F. B. Hagedorn

Dynamic conversion during magnetic bubble domain wall motion

The experimentally and previously observed erratic propagation of an individual magnetic bubble domain during repetitive bubble transport measurements has been attributed to the dynamic conversion of a normal bubble domain wall into a relatively immobile state. A model for dynamic conversion is presented in this paper. The model extends previous work of Slonczewski and Thiele and suggests that the immobile wall state contains both moving horizontal Bloch lines and stationary vertical Bloch lines, the latter of which are parallel with the cylindrical axis of the bubble domain. The model accounts qualitatively for the evolution of this state from a normal bubble and for its return to the normal bubble state when motion ceases. Interactions between the moving domain wall and material inhomogeneities are postulated to be important in initiating dynamic conversion, and it is suggested that the erratic characteristics associated with dynamic conversion arise from the statistical nature of these interactions. Me...

Domain Wall Mobility in Single-Crystal Yttrium Iron Garnet

Reasonable agreement between the damping constant inferred from the resonance linewidth and that obtained from the domain wall mobility has previously been found for ferrites. However, the recent linewidths reported for yttrium iron garnet (YIG) by Spencer, LeCraw, and Clogston are substantially narrower than those for ferrites. On using this narrow linewidth to calculate the YIG wall mobility, one obtains about 106 cm/sec oe. We have measured the YIG wall mobility as a function of temperature and find it to be less than 104 cm/sec oe. This discrepancy can be interpreted in terms of a model for domain wall motion which is based on a type of energy conversion process different from that usually assumed. The customary treatment requires that the domain wall dissipate entirely to the lattice all of the magnetostatic energy stored in a given region during the time that the wall passes through this region. For small damping such as exists in YIG, this requirement appears to be unreasonable. The wall motion mod...

Analysis of Exchange‐Coupled Magnetic Thin Films

Presented in this paper are some new analytical results for two exchange‐coupled magnetic thin films. The formulation of the problem which is used is similar to that of Goto et al., who reduced the determination of the magnetic configuration of the films in the presence of an external magnetic field to the evaluation of elliptic integrals. Derived herein is an expression for the second variation of the magnetic energy, thereby allowing an investigation of the stability of previously determined magnetic configurations. Evaluation of this expression, as well as determination of the magnetic configuration, must be done numerically, and tables giving magnetic configurations and critical fields are included for a variety of thickness combinations and magnetic parameters. In addition, new analytical results are presented for several limiting cases. Transcendental equations have been derived which give the threshold fields for arbitrary film parameters when the easy axes are mutually parallel in the two films an...

Magnetic Behavior of Some Orthoferrites in the Anisotropy Change Region

In a number of canted‐spin rare earth (RE) orthoferrites, the easy axis for the spontaneous magnetization changes from the a to the c axis with increasing temperature. We have studied the magnetic behavior in the transition region using both torque and vibrating sample magnetometers with applied fields (Ha) from about 0.1 to 6.0 kG. The measurements were made with Ha in the ab, bc, and ac planes. The use of small values of Ha makes it possible to separate the effects of the weak ferromagnetism from the paramagnetism of the RE lattice. In Sm orthoferrite the reorientation occurs over about 20°, centered at 175°C (Tr). For this material in the ac plane the iron lattice is well described by the energy expression E = +½Ku cos2θ+kb cos4θ. Substantially below Tr, Ku≫Kb and the magnetization has a strong uniaxially preferred axis along a. As the temperature increases, Ku decreases and the easy axis splits symmetrically in two, one on each side of a, and these rotate toward c with increasing T. At 175°C, Ku∼0 and...

Three garnet compositions for bubble domain memories

The choice of magnetic garnet compositions for bubble memories is always a compromise dictated by the material requirements generated by the specifications on the memories. The three compositions reported, Y2.62Smo.38Fe3.85Ga1.15O12, Gd2.lLuO.9Fe4.4Al0.6O12, and Yl.92Sm0.1Ca0.98Fe4.02Ge0.98O12, represent three examples of such a compromise. The first composition is excellent for use in circuits operating at 100 KHz over a temperature range of -20° to 80°C. The second has a mobility up to 5000 cm/sec/0e and is capable of very high speed operation at the sacrifice of stability toward temperature. The third exhibits excellent stability toward temperature and has operated at 1 MHz but is compositionally more complex.Melt compositions for film growth and a summary of magnetic properties are presented for the three compositions. Factors to be weighed in composition selection for bubble domain memories are discussed.

