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The deep impact of the work of V. L. Ginzburg in enhancing our understanding of the phenomena of superconductivity is briefly reviewed, and some recent measurements which clearly show an initially unexpected Coulomb blockade effect in superconducting nanowires are reported.

In this work we present resonant inelastic light scattering (Raman) studies of individual tubes suspended in air. Using high resolution micro-Raman spectroscopy with tunable filters for high throughput we have mapped the resonance Raman profiles for a series of individual SWNTs in the 2n+m = 22 and 29 families and found clear evidence of excitonic interactions from the Raman measurements. Individual suspended SWNTs are grown across etched trenches on a quartz substrate with the chemical vapor deposition technique. For a single suspended tube, the laser excitation energy is tuned to find the electronic resonance, indicated by an intensity maximum of the Raman radial breathing mode (RBM). The Stokes and anti-Stokes double-peaks are offset in energy as expected from incoming and outgoing light resonance with the electronic level. It is demonstrated that the double peaks in the resonance window are separated by the RBM phonon energy, determining the width of the resonance profile

The specific project demonstrates the photon-assisted tunneling process across the Coulomb blockade energy gap in mesoscopic tunnel junctions. Photon-assisted tunneling is well established in conventional macroscopic tunnel junctions, and forms the basis of very sensitive millimeter wave detectors for astrophysics applications. In this case, the photon supply the energy needed to tunnel in the presence of the superconducting energy gap, which is a single-particle property. We are trying to see if the same Tien-Gordon formalism that describes this process can also be applied to the case of the Coulomb blockade, where the energy barrier stems from the charging energy of an electron on a mesoscopic metallic island, which is a collective properly of the configuration, not of a single electron's energy levels.

We demonstrate electrical detection of spin currents in metallic nanostructures. In a conductor with nonzero spin-orbit coupling, a spin current is predicted in a direction perpendicular to the applied electric field, giving rise to a spin Hall effect, where electrons with opposite spin orientations accumulate at opposite edges of the sample. Conversely, when a spin current is present, a charge imbalance is expected, following the Onsager reciprocal relations between spin and charge currents. We report direct electronic measurements of this effect in a lateral geometry by using a ferromagnetic electrode in combination with a tunnel barrier to inject a spin-polarized current in a paramagnetic conductor. We observe a laterally induced voltage in the latter that results from the conversion of the injected spin current into charge imbalance owing to the spin-orbit coupling. Such a voltage is proportional to the component of the injected spins that is perpendicular to the plane defined by the spin-current dire...

The application of a new superconducting composite wire developed by C.C. Tsuei for high-field, high-current uses is explored. The importance of the dish continuous nature of the superconducting filaments in this material is analyzed. Our calculations indicate that practical wire may have a remnant resistivity of 10-14ohm-cm or less and we report our experiments to date in which we have tried to measure this quantity. We also report our observations of quantum coupling between filaments in this wire.

By digital simulations and experiment, we study a Josephson system in a highly nonlinear regime. High experimental noise values appear to correspond in simulations to intrinsic chaotic motion in some regions and to noise-induced hopping between periodic solutions in others. Focusing on the latter, we find correlation between high noise sensitivity and the fractal dimension of the boundary between the basins of the periodic attractors. We show that if enough noise is present to push the orbits into the basin boundary, behavior similar to intrinsic chaos results.

Theoretical step structures for ideal homogeneous filaments based on the interactions implicit in the simple phase-slip-center model of Skocpol, Beasley, and Tinkham are displayed explicitly.

The far-infrared (FIR) properties of niobium cat-whisker point contacts were studied using radiation from an optically pumped FIR laser. The reproducible behaviour of junctions with excellent high-frequency performance allowed a measurement of the FIR frequency dependence of the strength of the a.c. Josephson effect. The shape of the laser-induced steps was used to measure the effective noise temperatures, which increase with bias voltage in agreement with a heating model of metallic constrictions. The high-quality junctions were tested as frequency-selective, incoherent FIR detectors, with the d.c. bias in the vicinity of the incipient laser step. The response was found to be linear in the laser power, and the best measured responsivity at 604 GHz was $2 × 105 V/W, while the best noise equivalent power was $10p−13 W/Hz12, with a 450 Hz chopping frequency. The NEP is limited by the voltage noise in the junction, which was found to have an approximately 1f2 frequency dependence. The detector performance is degraded considerably at higher FIR frequencies. Also studied was the low-laser-power behaviour of the I–V curves near the critical current, which may be of importance for mixing applications with external local oscillators.

