Showing papers on "Spin-½ published in 1968"
TL;DR: In this paper, it was shown that there exists a localized excited state in the energy gap in a superconductor with a classical spin and at finite concentration localized excited states around classical spins form an "impurity band".
Abstract: It is shown that there exists a localized excited state in the energy gap in a superconductor with a classical spin. At finite concentration localized excited states around classical spins form an "impurity band". The process of growth of the "impurity band" and its effects on observable quantities are investigated. § I. Introduction Since the monumental paper by Abrikosov and Gorkov 1 ) many works have been done experimentally and theoretically concerning the thermodynamic and transport properties of superconductors with small amount of paramagnetic impUrItIes. Recently several authors 2 ),3) have been interested in whe'ther loca lized excited states in the energy gap exist in a superconductor with a paramag netic impurity or not. As is well known, a paramagnetic impurity in a normal metal or a superconductor brings about the so-called Kondo effect 4 ) (a kind of quantum mechanical effects of spins) and this makes complete solutions of the problem quite difficult. In this paper we restrict our discussions to the classical spins in supercon ductors. In the s~d interaction between conduction electrons and a localized spin
720 citations
TL;DR: In this paper, it is proved that a necessary and sufficient condition for a non-compact space-time M to admit a spinor structure is that M have a global field of orthonormal tetrads.
Abstract: In order to define spinor fields on a space‐time M, it is necessary first to endow M with some further structure in addition to its Lorentz metric. This is the spinor structure. The definition and the elementary implications of the existence of a spinor structure are discussed. It is proved that a necessary and sufficient condition for a noncompact space‐time M to admit a spinor structure is that M have a global field of orthonormal tetrads.
469 citations
410 citations
01 Jan 1968
344 citations
TL;DR: In this paper, the negative magnetoresistivity of dilute alloys containing magnetic transition impurities is calculated in the second Born approximation using an $s\ensuremath{-}d$ exchange model.
Abstract: The negative magnetoresistivity of dilute alloys containing magnetic transition impurities is calculated in the second Born approximation using an $s\ensuremath{-}d$ exchange model. Physically the variation of the magnetoresistivity is the product of: (a) the field and temperature dependence of the conduction-electron scattering amplitudes, (b) the freezing out of the impurity's spin degree of freedom by the magnetic field. In zero field, the former contribution leads to the well-known Kondo logarithmic series in $T$, whereas the latter remains constant in temperature. But in the presence of a magnetic field and for $\frac{g{\ensuremath{\mu}}_{B}H}{{k}_{B}T}\ensuremath{\lesssim}2$, the freezing out of the spins, mainly described by the square of the magnetization, varies, and much more rapidly than the perturbation expansion of the scattering amplitudes. This is verified experimentally in $\mathrm{Cu}\mathrm{Mn}$ alloys (for $T\ensuremath{\gg}{T}_{\mathrm{Kondo}}$), and allows us to phenomenologically extend our results to $T\ensuremath{\approx}{T}_{\mathrm{Kondo}}$, for which we get the same good fit with experiments in $\mathrm{Cu}\mathrm{Fe}$ alloys. For $\frac{g{\ensuremath{\mu}}_{B}H}{{k}_{B}T}\ensuremath{\gtrsim}4$, the impurity spins are completely aligned with the field; the scattering amplitudes become the main source of variation in the magnetoresistivity. In this case, as in absence of field, an exact theory in needed.
153 citations
TL;DR: In this paper, it was shown that the back-force of an electrically neutral magnet is a consequence of the relativistic corrections to the motion of the particles composing the magnet.
Abstract: Shockley and James have noted that an electrically neutral magnet whose moment is changing with time exerts a force on an electric charge of negligible velocity at a large distance from it, but that there is no obvious corresponding back-action of the charge on the magnet, although required by general considerations of the conservation of momentum. In the present paper, it is shown that the back-force is a consequence of the relativity corrections to the motion of the particles composing the magnet. The proof is given generally in terms of the relativistic theorem on the motion of the "center of energy" and explicitly in terms of a Lagrangian for a system of particles obtained many years ago by Darwin. The effect of spin is examined and found not to affect the action-reaction balance. In the Appendix, the properties of the center of energy are utilized to show how the Darwin Lagrangian should be modified when there are nonelectric classical forces acting between the particles of the magnet.
141 citations
TL;DR: In this paper, the time-scales characterizing spin relaxations near the magnetic transitions in isotropic Heisenberg spin systems are discussed, and the effect of spin relaxation on the magnetic transition is investigated.
Abstract: The time-scales characterizing spin relaxations near the magnetic transitions in isotropic Heisenberg spin systems are discussed.
