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An experimental and theoretical discussion is given of the results of cyclotron resonance experiments on charge carriers in silicon and germanium single crystals near 4\ifmmode^\circ\else\textdegree\fi{}K. A description is given of the light-modulation technique which gives good signal-to-noise ratios. Experiments with circularly polarized microwave radiation are described. A complete study of anisotropy effects is reported. The electron energy surfaces in germanium near the band edge are prolate spheroids oriented along $〈111〉$ axes with longitudinal mass parameter ${m}_{l}=(1.58\ifmmode\pm\else\textpm\fi{}0.04)m$ and transverse mass parameter ${m}_{t}=(0.082\ifmmode\pm\else\textpm\fi{}0.001)m$. The electron energy surfaces in silicon are prolate spheroids oriented along $〈100〉$ axes with ${m}_{l}=(0.97\ifmmode\pm\else\textpm\fi{}0.02)m$; ${m}_{t}=(0.19\ifmmode\pm\else\textpm\fi{}0.01)m$. The energy surfaces for holes in both germanium and silicon have the form $E(k)=A{k}^{2}\ifmmode\pm\else\textpm\fi{}{[{B}^{2}{k}^{4}+{C}^{2}({{k}_{x}}^{2}{{k}_{y}}^{2}+{{k}_{y}}^{2}{{k}_{z}}^{2}+{{k}_{z}}^{2}{{k}_{x}}^{2})]}^{\frac{1}{2}}.$ We find, for germanium, $A=\ensuremath{-}(13.0\ifmmode\pm\else\textpm\fi{}0.2)(\frac{{\ensuremath{\hbar}}^{2}}{2m})$, $|B|=(8.9\ifmmode\pm\else\textpm\fi{}0.1)(\frac{{\ensuremath{\hbar}}^{2}}{2m})$, $|C|=(10.3\ifmmode\pm\else\textpm\fi{}0.2)(\frac{{\ensuremath{\hbar}}^{2}}{2m})$; and for silicon, $A=\ensuremath{-}(4.1\ifmmode\pm\else\textpm\fi{}0.2)(\frac{{\ensuremath{\hbar}}^{2}}{2m})$, $|B|=(1.6\ifmmode\pm\else\textpm\fi{}0.2)(\frac{{\ensuremath{\hbar}}^{2}}{2m})$, $|C|=(3.3\ifmmode\pm\else\textpm\fi{}0.5)(\frac{{\ensuremath{\hbar}}^{2}}{2m})$. A discussion of possible systematic errors in these constants is given in the paper.

An exact theory of impurity states in crystals is developed, and an evaluation is given of the applicability of the Wannier equation to the donor states in Si and Ge in view of the multiple energy minima in the conduction band. The theory is extended to include degenerate bands, and it is shown by two different methods that the Wannier equation is to be replaced by a set of coupled wave equations. The theory is applied to acceptor states in Si and Ge. The agreement with experiment is fairly good for both donors and acceptors.

Two systems of biomolecules in solution are known to be represented by simple models which can be solved to give phase transitions in one dimension. The systems are double-stranded DNA and the helical polypeptides. We treat the very simple problem of the single-ended zipper. There is an interesting simialrity with the work of Nagle on the one-dimensional analog of the Slater model of KDP.

Synopsis This paper reviews the status of experiments bearing on the band structure of semiconductors, with particular reference to germanium and silicon. The situation in n-Ge is especially clear, as both cyclotron resonance and magnetoresistance experiments show that the energy surfaces at the bottom of the conduction band are prolate spheroids oriented along the [111] directions in k-space; the spheroids are highly anisotropic, with a mass ratio of about 15:1. In p-Ge the two isotropic lines in cyclotron resonance suggest that the band edge is at the center of the Brillouin zone; the multiplicity is explained by spin-orbit splitting. It appears that this model may account, qualitatively for the remarkable infra-red absorption of p-Ge, but it seems to be difficult to explain transport data. From magnetoresistance and from cyclotron resonance it is found that the energy surfaces in n-Si are prolate spheroids directed along [100] axes, while the structure of p-Si is like p-Ge.

This paper surveys current theoretical work on spin-spin and spin-lattice relaxation in ferromagnetic substances with reference to ferromagnetic resonance. It is shown that it is possible to give a reasonable explanation of the principal features of the experimental results. The calculations, carried out for nickel in particular, make use of a macroscopic spin-lattice interaction determined by the observed magnetostriction and a pseudo-dipolar spin-spin interaction determined by the observed anisotropy. It is not sufficient to use magnetic dipole coupling alone for either of the two relaxation processes. The zero-point fluctuations in the pseudo-dipolar field play a central role in the development of the theory.

