an example of tilted magnetic anisotropy. The 6-monolayer (111) film (about 1.3 nm thick) inclines the easy axis of magnetization of about 45 deg to the film plane, which can find use in applications. The (010) films show an in-plane easy magnetization axis in a unique L1 0 tetragonal direction. This is an unusual type of in-plane anisotropy, as the particular direction preference is very strong. The computational results encourage further experimental studies of L1 0 systems with tilted and in-plane fixed magnetic anisotropy.
The dynamic process of assisted magnetic switchings has been simulated to investigate the associated physics. The model uses a Voronoi construction to determine the physical structure of the nanogranular thin film recording media, and the Landau–Lifshitz–Bloch equation is solved to evolve the magnetic system in time. The reduction of the magnetization is determined over a range of peak system temperatures and for a number of anisotropy values. The results show that the heat-assisted magnetic recording process is not simply magnetization reversal over a thermally reduced energy barrier. To achieve full magnetization reversal (for all anisotropies investigated), an applied field strength of at least 6 kOe is required and the peak system temperature must reach at least the Curie point ( T c). When heated to T c, the magnetization associated with each grain is destroyed, which invokes the non-precessional linear reversal mode. Reversing the magnetization through this linear reversal mode is favorable, as the reversal time is two orders of magnitude smaller than that associated with precession. Under these conditions, as the temperature decreases to ambient, the magnetization recovers in the direction of the applied field, completing the reversal process. Also, the model produces results that are consistent with the concept of thermal writability; when heating the media to T c, the smaller grains require a larger field strength to reverse the magnetization.
A second-order perturbation (2PT) approach to the spin–orbit interaction (SOI) is implemented within a density-functional theory framework. Its performance is examined by applying it to the calculation of the magnetocrystalline anisotropy energies (MAE) of benchmark systems, and its efficiency and accuracy are compared with the popular force theorem method. The case studies are tetragonal FeMe alloys (Me=Co, Cu, Pd, Pt, Au), as well as FeMe (Me=Co, Pt) bilayers with (111) and (100) symmetry, which cover a wide range of SOI strength and electronic band structures. The 2PT approach is found to provide a very accurate description for 3d and 4d metals and, moreover, this methodology is robust enough to predict easy axis switching under doping conditions. In all cases, the details of the bandstructure, including states far from the Fermi level, are responsible for the finally observed MAE value, sometimes overruling the effect of the SOI strength. From a technical point of view, it is confirmed that accuracy in the MAE calculations is subject to the accuracy of the Fermi level determination.
We present density functional theory (DFT) calculations of the magnetic anisotropy energy (MAE) of FePt, which is of great interest for magnetic recording applications. Our data, and the majority of previously calculated results for perfectly ordered crystals, predict an MAE of $\sim 3.0$ meV per formula unit, which is significantly larger than experimentally measured values. Analyzing the effects of disorder by introducing stacking faults (SFs) and anti site defects (ASDs) in varying concentrations we are able to reconcile calculations with experimental data and show that even a low concentration of ASDs are able to reduce the MAE of FePt considerably. Investigating the effect of exact exchange and electron correlation within the adiabatic-connection dissipation fluctuation theorem in the random phase approximation (ACDFT-RPA) reveals a significantly smaller influence on the MAE. Thus the effect of disorder, and more specifically ASDs, is the crucial factor in explaining the deviation of common DFT calculations of FePt to experimental measurements.
We studied L10 ordered Fe50Pt50−x Ndx alloy films, which showed a large enhancement (~18.4% at room temperature and ~11.7% at 10 K) of magnetic moment with 6 atomic % of Nd. Analysis of the x-ray magnetic circular dichroism spectra at the Fe L 3,2 edges and Nd M 5,4 edges in Fe50Pt44Nd6 films indicated a significant contribution of the Nd orbital moment. The origin of the large enhancement of magnetic moment was attributed to the effect of ferromagnetic coupling of the total magnetic moments between Fe and Nd. Density functional theory based first principles calculations supported the experimental observations of increasing moment due to Nd substitution of Pt.