139 citations
137 citations
TL;DR: In this paper, the change in the easy axis of magnetization observed in some ferrimagnets has been studied using a phenomenological description, and it was found that two second-order phase transitions can occur.
Abstract: The change in the easy axis of magnetization observed in some ferrimagnets has been studied using a phenomenological description. It is found that two second-order phase transitions can occur.
112 citations
TL;DR: In this paper, the theory of spin fluctuations in nearly ferromagnetic metals is presented and their effect on the properties of such systems is discussed, and the importance of momentum-dependent exchange and band structure effects is stressed.
Abstract: The theory of spin fluctuations in nearly ferromagnetic metals is presented and their effect on the properties of such systems is discussed. The importance of momentum‐dependent exchange and band‐structure effects is stressed.
97 citations
TL;DR: The results of some progress made with the problem of evaluating the matrix elements of the Hamiltonian are reported, which may be very important in the calculation and interpretation of such quantities as nuclear spin-spin coupling and other hyperfine interactions.
Abstract: where Ep = ±1 is the parity of the permutation P and fsN is the dimension of the irreducible representation.' The notation used by Kotani et al.1 2 has been employed. The functions OS{MS;k(k = 1,2,...,f5N) are orthonormal and hence are indeterminate to within an orthogonal transformation. If one chooses the basis so as to generate the Young-Yamanouchi3 irreducible representation, then the indices k become the Yamanouchi symbols3 or, equivalently, the internal spin coupling indices of Kotani.' In this case the OsMS;k functions have the important property that the matrices U(P) for N 1, N -2,. . . ,2 particles appear in fully reduced form. Although functions of the form (1) are a significant improvement over the conventional Hartree-Fock functions, and may be very important in the calculation and interpretation of such quantities as nuclear spin-spin coupling and other hyperfine interactions, very little progress has been made hitherto due to the difficulty of evaluating the matrix elements of the Hamiltonian. We wish here to report the results of some progress we have made with this problem; further details will be given in a lengthier communication. Instead of choosing the standard Young-Yamanouchi basis in spin space, one may choose the following basis: N E SSMSS10N-M Om XS ,MS;k = (5152M514154 SM) 0S13,Ms,;k, 0S2,,MS2;k MS,3MS2
TL;DR: In this paper, high-spin wave functions, propagator numerators, and vertex functions are developed in a covariant, on-shell manner for massive bosons and fermions and for photons.
Abstract: High-spin wave functions, propagator numerators, and vertex functions are developed in a covariant, on-shell manner. General formulas are given for massive bosons and fermions and for photons. The application to dispersion theory is discussed.
31 Oct 1968
TL;DR: In this article, it is proposed that the phenomenological theory of particles be based on the source concept, which is abstracted from the physical possibility of creating or annihilating any particle in a suitable collision.
Abstract: It is proposed that the phenomenological theory of particles be based on the source concept, which is abstracted from the physical possibility of creating or annihilating any particle in a suitable collision. The source representation displays both the momentum and the space-time characteristics of particle behavior. Topics discussed include: spin and statistics, charge and the Euclidean postulate, massless particles, and $S{U}_{3}$ and spin. It is emphasized that the source description is logically independent of hypotheses concerning the fundamental nature of particles.
TL;DR: In this article, the effects of the mean free path on the spin susceptibility of almost ferromagnetic metals were investigated and the low-temperature specific heat contribution of the spin fluctuations was calculated.
Abstract: We investigate the effects of the mean free path on the spin susceptibility of almost ferromagnetic metals. Using these results, we calculate the low-temperature specific-heat contribution of the spin fluctuations. While the term linear in temperature $T$ is unaffected by the mean free path, we find that the ${T}^{3} \mathrm{ln} T$ contribution is rapidly modified by impurities, in contrast to the phonon case.
TL;DR: In this article, a theory of the first-order phase transition in U${\mathrm{O}}_{2}$ is presented and discussed in the molecular field approximation, where an isotropic nearest-neighbor exchange and local quadrupole-lattice interaction are taken as the basic interactions in the model.