The molecular field treatment of the magnetic properties of ferrites given by N\'eel is extended to take into account the antiferromagnetic exchange interactions within the two magnetic sublattices. On further subdividing the two lattices, we show that the ground state may, (1) have an antiparallel arrangement of the spins on the two sites; or (2) consist of a triangular arrangement of the spins on the sublattices; or (3) have antiferromagnetism in each of the two sites separately. We also show that transitions between various configurations may occur in the same substance at different temperatures, without the assumption of temperature-dependent interactions. Neutron diffraction experiments and specific heat measurements are suggested for the detection of the predicted arrangements.

It is shown that the observed width of the microwave electron spin resonance absorption lines associated with $F$ centers in KCl, NaCl, and KBr crystals can be attributed to hyperfine interactions between the $F$-center electron and the nuclear magnetic moments of the ions adjacent to the $F$ center. The width arises from the distribution of nuclear moment components. Theoretical calculations of the width are in good agreement with observation provided that the $F$-center wave function is treated as a linear combination of atomic orbitals; wave functions calculated on continuum models are shown to be unsatisfactory. The theory is confirmed by a comparison of observations on $F$ centers in crystals of ${\mathrm{K}}^{39}$Cl and ${\mathrm{K}}^{41}$Cl. If the width is attributed to interactions with the nearest sets of K and Cl ions, the experiments lead directly to quantitative values of the electronic charge density at the K and Cl nuclei: one finds ${|\ensuremath{\Psi}(\mathrm{K})|}^{2}=0.70\ifmmode\times\else\texttimes\fi{}{10}^{24}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ and ${|\ensuremath{\Psi}(\mathrm{Cl})|}^{2}=0.12\ifmmode\times\else\texttimes\fi{}{10}^{24}$ ${\mathrm{cm}}^{\ensuremath{-}3}$.

We extend the Monod-Wyman-Changeux of allosteric transitions in enzyme-substrate reactions to a membrane composed of identical units (protomers). It is supposed that each protomer can exist in two states. The interaction between protomers is treated in the molecular field approximation. It appears possible to have a first-order phase transition when the chemical potential of the substrate is varied, holding the temperature constant. The wide range of possible biological implications is discussed. (Author)

An explanation is given of the extreme sharpness of the electron spin resonance line in solutions of potassium in liquid ammonia, as reported by Hutchison and Pastor. Motional narrowing of the width associated with dipolar and hyperfine interactions results from the rotation and diffusion of ammonia molecules. The model of metal‐ammonia solutions used in the calculation is shown to be supported by thermal, magnetic, volumetric, and conductivity data. The model pictures the electrons removed from the potassium atoms as located in cavities in the liquid, the cavities having approximately the volume of two to four ammonia molecules. The electrons in the cavities are in equilibrium with respect to the reaction 2e⇆e2+0.2 ev, where e2 represents two electrons in a singlet state in one cavity. The electrons in cavities may perhaps be thought of as in molecular orbital states on the protons of the adjacent NH3 molecules.

A thermodynamic theory is given of a class of magnetic crystals which transform from ferromagnetic to antiferromagnetic states as the temperature is varied. Applications are suggested to ${\mathrm{Mn}}_{2\ensuremath{-}x}{\mathrm{Cr}}_{x}\mathrm{Sb}$ and to crystals having the nickel arsenide type structure. It is shown that the exchange magnetoelastic energy is often important in such transformations and leads to an additional interaction energy of the form ${({\mathrm{S}}_{A}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{S}}_{B})}^{2}$ in the effective spin Hamiltonian. It is suggested that one of the exchange constants goes linearly through zero near a critical value of some lattice coordinate characterizing the transition. There are important differences in the behavior of compact and noncompact antiferromagnetic lattices, under the assumption of nearest-neighbor interactions between sublattices. A triangular array is treated, such as might arise in crystal structures of the NiAs type.