We discuss simple models which appear to account quantitatively for the anomalous low-voltage resistance {ital R}{sub 0} observed in small, high-resistance Josephson tunnel junctions. We compare our predictions with both new and previously reported measurements. At high temperatures {ital R}{sub 0} is fit well by a model based on thermal activation. At low temperatures, our results are in good agreement with a model based on theoretical predictions for macroscopic quantum tunneling rates in the underdamped limit. The crossover temperature between the two regimes is dependent on magnetic field, as expected.

The London-Ginzburg-Landau concept of superconductivity as a macroscopic quantum state is reviewed. Experimental measurements are then discussed of resistance below ${T}_{c}$, and of enhanced diamagnetism above ${T}_{c}$, both caused by thermodynamic fluctuations away from the Ginzburg-Landau state of lowest free energy. Next the limitations on superconductivity at nonzero frequencies are reviewed: normal electron dissipation $\ensuremath{\propto}{\ensuremath{\omega}}^{2}$, and strong absorption above the energy gap frequency. Sum rule arguments relate the superfluid response at low frequencies to the gap; effects of strong electron-phonon coupling are also found. Finally, results of recent work on the resistive state of superconducting filaments above the critical current are summarized.

Superconducting sampling circuits have been used to investigate the transient response of long indium microbridges to current pulses in excess of their critical currents. For the first time, the rising-edge kinetic inductance spike and the nonzero minimum voltage have been observed, as well as the delay time until the normal state appears. These results are in reasonable agreement with a detailed theoretical model of the experiment and yield an estimate of 140 ps for tau/sub E/, the inelastic scattering time, in indium.

We have fabricated small superconducting tunnel junctions with a large single-electron charging energy E/sub c/ and measured the low-temperature current-voltage characteristics of devices having a wide range of ratios of E/sub c/ to the Josephson coupling energy E/sub J/. For E/sub c/approx. =E/sub J/, the I-V curve is resistive at all currents and the critical current is greatly reduced relative to that of conventional Josephson junctions. If E/sub J/<

Opportunities for research in the field of superconductivity are identifield in this report of a ‘Workshop on problems in superconductivity’ held at Copper Mountain, Colorado, August 22–23, 1983. Key problems in superconductivity, high payoff areas of research, barriers to progress, and the need for new facilities are outlined in the three areas of basic physics, materials, and devices.

We have observed an anomalous decrease of the measured Josephson critical current as temperature is decreased below 0.85T/sub c/ on small Sn-SnOx-Sn tunnel junctions. The results of analog and dig- ital simulations over a wide range of junction noise and damping parameters suggest that this anomalous temperature dependence of the critical current could be caused by the strongly temperature-dependent damping effect of the quasiparticle tunnel resistance below the gap voltage.

The effects of thermodynamic fluctuations near superconducting phase transitions are reviewed. Above Tc, fluctuations towards the superconducting state lead to the appearance of excess conductivity, diamagnetism, specific heat, and tunnelling currents. Below Tc, fluctuations towards the normal state lead to the appearance of resistance in thin wires and the breakdown of fluxoid quantization in small rings. These effects are generally small, but they can be measured experimentally, particularly in superconducting samples of reduced dimensionality (on the scale of the Ginzburg-Landau coherence length) such as thin films, whisker crystals, and powders. These phenomena are explained using Ginzburg-Landau theory (the salient features of which are developed concurrently), and the current status of theoretical and experimental studies of these effects is surveyed.