Abstract: A theory of the first-order phase transition in U${\mathrm{O}}_{2}$ is presented and discussed in the molecular-field approximation. An isotropic nearest-neighbor exchange and local quadrupole-lattice interaction are taken as the basic interactions in the model. Interesting behavior is obtained due to the two distinct ways in which the collective ground-state degeneracy can be removed at $T=0\ifmmode^\circ\else\textdegree\fi{}$K: a cooperative Jahn-Teller distortion or a polarization of the sublattice magnetization by the exchange field. Depending on the relative gain in free energy obtained by these two mechanisms, one obtains four different types of behavior near the critical point: (1) a second-order transition to a distorted state with no magnetic ordering; (2) a second-order transition to a distorted state followed by a second-order magnetic transition; (3) a first-order transition yielding a discontinuous change in lattice distortion and sublattice magnetization; (4) a second-order magnetic transition accompanied by a weak distortion. The temperature dependence of the elastic constant ${C}_{44}$ is also derived. The parameters required to give a first-order transition in agreement with the measured discontinuity in sublattice magnetization and the correct behavior for ${C}_{44}$ are found to be consistent with the parameters obtained from the measured spin-wave excitations.
TL;DR: In this paper, a set of coupled differential equations is obtained which represents an exact solution for the high-temperature spin autocorrelation function for spins in a liquid whose motion is governed by a classical isotropic rotational diffusion equation with a single diffusion constant, D. In this case, the dominant terms correspond to those in the well-known Redfield theory.
Abstract: A set of coupled differential equations is obtained which represents an exact solution for the high‐temperature spin autocorrelation function for spins in a liquid whose motion is governed by a classical isotropic rotational diffusion equation with a single rotational diffusion constant, D. If the diffusion is rapid, i.e., if D is large compared to the spin–lattice interaction, H1, then these equations can be solved by means of a perturbation expansion in (H1 / D). In this case, the dominant terms correspond to those in the well‐known Redfield theory; in the absence of spin degeneracy the spectrum consists of Lorentzian lines whose widths T2− 1 are of the order of H12τ2 where τ2 = (6D)− 1, and whose frequencies are shifted by an amount of the order of ω0τ2T2− 1(1 + ω02τ22)− 1 from the Zeeman frequency, where ω0 is a characteristic spectral frequency difference. The present theory introduces a number of corrections: The linewidth should be corrected by terms of the order of ω0(τ2 / T2)3 / 2 (1 + ω02τ22)− 1...
TL;DR: The spin density matrix for particles of arbitrary intrinsic angular momentum is explicitly expressed in terms of directly measurable quantities, such as expectation values of components of multipole moments, or the relative weights of partial beams split-up by a Stern-Gerlach apparatus according to eigenvalues of dipole projections in several directions.
TL;DR: In this article, the DWBA approximation with a deformed spin-dependent potential of the full Thomas form was used to calculate the spin flip probabilities and the spin asymmetries.
TL;DR: In this paper, the definition of the total momentum, position, and spin for two-free-particle systems is discussed by using the requirement that the generators of the respective invariance groups should have the same form expressed in terms of them as for a single particle.
Abstract: The definition of the total momentum, position, and spin for Galilean- or Lorentz-invariant two-free-particle systems is discussed by using the requirement that the generators of the respective invariance groups should have the same form expressed in terms of them as for a single particle. Internal c.m. dynamical variables are introduced by applying the singular transformation due to Gartenhaus and Schwartz on the basic single-particle dynamical variables, the transformation mapping the whole Hilbert space onto the c.m. subspace spanned by states of zero total momentum. The form of the internal c.m. position operator is given for particles with spin, for what appears to be the first time. Using these dynamical variables, it is shown how an interaction can be introduced while maintaining Galilean or Lorentz invariance and satisfying the asymptotic condition of freely propagating particles for large separations.
TL;DR: In this paper, an approximate expression for the wave number and frequency-dependent spin susceptibility χ(Q, ω) of a system of interacting electrons in a narrow s band was derived.
Abstract: An approximate expression has been derived for the wave number and frequency-dependent spin susceptibility χ(Q, ω) of the paramagnetic phase of a system of interacting electrons in a narrow s band. This expression has the property of reducing to the random phase result in the weak-interaction (band) limit and gives a Curie law for the ordinary susceptibility in the strong-interaction (atomic) limit. When the number of electrons per atom is small, χ(Q, ω) is expressible in terms of an effective electron-electron interaction similar to that of Kanamori. The stability of the paramagnetic phase relative to ferromagnetic ordering is discussed.
TL;DR: In this paper, a generalized self-consistent cluster treatment of the narrow-band Hamiltonian was used to study the magnetic properties of a narrow band ionic system and its transition from an antiferromagnetic insulator to metal.
