Ultrathin Ferromagnetic Films Research Articles

Investigation of anisotropy constants dependence of ultra-thin ferromagnetic films with second order perturbed Heisenberg Hamiltonian

The variation of energy of ferromagnetic ultra-thin films with second and fourth order anisotropy was investigated using Heisenberg Hamiltonian with second order perturbation. The study was limited to sc(001) film with three layers. Graphs indicate energy minimums at certain values of second order anisotropy, fourth order anisotropy and angle. Films with fourth order anisotropy (Dm(4))/ω=4 can be easily oriented in the direction given by angle of 2.66 radians for the values of other energy terms used in this simulation. When the second order anisotropy (Dm(2))/ω is 3.1, preferred direction is 0.754 radians. When the second order anisotropy varies at a constant value of fourth order anisotropy, the graph indicates more energy minimums.Keywords: Heisenberg Hamiltonian; magnetic thin films; magnetic anisotropies; spinDOI: 10.4038/josuk.v3i0.2740J. Sci. Univ. Kelaniya 3 (2007) : 73-82

Complex anisotropy and magnetization reversal on stepped surfaces probed by the magneto-optical Kerr effect

So-called split hysteresis loops have been measured for ultrathin ferromagnetic films grown on stepped surfaces. Since the shape of the loops is sensitive to the direction in which the magnetic field is applied with respect to the steps, the sample orientation against the field is particularly important. We performed systematic magneto-optical Kerr effect studies for 15 and 58 ML of Fe grown on Au(1,1,13). In view of the complex magnetic anisotropy of such systems we discuss representative hysteresis loops taken at sample orientations misaligned from the field (and laser beam) direction. In particular, the presence of a so-called low field component to the hysteresis loops is discussed and its reversed polarity is explained.

Scaling hypothesis for modulated systems

We propose a scaling hypothesis for pattern-forming systems in which modulation of the order parameter results from the competition between a short-ranged interaction and a long-ranged interaction decaying with some power $\alpha$ of the inverse distance. With L being a spatial length characterizing the modulated phase, all thermodynamic quantities are predicted to scale like some power of L. The scaling dimensions with respect to L only depend on the dimensionality of the system d and the exponent \alpha. Scaling predictions are in agreement with experiments on ultra-thin ferromagnetic films and computational results. Finally, our scaling hypothesis implies that, for some range of values \alpha>d, Inverse-Symmetry-Breaking transitions may appear systematically in the considered class of frustrated systems.

Field‐induced magnetic reorientation in ultrathin ferromagnetic films: Phase diagrams

AbstractThe magnetic reorientation transition can be induced by applying an external transverse magnetic field. The magnetic field at which the magnetization reaches the field direction is called the reorientation magnetic field. The reorientation magnetic field in ultrathin ferromagnetic films is studied within the framework of the many‐body Green function theory. The model Hamiltonian includes a Heisenberg term with different surface exchange couplings with respect to the bulk one, a second‐order single‐ion anisotropy, and a transverse external magnetic field in the x‐direction. The single‐ion anisotropy term is treated by the generalized Anderson–Callen decoupling scheme. We investigate the reorientation magnetic field $h_{0R}^x$ as a function of the surface single‐ion anisotropic parameter $K_{2,S} (T \to 0)$ for different: film thicknesses L, surface exchange coupling enhancements ΔS, temperatures, T and as a function of the temperature for different film thicknesses L.

Vortex energy and 360° Néel walls in thin‐film micromagnetics

AbstractWe study the vortex pattern in ultrathin ferromagnetic films of circular crosssection. The model is based on the following energy functional: for in‐plane magnetizations m: B2 → S1 in the unit disc $\font\open=msbm10 at 10pt\def\R{\hbox{\open R}}B^2 \subset \R^2$. The avoidance of volume charges ▿ · m ≠ 0 in B2 and surface charges m · ν ≠ 0 on δB2 leads to the formation of a vortex in the limit ε → 0. At the level ε > 0 the vortex is regularized by the formation of a 360° Néel wall (a one‐dimensional transition layer with core of scale ε) concentrated along a radius of B2. We derive the limiting energy of the vortex by matching upper and lower bounds. Our analysis on the lower bound is based on a dynamical system argument and an interpolation inequality with sharp leading‐order constant, while the upper bound uses the leading‐order energy for 360° Néel walls. © 2010 Wiley Periodicals, Inc.