We have measured the change in absorption of microwave radiation by superconducting indium, tin, and lead films as a function of magnetic field. Experiments have been conducted on films 145-700 \AA{} thick using 8-mm- and 4-mm-wavelength microwave radiation, primarily with the magnetic field parallel to the plane of the film, but also as a function of angle between the magnetic field and the plane of the film. We observe a second-order phase change in the magnetic field, as is to be expected for films of this thickness according to the theories of Ginzburg and Landau and of Nambu and Tuan. The angular dependence of the critical field found in our measurements is in good agreement with the theory of one of the authors, which predicts an angular dependence given by the formula $(\frac{{H}_{c}sin\ensuremath{\theta}}{{H}_{c\ensuremath{\perp}}})+{(\frac{{H}_{c}cos\ensuremath{\theta}}{{H}_{c\mathrm{II}}})}^{2}=1$.We have attempted to infer the magnetic-field dependence of the effective energy gap $\ensuremath{\Delta}$ from our absorption measurements in a parallel magnetic field. This inference was made by using the calculations of Miller, based on the theory of Mattis and Bardeen. The magnetic-field dependence of $\ensuremath{\Delta}$ which we found is not in agreement with previous experiment and theory, as $\ensuremath{\Delta}$ decreases much more rapidly in low magnetic fields in our experiments, nor is it completely consistent for the two frequencies used. Thus, it appears from our experimental absorption measurements that the effect of a magnetic field on a superconducting film cannot be adequately described simply by introducing a field-dependent energy-gap parameter.

The real and imaginary parts of the dielectric constant of SrTi${\mathrm{O}}_{3}$ have been obtained for the region 2.5 to 3000 ${\mathrm{cm}}^{\ensuremath{-}1}$ from an analysis of the reflectivity. The imaginary part exhibits a very strong peak at 100 ${\mathrm{cm}}^{\ensuremath{-}1}$ at room temperature which shifts to 40 ${\mathrm{cm}}^{\ensuremath{-}1}$ at 93\ifmmode^\circ\else\textdegree\fi{}K. This mode is of sufficient strength to account for more than 90% of the low-frequency dielectric constant. The accompanying dispersion of the real part of the dielectric constant is of resonant form. The connection of this mode with Cochran's theory of ferroelectricity is discussed.

We describe measurements of the far-infrared conductivity ${\ensuremath{\sigma}}_{1}\ensuremath{-}i{\ensuremath{\sigma}}_{2}$ of thin superconducting lead films with resistances of about $\frac{200\ensuremath{\Omega}}{\mathrm{square}}$ in the normal state. The conductivity is inferred from measurements of the transmittance and reflectance of a thin film of lead which has been evaporatively deposited on a quartz crystal. We report results for the real part of the conductivity of lead over the frequency range 9 to 120 ${\mathrm{cm}}^{\ensuremath{-}1}$. From these we infer an energy gap for lead films at $T=0$ of 22.5\ifmmode\pm\else\textpm\fi{}0.5 ${\mathrm{cm}}^{\ensuremath{-}1}$, or $(4.5\ifmmode\pm\else\textpm\fi{}0.1)k{T}_{c}$, where $k$ is the Boltzmann constant and ${T}_{c}$ is the superconducting transition temperature. The measurements were made at 2.0, 4.3, and 5.5\ifmmode^\circ\else\textdegree\fi{}K, and the energy gap varies with temperature in the manner predicted by the Bardeen-Cooper-Schrieffer theory. The frequency dependence of the real part of the conductivity also is in good agreement with the theory. No evidence is found of the strong precursor absorption which had been previously reported in the energy gap in lead, but ${\ensuremath{\sigma}}_{2}$ is found to be anomalously low (by \ensuremath{\sim}25%) near and below the gap frequency. This is believed to result from the strong-coupling anomalies discussed by Nam. This anomalously low ${\ensuremath{\sigma}}_{2}$ would also account for the anomalously steep absorption edge observed in other experiments on lead.