We have studied the ferromagnetic resonance response in a series of atomically disordered FePt thin films as a function of film thickness (9–200 nm) and excitation frequency (9.5 and 24 GHz). These films are characterized by a perpendicular anisotropy that promotes a stripelike magnetic domain structure above a critical thickness dcr~30 nm. All films display a resonant absorption due to the uniform precession of the magnetization vector. The analysis of the linewidth as a function of film thickness shows that the line broadens considerably above dcr. In the thinner films (d<28 nm) we have only observed the absorption related to the uniform precession mode, but thicker films, in which a stripe domain pattern is observed at zero field in static magnetic measurements, show an additional resonance line when the magnetic field is applied at, or very close to, the film plane normal. This line appears at fields below the main resonance and is observed at both X and K bands with approximately the same field separation from the uniform mode. We have also found that the line separation between the two resonances varies with the film thickness, indicating that the appearance of an additional resonance is related to confinement effects, but does not follow the quadratic law expected for infinite surface pinning. The ferromagnetic resonance results have been interpreted within a model of standing spin waves with finite surface pinning. From the angular variation of the pinning parameter close to the film normal we have found that the surface anisotropy is perpendicular to the film plane and increases with film thickness. The origin of the surface anisotropy seems to be related to a substrate-induced strain produced in the fabrication process and to a surface layer with a reduced magnetization. Annealing the samples at relatively low temperatures produces important changes in the resonance spectra. The overall observed behavior suggests that even though the resonance experiments are made at fields large enough to be in a magnetically saturated state, the formation of a stripe structure and the changes observed in the ferromagnetic resonance spectra above dcr are not completely uncorrelated phenomena.
Using first-principles density-functional theory calculations, we systematically investigate the magnetic anisotropy of the multilayer system Cu/(FePt)n/MgO, a promising spintronics structure. Particularly, we have studied the influence of the epitaxial strain, thickness of the ferromagnetic layer, and different interfaces on the magnetic anisotropy energy (MAE) of the system. It is found that the thickness of FePt has slight influence on the MAE, while the increase of the in-plane lattice constant a, or tensile strain, can significantly reduce and even change the sign of the MAE. The calculated density of states shows that the occupation number of the minority spin channel of Fe dx(2)-y(2) orbital decreases with the increase of a, which leads to the reduction of the orbital moment anisotropy of the Fe atom and therefore the decrease of MAE. We also consider the influence of the Cu/FePt and FePt/MgO interfaces on the MAE, and find that both interfaces can reduce the MAE. Especially, the effect of the Cu/FePt interface is more pronounced due to the increased occupation number of the minority spin channel of Fe dz(2) orbital.
The magnetocrystalline anisotropy (MCA) of bulk and thick films of FePt is calculated from a 'first-principles' theory. The starting point is a description from electronic density functional theory for systems of interacting electrons moving in lattices of ions. Relativistic effects such as spin-orbit coupling are included. FePt readily transforms into a CuAu-type (L 10) ordered phase and this coincides with the material's high anisotropy. Here we describe how to calculate the MCA of a partially ordered alloy and to extract its dependence on the long range chemical order parameter eta. We present calculations of the MCA of FePt as a function of eta and find excellent agreement with the experimental data of Okamoto et al (2002 Phys. Rev. B 66 024413) and others with respect to the magnetic easy axis, the magnitude of the MCA and its trend with decreasing eta. We also study the paramagnetic phase of the ordered alloy using the 'disordered local moment' picture of metallic magnetism at finite temperatures. We calculate a Curie temperature of 935 K in reasonable agreement with experiment (710 K) and find the easy axis for the onset of ferromagnetic order to coincide with the magnetic easy axis found at low temperatures.
The temperature dependence of magnetocrystalline anisotropy constants and the saturation magnetization in a single variant state have been investigated for L10-type Fe60Pt40 bulk single crystal prepared under compressive stress. The uniaxial magnetocrystalline anisotropy constant Ku evaluated from the magnetization curve is 6.9×107 erg cm−3 at 5 K. The values of the second- and fourth-order magnetocrystalline anisotropy constants K1 and K2 at 5 K determined by the Sucksmith–Thompson method are 7.4 and 0.13×107 erg cm−3, respectively. Both the values of Ku and K1 decrease with increasing temperature T, while K2 is almost independent of T. The difference between the power law of the Callen and Callen model is described by the dimensionality and the thermal variation of the axial ratio c/a due to the thermal expansion.
In a recent experiment, Weisheit et al (2007 Science 315 349) demonstrated that the coercivity of thin L10 FePt and FePd films can be modified by the external electric field in an electrochemical environment. Here, this observation is confirmed by density functional calculations for the intrinsic magnetic anisotropy. The origin of the effect is clarified by means of a general and simple method to simulate charged metal surfaces. It is predicted that the coercivity of thin CoPt films is much more susceptible to electric field than that of FePt films.
An efficient tight-binding model including magnetism and spin-orbit interactions is extended to metallic alloys. The tight-binding parameters are determined from a fit to bulk ab initio calculations of each metal and rules are given to obtain the heteroatomic parameters. The spin and orbital magnetic moments as well as the magneto-crystalline anisotropy are derived. We apply this method to bulk FePt L1(0) and the results are compared with success to ab initio results where available. Finally this model is applied to a set of FePt L1(0) clusters and physical trends are derived.