SPIN WAVES TRANSMISSION VIA A MOLECULAR JUNCTION CONNECTING TWO QUASI-2D HEISENBERG FERROMAGNETS

A theoretical investigation of spin wave dynamics and scattering at a molecular junction between two Heisenberg ferromagnets is presented. The model system consists of two ferromagnetic ultrathin films with equal thickness of three atomic layers, joined together by a magnetic molecule. No electronic effects are considered, but local changes in the magnetic exchange field are assumed to be dominant. The mathematical framework of the matching method is used with nearest neighbor magnetic exchange interactions, to analyze both the spin fluctuation dynamics and the spin wave scattering phenomena at the junction boundary. The coherent reflection and transmission probabilities and the conductance of spin waves incident from the interior of the films onto the boundary are calculated in accordance with the Landauer–Büttiker formalism, and numerical results are presented for representative sets of system parameters for a large range of scattering frequencies. The scattered spectra show interesting sharp features, with associated Fano resonances, as a function of scattering frequencies, system parameters, and spin wave incidence angle. Moreover, a frequency selective conductance of the spin waves via Fano resonances can be obtained by an appropriate choice of the spin wave incident angle and system parameters.

Determination of perpendicular magnetic anisotropy in ultrathin ferromagnetic films by extraordinary Hall voltage measurement

A magnetometric technique for detecting the magnetic anisotropy field of ferromagnetic films is described. The technique is based on the extraordinary Hall voltage measurement with rotating the film under an external magnetic field. By analyzing the angle-dependent Hall voltage based on the Stoner-Wohlfarth theory, the magnetic anisotropy field is uniquely determined. The present technique is pertinent especially for ultrathin films with strong intrinsic signal, in contrast to the conventional magnetometric techniques of which the signal is in proportion to the sample volume and geometry.

The reorientation temperature in ultrathin ferromagnetic films

AbstractThe reorientation temperature in ultrathin ferromagnetic films is studied within the framework of the many‐body Green function theory. The model Hamiltonian includes a Heisenberg term with the different surface exchange couplings with respect to the bulk one, a second‐order single‐ion anisotropy, and a transverse external magnetic field in the x‐direction. The single‐ion anisotropy term is treated by the generalized Anderson–Callen decoupling scheme. We investigate the reorientation temperature TR (a) as a function of the surface single‐ion anisotropic parameter K2,S(T → 0) for different: film thicknesses L, surface exchange coupling enhancements ΔS, transverse magnetic fields h and (b) as a function of the transverse magnetic field h for different: film thicknesses L, surface exchange coupling enhancements ΔS, surface single‐ion anisotropic parameters K2,S(T → 0).

Chemically selective modification of spin polarization in ultrathin ferromagnetic films: Microscopic theory and macroscopic experiment

Modulation of thin-film magnetic properties will be key to the design of future magnetoelectronic (spintronic) devices. Here, we report the influence of atomic adsorbates upon ultrathin cobalt films on copper, employing secondary electron spin polarization as an incisive experimental probe. We observe that nitrogen suppresses measured polarization by $\ensuremath{\sim}20%$ for the thickest layers; oxygen has little impact in this regime. Moreover, we develop a model capable of predicting these effects, forging a crucial link between microscopic theory and an observable macroscopic magnetic phenomenon.

Dynamic magnetization properties of a superferromagnetic metal-insulator multilayer observed by magneto-optic Kerr microscopy

Longitudinal magneto-optical Kerr effect (MOKE) magnetometry and microscopy have been performed on a superferromagnetic (SFM) metal-insulator multilayer of [Co80Fe20(tn=1.3 nm)/Al2O3(3 nm)]10 to understand the dynamic behavior of the SFM domains. Frequency dependent hysteresis loops measured by MOKE show that the coercive field Hc increases as the rate (frequency) of magnetization reversal is increased similar to dynamic hysteresis loops observed on conventional ferromagnetic ultrathin films. This dynamic hysteresis behavior arises due to SFM friction-controlled domain wall motion which is observed by MOKE microscopy. We see that the nucleation field for SFM domains increases for hysteresis loops with higher frequency as expected for a ferroic system.

