E. J. Torok

Measurement of the Easy‐Axis and Hk Probability Density Functions for Thin Ferromagnetic Films Using the Longitudinal Permeability Hysteresis Loop

A new method of measuring the inhomogeneity in easy‐axis orientation and in the magnitude of the uniaxial anisotropy in thin ferromagneticfilms has been found. Correlation between the two can also be obtained by this method. Apparatus has been built to measure the probability density of finding a part of the film with a given easy‐axis orientation, as well as a given Hk , and to plot this probability density function on an x‐y recorder. The Hk probability density function is found to be symmetric, contrary to popular belief. Measured values of easy‐axis inhomogeneity agree within experimental error with values obtained by conventional methods. Previous methods of measuringHk inhomogeneity, based on either radio‐frequency resonance linewidth or on reversible limit, are discussed and found to be questionable.

Local Regions with Biaxial Anisotropy in Thin Polycrystalline Ferromagnetic Films with Uniaxial Anisotropy

Deposited thin ferromagnetic films with uniaxial anisotropy have local regions with admixed biaxial anisotropy, although there is no biaxial component to the average anisotropy field of the whole film. Two methods are presented for measuring the biaxial contribution to the inhomogeneity in the anisotropy field. The effect of this biaxial inhomogeneity is investigated theoretically and found to explain much puzzling data: the various negative anisotropy effects, the relationship between α90 and Δ90 (the inhomogeneity in orientation and in magnitude of the anisotropy, respectively), the internal biasing field, the compositional dependence of the inhomogeneity and negative anisotropy, the deposition substrate temperature dependence of negative anisotropy, the position of the negative anisotropy peak, the shape of the probability density function for films with both large and small inhomogeneities, the ratio of positive to negative anisotropy, and the skew of the Δ90 probability density curves. Theoretical sw...

Variation of Stripe‐Domain Spacing in a Faraday Effect Light Deflector

Stripe‐domain ferromagnetic films with high Faraday rotation and low optical absorption will rotate the angle of polarization of light transmitted through even‐numbered domains an angle φ = FT and through odd‐numbered domains an amount −φ, where F is the Faraday constant and T is the film thickness. The result of the differential rotation is that the film will act like a transmission diffraction grating. Since the orientation and spacing of the stripes may be altered by appropriate applied fields, the film may be used as a laser light deflector. A two dimensional model is proposed for stripe domains in some ferromagnetic films. This model differs from previous models (see Ref. 4–8) in that it includes the dependence of wall width on wall angle and thereby shows that variations in stripe‐domain spacing of more than an order‐of‐magnitude are possible. Variations of this amount were observed experimentally in a YIG platelet which was used as a stripe‐domain light deflector.

Transition between Bloch and Néel Walls

The transition between Neel and Bloch walls is shown to be gradual rather than abrupt, resulting in a wall with Neel and Bloch components superposed. For films thick enough so that such a transition can occur, the wall is a pure Neel wall if φf, the acute angle between the wall normal in the plane of the film and the magnetization at the edge of the wall (half the angle between the magnetization vectors in the two domains separated by the wall) is less than a critical value. For φf larger than that critical value but less than π/2, the wall contains both Neel and Bloch components. When φf is π/2, i.e., a 180° wall, the wall is of the pure Bloch type; however, this situation is often unstable, resulting in a transition wall with the Neel component reversing periodically in distance along the wall in a crosstie‐like structure. These conclusions are supported by Lorentz micrographs.

Polarization-sensitive thermal imaging

In order to recognize 3-D objects, conventional methods in robot vision perform shape extraction by sensing the intensity of light reflected by objects. A fundamental problem associated with sensing the intensity of reflected light is that intensity gives one parameter while the surface orientation of objects has two degrees of freedom. Physics Innovations Inc. is developing a thermal imaging technique for determining surface orientation where, in each image pixel, two parameters are sensed simultaneously. The two parameters, percent of polarization P and angle of the plane of polarization (phi) , are directly related to the two angles of surface orientation. In this paper the uncertainties in determining P, and (phi) using the Physics Innovations sensor are made explicit by analytical expressions and by computer simulations of the images. These uncertainties are related to temporal and spatial noise characteristics of the imaging system and to the polarization efficiencies of the polarizers. Automatic object recognition using polarization information is dependent on the uncertainties in determining P, and (phi) .