The computational framework of this study is based on the local-spin-density approximation with first-principles full-potential linear muffin-tin orbital calculations including orbital polarization OP correction. We have studied the magnetic anisotropy for a series of bilayer CuAuI-type materials such as FeX, MnX (X Ni,Pd,Pt), CoPt, NiPt, MnHg, and MnRh in a ferromagnetic state using experimental structural parameters to understand the microscopic origin of magnetic-anisotropy energy MAE in magnetic multilayers. Except for MnRh and MnHg, all these phases show perpendicular magnetization. We have analyzed our results in terms of angular momentum-, spin-and site-projected density of states, magnetic-angular-momentum-projected density of states, orbital-moment density of states, and total density of states. The orbital-moment number of states and the orbital-moment anisotropy for FeX (XNi,Pd,Pt) are calculated as a function of band filling to study its effect on MAE. The total and site-projected spin and orbital moments for all these systems are calculated with and without OP when the magnetization is along or perpendicular to the plane. The results are compared with available experimental as well as theoretical results. Our calculations show that OP always enhances the orbital moment in these phases and brings them closer to experimental values. The changes in MAE are analyzed in terms of exchange splitting, spin-orbit splitting, and tetragonal distortion/crystal-field splitting. The calculated MAE is found to be in good agreement with experimental values when the OP correction is included. Some of the materials considered here show large magnetic anisotropy of the order of meV. In particular we found that MnPt will have a very large MAE if it could be stabilized in a ferromagnetic configuration. Our analysis indicates that apart from large spin-orbit interaction and exchange interaction from at least one of the constituents, a large crystal-field splitting originating from the tetragonal distortion is also a necessary condition for having large magnetic anisotropy in these materials. Our calculation predicts large orbital moment in the hard axis in the case of FePt, MnRh, and MnHg against expectation.
We present an efficient scheme for calculating the Kohn-Sham ground state of metallic systems using pseudopotentials and a plane-wave basis set. In the first part the application of Pulay's DIIS method (direct inversion in the iterative subspace) to the iterative diagonalization of large matrices will be discussed. Our approach is stable, reliable, and minimizes the number of order N-atoms(3) operations. In the second part, we will discuss an efficient mixing scheme also based on Pulay's scheme. A special ''metric'' and a special ''preconditioning'' optimized for a plane-wave basis set will be introduced. Scaling of the method will be discussed in detail for non-self-consistent calculations. It will be shown that the number of iterations required to obtain a specific precision is almost independent of the system size. Altogether an order N-atoms(2) scaling is found for systems up to 100 electrons. If we take into account that the number of k points can be implemented these algorithms within a powerful package called VASP (Vienna ab initio simulation package). The program and the techniques have been used successfully for a large number of different systems (liquid and amorphous semiconductors, liquid simple and transition metals, metallic and semiconducting surfaces, phonons in simple metals, transition metals, and semiconductors) and turned out to be very reliable.
We present experimental and theoretical investigations on the magnetic anisotropy of Co ultrathin films sandwiched by Au. Ferromagnetic resonance experiments revealed the presence of a large perpendicular surface anisotropy that makes the easy magnetization direction become perpendicular to the film plane for Co thicknesses lower than 11 Å, as is observed in magnetization measurements. In order to explain this surface anisotropy, we propose various models, taking into account the imperfections of the films. For thicknesses below 11 Å, there is a large increase of the coercive field with decreasing thickness. This effect is tentatively interpreted in a model of propagating Bloch walls, where the interfacial roughness plays an important role.
Growth of epitaxial films of the L1 0 phase of FePt, with the tetragonal c axis along either the film normal or in‐plane, is described. Films were grown by coevaporation of Fe and Pt, under ultrahigh vacuum conditions, onto a seed film of Pt grown on MgO or SrTiO 3 substrates. The perpendicular or in‐plane orientation of the c axis was controlled by selecting the (001) or (110) substrate plane, respectively. Nearly complete chemical ordering was achieved for growth at 500 °C for both orientations. Magnetic and magneto‐optical characterization of these films confirmed the huge magnetic anisotropy expected for this phase. In the most highly ordered films, anisotropy fields in excess of 120 kOe were measured. © 1996 American Institute of Physics.
The formal relationship between ultrasoft (US) Vanderbilt-type pseudopotentials and Blöchl's projector augmented wave (PAW) method is derived. It is shown that the total energy functional for US pseudopotentials can be obtained by linearization of two terms in a slightly modified PAW total energy functional. The Hamilton operator, the forces, and the stress tensor are derived for this modified PAW functional. A simple way to implement the PAW method in existing plane-wave codes supporting US pseudopotentials is pointed out. In addition, critical tests are presented to compare the accuracy and efficiency of the PAW and the US pseudopotential method with relaxed core all electron methods. These tests include small molecules (H2, H2O, Li2, N2, F2, BF3, SiF4) and several bulk systems (diamond, Si, V, Li, Ca, CaF2, Fe, Co, Ni). Particular attention is paid to the bulk properties and magnetic energies of Fe, Co, and Ni.