It is known from neutron scattering experiments that alpha-CoSO4 is a four-sublattice canted antiferromagnet with no net magnetic moment. In this paper the magnetic properties of this material are analyzed using a model in which an isotropic fictitious spin of 1/2 is assigned to each Co(++) ion. The large canting angle of 25 degrees is interpreted in terms of antisymmetric terms in the Hamiltonian due to anisotropic superexchange and the large anisotropy in the g values. Corresponding to the four sublattices, there are four spin-wave modes at k=0. Calculations indicate that the resonant frequencies of these modes should lie in the far infrared, and that only three of the modes should be observable spectroscopically. In addition, static susceptibilities of the system have been calculated for T=0 and T>>Tn(12K), and the g values were estimated. Far-infrared transmission experiments resulted in the observation of three lines at 20.6, 25.4 and 35.8 cm, with relative intensities 1:1:0.1. Although these lines are presumed to be the three expected resonances, an unambiguous fitting for all the parameters of the model has not been possible. The temperature dependence of the resonance lines is anomalous. (Author)

The recent observation of two-, three-, four-, and five-magnon bound states in the linear chains of Co${\mathrm{Cl}}_{2}$\ifmmode\cdot\else\textperiodcentered\fi{}2${\mathrm{H}}_{2}$O has prompted a theoretical examination of such states in an anisotropic linear ferromagnetic chain with $S=\frac{1}{2}$. A new method called the Ising-basis-function (IBF) method is developed. This method treats the conventional, localized Ising wave functions as Wannier functions, from which a complete, orthonormal set of Bloch functions (IBF's) is formed. Using these IBF's as basis functions, we obtain the expression for the energy of the two-magnon bound state originally found by Orbach for general longitudinal exchange anisotropy. Furthermore, we can calculate the energy of the ($ng2$)-magnon bound states for the case of strong longitudinal anisotropy. The method is also applied to describe the effect of transverse exchange anisotropy. It is shown that this anisotropy causes an interaction between bound states, particularly important near zero field, and gives rise to a finite probability of exciting the bound states by photon absorption. The generalization of this method to treat bound states in two and three dimensions and for $Sg\frac{1}{2}$ is also discussed. The method is simple and has a direct physical interpretation. As an example, a physical description of the two-magnon bound state in a general system is given. Since the IBF method automatically contains some of the magnon-magnon interactions in zero order, it should be useful in other problems where these interactions are important.

A report is given of the paramagnetic resonance spectra of Mn 2+ , Fe 2+ , Co 2+ and Cr 3+ ions present substitutionally in a ZnF 2 lattice. The temperature-dependence of the anisotropy of the susceptibility in the case of Fe was also studied. In addition to the usual spin Hamiltonian tensor parameters g , D and A , there are data on the hyperfine structure coupling tensors A N between the magnetic electrons and the surrounding six fluorine nuclei. In all cases except Cr 3+ , where there are no σ -bonding electrons, the fluorine h.f.s. intervals are of between 10 and 20 G. With Cr 3+ , no fluorine h.f.s. is resolved. It is suggested that the two types of Cr 3+ spectra observed correspond to the two most natural sites for a monovalent charge-compensating cation.

The data on the g, A and D tensors and on the fluorine hyperfine structure coupling tensors for paramagnetic ions in a ZnF 2 lattice are interpreted in terms of 3 d orbitals augmented by attached fluorine wave functions of appropriate symmetry. It is suggested that fluorine 3 s and 3 p functions are required, in addition to the 2 s and 2 p functions usually assumed, to give quantitative agreement between the fluorine h.f.s. coupling and the spin-orbit coupling reduction effects. The presence of n = 3 functions also renders the dependences on internuclear distance more easily understood. Charge transfer by π - and σ -bonding seems to be of the same order, but the s -electron contact interaction of the σ -bonding electrons gives the dominant h.f.s. interaction. Particularly complete analyses are possible for Mn 2+ and Fe 2+ . In these cases, we estimate that the magnetic electrons have a probability of about 6% of being in fluorine n = 2 orbitals, about the same of being in fluorine n = 3 orbitals, roughly 25% of being in the overlap region, leaving only about (60 ± 10)% probability of being on the central ion. The charge transfer in the case of Co 2+ is believed to be less, and perhaps more typical of the situation when the ions are in their own lattices, with proper lattice parameter. The absence of resolved fluorine h.f.s. with Cr 3+ is consistent with the absence of dγ electrons in the 3 d 3 configuration in an octahedral environment.