Instability of an Isolated Straight Magnetic Domain Wall

An isolated straight magnetic domain wall along the y axis results when a thin slab of magnetic material in the xy plane is exposed to a nonuniform z axis magnetic field of the form Hz=βx, if β is sufficiently large. The behavior of this magnetic system as β decreases is discussed. A magnetic energy calculation shows that sinusoidal deviations from the straight wall become energetically favorable at a critical value βc. The wavelength of this distortion at βc and βc are both expressed in terms of magnetic material properties. Experimental observations of this instability in YbFeO3 are given, and the magnetic parameters determined this way are in reasonable agreement with those obtained by using other methods. Effects of material inhomogeneieties are discussed, and the transition from the initially distorted straight wall to the demagnetized state of stripe domains is shown.

The temperature dependence of the anisotropy field and coercivity in epitaxial films of mixed rare‐earth iron garnets

The temperature dependence of the anisotropy field Hk and the domain‐wall coercivity Hc have been measured for three different epitaxial films of mixed rare‐earth iron garnets with the nominal compositions Er2Eu1Ga0.7Fe4.3O12, Y1Eu1.85Yb0.15Al1.1Fe3.9O12, and Eu1.7Er1.3Al0.7Ga0.8Fe3.5O12. Each of these garnets supports bubble domains. The anisotropy field was measured using an optical magnetometer, and analytical expressions are developed which relate the optical magnetometer parameters to the anisotropy field. These measurements show that the anisotropy field decreases with increasing temperature at about −1%/°C at 20°C for all three samples. The coercivity, again measured by an optical technique, was also found to decrease with increasing temperature. The coefficient ranged from −1.3%/°C to −3.0%/°C at 20°C depending on the sample. The largest total change in Hc for one of the samples was a factor of 310 over the temperature range −106°C to +80°C. The temperature variation of the saturation magnetizatio...

Exchange Anisotropy in Oxidized Permalloy Thin Films at Low Temperatures

Oxidized Permalloy thin films exhibit uniaxial anisotropy at room temperature, but at low temperatures develop a mixture of uniaxial and unidirectional anisotropies. Exchange coupling between the ferromagnetic permalloy and the antiferromagnetic oxide, at temperatures below the latters Neel temperature, account for this phenomenon. New observations and interpretations of low‐temperature hysteresis‐loop effects in oxidized Permalloy films are reported in this paper. The initial susceptibility in the original uniaxial hard direction has been measured at 4.2°K for various combinations of Permalloy and oxide‐layer thicknesses. While the results are found to be in qualitative agreement with a model based on a simple mixture of anisotropies, a semiquantitative understanding is found possible only after assuming that reversal of the Permalloy magnetization direction also reverses the spin orientations in a large fraction of the antiferromagnetic material. For very thin (∼10 A) oxide layers, this fraction is lar...

Right‐Angle Bends in Thin Strip Conductors

Current density and resistance expressions are obtained by means of a conformal transformation for a strip conductor which contains a right‐angle bend. The approach, similar to that applied by Cockcroft to the problem of rectangular coaxial capacitors, is sufficiently general to take into account the effects arising both from a width change at the bend and from a small radius on the inside corner. It is suggested that the current density expressions can be applied in some cases to superconducting thin film strips, and the effect of a right‐angle bend on the supercurrent‐carrying capacity of such a strip is discussed. A typical result is that the critical current of a bent superconducting strip may be only 1/6 that of a similar but straight strip if the radius of the inside corner of the bend is 1% of the strip width. A specially shaped right‐angle bend is then described, the critical current for which is identical to the corresponding straight strip. Current density nonuniformity somewhat away from the co...

Growth‐induced magnetic anisotropy in seven different mixed rare‐earth iron garnets

We have measured the noncubic magnetic anisotropy in seven different compositions of rare‐earth iron garnets, using bulk single‐crystal samples grown from a flux. Several of these compositions supported magnetic bubble domains. The noncubic anisotropy is growth induced, and for each composition we investigated samples from both types of growth facets which occur in bulk garnet growth. Anisotropy energies as large as 7×104 erg/cm3 were found, and three distinct anisotropy orientations were resolved. The results have been analyzed within the framework of a two‐parameter model for growth‐induced anisotropy, and we find general agreement although there are some discrepancies. For one composition, Y2Gd1Al0.8Fe4.2O12, we have measured the dependence of the noncubic anisotropy on temperature over the range 4.2–300°K. Only part of the observed temperature dependence is in good agreement with a microscopic calculation done by Sturge. Finally, we report on the annealing characteristics of the noncubic anisotropy. T...