Magnetic nanoparticles are of immense current interest because of their possible use in biomedical and technological applications. Here we demonstrate that the large magnetic anisotropy of FePt nanoparticles can be significantly modified by surface design. We employ X-ray absorption spectroscopy offering an element-specific approach to magnetocrystalline anisotropy and the orbital magnetism. Experimental results on oxide-free FePt nanoparticles embedded in Al are compared with large-scale density functional theory calculations of the geometric- and spin-resolved electronic structure, which only recently have become possible on world-leading supercomputer architectures. The combination of both approaches yields a more detailed understanding that may open new ways for a microscopic design of magnetic nanoparticles and allows us to present three rules to achieve desired magnetic properties. In addition, concrete suggestions of capping materials for FePt nanoparticles are given for tailoring both magnetocrystalline anisotropy and magnetic moments.
We have calculated surface energies and surface magnetic order of various low-indexed surfaces of monoatomic Fe, Co, and Pt, and binary, ordered FePt, CoPt, and MnPt using density functional theory. Our results for the binary systems indicate that elemental, Pt-covered surfaces are preferred over Fe- and Co-covered and mixed surfaces of the same orientation. The lowest energy orientation for mixed surfaces is the highly coordinated (111) surface. We find Pt-covered (111) surfaces, which can be realized in the L11 structure only, to be lower in energy by about 400 meV/atom compared to the mixed L10 (111) surface. We conclude that this low surface energy stabilizes the L11 structure in small nanoparticles, which is suppressed in bulk alloys, but has been recently synthesized as thin film for CoPt. From the interplay of surface and bulk energies, equilibrium shapes of single-crystalline ordered nanoparticles and crossover sizes between the different orderings can be estimated. Comment: 17 pages, 15 figures, revised version accepted for publication at Phys. Rev. B
We investigated the magnetic anisotropy of an iron layer on a Pt(001) surface and some related systems by employing the local spin density approximation in a theoretical ab initio approach. We found that the surface system Pt/Fe/Pt (001) showed a perpendicular magnetic anisotropy and its anisotropy energy per iron atom amounted to a value which is 2 times larger than the value of bulk FePt. The surface relaxation much enhances the anisotropy energies, related to a large attractive force between the iron and platinum layers. A remarkable cap effect-that the covering platinum layer changes anisotropy energy-was also found to exist. We investigated the microscopic origin of the perpendicular anisotropy in relation to the local densities of states of the Fe atom. These quantities were discussed as a fingerprint of magnetic anisotropy in comparison with the results of the Fe chain at the step edge on a vicinal surface Pt(664). The atomic orbital magnetic moments were enhanced at the respective surface atoms. © 2008 The American Physical Society.
We present a method to calculate the magnetic anisotropy parameters which is based on a perturbative treatment of the spin-orbit interaction and a Green’s function technique in real space. It allows us to interpret the magnetocrystalline anisotropy energy (MAE) in terms of interatomic interactions in the crystal. The method is applied to analyze orbital magnetism and MAE in TX ordered alloys (T=Fe,Co and X=Pd,Pt). The convergence of the orbital moments and MAE in real space and its relation to the problems of Brillouin-zone integration and of oscillatory behavior of MAE as a function of band filling are discussed. A comparison with results obtained by other methods is also given.
High K<sub>u</sub>, uniaxial magnetocrystalline anisotropy, materials are generally attractive for ultrahigh density magnetic recording applications as they allow smaller, thermally stable media grains. Prominent candidates are rare-earth transition metals (Co<sub>5</sub>Sm,...), and tetragonal intermetallic compounds (L1<sub>0</sub> phases FePt, CoPtY,...), which have 20-40 times higher K<sub>u</sub> than today's hexagonal Co-alloy based media. This allows for about 3 times smaller grain diameters, D, and a potential 10-fold areal density increase (∝1/D<sup>2</sup>), well beyond the currently projected 40-100 Gbits/in<sup>2</sup> mark, Realization of such densities will depend on a large number of factors, not all related to solving media microstructure problems, In particular it is at present not known how to record into such media, which may require write fields in the order of 10-100 kOe. Despite this unsolved problem, there is considerable interest in high Ku alternative media, both for longitudinal and perpendicular recording. Activities in this area will be reviewed and data on sputtered and evaporated thin FePt films, with coercivities exceeding 10000 Oe will be presented.
We report magnetocrystalline anisotropy (MCA) calculations of Fe, Co, and Ni slabs of various thicknesses and crystallographic orientations from two density functional theory codes based either on a plane wave or a local atomic basis set expansion and a magnetic tight-binding method. We analyze the evolution of the MCA with the number of layers of the slabs. The decomposition of MCA into contributions of atomic sites helps understanding the oscillatory behavior of the MCA with the slab thickness and highlights the role of finite size effects. We also identify some specific systems with enhanced MCA. A k space as well as a band-filling analysis show very rich features of the MCA that could be used to tailor systems with enhanced magnetic properties. Finally, this work can serve as a benchmark for MCA calculations.