High‐speed transportation vehicles (trains) carrying superconducting magnets can be levitated by repulsion from diamagnetic currents induced in a conducting track. Various approximate methods are presented for calculating the lift and drag forces for such magnetic suspensions. Fourier analysis of periodic train magnet fields is used to analyze ``image‐force'' and ``hybrid null‐flux'' systems which involve homogeneous conducting sheet tracks. A lumped circuit analysis is used to discuss the ``null‐flux'' principle and related systems with structured tracks. The stability and efficiency of linear induction and linear synchronous motor propulsion systems are studied using related methods.

The theory of electron tunneling is extended to treat the generation and detection of an imbalance $Q$ between electronlike and holelike quasiparticle populations in superconductors. The equilibration of injected high-energy quasiparticles owing to inelastic phonon processes is discussed, and it is shown that in tin, $Q$ relaxes in ${\ensuremath{\tau}}_{Q}\ensuremath{\approx}[\frac{\ensuremath{\Delta}(0)}{\ensuremath{\Delta}(T)}](2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10})$ sec. It is also shown that even a small (\ensuremath{\sim}1%) anisotropy of the gap can lead to significant $Q$ relaxation by elastic scattering processes. This discussion extends our previous brief interpretation of the pairquasiparticle potential difference measured by Clarke.

The spin-wave spectra of simplified two- and three-sublattice models of the rare-earth iron garnets are obtained, and shown to contain an iron spin-wave spectrum similar to that in ytrrium iron garnet, together with one and two optical branches, respectively. Intensities for optical excitation of $k=0$ spin waves are computed, and the effect of an external magnetic field on the resonant frequencies is also found. The consequences of anisotropic $g$ values, which can be very different from the Land\'e ${g}_{J}$, are explored. Whereas frequencies are determined by the $g$ values along the exchange field produced by the iron, selection rules depend on transverse $g$ values. This results in absorption at single-ion splitting frequencies as well as at the Kaplan-Kittel exchange resonance frequency ${\ensuremath{\omega}}_{e}=\ensuremath{\lambda}({\ensuremath{\gamma}}_{2}{M}_{1}\ensuremath{-}{\ensuremath{\gamma}}_{1}{M}_{2})$. The anisotropy in the $g$ values also produces a shift in the exchange resonance frequency, which can be related to the macroscopic anisotropy energy deduced from the anisotropic single-ion exchange splittings. Agreement with experimental data on ytterbium iron garnet, given in an accompanying paper, is excellent. Application of the theory to anisotropy effects in ferrimagnetic resonance of rare-earth-doped yttrium iron garnet is also considered. Finally, the specific heat capacity is considered and shown to be well approximated by the single-ion Shottky anomaly approximation used by Meyer and Harris.

We have measured the absorption of far-infrared radiation in a cavity by superconducting lead films as a function of magnetic field up to the critical field. The experiments were conducted over a frequency range of 8 to 60 ${\mathrm{cm}}^{\ensuremath{-}1}$ on films approximately 100 \AA{} thick in a magnetic field nearly parallel to the film plane. Even for fields well below the critical value, we observed substantial absorption below the gap frequency and apparently extending down to very low frequencies. This low-frequency absorption is much stronger than we can account for in terms of a spatially uniform order parameter being depressed by the field. Rather, we postulate that vortices with normal cores resulting from the unavoidable, though small, perpendicular-field component play an essential role. In this way we can qualitatively interpret our data, but at present no available theory is capable of giving a quantitative account of them.

