Magnetization of left-handed metamaterials

We propose a possible mechanism for the generation of magnetic fields in negative refraction index composite metamaterials. Considering the propagation of a high-frequency modulated amplitude electric field in a left-handed material (LHM), we show that the ponderomotive interaction between the field and low-frequency potential distributions leads to spontaneous generation of magnetic fields, whose form and properties are discussed.

Improved magnetization in sputtered dysprosium thin films

50nm thick nanogranular polycrystalline dysprosium thin films have been prepared via ultra-high vacuum DC sputtering on SiO2 and Si wafers. The maximum in-plane spontaneous magnetization at T = 4K was found to be µ₀M_S,4K^(C) = (3.28±0.26)T for samples deposited on wafers heated to 350°C with a Neel point of T_N^(C) = (173±2)K and a ferromagnetic transition at T_C^(C) = (80±2)K, measured via zero-field-cooled – field-cooled magnetization measurements, close to single-crystal values. The slightly reduced magnetization is explained in the light of a metastable face-centered cubic crystal phase which occurred at the seed interface and granularity related effects, that are still noticeably influential despite an in-plane magnetic easy axis. As deposited samples showed reduced magnetization of µ₀M_S,4K^(A) = (2.26±0.18)T, however their ferromagnetic transition shifted to a much higher temperature of T_C^(A) = (172±2)K and the antiferromagnetic phase was completely suppressed probably as a result of strain.

A variational approach to the relaxation of single domain magnetic particles based on Brown's model

Brown's model for the relaxation of the magnetization of a single domain ferromagnetic particle is considered. This model results in the Fokker-Planck equation of the process. The solution of this equation in the cases of most interest is non- trivial. The probability density of orientations of the magnetization in the Fokker-Planck equation can be expanded in terms of an infinite set of eigenfunctions and their corresponding eigenvalues where these obey a Sturm-Liouville type equation. A variational principle is applied to the solution of this equation in the case of an axially symmetric potential. The first (non-zero) eigenvalue, corresponding to the largest time constant, is considered. From this we obtain two new results. Firstly, an approximate minimising trial function is obtained which allows calculation of a rigorous upper bound. Secondly, a new upper bound formula is derived based on the Euler-Lagrange condition. This leads to very accurate calculation of the eigenvalue but also, interestingly, from this, use of the simplest trial function yields an equivalent result to the correlation time of Coffey et at. and the integral relaxation time of Garanin. (C) 2004 Elsevier B.V. All rights reserved.

Interpolation formula between very low and intermediate-to-high damping Kramers escape rates for single-domain ferromagnetic particles

It is shown that the Mel'nikov-Meshkov formalism for bridging the very low damping (VLD) and intermediate-to-high damping (IHD) Kramers escape rates as a function of the dissipation parameter for mechanical particles may be extended to the rotational Brownian motion of magnetic dipole moments of single-domain ferromagnetic particles in nonaxially symmetric potentials of the magnetocrystalline anisotropy so that both regimes of damping, occur. The procedure is illustrated by considering the particular nonaxially symmetric problem of superparamagnetic particles possessing uniaxial anisotropy subject to an external uniform field applied at an angle to the easy axis of magnetization. Here the Mel'nikov-Meshkov treatment is found to be in good agreement with an exact calculation of the smallest eigenvalue of Brown's Fokker-Planck equation, provided the external field is large enough to ensure significant departure from axial symmetry, so that the VLD and IHD formulas for escape rates of magnetic dipoles for nonaxially symmetric potentials are valid.

Boundary conditions in the simplest model of linear and second harmonic magneto-optical effects

This paper is concerned with linear and nonlinear magneto- optical effects in multilayered magnetic systems when treated by the simplest phenomenological model that allows their response to be represented in terms of electric polarization, The problem is addressed by formulating a set of boundary conditions at infinitely thin interfaces, taking into account the existence of surface polarizations. Essential details are given that describe how the formalism of distributions (generalized functions) allows these conditions to be derived directly from the differential form of Maxwell's equations. Using the same formalism we show the origin of alternative boundary conditions that exist in the literature. The boundary value problem for the wave equation is formulated, with an emphasis on the analysis of second harmonic magneto-optical effects in ferromagnetically ordered multilayers. An associated problem of conventions in setting up relationships between the nonlinear surface polarization and the fundamental electric field at the interfaces separating anisotropic layers through surface susceptibility tensors is discussed. A problem of self- consistency of the model is highlighted, relating to the existence of resealing procedures connecting the different conventions. The linear approximation with respect to magnetization is pursued, allowing rotational anisotropy of magneto-optical effects to be easily analyzed owing to the invariance of the corresponding polar and axial tensors under ordinary point groups. Required representations of the tensors are given for the groups infinitym, 4mm, mm2, and 3m, With regard to centrosymmetric multilayers, nonlinear volume polarization is also considered. A concise expression is given for its magnetic part, governed by an axial fifth-rank susceptibility tensor being invariant under the Curie group infinityinfinitym.