A discussion is given of the connection between the results of microwave resonance absorption experiments and gyromagnetic ratio experiments on ferromagnetic substances. A review of the experimental data indicates that the microwave experiments usually give $gg2$, while gyromagnetic measurements usually give values of the related quantity ${g}^{\ensuremath{'}}$ which are 2. The analogous situation obtaining in paramagnetic salts is explained by means of a simple example, and the application of the argument to ferromagnetic substances is indicated. The validity of the use of $g$ in the macroscopic equations of motion in the resonance experiment is justified as a consequence of the approximate mutual cancellation of the orbital and lattice angular momenta. A critical discussion is given of other attempts to explain the $g\ensuremath{\ne}{g}^{\ensuremath{'}}$ effect.

A scheme is proposed for the relaxation processes at low temperatures accompanying excitation of uniform precession spin waves in a ferromagnetic resonance experiment, with particular reference to highly pure yttrium iron garnet. The processes are: (1) scattering of uniform precession spin waves into the degenerate spin-wave modes by polishing imperfections on the sample surface; (2) equalization of the populations of the degenerate spin-wave modes, also by surface imperfections; and (3) relaxation of the degenerate modes by Raman scattering of thermal spin waves through the magnetic dipole interaction. Relaxation times for the three processes are calculated and compared with experimental values with reasonable agreement.

The giant sharp anisotropy anomalies in YIG discovered by Dillon and attributed to rare earth ions are explained in terms of the crossovers or, most probably, near crossovers of the energy levels of the rare earth ions in the combined crystal and exchange fields. The central consequence deduced by the theory, independent of the detailed behavior of the energy levels, is that $\ensuremath{-}{H}_{\ensuremath{\alpha}}{(\ensuremath{\Delta}{\ensuremath{\theta}}_{\frac{1}{2}})}^{2}\ensuremath{\approx}\frac{\mathrm{kT}{N}^{\ensuremath{'}}}{M}$, where ${H}_{\ensuremath{\alpha}}$ is the anisotropy field; $\ensuremath{\Delta}{\ensuremath{\theta}}_{\frac{1}{2}}$ the angular width of the peak; ${N}^{\ensuremath{'}}$ the concentration of rare earth ions at the crossover; $M$ is the total magnetization; the result assumes $\mathrm{kT}\ensuremath{\gg}\mathrm{level}$ splitting at apparent crossover. This and other results appear to be in satisfactory agreement with the available experimental data. Crystals with giant anomalies have useful properties for adiabatic demagnetization experiments---the ferric-rare earth exchange field of 100 koe can be effectively turned on or off by rotation of the magnetic moment of the crystal. In an appendix we examine the validity of the molecular field approximation to the ferric-rare earth ion interaction, and we find that the approximation is excellent. A further appendix discusses the question of crossing or noncrossing of energy levels in static fields.

The ferromagnetic transition is considered in detail for the Heisenberg Hamiltonian with all spins coupled equally. For this special model the statistical problem is solved exactly. The transition develops very slowly as the number $N$ of particles in the system is increased; the spin order at the nominal Curie temperature is proportional to ${N}^{\ensuremath{-}\frac{1}{4}}$. The order in the most probable state differs from the mean value of the order, except for $N\ensuremath{\rightarrow}\ensuremath{\infty}$. The connections are studied with the molecular-field, spin-wave, and self-consistent approximations. The failure of the self-consistent approximation is relatively severe as compared with the nearest-neighbor problem. The antiferromagnetic ground state is very close in energy to the N\'eel state.

A calculation is given of the indirect exchange ${\mathrm{I}}_{i}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{I}}_{j}$ type coupling of nuclear magnetic moments in a metal by means of the hyperfine interaction with the conduction electrons. The interaction appears to account qualitatively for the broad nuclear spin resonance lines observed in natural metallic silver. It is expected that the interaction may sharpen the resonances in pure isotopic specimens. The line shape of the minority isotope in a binary mixture may tend to be Gaussian, while that of the majority isotope may tend to be Lorentzian, if the indirect exchange interaction is dominant.

A survey is given of the indirect coupling of nuclear magnetic moments in metals via the hyperfine interaction with conduction electrons. The treatment is given in terms of the wavevector‐dependent static susceptibility of the conduction electrons. The criterion for the absence of a long‐range uniform magnetization is discussed. The usual divergence in the self‐energy of a single nuclear magnetic moment in a metal is shown to be caused by the attribution of a zero range to the contact interaction, whereas the appropriate range is ħ/mc. The divergence recently claimed in the interaction between two nuclear moments at absolute zero is believed to be a manifestation of the Kondo effect. Mean free path and correlation effects are considered.

