Volume 37, Issue 3, 01 March 1966
 GENERAL SESSION


Theory of Linear Ferrite Devices for Microwave Applications
View Description Hide DescriptionLinear ferrite devices for microwave applications include phase shifters, switches, isolators, circulators, and others whose operation is independent of the applied rf signal level. In this paper, propagation through an infinite ferrite medium is treated first, and points of operation for various ferrite devices are established on a normalized plot of effective permeability vs biasing field. Transfer matrix techniques are used to analyze slab configurations with transverse magnetization, such as those found in differential phase shifters for circulators, field‐displacement isolators, and certain latching phase shifters. These techniques permit computation of optimum geometry, field configurations, phase shift, and cutoff conditions. Suhl and Walker's analysis of the completely filled cylindrical waveguide is applied to the ferrite‐filled coaxial line and extended to study Faraday rotation, phase shift, and cutoff conditions in cylindrical rod geometries. Of particular interest is a simplified analysis of the Reggia‐Spencer phase shifter which predicts frequency dependence and critical geometry with good accuracy.

Electron Microscopic Observation of Domain Wall‐Inclusion Interactions in Iron
View Description Hide DescriptionTransmission electron microscopic observations of the dynamic behavior of domain walls in thin polycrystalline foils of iron containing inclusions of varying sizes have been carried out under conditions of known applied field.^{1} The field component in the plane of the specimen was varied over the range 0→±10 Oe, traversing hysteresis loops in times of the order of 10 sec.
The observations show that inclusions affect the mobility of domain walls not only through the formation of individual Néel spike domains, but also by acting as tie points for domain wall intersections and by the formation of ``ladder'' domain structures connecting closely spaced inclusions.
The detailed domain structures observed during the cutting of large (about 1 μ) inclusions by 180° domain walls correspond closely to the structures predicted by detailed theoretical models of this process.^{2}
New domains are readily formed at grain boundaries. A frequently observed alternative to the cutting of an inclusion by a domain wall is the formation of one or more new domains in other parts of the same grain.
Continuity of the normal component of magnetization across grain boundaries is accomplished either by echelon structures of the sort observed in thin nickel platelets^{3} or by individual spike domains extending from the boundary. A 16‐mm motion picture film illustrating these points has been prepared and was presented at the conference.

Cu, Ni, Ag, and Fe Densities of States
View Description Hide DescriptionAn experimental method for determining the densities of states in solids based on photoemission and optical measurements is described and illustrated with data from Cu and Ni.Densities of states for Cu, Ag, Ni, and Fe determined by this technique are presented. The Cudensity of states is found to be in reasonable agreement with the band calculations of Burdick except for the appearance of a rather large peak in the experimentally determined density of states 6.2 eV below the Fermi surface. The Nidensity of states is dominated by a strong maximum 4.5 eV below the Fermi level. This maximum is not predicted either by recent band calculations or by the rigid band model using the Cudensity of states. Recent suggestions of Phillips and Mott concerning this are outlined.

Study of the Lattice of Vortex Lines in Superconducting Niobium by Neutron Diffraction
View Description Hide DescriptionThe magnetic behavior of type II superconductors in the mixed state is well explained by the model of vortex lines. Following A.A. Abrikosov, the superconductor in an applied field H (H _{ c1} < H < H _{ c2}) is divided in regions where superconductivity is strongly perturbated, the magnetic field penetrates inside a hard core surrounded by rings of supercurrents which screen the field (vortex lines). Moreover, there should exist a regular two‐dimensional lattice of these lines: the field is periodical. Each line carries a flux quantum φ_{0} = ch/2e; the total magnetic inductionB = αφ_{0}/d ^{2}; α is a geometrical coefficient depending on the lattice type and d the lattice parameter. In a preliminary report^{1} a periodicity of the field was detected and the flux quantization was proved. Actually the experiments yielded √3/2>α> 1. A new set of experiments with better angular and wavelength definition of the neutron beam has given more accurate results. The main points are: (1) The Bragg peak is very sharp so that there exists a long‐range order. (2) The second‐order Bragg peak is unobservable, i.e., that the periodical variation of the field is well represented by the first Fourier component. (3) The value of α is given by 2α = √3 for a set of magnitude of B when applied field H is far from H _{ c1} and H _{ c2}. The lattice is thus triangular.