Dynamic, in situ optical, magnetic and magneto-optical monitoring of the growth of Co/Au and Pd/Co/Au multilayer systems

The growth of magnetron sputtered Co/Au and Pd/Co/Au superlattices on Au and Pd buffer layers, deposited onto glass substrates, has been monitored optically and magneto-optically in real time, using rotating analyser ellipsometry and Kerr polarimetry, at a wavelength of 633 nm. The magneto-optical traces, combined with ex situ and in situ hysteresis loops, provide a detailed and informative fingerprint of the optical and magnetic properties of the films as they evolve during growth. For Co/Au, oscillations in the polar magneto-optical effect developed during the deposition of An overlayers on Co and these may be attributed to quantum well states. However, the hysteresis measurements show that the magnetic field required to maintain saturation magnetization throughout the experiment was larger than available in situ, introducing a degree of confusion concerning the interpretation of the data. This problem was overcome by the incorporation of Pd layers into the Co/Au structure, thereby eliminating variation in magnetic orientation during growth of the Au layers as a contributory factor to the observations.

Current-driven magnetic rearrangements in spin-polarized point contacts

A method for investigating the dynamics of atomic magnetic moments in current-carrying magnetic point contacts under bias is presented. This combines the nonequilibrium Green's function (NEGF) method for evaluating the current and the charge density with a description of the dynamics of the magnetization in terms of quasistatic thermally activated transitions between stationary configurations. This method is then implemented in a tight-binding (TB) model with parameters chosen to simulate the main features of the electronic structures of magnetic transition metals. We investigate the domain wall (DW) migration in magnetic monoatomic chains sandwiched between magnetic leads, and for realistic parameters find that collinear arrangement of the magnetic moments of the chain is always favorable. Several stationary magnetic configurations are identified, corresponding to a different number of Bloch walls in the chain and to a different current. The relative stability of these configurations depends on the geometrical details of the junction and on the bias; however, we predict transitions between different configurations with activation barriers of the order of a few tens of meV. Since different magnetic configurations are associated with different resistances, this suggests an intrinsic random telegraph noise at microwave frequencies in the I-V curves of magnetic atomic point contacts at room temperature. Finally, we investigate whether or not current-induced torques are conservative.

Evolution of Clay Morphology in Polypropylene/Montmorillonite Nanocomposites upon Equi-biaxial Stretching: A Solid-State NMR and TEM Approach

Solid-state NMR and TEM were used to quantitatively examine the evolution of clay morphology upon equibiaxial stretching of polypropylene/montmorillonite (PP-MMT) nanocomposites up to a stretch ratio (?= final length/initial length) of 3.5. 1 H spin-lattice relaxation times were measured by the saturation-recovery sequence. For the nanocomposites, initial portions of the magnetization recovery
curves (e~20 ms) were found to depend on v t, indicative of diffusion-limited relaxation and in agreement with calculations based on estimates of the spin-diffusion barrier radius surrounding the paramagnetic centers in the clay, the electron-nucleus coupling constant, and the spin-diffusion coefficient. Initial slopes of these magnetization recovery curves directly correlated with the fraction of clay/polymer interface. New clay surface was exposed as a near linear function of strain. Long-time portions of the magnetization recovery curves yielded information on the average interparticle separations, which decreased slowly before reaching a plateau at ?=~2.5 as particles aligned. TEM images supported these findings and were used to define and quantify degrees of exfoliation and homogeneity from the NMR data. Exfoliation, defined as (platelets/ stack)-1, increased from 0.38 (unstretched) to 0.80 at ? = 3.5 for PP-MMT nanocomposites stretched at
150 C and 16 s-1. A lower stretch temperature, 145 C, which is slightly below melting onset, led to an exfoliation degree of 0.87 at ?= 2.8, consistent with the ability of higher melt viscosities to allow for higher shear stress transfer. Exposure of new clay surface is attributed to aggregate breakup and orientation at low strains (? e ~2) and to platelets sliding apart at higher strains.