The strong perpendicular magnetic anisotropy of $L{\rm1_0}$-ordered FePt has been the subject of extensive studies for a long time. However, it is not known which element, Fe or Pt, mainly contributes to the magnetic anisotropy energy (MAE). We have investigated the anisotropy of the orbital magnetic moments of Fe 3$d$ and Pt 5$d$ electrons in $L{\rm1_0}$-ordered FePt thin films by Fe and Pt $L_{2,3}$-edge x-ray magnetic circular dichroism (XMCD) measurements for samples with various degrees of long-range chemical order $S$. Fe $L_{2,3}$-edge XMCD showed that the orbital magnetic moment was larger when the magnetic field was applied perpendicular to the film than parallel to it, and that the anisotropy of the orbital magnetic moment increased with $S$. Pt $L_{2,3}$-edge XMCD also showed that the orbital magnetic moment was smaller when the magnetic field was applied perpendicular to the film than parallel to it, opposite to the Fe $L_{2,3}$-edge XMCD results although the anisotropy of the orbital magnetic moment increases with $S$ like the Fe edge. These results are qualitatively consistent with the first-principles calculation by Solovyev ${\it et\ al.}$ [Phys. Rev. B $\bf{52}$, 13419 (1995).], which also predicts the dominant contributions of Pt 5$d$ to the magnetic anisotropy energy rather than Fe 3$d$ due to the strong spin-orbit coupling and the small spin splitting of the Pt 5$d$ bands in $L{\rm1_0}$-ordered FePt.
The magnetism of FeRh (001) films strongly depends on film thickness and surface terminations. While the magnetic ground state of bulk FeRh is G-type antiferromagnetism, the Rh-terminated films exhibit ferromagnetism with strong perpendicular magnetocrystalline anisotropy whose energy +2.1 meV/ is two orders of magnitude greater than bulk 3d conventional magnetic metals (is the area of a two-dimensional unit cell). While the Goodenough-Kanamori-Anderson rule on the superexchange interaction is crucial in determining the magnetic ground phases of FeRh bulk and thin films, the magnetic phases are the results of interplay and competition between three mechanisms—the superexchange interaction, the Zener-type direct interaction, and energy gain by Rh magnetization.
The temperature dependence of the crystallographic anisotropy constant K//1 and saturation magnetization I//s of an ordered FePt alloy were determined in the temperature range 20-450 degree C. The magnetic properties of powders were examined. The highly coercive state is found to be due to a transition domain structure which forms inside the grains of all sized particles when the anisotropy field reaches a high level.
A method is given for generating sets of special points in the Brillouin zone which provides an efficient means of integrating periodic functions of the wave vector. The integration can be over the entire Brillouin zone or over specified portions thereof. This method also has applications in spectral and density-of-state calculations. The relationships to the Chadi-Cohen and Gilat-Raubenheimer methods are indicated.
Magnetism of FeRh (001) films strongly depends on film thickness and surface
terminations. While magnetic ground state of bulk FeRh is G-type
antiferromagnetism, the Rh-terminated films exhibit ferromagnetism with strong
perpendicular MCA whose energy +2.1 meV/$\Box$ is two orders of magnitude
greater than 3$d$ magnetic metals, where $\Box$ is area of two-dimensional unit
cell. While Goodenough-Kanamori-Anderson rule on the superexchange interaction
is crucial in determining the magnetic ground phases of FeRh bulk and thin
films, the magnetic phases are results of interplay and competition between
three mechanisms - the superexchange interaction, the Zener direct-interaction,
and magnetic energy gain.
Highly chemically ordered L10 FePtX–Y nano-granular films with high perpendicular magnetic anisotropy are key media approaches for future heat-assisted magnetic recording (HAMR). They are sputtered at elevated temperature on glass disks coated with adhesion, heat sink, and texturing layers. Adding X = Ag reduces the required deposition temperature and X = Cu lowers the Curie temperature. Current seed layers are NiTa for adhesion and heat sink and well-oriented MgO (002) layers for highly textured FePtX(002) grains surrounded by Y = carbon and/or other segregants. Magnetic anisotropies larger than 4.5 × 107 erg cm−3 and coercivities beyond 5 Tesla have been achieved. The combination of thermal conductivity and Curie temperature determines the required laser power during recording. Key goals are to optimize media, heads, head-disk-spacing, and read-back channels to extend the areal density to 1.5–5 Tb in−2.
Head and media in heat-assisted magnetic recording1. LD, laser diode; TFC, thermal fluctuation control; NFT, near field transducer. 1Lidu Huang et al., “HAMR Thermal Modeling Including Media Hot Spot”, APMRC 2012.
