FUNDAMENTALS OF PARAMETER ESTIMATION

Since the time that man first became involved with measurements, he has had to deal with the problems caused by discrepancies in different measurements of the same object. The attempt for reducing the effects of these discrepancies had led to the development of estimation theory. The discrepancies or errors are generally regarded as being unknowable or random. To reduce their effect with respect to the quantity of interest one is led to the problem of defining an estimator. The problem of estimating parameters from observational data can be traced from antiquity. From about 300 B.C. Babylonian astronomers dealt with this problem. Up to present times astronomical studies have provided a major stimulus for the development of estimation theory. In the 18. and 19. century we find essential contributions by Bernoulli, Euler, Legendre, Gauss and Bayes. In these days we recognize wide applications in the space technology, control and measurement theory

Effect of rounded corners on the magnetic properties of pyramidal-shaped shell structures

In recent years, the advance of novel chemical growth techniques has led to the fabrication of complex, three-dimensional magnetic nanostructures. The corners and edges of such realistic geometries are generally not sharp but rounded. In a previous article we have argued that high demagnetization fields in the vicinity of sharp edges lead to the formation of an asymmetric vortex state in pyramidal-shaped magnetic shell structures. The asymmetric vortex state is potentially interesting with respect to future magnetic memory devices. In this work a micromagnetic model is used to investigate the effect of rounded corners and edges on the magnetic reversal process within these pyramidal-shaped magnetic shell structures. In particular, we explore the degree of rounding, which has to be introduced in order to suppress the asymmetric vortex state. Another emphasis is placed on the magnetic reversal of (quasi-)homogeneous states within these structures. We demonstrate that the rounding of corners significantly reduces the coercivity. This complies with former studies on cuboidal structures, which suggest the important effect of corners on the magnetic reversal of homogeneous magnetic states. The present study uses a finite-element discretization for the numerical solution of the micromagnetic equations, which provides flexibility with respect to the modeling of complex shapes. In particular, this method is very accurate with respect to structures with a smooth surface

Power-law decay in first-order relaxation processes

Starting from a simple definition of stationary regime in first-order relaxation processes, we obtain that experimental results are to be fitted to a power-law when approaching the stationary limit. On the basis of this result we propose a graphical representation that allows the discrimination between power-law and stretched exponential time decays. Examples of fittings of magnetic, dielectric and simulated relaxation data support the results.Comment: to appear in Phys. Rev. B; 4 figure

Fundamental Magnetic Properties and Structural Implications for Nanocrystalline Fe-Ti-N Thin Films

The magnetization (M) as a function of temperature (T) from 2 to 300 K and in-plane field (H) up to 1 kOe, room temperature easy and hard direction in-plane field hysteresis loops for fields between -100 and +100 Oe, and 10 GHz ferromagnetic resonance (FMR) profiles have been measured for a series of soft-magnetic nano-crystalline 50 nm thick Fe-Ti-N films made by magnetron sputtering in an in-plane field. The nominal titanium concentration was 3 at. % and the nitrogen concentrations (xN) ranged from zero to 12.7 at. %. The saturation magnetization (Ms) vs. T data and the extracted exchange parameters as a function of xN are consistent with a lattice expansion due to the addition of interstitial nitrogen in the body-centered-cubic (bcc) lattice and a structural transition to body-centered-tetragonal (bct) in the 6-8 at. % nitrogen range. The hysteresis loop and FMR data show a consistent picture of the changes in both the uniaxial and cubic anisotropy as a function of xN. Films with xN > 1.9 at. % show an overall uniaxial anisotropy, with an anisotropy field parameter Hu that increases with xN. The corresponding dispersion averaged uniaxial anisotropy energy density parameter = HuMs/2 is a linear function of xN, with a rate of increase of 950 erg/cm3 per at. % nitrogen. The estimated uniaxial anisotropy energy per nitrogen atom is 30 J/mol, a value consistent with other systems. For xN below 6 at. %, the scaling of coercive force Hc data with the sixth power of the grain size D indicate a grain averaged effective cubic anisotropy energy density parameter that is about an order of magnitude smaller that the nominal K1 values for iron, and give a quantitative vs. D response that matches predictions for exchange coupled random grains with cubic anisotropy.Comment: 13 pages, 7 figure

Multiscale nature of hysteretic phenomena: Application to CoPt-type magnets

We suggest a workable approach for the description of multiscale magnetization reversal phenomena in nanoscale magnets and apply it to CoPt-type alloys. We show that their hysteretic properties are governed by two effects originating at different length scales: a peculiar splitting of domain walls and their strong pinning at antiphase boundaries. We emphasize that such multiscale nature of hysteretic phenomena is a generic feature of nanoscale magnetic materials.Comment: 4 pages (revtex 4), 2 color EPS figure

Layer charge instability in unbalanced bilayer systems in the quantum Hall regime

Measurements in GaAs hole bilayers with unequal layer densities reveal a pronounced magneto-resistance hysteresis at the magnetic field positions where either the majority or minority layer is at Landau level filling factor one. At a fixed field in the hysteretic regions, the resistance exhibits an unusual time dependence, consisting of random, bidirectional jumps followed by slow relaxations. These anomalies are apparently caused by instabilities in the charge distribution of the two layers.Comment: 4 pages, 4 figure

Electrically-Controlled Nuclear Spin Polarization and Relaxation by Quantum-Hall states

We investigate interactions between electrons and nuclear spins by using the resistance (Rxx) peak which develops near filling factor n = 2/3 as a probe. By temporarily tuning n to a different value, ntemp, with a gate, the Rxx peak is shown to relax quickly on both sides of ntemp = 1. This is due to enhanced nuclear spin relaxation by Skyrmions, and demonstrates the dominant role of nuclear spin in the transport anomaly near n = 2/3. We also observe an additional enhancement in the nuclear spin relaxation around n = 1/2 and 3/2, which suggests a Fermi sea of partially-polarized composite fermions.Comment: 6 pages, 3 figure

Probing fractal magnetic domains on multiple length scales in Nd2Fe14B

Using small-angle neutron scattering, we demonstrate that the complex magnetic domain patterns at the surface of Nd2Fe14B, revealed by quantitative Kerr and Faraday microscopy, propagate into the bulk and exhibit structural features with dimensions down to 6 nm, the domain wall thickness. The observed fractal nature of the domain structures provides an explanation for the anomalous increase in the bulk magnetization of Nd2Fe14B below the spin-reorientation transition. These measurements open up a rich playground for studies of fractal structures in highly anisotropic magnetic systems.Comment: Accepted for publication in Phys. Rev. Lett. (4 pages, 4 figures

Buckling instability in type-II superconductors with strong pinning

We predict a novel buckling instability in the critical state of thin type-II superconductors with strong pinning. This elastic instability appears in high perpendicular magnetic fields and may cause an almost periodic series of flux jumps visible in the magnetization curve. As an illustration we apply the obtained criteria to a long rectangular strip.Comment: Submitted to Phys. Rev. Let