Stripe Domains in Thin Magnetic Films and Their Application to Magneto‐Optical Displays
View Description Hide DescriptionA thin magnetic film display element is described which consists of a planar, hermetically sealed unit containing a RIS 1 magnetic film and an overlying colloidalsuspension of iron oxide. The effect of the ``stripe'' domain structure of the magnetic film upon the colloid is such as to furnish an element which is capable of diffracting light incident upon the surface of the element in a manner similar to that of a diffraction grating. The interference phenomena are, however, controllable by a magnetic field applied so as to cause changes in the distribution of the magnetization within the film. Both the intensity and color of the diffracted light can be modified by the applied field and such modification, once produced, is permanent until subsequent alteration is required. Command of the element can be accomplished by coincident drive currents in matrix fashion as is common in the operation of planar magnetic memories. Measurements performed on experimental RIS 1 display panels indicate an element switching speed of less than 10 μsec, a brightness of over 30 ft·L and a contrast ratio of greater than 70:1. The feasibility of manual entry of information and electrical read of the latter has been demonstrated as well.
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 ANTIFERROMAGNETISM I


Antiferromagnetism of the Spinel MnGa_{2}O_{4}
View Description Hide DescriptionThe cubic spinel MnGa_{2}O_{4} is partially inverse with 87% of the Mn atoms on tetrahedral A sites. Neutron diffraction with a powder has shown that, at low temperatures, the spin moments on A sites are antiferromagnetically coupled (T_{N} =33°K). The variation of the (200) magnetic reflection as a function of the magnetic field allows the determination of both the direction of the magnetic moments along [111] and the value (K _{1}=−4.10^{4} erg/cm^{3}) of the anisotropy constant. The 1/χ(T) curve does not show the typical minimum at the Néel point but instead decreases rapidly at low temperatures. We explain that phenomenon by taking into account the paramagnetism of the spins on octahedral sites.

Reduced Manganese Moment in Manganese Chromite
View Description Hide DescriptionThe net magnetization, magnetic susceptibility,^{55}Mn nuclear magnetic resonance, and neutron‐diffraction properties of MnCr_{2}O_{4} have been reinvestigated. Our results are in general agreement with earlier findings. The neutron‐diffraction pattern of MnCr_{2}O_{4} evidences appreciable deviation from a pure spiral configuration. Furthermore, the susceptibility data indicate that the Mn^{+ +} ions possess a reduced magnetic moment of about 4.3_{μB }, rather than the previously assumed value of 5.0_{μB }. Given the hypothesis of an admixture of quartet states with quenched orbital momentum into the ^{6} S free‐ion ground state, the reduced value of the ^{55}Mn hyperfine field observed in manganese chromite is consistent with this low value for the manganese moment.
The interpretation of the NMR result in terms of a ferrimagnetic spiral ground‐state spin configuration remains essentially unchanged, a manganese cone angle of about 61° being indicated. The use of 4.3_{μB } for the Mn^{+ +} moment improves the agreement between the theoretical and observed neutron‐diffraction patterns, but the best fit is still obtained with a much smaller value for this cone angle, namely 33°. Within the spiral model, the observed magnetic‐diffraction intensities are incompatible with the larger cone angle; the NMR findings are incompatible with the smaller. Other discrepancies are also discussed.

Neutron Diffraction Study of Helimagnetic Spinel ZnCr_{2}Se_{4}
View Description Hide DescriptionNeutron diffraction experiments under magnetic fields up to 15 kOe are performed on the helimagnetic spinel ZnCr_{2}Se_{4}. For fields of about 3 to 4 kOe, switching of 90° antiferromagnetic domains occurs. In the same field range, there is also a tilting of the spins rotation axis towards the field direction. In the field range 10 to 15 kOe, canting of the spins towards the field direction occurs as shown experimentally. Hysteresis effects of the boundaries motions are studied. Exchange coefficients are determined, together with estimates of the potential energy associated with the Bloch walls and of the magnetic anisotropy energy.