The effect of surface anisotropy on the magnetic ground state of a ferromagnetic nanoparticle is investigated using atomic Monte Carlo simulation for spheres of radius R=6a and R=15a, where a is the interatomic spacing. It is found that the competition between surface and bulk magnetocrystalline anisotropy imposes a ``throttled'' spin structure where the spins of outer shells tend to orient normal to the surface while the core spins remain parallel to each other. For large values of surface anisotropy, the spins in sufficiently small particles become radially oriented either inward or outward in a ``hedgehog'' configuration with no net magnetization. Implications for FePt nanoparticles are discussed.
The effect of surface anisotropy and vacancies upon the ground magnetic state of ferromagnetic nanoparticles is discussed. Our study is based on a random site-diluted classical Heisenberg Hamiltonian with nearest-neighbor interactions, surface and core anisotropies, and a Monte Carlo–Metropolis approach with simulated annealing for energy minimization. Results reveal severe variations with respect to a single domain phenomenology and wider ranges of metastability resembling a multi-valley energy landscape as vacancies are considered and surface anisotropy increases.
The spin-polarized band calculations including spin-orbit interaction for L10-FePt and CoPt ordered alloys have been performed with LMTO-ASA method in the frame of local spin density functional approximation. It has been shown that strong uniaxial magnetic anisotropy of both alloys is brought about by a large spin-orbit coupling of Pt atom and a strong hybridization of Pt d bands with highly polarized Fe (Co)d bands. The obtained magnetocrystalline anisotropy energy (MAE) is about 16×106 J/m3 for FePt and 9×106 J/m3 for CoPt. It is also found that both MAE's have a trend of increase with increasing axial ratio c/a in the vicinity of measured c/a. This can be regarded as being associated with the behavior that the MAE's decrease with increasing band filling.
The uniaxial magnetic anisotropy energy (MAE) of L10 FePt and Fe1−xMnxPt, x=0−0.25, was studied from first principles using two fully relativistic computational methods, the full-potential linear muffin-tin orbitals method and the exact muffin-tin orbitals method. It was found that the large MAE of 2.8 meV/f.u. is caused by a delicate interaction between the Fe and Pt atoms, where the large spin-orbit coupling of the Pt site and the hybridization between Fe 3d and Pt 5d states is crucial. The effect of random order on the MAE was modeled by mutual alloying of the sublattices within the coherent potential approximation (CPA), and a strong dependence of the MAE on the degree of chemical long-range order was found. The alloying of FePt with Mn was investigated with the virtual crystal approximation and the CPA as well as supercell calculations. The MAE increases up to 33% within the concentration range studied here, an effect that is attributed to band filling. Furthermore, the dependence of the MAE on the structural properties was studied.
Using the state-of-the-art relativistic full-potential version of the linear-muffin-tin orbital method we have performed ab initio calculations to study the magnetic properties of eight transition-metal binary alloys (FePt, CoPt, FePd, FeAu, MnPt3, CoPt3, VAu4, and MnAu4). Both the local-spin-density approximation (LSDA) and the generalized gradient approximation (GGA) to the exchange-correlation potential are used in the computation. The resulting spin and orbital magnetic moments of both approximations are similar and agree nicely with experiment, however, different values are found for the magnetocrystalline anisotropy energy (MCA), especially for MnPt3, CoPt3, and MnAu4. For all the other alloys the difference between the MCA values calculated within LSDA and GGA is less than 1 meV. The volume shape anisotropy is found to be important for the FePd and MnPt3 thick films, while it is negligible for the other binary alloys.
The dependence of the magnetic moments on the compositional order in Fe–Pt alloys was studied by neutron powder diffraction. For alloys with almost perfect L10-type long-range order the experimental value of the Fe magnetic moment was determined to be 2.8±0.1μB (extrapolated to zero temperature). Combined analysis of experimental and density functional data shows that the Fe moment drops with increasing Fe content, but is less sensitive to the degree of order, in contrast to the well-known behavior of Fe–Al alloys.
Materials with perpendicular magnetic anisotropy (PMA) are being investigated for magnetic random access memory (MRAM) and other spintronics applications. This article is an overview of the developments in this topic. At first, a historical overview of the magnetic memory is presented along with the fundamentals of MRAM using the field-assisted scheme. Later on, the principle of spin-transfer torque (STT) is explained briefly along with the STT-MRAM design requirements. Here, it is described that the MRAM design is a challenge where a choice has to be made to meet five criteria, a phenomenon called MRAM pentalemma. The main part of the article focuses on the discussion of materials with PMA. The focus is made first on multilayers such as Co/Pd and Co/Pt which have been widely investigated, followed by the recent observation of PMA in FeCoB. In subsequent sections, the progress in future candidates such as FePt is discussed. The article concludes with a summary of the challenges and future directions in this research topic. (C) 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Magnetocrystalline anisotropy (MA) energy of (001) face-centred-cubic Co(N) films is calculated for film thicknesses N = 1–28 in a realistic tight-binding model with and without sp–d orbital hybridization included. The obtained results show that the average MA energy is not largely influenced by the sp–d hybridization. On the other hand, the oscillation pattern is remarkably changed when the sp–d hybridization is included: in this case the MA energy has oscillations with a clear period of 2 atomic layers (AL), similar to the previous ab initio calculations (Szunyogh L, Újfalussy B, Blaas C, Pustugova U, Sommers C and Weinberger P 1997 Phys. Rev. B 56 14036). A careful analysis in k- and N-spaces reveals that the total MA oscillations are a superposition of two oscillatory contributions: one coming from the neighbourhood of the -point with period close to 2 AL (regardless whether the sp–d hybridization is present or not) and the other originating in the region around the -point. The -point contribution has a larger period and its amplitude is significantly smaller than that of the -point contribution when the sp–d hybridization is included so that the 2 AL -point contribution is dominant in this case. The two oscillatory MA contributions are attributed to quantum-well states and the corresponding oscillation periods are related to the extremal radii of the minority-spin bulk Co Fermi surface.