MAGNONS TRANSMISSION THROUGH AN ATOMIC WIRE CONNECTING TWO ULTRATHIN HEISENBERG FERROMAGNETS

The magnons transport properties of molecular wires connecting two Heisenberg ferromagnets are studied within the framework of the matching method and with use of a realistic atomic structure. The model system consists of two nanostructured ferromagnetic films on either side of the junction and the atomic wire consists of a linear molecule connecting two ultrathin solid ferromagnetic films. A theoretical model is presented for the study of the transmission and the reflection of spin waves at the atomic wire junction. The calculation was made at the atomic scale for two identical waveguides with ordered spins and coupled by Heisenberg exchange interaction between first neighbors. Our analysis yields a detailed understanding of the spin-wave coherent scattering at the linear molecular junction. We calculate, in particular, the coherent reflection R and transmission T coefficients, which constitute the elements of the scattering matrix in accordance with the Landauer–Büttiker scattering formalism, as well as the magnon transmittance of the atomic wire for spin-waves incident from the interior of the film on the junction. The most representative numerical results obtained for the system of two slabs made up of three Fe ferromagnetic atomic layers connected with an Fe or Gd atomic wire are presented as function of the dimensionless frequency Ω in the magnons energy band. The coherent reflection and transmission scattering cross sections show characteristic spectral features, depending on the length of the wire, on the cut-off frequencies for the propagating magnons, as well as on the magnons incidence angle. The results illustrate the occurrence of Fano resonances in the transmitted spectra due to the interaction of localized spin states on the atomic wire with the propagating spin waves of the waveguide. An interesting physical effect is observed for this magnetic atomic junction, namely the frequency selective conductance of the spin waves via Fano resonances, by an appropriate choice of the spin-wave incident angle.

Magnetization direction reorientation in ultrathin ferromagnetic films: Spin reorientation transition by H adsorption in the Valenta model

The magnetization of ultrathin ferromagnetic films depends in a very sensitive way on anisotropy fields which favor its particular orientation. We consider the spin reorientation transition in the ferromagnetic thin films within the Valenta model investigating the influence of different anisotropy fields on their magnetization behavior. It is shown that for certain values of the parameters a temperature-driven, a thickness-induced, and a H-induced switching transition from an in-plane to an out-of-plane ordered state may be observed. The use of the Valenta model allows us to present all dependences in the layer resolved mode which leads to the kinetics of the spin reorientation.

Spin-charge coupling in a band ferromagnet: Magnon-energy reduction, anomalous softening, and damping

The effects of correlation-induced coupling between spin and charge fluctuations on spin-wave excitations in a band ferromagnet are investigated by including self-energy and vertex corrections within a systematic inverse-degeneracy expansion scheme which explicitly preserves the Goldstone mode. Arising from the scattering of a magnon into intermediate spin-excitation states (including both magnon and Stoner excitations) accompanied with charge fluctuations in the majority-spin band, this spin-charge coupling results not only in a substantial reduction of magnon energies but also in anomalous softening and significant magnon damping for zone-boundary modes lying within the Stoner gap. Our results are in good qualitative agreement with recent spin-wave excitation measurements in colossal magnetoresistive manganites and ferromagnetic ultrathin films of transition metals.

Spin Dynamics of Itinerant Electron Ferromagnetic Nanostructures

We review our theoretical studies of the spin dynamics of ultrathin ferromagnetic films adsorbed on metallic substrates. Of interest are the spin waves with wave vector from the center of the Brillouin zone to its boundary. We utilize a realistic electronic structure for the substrate/adsorbate combination through an empirical tight binding description of the electronic structure of the materials involved, and the spin excitations are explored through the random phase approximation. We can examine very large systems with this scheme, such as multilayer films placed on fully semi-infinite substrates. One principal finding is the adiabatic approximation breaks down qualitatively for these systems. We illustrate for Co films on Cu(100) where we also find excellent agreement with experiment. We conclude by discussing recent data for the Fe bilayer on W(110) where, after an excellent account of the measured exchange stiffness, we find the large wave vector spin waves generated by theory to be far too stiff.

Spin reorientation transition and phase diagram of ultrathin ferromagnetic films

We show results from Monte Carlo simulations of a two-dimensional Heisenberg model for ultrathin films with perpendicular anisotropy. A complete phase diagram is obtained as a function of anisotropy and temperature, spanning a wide range of behavior. We discuss our results in relation to experimental findings in different ultrathin films. We observe and characterize a line of spin reorientation transitions. This transition from out-of-plane stripe order to in-plane ferromagnetic order presents an intermediate paramagnetic gap in a finite region of parameter space, as reported in experiments. For large anisotropies, direct transitions from a low temperature stripe phase to a paramagnetic or tetragonal phase with dominant perpendicular magnetization is observed, which is also in agreement with experiments. We also show the phase diagram for a system without exchange, i.e., with pure dipolar and anisotropy interactions. It shows a similar behavior to the ferromagnetic case with antiferromagnetic instead of stripe phases at low temperatures. A spin reorientation transition is also found in this case.