Magnetic Ordering in VF_{2}
View Description Hide DescriptionThe compound VF_{2} has been prepared by treatment of vanadium metal with HF gas at 1250°C to form VF_{3}, and subsequent reduction to VF_{2} at 1150°C with a controlled mixture of HF and H_{2}. Debye—Scherrer photographs show VF_{2} to have the rutile structure, isomorphic with MnF_{2}, FeF_{2}, CoF_{2}, NiF_{2}, and ZnF_{2}. Heat‐capacity measurements from room temperature to 5°K, using a platinum resistance thermometer, show a peak in heat capacity at 7.0°K, presumably associated with long‐range magnetic ordering, and a large magnetic contribution to the heat capacity at higher temperatures. The major fraction of the magnetic entropy of Rln4 is acquired in the short‐range‐order region. The behavior of the magnetic entropy is similar to that found in CuCl_{2} and CrCl_{2} where there is extensive short‐range magnetic ordering in one‐dimensional chains of metal atoms coupled by relatively strong exchange forces. This suggests that in VF_{2}, unlike the other iron group fluorides, the strong exchange interactions are between neighboring vanadium atoms which form one‐dimensional chains parallel to the tetragonal axis and that the exchange forces between a vanadium atom and its eight nearest neighbors in 〈111〉 directions are relatively weak.

Magnetic Ordering in Eu_{3}O_{4} and EuGd_{2}O_{4}
View Description Hide DescriptionThe magnetic susceptibilities of single crystalline and polycrystalline Eu_{3}O_{4} and of polycrystalline EuGd_{2}O_{4} in the range between 2° and 300°K are reported. The compounds are antiferromagnetic with T_{N} =5.0° and 4.5°K, respectively. Above T_{N} the susceptibilities follow Curie—Weiss laws, with θ_{ P }=−5° and +2°K, respectively. Eu_{3}O_{4} is metamagnetic below T_{N} with H_{c} =2.4 kOe at 2°K. Possible magnetic structures for Eu_{3}O_{4} are discussed.

Structure and Magnetic Properties of Dy_{2}Mn_{4}O_{9}
View Description Hide DescriptionSingle crystals of Dy_{2}Mn_{4}O_{9}, a new rare‐earth transition metal oxide, were grown by a three‐component flux method. X‐ray studies indicate that the space group of this crystal is P_{bam} and the dimensions of the orthorombic unit cell are; a=7.24, b=8.44, c=5.62 Å. Magnetization measurements at 1.3° to 300°K in a magnetic field of 14.2 kOe show that an antiferromagnetic transition takes place in Dy_{2}Mn_{4}O_{9} at about 8°K. Large magnetic anisotropy is observed, the easy direction of magnetization lying along the a axis. At 4.2°K in a field of 100 kOe the magnetization along the c axis is less than 50% of that along the a‐axis. In Mössbauer studies of the 26‐keV γ‐transition in ^{161}Dy typical paramagnetic relaxation spectra were observed, from which the ``g'' tensor of the ground stark level of the Dy^{3+} ions was deduced; g_{z} =18.5g_{x} ≈0, g_{y} ≈0. The spin‐relaxation time of the Dy ions at 5°K was estimated to be 2×10^{−9} sec.

Antiferromagnetic—Ferromagnetic Transition in the Compound Mn_{3}GaC
View Description Hide DescriptionThe compound Mn_{3}GaC has been found to have a crystal structure of the perovskite type and a ferromagneticCurie point of 246°±2K°. At a lower temperature, about 150°K, it exhibits a rather abrupt transition to an antiferromagnetic state. At this transition, there is a rapid decrease of lattice parameter and of resistivity with increasing temperature. The transition has been studied as a function of magnetic field up to 200 kOe while both transitions have been examined in hydrostatic pressures up to 4000 bar. From these data, the latent heat of the abrupt transition is calculated to be about 1 cal/g.