An approach for electronic structure calculations is described that generalizes both the pseudopotential method and the linear augmented-plane-wave (LAPW) method in a natural way. The method allows high-quality first-principles molecular-dynamics calculations to be performed using the original fictitious Lagrangian approach of Car and Parrinello. Like the LAPW method it can be used to treat first-row and transition-metal elements with affordable effort and provides access to the full wave function. The augmentation procedure is generalized in that partial-wave expansions are not determined by the value and the derivative of the envelope function at some muffin-tin radius, but rather by the overlap with localized projector functions. The pseudopotential approach based on generalized separable pseudopotentials can be regained by a simple approximation.
Flat epitaxial 48Ni/52Fe(111) films are prepared by evaporation onto atomically flat Cu(111) films. All films consisting of three or more layers (d ≧ 6 Å) show a far-reaching fit to the model structure of a flat single crystal. The magnetic properties are determined for (70 ≦ T ≦ 400) °K with an oscillation type torsion magnetometer, which can detect a moment of 5 × 10−8 G cm3. All films of three or more layers are ferromagnetic without any indication of superparamagnetism; Curie-temperature and magnetization decrease monotonously with film thickness; there is good qualitative agreement with spin-wave theory and Green's function theory; the magnetization is independent of the field, however, within 1%, for (300 ≦ H ≦ 5000) Oe, while the theory predicts considerable dependence on the field. Strong anisotropies relating to the surface normal as easy axis may easily be interpreted as Néel-type surface anisotropies.
Flache epitaktische 48Ni/52Fe(111)-Schichten wurden durch Aufdampfen auf atomar ebene Cu(111)-Schichten präpariert. Alle Schichten aus 3 oder mehr Atomlagen (d ≧ 6Å) entsprechen weitgehend dem Strukturmodell des ebenen Einkristalls. Die magnetischen Eigenschaften wurden für (70 ≦ T ≦ 400) °K bestimmt in einem Torsions-Schwingungs-Magnetometer, welches den Nachweis eines Moments von 5 × 10−8 G cm3 erlaubt. Alle Schichten aus 3 oder mehr Atomlagen sind ferromagnetisch ohne jedes Anzeichen von Superparamagnetismus. Curie-Temperatur und Magnetisierung fallen monoton mit der Schichtdicke, in guter qualitativer Übereinstimmung mit Spinwellentheorie und Greenscher Funktionentheorie. Die Magnetisierung ist jedoch für (300 ≦ H ≦ 5000) Oe innerhalb 1% vom Feld unabhängig, während die Theorie eine beträchtliche Feldabhängigkeit postuliert. Starke Anisotropien bezüglich der Flächennormalen als leichter Achse lassen sich zwanglos als Oberflächenanisotropien nach Néel interpretieren.