Langevin simulations of a model for ultrathin magnetic films

We show results from simulations of the Langevin dynamics of a two-dimensional scalar model with competing interactions for ultrathin magnetic films. We find a phase transition from a high temperature disordered phase to a low temperature phase with both positional and orientational orders. Both kinds of order emerge at the same temperature, probably due to the isotropy of the model Hamiltonian. In the low temperature phase orientational correlations show long range order while positional correlations show only quasi-long-range order in a wide temperature range. The orientational correlation length and the associated susceptibility seem to diverge with power laws at the transition. While at zero temperature the system exhibits stripe long range order, as temperature grows we observe the proliferation of different kinds of topological defects that ultimately drive the system to the disordered phase. The magnetic structures observed are similar to experimental results on ultrathin ferromagnetic films.

Application of two-electron spectroscopy in reflection for studying electronic structure of surfaces and thin films

Since first observations of the (e,2e) reaction in reflection geometry on solid surfaces this phenomenon was thoroughly investigated in order to understand the mechanism of two correlated electrons emission. At the same time this technique has been developing to become a spectroscopic tool for studying solid surfaces. In this contribution we present two examples of how valuable information on electronic structure of solid surface can be extracted from the (e,2e) spectra. The first concerns a dielectric LiF film and the second a ferromagnetic ultra-thin Co film. The combination of (e,2e) and electron energy loss spectroscopy allows the measurement of the energy gap E g, valence bandwidth Δ E, electron affinity χ and excitonic levels position E ex of the dielectric. These parameters depend on the thickness, morphology and crystallinity of the film that were studied by transmission and scanning electron microscopy. In case of the Co film a spin-polarized incident electrons were used to probe spin-dependent features of the cobalt valence band.

Ultrathin manganite films grown by pulsed-plasma deposition

Ultrathin ferromagnetic films of La 0.7Sr 0.3MnO 3 were deposited by electron-beam ablation on standard SrTiO 3(1 0 0) and NdGaO 3(1 1 0) substrates. Even 4 nm films are metallic and develop spontaneous magnetization at room temperature: similar hysteresis cycles were measured by magneto optical Kerr effect (MOKE) in the longitudinal configuaration and by SQUID magnetometry. To the best of our knowledge the 4 nm thickness corresponds so far to the thinnest manganite film showing room-temperature ferromagnetism.

Spin dynamics across an inhomogeneous atomic boundary separating ultrathin Heisenberg ferromagnetic films

A theoretical model is presented for the study of the scattering and the localisation of spin-waves at an extended inhomogeneous structural and magnetic boundary separating ultrathin Heisenberg ferromagnetic films. The model system consists of two different magnetic materials A and B with different thickness of two and three atomic layers, on either side of a defect atomic step. The matching technique is used with nearest neighbour magnetic exchange to analyse both the localisation and the scattering spin dynamics. The localised spin states that manifest themselves as Rayleigh branches, and the local densities of spin states are calculated on this boundary. The coherent reflection and transmission scattering properties of spin-waves incident from the interior of the ultrathin films on the inhomogeneous boundary are also calculated. The numerical calculations are applied in particular to a system of three Fe ferromagnetic atomic layers and two Gd ferromagnetic atomic layers, across a defect atomic step. The results illustrate the occurrence of Fano resonances in the transmitted spectra due to the localised spin states on the inhomogeneous boundary. An interesting physical effect is observed for this magnetic and atomic step boundary, namely the frequency selective conductance of the spin-waves via Fano resonances, by an appropriate choice of the angle of spin-wave incidence on the boundary.

Observation of unusual magnetic behavior: Spin reorientation transition in thick Co–Fe–Ta–B glassy films

Atomically smooth Co–Fe–Ta–B glassy films were deposited on variety of substrates (Si, SiO2, and keptone). An extensive magnetic characterization in the temperature range from 5to330K is reported for the films of thickness up to ∼5.5μm. A reversible spin reorientation transition (SRT) from in-plane single domainlike state to out-of-plane multidomain state with increase in measuring temperature from 5to330K was observed in the films of thickness up to ∼2.5μm, in contrast to previously reported ultrathin ferromagnetic films of transition metals consisting of about half a dozen of monolayers. The SRT temperature (TSRT) is dependent on the film thickness and the applied magnetic field and is not governed by the temperature dependent magnetocrystalline anisotropy or the anisotropy at the film-substrate interface, which are the most common cause for the SRT in magnetic materials. Atomic relaxation has significant influence on SRT. The relaxed state results in a shift in TSRT to higher temperature or disappearance of SRT. We have compared our results with the reported data on ultrathin ferromagnetic films and shown that the atomic randomness and the strains/stress are responsible for the SRT in present case.