Magnetic Structures in CrTe—CrSb Solid Solutions
View Description Hide DescriptionNeutron diffraction studies have been made of solid solutions of ferromagnetic CrTe and antiferromagnetic CrSb which crystallize in the hexagonal NiAs structure. Similarities are found with the isostructural system MnSb‐CrSb, in which good agreement is obtained with de Gennes predictions for the effects of double exchange on an antiferromagnetic system. The most striking feature is the formation of a canted spin structure with cosine of the cant angle varying as a linear function of composition. The variation of angles and transition points when analyzed in terms of double exchange theory gives about the same value of b/J S ^{2} in the two systems. At very high CrTe contents, a different type of canted spin structure occurs.
The possibility of deviations from the ideal structure as can occur in CrTe is examined. A least‐squares structure analysis was made which indicated the absence of distortions in most of the solid solutions.

Magnetic Properties of RbFeF_{3}
View Description Hide DescriptionThe magnetic susceptibility of a powder sample of RbFeF_{3} has been measured from 12° to 300°K in magnetic fields up to 11 kOe. Its Curie constant agrees with S=2 and g=2.17 for an Fe^{2+} ion. Its Néel point is 75°K. The data yield the exchange interactions for a two‐sublattice model: W _{12}=−43.9°K, W _{11}=+4.5°K, and W _{22}=−7.5°K. The ratios of θ to T_{N} (1.17) and of W _{11} to W _{12} (0.10) are consistent with a magnetic ordering of the first kind. Weak ferromagnetism occurs around 74°K. The weak ferromagnetic moment extrapolates to about 0.27 μ_{B} (Bohr magnetons) at 0°K and corresponds to a canting angle of 1°56′.

Effect of Electron Concentration on Magnetic Properties of EuTe—GdTe
View Description Hide DescriptionThe systems EuSe—GdSe and EuS—GdS show a strong increase in the positive value of the paramagneticCurie temperature (θ) as a function of the Gd^{3+} concentration. The pure europiumchalcogenides in both systems have positive θ values. This paper discusses the effect of the increase of electron concentration on magnetic interactions in EuTe, which is antiferromagnetic in its pure state. We find that θ increases from −10°K for EuTe to a maximum of +28°K for Eu_{0.8}Gd_{0.2}Te and then decreases monotonically with increasing Gd content to θ=−90°K for GdTe. The variation of θ is interpreted as a result of a Ruderman‐Kittel‐Yosida type interaction via the conduction electron donated by Gd^{3+}. In contrast to the selenide and sulfide systems, no true ferromagnetic order occurs in EuTe‐GdTe at 4.2°K for any composition. As an example, the magnetization of Eu_{0.8}Gd_{0.2}Te (θ=+28°K) saturates at 4.2°K for magnetic fields only above 45 000 Oe, which may be due to either spin canting or a more complex magnetic structure involving ferromagnetic clusters.

Neutron‐Diffraction Study of Magnetic Ordering in K_{2}ReCl_{6}
View Description Hide DescriptionNeutron‐diffraction measurements have been made on single‐crystal and powder specimens of K_{2}ReCl_{6} at temperatures from 295° to 4.2°K. This compound is fcc at room temperature but becomes primitive cubic below 76°K. In both structures the Re ions are in an fcc arrangement, and, although the over‐all symmetry is reduced at low temperatures, the immediate environment of the Re ion (i.e., the six bonding Cl ions) has essentially octahedral symmetry. Previous specific heat and magnetic susceptibility measurements have indicated an antiferromagnetic transition at 11.9°K, and the neutron‐diffraction patterns confirm that an ordered antiferromagnetic structure exists at 4.2°K. Because of the rapid decrease of the magnetic form factor associated with the 5d electrons, only four antiferromagnetic reflections could be measured. These reflections indicate magnetic ordering of the first kind, i.e., the moments are ferromagnetically aligned in (001) planes and adjacent planes are oriented antiparallel. Both the moment value of 2.6±0.5 Bohr magnetons and the magnetic form factor are consistent with a spin‐only value for the magnetic moment.