Atomic ordering in nano-layered FePt: Multiscale Monte Carlo simulation

Nano- and meso-scale simulation of chemical ordering kinetics in nano-layered L1(0)-AB binary intermetallics was performed. In the nano- (atomistic) scale Monte Carlo (MC) technique with vacancy mechanism of atomic migration implemented with diverse models for the system energetics was used. The meso-scale microstructure evolution was, in turn, simulated by means of a MC procedure applied to a system built of meso-scale voxels ordered in particular L1(0) variants. The voxels were free to change the L1(0) variant and interacted with antiphase-boundary energies evaluated within the nano-scale simulations. The study addressed FePt thin layers considered as a material for ultra-high-density magnetic storage media and revealed metastability of the L1(0) c-variant superstructure with monoatomic planes parallel to the (001)-oriented layer surface and off-plane easy magnetization. The layers, originally perfectly ordered in the c-variant, showed discontinuous precipitation of a- and b-L1(0)-variant domains running in parallel with homogeneous disordering (i.e. generation of antisite defects). The domains nucleated heterogeneously on the free monoatomic Fe surface of the layer, grew inwards its volume and relaxed towards an equilibrium microstructure of the system. Two

Atomic ordering in nano-layered FePt

Monte Carlo simulation of chemical ordering kinetics in nano-layered L1₀ AB binary intermetallics was performed. The study addressed FePt thin layers considered as a material for ultra-high-density magnetic storage media and revealed metastability of the L1₀ c-variant superstructure with monoatomic planes parallel to the surface and off-plane easy magnetization. The layers, originally perfectly ordered in a c-variant of the L1₀ superstructure, showed homogeneous disordering running in parallel with a spontaneous re-orientation of the monoatomic planes leading to a mosaic microstructure composed of a- and b-L1₀-variant domains. The domains nucleated heterogeneously on the surface of the layer and grew discontinuously inwards its volume. Finally, the domains relaxed towards an equilibrium microstructure of the system. Two “atomistic-scale” processes: (i) homogeneous disordering and (ii) nucleation of the a- and b-L1₀-variant domains showed characteristic time scales. The same was observed for the domain microstructure relaxation. The discontinuous domain growth showed no definite driving force and proceeded due to thermal fluctuations. The above complex structural evolution has recently been observed experimentally in epitaxially deposited thin films of FePt.

Large-scale density functional calculations of the surface properties of the Wigner crystal

The surface properties of the jellium model have been investigated by large supercell computations in the density functional theory-local spin-density (DFT-LSD) approach for planar slabs with up to 1000 electrons. A wide interval of densities has been explored, extending into the stability range of the Wigner crystal. Most computations have been carried out on nominally paramagnetic samples with an equal number of spin-up and spin-down electrons. The results show that within DFT-LSD spontaneous spin polarization and charge localization start nearly simultaneously at the surface for r(s) similar to 20, then, with decreasing density, they progress toward the center of the slab. Electrons are fully localized and spin polarized at r(s) = 30. At this density the charge distribution is the superposition of disjoint charge blobs, each corresponding to one electron. The distribution of blobs displays both regularities and disorder, the first being represented by well-defined planes and simple in-plane geometries, and the latter by a variety of surface defects. The surface energy, surface dipole, electric polarisability, and magnetization pattern have been determined as a function of density. All these quantities display characteristic anomalies at the density of the localization transition. The analysis of the low-frequency electric conductivity shows that in the fluid paramagnetic regime the in-plane current preferentially flows in the central region of the slab and the two spin channels are equally conducting. In the charge localized, spin-polarized regime, conductivity is primarily a surface effect, and an apparent asymmetry is observed in the two spin currents.