Critical magnetic fields of superconducting vacuum-evaporated tin films were measured for all angles $\ensuremath{\theta}$ between the magnetic field and the film surface at temperatures from $0.4{T}_{c}$ to ${T}_{c}$. The experimental results were found to be consistent with Ginzburg-Landau theory provided that the original theory was modified to account for the extended temperature range and the nonlocal nature of superconducting electrodynamics. Measurements of the temperature dependence of the parallel and perpendicular critical fields supported the extensions of Ginzburg-Landau theory developed, most notably, by Maki and de Gennes. The angular dependence of the critical field for $0l\ensuremath{\theta}l\frac{1}{2}\ensuremath{\pi}$ at different temperatures was found to be in agreement with Tinkham's original formula for several sufficiently thin films, $d\ensuremath{\ll}{\ensuremath{\xi}}_{T}$; a detailed derivation of that formula is given here, with discussion of its range of validity. For thicker films the corrections found by Yamafuji et al. were necessary to obtain agreement with the data. The critical fields were carefully measured for $\ensuremath{\theta}\ensuremath{\approx}0$, and evidence of surface superconductivity was found in the thickest film studied, but not in thinner films. This is consistent with the numerical calculations of St. James and de Gennes.

We have measured the change in the thermal conductivity of superconducting tin, indium, and lead films upon application of a magnetic field in the plane of the film. These experiments were undertaken to explore the dependence of the energy gap upon magnetic field and to determine the thermodynamic order of the field-induced transition in films. Within the range of temperatures available to us ($0.35{T}_{c}$ to $0.65{T}_{c}$) the thermal conductivity of indium and tin films increases nearly as ${H}^{2}$. In films of thickness $d\ensuremath{\geqq}2800$ \AA{} the thermal conductivity jumps at ${H}_{c}$ to the normal state value, indicating a first-order phase transition in thin films, consistent with the Ginzburg-Landau (GL) theory. If the effect of a field upon the superconducting state can be adequately represented as a change of the ${\ensuremath{\epsilon}}_{0}$ of BCS, we may use the theory of Bardeen, Rickayzen, and Tewordt to compute ${\ensuremath{\epsilon}}_{0}(H)$ from our data. At $T=0.65{T}_{c}$ we find $\frac{{\ensuremath{\epsilon}}_{0}(H)}{{\ensuremath{\epsilon}}_{0}(H=0)}={[1\ensuremath{-}{(\frac{H}{{H}_{c}})}^{2}]}^{\frac{1}{2}}$ in agreement with the GL prediction. At $T=0.35{T}_{c}$ however, $\frac{{\ensuremath{\epsilon}}_{0}(H)}{{\ensuremath{\epsilon}}_{0}(0)}=1\ensuremath{-}{(\frac{H}{{H}_{c}})}^{2}$ provides a more satisfactory fit to our data. Orientation of the field \ensuremath{\perp} and \ensuremath{\parallel} to the direction of heat flow produces the same effect on the thermal conductivity to \ifmmode\pm\else\textpm\fi{}1%. This is interesting in view of Bogoliubov's prediction of a ${\mathrm{p}}_{F}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{v}}_{\mathrm{drift}}$ term in the excitation spectrum of a current-carrying superconductor. When the field is not parallel to the surface of the film the thermodynamic transition is still sharply defined, but ${H}_{c}$ is reduced. Thin lead films gave results similar to those of indium and tin films except that at low fields the field-dependent conductivity increased more slowly than ${H}^{2}$ at low temperatures.

The far infrared spectral region (~ 10–100 cm−1) corresponds to kT for T = 15–150°K or βH for H = 105–106 oe. Materials with characteristic temperatures or fields of these orders of magnitude may have interesting far infrared spectra. We have studied far infrared resonance spectra in antiferromagnetic and in ferromagnetic rare-earth iron garnets.

Polarized reflection spectra have been made of single crystal KH2PO4, TGS, TiO2, and KD2PO4. KH2PO4 and TiO2 were studied in the range 2.5 to 1500 cm—1, TGS and KD2PO4 over a somewhat smaller range. The reflectivity data were analyzed using dispersion theory and classical‐oscillator fits to obtain the optical constants. The hydrogen bonded ferroelectrics show a behavior quite different from the perovskite ferroelectrics studied earlier. A highly overdamped ferroelectric mode is found in KH2PO4 near 50 cm—1 at room temperature. The close similarities of certain modes in KH2PO4 and KD2PO4 do not support previous speculations on proton tunneling. An analysis of the mode strengths in TGS shows that the major dispersion which contributes to the low‐frequency dielectric constant takes place below 14 cm—1. TiO2 exhibits strong modes near 190 cm—1 which are connected with its large value of low‐frequency dielectric constant, and are quite similar to the low‐frequency mode in SrTiO3.