Magnetic Structure of EuTiO_{3}
View Description Hide DescriptionEuropium titanate has the cubic perovskite structure containing divalent Eu (7 μ_{B}) and tetravalent Ti. From magnetic measurements we find that EuTiO_{3} is one of the few antiferromagnetic materials with a positive θ (T_{N} =5.3°K, θ=3.8°K). At 1.3°K the magnetic moment (σ) increases linearly with field to 10 kOe; above 14 kOe the moment saturates and σ=156 emu/gm (6.93 μ_{B}) at 20 kOe. Powder neutron‐diffraction work indicates that EuTiO_{3} has the Type G magnetic structure in which a given Eu^{++} has six nearest‐neighbor europium ions antiparallel and 12 next‐nearest‐neighbor europium ions parallel. In a perovskite structure where only the 12‐coordinated ion is magnetic, i.e., Eu^{++}, the molecular field relations for a two sublattice model yield J _{1}/k=−0.021°K, where J _{1} is the effective intersublattice exchange interaction, and J _{2}/k=0.040°K, where J _{2} is the effective intrasublattice exchange interaction. The signs of J _{1} and J _{2} are opposite to those found in the europium chalcogenide series. The chalcogenides, however, have the rocksalt structure in which the number of 90° cation‐anion‐cation interactions differs from the perovskite structure.
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 MAGNETOELASTIC PHENOMENA


Internal Magnetic Field Analysis and Synthesis for Prescribed Magnetoelastic Delay Characteristics
View Description Hide DescriptionA systematic procedure is given for synthesizing the internal magnetic field required to realize prescribed magnetoelastic delay characteristics. The method is based on the expression T_{r} = (2/c) {y+ω[γH_{i} ′(y, H_{e} )]^{−1}} for the transit time of magnetoelastic waves in ferromagnetic insulators. Here H_{i} ′(y, H_{e} ) is the gradient of the internal magnetic field at the turning point, and H_{e} is the external magnetic field. Some necessary conditions for physical realizability are discussed and a delay‐bandwidth invariant is demonstrated. Field distributions are obtained having the characteristics: (a) ∂T_{r} /∂ω = 0, independent of ω at specified H_{i} (0, H_{e} ), and (b) ∂T_{r} /∂ω = 0, independent of H_{i} (0, H_{e} ) at specified ω. The last case is used as a basis for evaluating the bandwidth capabilities of magnetoelastic variable delay lines. Limitations on the bandwidth, delay variation, and delay distortion are discussed.
Realization of a desired internal magnetic field is greatly simplified by a method for determining the field from measurements of the transit time T_{r} (ω, H_{e} ) of magnetoelastic pulses and the separation S_{m} (ω, H_{e} ) in magnetic field between adjacent standing‐wave modes. The relation H_{i} ′ = ωS_{m} /πc gives y = Φ(ω/γ, H_{e} ) = (c/2)[T_{r} −2π/γS_{m} ] in terms of measurable quantities; inversion of the function Φ at constant H_{e} recovers the internal field in the form ω/γ = H_{i} (y, H_{e} ). This method has been applied to data from an yttrium iron garnet rod immersed in a steady, uniform, axial field H_{e} ; a comparison of the measured results with existing theory is presented.

Analysis of Magnetoelastic Conversion Efficiency
View Description Hide DescriptionCoupling of spin waves and elastic waves in ferrimagnetic materials is investigated theoretically. The magnetoelastic equations are transformed into coupled equations for fast and slow hybrid waves; the magnetoelastic coupling mechanism is then treated as a distributed directional coupler where the velocities of quasinormal modes are slowly tapered over the coupling length. Solution of the hybrid wave equations using a computerized numerical integration yielded conversion efficiencies versus magnetic field gradient. Over the efficiency range from 10% to 99.4% the conversion efficiency is equal to 1 − exp (−H′ _{crit}/ H′), to within one‐half of one percent. The results provide a complete curve of conversion efficiency versus field gradient, and at the limits agree with Schlömann's strong and weak coupling approximations.