An antiferroelectric state is defined as one in which lines of ions in the crystal are spontaneously polarized, but with neighboring lines polarized in antiparallel directions. In simple cubic lattices the antiferroelectric state is likely to be more stable than the ferroelectric state. The dielectric constant above and below the antiferroelectric curie point is investigated for both first- and second-order transitions. In either case the dielectric constant need not be very high; but if the transition is second order, $\ensuremath{\epsilon}$ is continuous across the Curie point. The antiferroelectric state will not be piezoelectric. The thermal anomaly near the Curie point will be of the same nature and magnitude as in ferroelectrics. A susceptibility variation of the form $\frac{C}{(T+\ensuremath{\theta})}$ as found in strontium titanate is not indicative of antiferroelectricity, unlike the corresponding situation in antiferromagnetism.

Heat and momentum exchanges at the Southern Ocean surface are crucial for the Earth’s Climate, but the importance of the small-scale spatial variability of these surface fluxes is poorly understood. Here, we explore how small-scale heterogeneities of the surface conditions due in particular to ocean eddies affect the atmosphere–sea ice–ocean interactions off Adélie Land, in East Antarctica. To this end, we use a high-resolution regional atmosphere–sea ice–ocean coupled model based on the NEMO-LIM and MAR models. We explore how the atmosphere responds to small-scale heterogeneity of the ocean or sea ice surface conditions, how eddies affect the sea ice and atmosphere, and how the eddy-driven surface fluxes impact the heat, freshwater, and momentum budget of the ocean. The atmosphere is found to be more sensitive to small-scale surface temperature gradients above the ice-covered than above the ice-free ocean. Sea ice concentration is found to be weaker above anticyclonic than cyclonic eddies due to increased sea ice melting or freezing (0.8 cm/day) partly compensated by sea ice convergence or divergence. The imprint of ice-free eddies on the atmosphere is weak, but in the presence of sea ice, air warming (+ 0.3 $$^{\circ }$$ ∘ C) and wind intensification (+ 0.1 m/s) are found above anticyclonic eddies, while cyclonic eddies have the opposite effects. Removing the interactions of eddies with the sea ice or atmosphere does not affect the total sea ice volume, but increases the ocean kinetic energy by 8% and weakens northward advection of sea ice, leading to a 15% decrease in freshwater flux north of 62.5 $$^{\circ }$$ ∘ S and weaker ocean restratification.

Alfv\'en-wave resonances are used to measure time decay of the electron-hole drop radius in stressed Ge, and striking new properties of the condensate are observed. Compared to standard results, the drop volume is larger by more than 1000, and the drop lifetime is increased from 40 \ensuremath{\mu}sec to over 400 \ensuremath{\mu}sec. We believe the long-lived condensate corresponds to low-density Ge $〈111〉$ or Ge $〈110〉$ phases with one or two electron ellipsoids occupied.

In Brownian motion the ensemble average of the product of the displacement and the random force is zero. This result was assumed by Langevin to be true, although it appears to contradict the intuitive feeling that the net displacement should be in the direction of the net impulse. The literature contains a statement that the Langevin assumption is incorrect, and this led us to an examination of the question. We show that the relevant correlation function in one dimension is 〈x (t) A (t−τ) 〉=2(kBT/M)[1−exp(−βτ)] which is zero at equal times and approaches 2(kBT/M) as τ→∞.

A theory is given that accounts qualitatively for the observations of thin and thick domain walls in ferroelectric and ferroelastic crystals, with special reference to the 90° walls in BaTiO 3 and to the 180° walls in GMO.

A review is given of the theory of spin waves and of the principal physical effects associated with spin waves. It is shown that the boundary condition mx = 0 at the surface permits the excitation of spin waves by a uniform r-f field. (auth)

An elementary discussion for physicists is given of the thermodynamic instability of proteins and DNA. The biochemical explanation is given of how these molecules are grown in the face of a large unfavorable free energy difference, as much as 0.2 MeV for DNA of 106 bonds. The role of ATP is described as the major fuel of the biological world.

The transfer of momentum between a conduction electron and a crystal lattice is examined in detail. By physical considerations we are led to the expression (mm*)ij = δij+ ∑ GGiδδkj|aG(k)|2 for the reciprocal effective mass tensor, where G is 2π times a reciprocal lattice vector and aG(k) is a coefficient in the momentum representation of the Bloch eigenfunction: ψk = ∑ GaG(k) exp[i(G+k)·r]. This expression for the effective mass tensor is shown to be completely equivalent to the usual definition.