Dans la première partie de ce Mémoire, on propose de considérer l'énergie magnétocristalline et magnétoélastique d'un corps ferromagnétique comme la somme de termes élémentaires relatifs chacun à une liaison, c'est-à-dire à un couple de deux atomes proches voisins. Sur cette base, on développe la théorie de la magnétostriction et de l'anisotropie magnétocristalline et, de sa comparaison avec les résultats expérimentaux, on déduit les valeurs des paramètres qui caractérisent l'énergie de liàison. Des mêmes prémices, on déduit qu'il doit exister dans les corps ferromagnétiques, une énergie d'anisotropie superficielle, dépendant de l'orientation de l'aimantation spontanée par rapport à la surface et ne présentant d'ailleurs aucun rapport avec le phénomène classique de champ démagnétisant de forme. Cette énergie de surface, de l'ordre de O, I à I erg/cm2, est susceptible de jouer un rôle important dans les propriétés des substances ferromagnétiques dispersées en éléments de dimensions inférieures à I00 Å. Dans la seconde partie, on montre, en adoptant le point de vue précédent, que dans les solutions solides ferromagnétiques à deux constituants au moins, traitées à chaud dans un champ magnétique, les atomes proches voisins d'un atome donné doivent se répartir d'une façon anisotrope autour de ce dernier et donner naissance à une surstructure d'orientation. Par trempe, cette surstructure est susceptible de se conserver en faux équilibre à basse température et se manifeste par l'apparition d'une anisotropie magnétique de caractère uniaxial. Les phénomènes sont précisés par le calcul, notamment le rôle de la concentration, dans le cas de différents réseaux cubiques simples et dans le cas d'une substance isotrope par compensation. L'anisotropie calculée est de l'ordre de I03 à I05 ergs/cm2, mais paraît dépasser largement ces valeurs dans des cas exceptionnels. Cette théorie rend compte des propriétés des ferronickels traités à chaud dans un champ magnétique et, en particulier, des monocristaux de permalloy. On suggère le rôle possible de ces effets dans l'alnico V et les ferrites de cobalt orientés. Dans une troisième partie, on montre que l'on peut créer une surstructure d'orientation dans une solution solide quelconque au moyen d'une déformation élastique à chaud et la conserver par trempe. Si la solution solide est ferromagnétique, les surstructures ainsi créées donnent naissance à une anisotropie magnétique de caractère uniaxial. En s'appuyant sur une théorie sommaire des propriétés élastiques des solutions solides développée à cet effet, le phénomène est soumis au calcul : on trouve des anisotropies de I04 ergs/cm3 pour des tensions de I0 kg/mm2 , dans le cas des ferronickels. On propose d'interpréter par la création de telles surstructures l'anisotropie magnétique uniaxiale des ferronickels quasi unicristallins laminés à froid, la déformation plastique permettant aux atomes de prendre la répartition d'équilibre correspondant au système des tensions appliquées. Dans les ferronickels polycristallins laminés ou étirés, l'anisotropie est de signe contraire à la précédente; on propose de l'expliquer selon le même mécanisme que les phénomènes de restauration après fluage.
A perturbative theory of magnetocrystalline anisotropy and orbital moment in itinerant ferromagnets is presented that clearly outlines the close connection between these two quantities. The theory is used to study the magnetocrystalline anisotropy in transition-metal monolayers. The importance of the crystal-field energy and of the filling of the valence band is emphasized. For the first time the orbital contribution to the magnetization in monolayers is estimated; it is shown that it may produce an anisotropy in the magnetization of the order of 0.1μB per atom.
The magnetocrystalline anisotropy energy and anisotropy of the orbital angular momentum have been calculated from first prinicples for Co and for a variety of intermetallic compounds including YCo5. For all compounds the predicted easy axes are in agreement with experiment. A strong correlation between the anisotropy of the orbital angular momentum and the energy is found for the compounds that do not contain Pt. For those that do contain Pt, Pt is shown to contribute significantly to the anisotropy energy.
Generalized gradient approximations (GGA{close_quote}s) for the exchange-correlation energy improve upon the local spin density (LSD) description of atoms, molecules, and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental constants. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential. {copyright} {ital 1996 The American Physical Society.}
First principles calculations based upon density functional theory have been used to investigate the magnetic properties of various Fe-Pt and Co-Pt alloys. At the 50:50 composition, the technologically important L1<sub>0</sub> alloys CoPt and FePt show large magnetocrystalline anisotropies consistent with the natural layering of the crystal structure. Calculated values for the magnetocrystalline anisotropy and magnetizations are found to be in close agreement with measured values. Since the L1<sub>0</sub> phase forms over a range of compositions, the influence of composition on magnetic properties has also been examined. A simple expression, derived from the Ne´el model, relates the anisotropy to the composition, or degree of disorder in the structure, and is found to be of value for understanding anisotropy in imperfect structures. At greater Fe of Co compositions there are several interesting crystal structures including the metastable pmm<sub>2</sub> phase that is composed of alternating pure and mixed planes. Again, fairly large anisotropies are seen as a consequence of layering and symmetry. Growing Fe<sub>3</sub>Pt pmm<sub>2</sub> films seems less promising than Co<sub>3</sub>Pt pmm<sub>2</sub> films given the larger energy difference between the pmm<sub>2</sub> and cubic L1<sub>2</sub> phases.
FePt heat assisted magnetic recording media
- Weller
Magnetic anisotropy of L10 FePt and Fe1- xMnxpt
- Burkert
FePt heat assisted magnetic recording media
- D Weller
- G Parker
- O Mosendz
- A Lyberatos
- D Mitin
- N Y Safonova
- M Albrecht
D. Weller, G. Parker, O. Mosendz, A. Lyberatos, D. Mitin, N.Y. Safonova,
M. Albrecht, FePt heat assisted magnetic recording media, J. Vac. Sci. Technol. B,
Nanotechnology and Microelectronics: Materials, Processing, Measurement, and
Phenomena 34 (6) (2016) 060801.