This paper discusses the critical field of superconducting particles, or films, much smaller in size than the coherence length and the penetration depth; it is restricted to situations where the order parameter may be taken as constant in space, and where the superconducting transition in the presence of the field is of second order. The critical field calculation is then reduced to a study of the magnetic flux $\mathrm{\ensuremath{\Phi}}$ enclosed by all one-electron trajectories in the normal state during a prescribed time interval $\mathrm{t}$. We show that (1) if $\mathrm{\ensuremath{\Phi}}$ does not have a completely ergodic behavior at large times, the equation of state is of the BCS type, but with a renormalized, field dependent coupling constant $\mathrm{N}(0)\mathrm{V}$ $\ensuremath{\eta}(\mathrm{H})$. (2) if $\mathrm{\ensuremath{\Phi}}$ has a certain ergodic property, the effect of the field is comparable to the effect of paramagnetic impurities, as first pointed out in a particular example by Maki. Among other things there is a region of gapless superconductivity in the $(\mathrm{HT})$ plane.A thin film in a parallel field with diffuse boundary scattering but no volume defects belongs to case (1). This surprising result is due to a geometrical cancellation of successive contributions to $\mathrm{\ensuremath{\Phi}}$. However, a rather small amount of scattering in the bulk is enough to restore case (2). Numerical values of the resulting critical field are discussed in detail for various ratios of the bulk mean free path 1 to the film thickness $\mathrm{d}$. In the situations of major physical interest the theoretical values are proportional to ${\mathrm{d}}^{\ensuremath{-}3/2}$ and are in rather good agreement with the experimental data.

A rather general relation is derived between vertical accelerations of the train and cryogenic power dissipation due to ac currents induced in the superconducting suspension magnets. Our theoretical results account for the order of magnitude of the rather large losses observed in the Fuji Electric test vehicle, which used less than state‐of‐the‐art conductors. Even with parameters estimated to represent the best commercially available materials, however, it appears that these losses may be comparable with the total heat leak due to all other causes if the accelerations are as large as permitted by subjective human ride quality considerations. Empirical data on losses under appropriate conditions of B, Ḃ, and I/Ic may be needed to ascertain whether improved materials will be required to avoid serious design constraints by cryogenic heating.

The results of far-infrared transmission measurements on Co${\mathrm{Cl}}_{2}$\ifmmode\cdot\else\textperiodcentered\fi{}2${\mathrm{H}}_{2}$O at helium temperatures are reported and compared with theoretical predictions. Antiferromagnetic resonance, ferrimagnetic resonance, and ferromagnetic resonance have been observed in the respective metamagnetic phases of this material. Furthermore, these magnons appear to interact with an unexpected excitation which is believed to be an optical phonon. The most striking feature of the data, however, is the appearance of absorption lines in each phase which shift with magnetic field at a rate corresponding to $g$ values of about 14, 21, 28, and even 35, as compared to the $g$ value of \ensuremath{\sim}7 for the single magnons. Furthermore, the energy of each of these $n$-fold multiple excitations is markedly less than $n$ times the energy of a onefold one. These excitations are identified as clustered spin reversals or magnon bound states, and this is the first direct observation of such states. In the simple Ising-model approximation, such clusters of $n$ adjacent spin reversals are eigen-states, and the Ising-model energies qualitatively describe the observed energy spectra in all three phases. Using the theoretical results of the preceding paper, the small non-Ising terms are included in the theory, and excellent quantitative agreement is obtained. The reasons why bound states can be observed in Co${\mathrm{Cl}}_{2}$\ifmmode\cdot\else\textperiodcentered\fi{}2${\mathrm{H}}_{2}$O are also discussed.