Mesoscale flux-closure domain formation in single-crystal BaTiO3

Over 60 years ago, Charles Kittel predicted that quadrant domains should spontaneously form in small ferromagnetic platelets. He expected that the direction of magnetization within each quadrant should lie parallel to the platelet surface, minimizing demagnetizing fields, and that magnetic moments should be configured into an overall closed loop, or flux-closure arrangement. Although now a ubiquitous observation in ferromagnets, obvious flux-closure patterns have been somewhat elusive in ferroelectric materials. This is despite the analogous behaviour between these two ferroic subgroups and the recent prediction of dipole closure states by atomistic simulations research. Here we show Piezoresponse Force Microscopy images of mesoscopic dipole closure patterns in free-standing, single-crystal lamellae of BaTiO3. Formation of these patterns is a dynamical process resulting from system relaxation after the BaTiO3 has been poled with a uniform electric field. The flux-closure states are composed of shape conserving 90° stripe domains which minimize disclination stresses.

Structural and magnetic properties of sol-gel Co2xNi0.5-xZn0.5-xFe2O4 thin films

Nanocrystalline Co2xNi0.5-xZn0.5-xFe2O4 (x = 0-0.5) thin films have been synthesized with various grain sizes by a sol-gel method on polycrystalline silicon substrates. The morphology as well as magnetic and microwave absorption properties of the films calcined at 1073 K were studied using X-ray diffraction, scanning electron microscopy, X-ray photoelectron spectroscopy, and vibrating sample magnetometry. All films were uniform with out microcracks . The Co content in the Co-Ni-Zn films resulted in a grain size ranging from 15 to 32 nm while it ranged from 33 to 49 nm in the corresponding powders. Saturation and remnant magnetization increased with increase in grain size, while coercivity demonstrated a drop due to multidomain behavior of crystallites for a given value of x. Saturation magnetization increased and remnant magnetization had a maximum as a function of grain size in dependent of x. In turn, coercivity increased with x independent of grain size. Complex permittivity of the Co-Ni-Zn ferrite films was measured in the frequency range 2-15 GHz. The highest hysteretic heating rate in the temperature range 315-355 K was observed in CoFe2O4. The maximum absorption band shifted from 13 to 11GHz as cobalt content increased from x = 0.1 to 0.2.

Structural investigations and magnetic properties of sol-gel Ni0.5Zn0.5Fe2O4 thin films for microwave heating

Nanocrystalline Ni0.5Zn0.5Fe2O4 thin films have been synthesized with various grain sizes by a sol-gel method on polycrystalline silicon substrates. The morphology, magnetic, and microwave absorption properties of the films calcined in the 673-1073 K range were studied with x-ray diffraction, scanning electron microscopy, x-ray photoelectron spectroscopy, atomic force microscopy, vibrating sample magnetometry, and evanescent microwave microscopy. All films were uniform without microcracks. Increasing the calcination temperature from 873 to 1073 K and time from 1 to 3 h resulted in an increase of the grain size from 12 to 27 nm. The saturation and remnant magnetization increased with increasing the grain size, while the coercivity demonstrated a maximum near a critical grain size of 21 nm due to the transition from monodomain to multidomain behavior. The complex permittivity of the Ni-Zn ferrite films was measured in the frequency range of 2-15 GHz. The heating behavior was studied in a multimode microwave cavity at 2.4 GHz. The highest microwave heating rate in the temperature range of 315-355 K was observed in the film close to the critical grain size.

Bats use magnetite to detect the earth's magnetic field

While the role of magnetic cues for compass orientation has been confirmed in numerous animals, the mechanism of detection is still debated. Two hypotheses have been proposed, one based on a light dependent mechanism, apparently used by birds and another based on a "compass organelle" containing the iron oxide particles magnetite (Fe3O4). Bats have recently been shown to use magnetic cues for compass orientation but the method by which they detect the Earth's magnetic field remains unknown. Here we use the classic "Kalmijn-Blakemore" pulse re-magnetization experiment, whereby the polarity of cellular magnetite is reversed. The results demonstrate that the big brown bat Epteskus fuscus uses single domain magnetite to detect the Earths magnetic field and the response indicates a polarity based receptor. Polarity detection is a prerequisite for the use of magnetite as a compass and suggests that big brown bats use magnetite to detect the magnetic field as a compass. Our results indicate the possibility that sensory cells in bats contain freely rotating magnetite particles, which appears not to be the case in birds. It is crucial that the ultrastructure of the magnetite containing magnetoreceptors is described for our understanding of magnetoreception in animals.