This paper gives an elementary discussion of the theory of g values and line widths in ferromagnetic resonance in certain rare earth garnets. The experimental facts are reviewed briefly.

The thermal conductivity of glasses decreases with decreasing temperature, while the conductivity of crystalline substances increases with decreasing temperature. The behavior of glasses is interpreted in terms of an approximately constant free path for the lattice phonons, so that the conductivity decreases roughly with the specific heat. The value of the phonon mean free path at room temperature is of the order of magnitude of the scale of the disorder in the structure of glasses as determined from x-ray evidence---that is, of the order of 7A. This is about the size of the unit cell of the crystalline forms of silica.

The linearized Landau-Ginzburg equation is used to calculate H c3 for a cylindical cavity in a type II material H c3 exhibits oscillations as a function of the cavity radius R when R is if the order of the coherence length. H c3 increase to the Saint-James and De Gennes limit for large R .

A discussion is given of the dispersion relation, magnetization distribution, and group velocity of magnetostatic waves in an infinite circular cylinder with the static magnetic field parallel to the cylinder axis. The dispersion relation of the modes with ${e}^{i\ensuremath{\phi}}$ angular dependence is, for $\mathrm{kR}\ensuremath{\gg}1$, $\ensuremath{\omega}\ensuremath{\cong}\ensuremath{\gamma}{H}_{0}+\ensuremath{\gamma}2\ensuremath{\pi}{M}_{s}{(\frac{{x}_{i}}{\mathrm{kR}})}^{2}+(\frac{D}{\ensuremath{\hbar}}){k}^{2},$ where ${x}_{i}$ is a root of ${J}_{0}(x)=0$; $R$ is the cylinder radius; and $D$ is the exchange constant. The group velocity of magnetostatic pulses at low wave vectors is shown to be considerably higher than magnon velocities.

Publisher Summary This chapter reviews the indirect exchange interactions in a metal. The indirect interaction in a metal proceeds as follows: The magnetic moment of one nucleus of spin I 1 scatters a conduction electron of spin s by means of the hyperfine interaction between electronic and nuclear magnetic moments, and then the magnetic moment of the second nucleus of spin I 2 sees the scattered electron. The two nuclear moments see each other in this way. When the contact I.s part of the hyperfine interaction is dominant, the indirect exchange is isotropic, of the form I 1 .I 2 . The primary emphasis is on the coupling between two nuclear magnetic moments, and secondary emphasis is on the coupling between the electronic magnetic moments of substitutional paramagnetic ions in a dilute alloy. The primary area is the simpler to handle theoretically; the secondary area is of wider scientific and technological importance because of the application to magnetic order in the rare-earth metals.

Publisher Summary The chapter presents a study on ferromagnetic domain theory. The chapter presents a broad review of the physical principles of domain theory and of the crucial experiments which bear directly on the foundations of the subject of ferromagnetic domains. The chapter is organized in two stages. There is first an introductory survey, which describes the basic physical concepts of domain theory in general nonmathematical terms. The ideas are then developed in detail. The essential aspects of ferromagnetism are illustrated by the implications of the following experimental fact: It is possible to change the overall magnetization of a suitably prepared ferromagnetic specimen from a n initial value of zero (in the absence of an applied magnetic field) to a saturation value of the order of 1000 gauss, by the application of a field whose strength may be of the order of 0.01 oersted. This fact contains two significant observations: (1) it is possible in some cases to attain saturation magnetization by the application of a very weak magnetic field. (2) It is possible for the magnetization of the same specimen to be zero in zero (or nearly zero) applied field. The chapter discusses that domain structure is a natural consequence of the various contributions to the energy-exchange, anisotropy, and magnetic-of a ferromagnetic body. The chapter presents a discussion on coercive force, hysteresis, and reversible permeability, including reversible permeability and Barkhausen effect.

An explanation is given for the long time delay in the formation of gamma phase EHD in germanium. The Cerenkov radiation of phonons by moving alpha drops at velocity mach 0.2–0.3 is calculated to be the controlling process in the time delay.

Many realizations of infinitely adaptive crystal structures have been reported recently. It is shown that the elastic energy associated with the forced coherent registration of two types of lattice planes gives a long range repulsive interaction that can account for the observations.

We consider the Kroemer experiments on explosive instabilities in EHD in Ge in the light of an extension of the Altukhov theory to encompass general values of ωτ and of the ratio of drop radius to rf penetration depth. We suggest that the drops were heated above their critical temperature, but by a monotonic path.