The far infrared transmission through films of superconducting and normal lead, tin, indium, and mercury has been measured in the wavelength region between 0.1 and 1.1 mm. The transmission data have been analyzed to find the ratio of the complex conductivity in the superconducting state to that in the normal state, as a function of frequency. The width of the energy gap at 0\ifmmode^\circ\else\textdegree\fi{}K may be estimated from the frequency of the extrapolated cutoff of the real part, ${\ensuremath{\sigma}}_{1}(\ensuremath{\omega})$, of the superconducting conductivity. The values so obtained are 4.0\ifmmode\pm\else\textpm\fi{}0.5, 3.3\ifmmode\pm\else\textpm\fi{}0.2, and $3.9\ifmmode\pm\else\textpm\fi{}0.3k{T}_{c}$ for lead, tin, and indium, respectively. These values are in good agreement with those obtained in other experiments on bulk samples. The frequency dependence of $\frac{{\ensuremath{\sigma}}_{1}(\ensuremath{\omega})}{{\ensuremath{\sigma}}_{N}}$ is in qualitative agreement with the results of a calculation by Mattis and Bardeen based on the theory of Bardeen, Cooper, and Schrieffer, except for an unexpected hump in ${\ensuremath{\sigma}}_{1}(\ensuremath{\omega})$ for lead and (tentatively) mercury at low frequencies. This hump may be due to the production of collective excitations or an anisotropy in the energy gap. It has also been found that a magnetic field as high as 8000 gauss applied in the plane of a lead film about 12 A thick has only a very small effect on the electromagnetic properties of the film. This is not surprising, in view of the results of the microwave experiments of Pippard and of Spiewak.

Apparatus especially designed for studying electron paramagnetic resonance is described and discussed. A magnet of novel yokeless design is presented. Field stabilization and modulation procedure is considered. The microwave sample cavity is analyzed to determine conditions for optimum operation. The klystron stabilization problem is examined. Appropriate lumped circuits for low‐frequency operation are described. The signal amplification and presentation system is treated in detail.

Antiferromagnetic resonance in single crystals of Fe${\mathrm{F}}_{2}$ was observed between 1.5\ifmmode^\circ\else\textdegree\fi{} and 66\ifmmode^\circ\else\textdegree\fi{}K (${T}_{N}=78.4\ifmmode^\circ\else\textdegree\fi{}$K) in the far-infrared region. The resonance frequency at $T\ensuremath{\approx}0$ was found to be $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\nu}}(0)=52.7\ifmmode\pm\else\textpm\fi{}0.2$ ${\mathrm{cm}}^{\ensuremath{-}1}$. Using the antiferromagnetic resonance relation derived by Kittel, Nagamiya, Keffer, and others, and using the experimental value for the static susceptibility, the uniaxial anisotropy constant at absolute zero, $K(0)$, was inferred to be 1.1\ifmmode\times\else\texttimes\fi{}${10}^{8}$ ergs/${\mathrm{cm}}^{3}$ (40 ${\mathrm{cm}}^{\ensuremath{-}1}$/atom). Measurements of the splitting of the line caused by an external magnetic field gave ${g}_{\ensuremath{\parallel}}=2.25\ifmmode\pm\else\textpm\fi{}0.05$. The anisotropy energy in Fe${\mathrm{F}}_{2}$, being primarily due to the crystalline field-spin-orbit interaction, may be described by a term $\ensuremath{\Sigma}{i}^{}D{{S}_{\mathrm{zi}}}^{2}$ in the Hamiltonian. By including this interaction in the molecular-field treatment, we have determined $D=\ensuremath{-}9\ifmmode\pm\else\textpm\fi{}2$ ${\mathrm{cm}}^{\ensuremath{-}1}$, and have calculated the temperature dependences of the sublattice magnetization, the anisotropy constant, the resonance frequency, and the line width. The last two were compared with the experimental results and found to be in reasonable agreement. The linewidths were found to follow a ${T}^{4}$ law above 15\ifmmode^\circ\else\textdegree\fi{}K. The search over a frequency region of 13-70 ${\mathrm{cm}}^{\ensuremath{-}1}$ for the absorption lines expected in the paramagnetic region was unsuccessful, possibly indicating a relaxation time of less than ${10}^{\ensuremath{-}12}$ sec.