Origin and Effects of Local Regions of Complex Biaxial Anisotropy in Thin Ferromagnetic Films with Uniaxial Anisotropy

Besides the uniform field‐induced anisotropy field in a thin ferromagnetic film, there are perturbation anisotropy fields due to the magnetocrystalline anisotropy of the randomly oriented crystallites, their shape anisotropy, the shape anisotropy of the film at the edge, and from the locally anisotropic strains on the crystallites. These perturbations are of great importance in determining the magnetic behavior of the film. Because of exchange and magnetostatic coupling, uniaxial perturbation anisotropy fields of great magnitude in crystallite‐sized areas appear instead as complex biaxial perturbation anisotropy fields of small magnitude in areas the size of small domains. The size and shape of these regions are calculated. Most interactions between these areas are automatically included in the randomly oriented complex biaxial perturbation anisotropy fields. These fields can explain the various negative anisotropy effects, the internal biasing field, the relationship between the angular and magnitude inh...

Longitudinal Permeability in Thin Permalloy Films

Longitudinal permeability is defined as μL=(∂BL/∂HL)HT=const, where BL is the component of applied field parallel to the easy axis, and HT is a bias field applied perpendicular to the easy axis of a magnetic film with uniaxial anisotropy. The longitudinal permeability is also the hard axis resonance amplitude in the low frequency limit.The longitudinal permeability is calculated using three different models. The first, that of an ideal single domain film, yields an infinite value when the bias equals HK. Considering the effect of inhomogeneity in easy axes, resulting in many noninteracting domains, gives a maximum μL/μT=22α90−23, where μT=4πM/HK and α90 is so defined that 90% of the film has a local easy axis within α90 degrees of the average easy axis. Including variation of HK within a film lowers μL/μT at HT=HK to 22α90−23−34α90−1Δ9012, where Δ90 is defined so that 90% of the film has an HK within Δ90 HK of the average HK of the film.Comparison with experimental curves for films with measured values of...

Magnetization Creep of Cross‐Tie Walls

Cross‐tie walls are known to have lower creep thresholds than non‐cross‐tie walls. This indicates that a special creep mechanism exists for cross‐tie walls but does not for non‐cross‐tie walls. Such a mechanism is described: In the presence of a pure dc easy‐axis field the magnetization antiparallel to the field buckles more, while the magnetization on the other side of the wall buckles less. This causes magnetostatic charges on the wall which cause the main wall itself to buckle in a zig‐zag fashion with bends at the Bloch lines between the cross‐ties and at the Bloch lines in the cross‐ties. When a hard‐axis field is applied, the Bloch lines between the (fixed) cross‐ties move along the wall, a situation resulting in magnetostatic charges causing the apex of the zig‐zags to move along with the Bloch lines. This distorts the symmetrical zig‐zags into asymmetrical ones having alternately long and short legs. At this point, each segment of the zig‐zag lies at a different angle from the easy axis than it di...

Calculations of the Structure of Néel, Bloch, and Intermediate Walls and the Influence of Their Stray Fields on Bitter Powder Patterns

A comprehensive computer investigation of Neel, Bloch, and intermediate walls in films 200 A to 2000 A thick was made by letting the computer adjust the magnetization direction in small segments of the wall until the sum of the torques on the magnetization in each segment was minimal. Many parallel walls lying parallel to the easy axis were assumed to exist as in a real film during hard axis remagnetization. The Neel wall width was found to be approximately proportional to φf−1, where φf is the angle between the magnetization in the center of the domain and the hard axis. Intermediate walls were found to exist for 90° > φf > φc, where φc is a critical angle dependent on thickness. For φf ≤ φc pure Neel walls exist and only for φf = 90° can pure Bloch walls exist. Once the magnetization distribution was known, the stray field from the wall was calculated. For Neel walls, the magnitude of the stray field was found to increase slightly as the film thickness increased (500 < T < 2000 A) for a fixed‐angle wall...

Steady‐State B‐H Hysteresigraph for Thin Ferromagnetic Films Using a Torque Magnetometer

An ordinary torque magnetometer can be used to obtain dc B‐H hysteresis loops of thin ferromagnetic films simply by replacing the rotating set of Helmholtz coils with a stationary set of three mutually perpendicular coils and by mounting the film edgewise on the suspension. When the magnetometer is used in this mode, the signal and signal‐to‐noise ratio are directly proportional to the field normal to the film; thus one can measure the anisotropy field of film samples many times smaller than previously possible with a torque magnetometer, as well as the various loop properties previously not obtainable with a torque magnetometer. All sections of the film are sensed uniformly in marked contrast to coil sensing devices. Unlike the usual ac B‐H hysteresigraph, the torque B‐H hysteresigraph is not affected by eddy currents in metal substrates.