Abstract: Correlation and magnetic effects in narrow bands are studied using a generalized self-consistent cluster treatment of the narrow-band Hamiltonian. Here the dynamics consists of electron hopping between nearest-neighbor sites and Coulomb interaction between electrons on the same site and nearest-neighbor sites. In the simpler case, where the neighbor interactions are neglected, i.e., the Hubbard model, the environment of the cluster is regarded as a particle reservoir, one for each spin. Hopping between the cluster and reservoirs is described by fermion source terms. It is required that the thermodynamic average of the particle currents of each spin within the cluster equal the corresponding particle exchange between cluster and reservoir. Electron motion in the system is examined for varying ratios of the strength of the hopping to the intrasite Coulomb repulsion. A discontinuous transition from an antiferromagnetic insulator to a metal is found under dynamical conditions close to those predicted by Hubbard and Kemeny. The effect of the intersite Coulomb interaction on the transition is next studied. These added terms are seen greatly to influence the transition and the magnetic properties of the cluster.
TL;DR: In this article, a quasi-potential equation for relativistic scattering amplitude and the wave function of two interacting particles with spin 1/2 was constructed with the help of specific covariant extrapolation of the scattering amplitude off the energy-momentum shell.
Abstract: Quasi-potential equations are constructed for the relativistic scattering amplitude and the wave function of two interacting particles with spin 1/2. This is done with the help of specific covariant extrapolation of the scattering amplitude off the energy-momentum shell. Suitable diagram techniques are developed. The quasi-potential is defined as a sum of «irreducible» diagrams. The free part of the wave equation is spin independent and all features connected with spin appear in the interaction (quasi-potential). The spin structure of the quasipotential is investigated.
TL;DR: In this article, a new type excitation of localized magnons in the Ising-like spin system is reported, where the selection rule Δ m = ± 1, where m is the number of spins in the short range order spin cluster directed oppositely to the majority spins, can be used.
Abstract: A new type excitation of localized magnons in the Ising-like spin system is reported. It was found that in a strongly anisotropic ferro- or antiferromagnetic crystal such as CoC122H2O, nonuniform magnetic resonances with the selection rule Δ m = ± 1, where m is the number of spins in the short range order spin cluster directed oppositely to the majority spins, can be excited. Examples of such a localized spin wave excitation observed in FeCl2 and CoCl22H2O is discussed using a model of the Ising spin system.
TL;DR: In this article, the authors derived kinetic equations for the spin autocorrelation function for a paramagnetic spin system using the resummation procedure introduced by R\'esibois and De Leener in the framework of the statistical mechanics of irreversible processes.
Abstract: In a recent work, the authors derived kinetic equations for the spin autocorrelation function for a paramagnetic spin system using the resummation procedure introduced by R\'esibois and De Leener in the framework of the statistical mechanics of irreversible processes due to Prigogine and co-workers. These equations are non-Markovian and nonlinear in the high-field, high-temperature, and Weiss-limit approximations. In the present paper, methods of approximation are given to solve such kinetic equations and are applied to the study of two important NMR problems, namely, free induction decay (FID) and spin diffusion. The general characteristics of the FID are obtained even in the lowest order of approximation owing to the resummation procedure, whereas the next higher-order correction leads to very good agreement with the experimental results given by Barnaal and Lowe. The following asymptotic form is also derived: $\ensuremath{\Gamma}(t)=(acos\ensuremath{\alpha}t+bsin\ensuremath{\alpha}t){e}^{\ensuremath{-}\ensuremath{\beta}t}$ A diffusion equation is obtained for the magnetization. From this the diffusion coefficient is computed and is found to be in agreement with that proposed by several authors. However, consideration of higher-order corrections does not seem to explain the strong dependence on the orientation of the external magnetic field which was observed experimentally by Leppelmeier.
TL;DR: In this article, the partition function z, the pair correlation function ρ, and the zero-field susceptibility χ for the one-dimensional Ising model with infinite spin are expressed in terms of the eigenvalues and eigenfunctions of an integral equation.
Abstract: The partition function z, the pair correlation function ρ, and the zero‐field susceptibility χ for the one‐dimensional Ising model with infinite spin, are expressed in terms of the eigenvalues and eigenfunctions of an integral equation. The eigenfunctions of the integral equation are shown to be the oblate spheroidal wavefunctions, and, from known asymptotic expansions, high‐ and low‐temperature expansions are given for z, ρ, and χ. It is shown that the low‐temperature behavior of z, ρ, and χ differs qualitatively from the corresponding behavior for all finite spin.
TL;DR: In this article, a diagrammatic-perturbational approach to derive Wick's theorems for operators of spin \textonehalf{} and 1 (in units of $\ensuremath{\hbar}$) using the drone-fermion representation is applied to the Heisenberg model.
Abstract: Earlier derivations of simple Wick's theorems for operators of spin \textonehalf{} and 1 (in units of $\ensuremath{\hbar}$) using the drone-fermion representation are applied to the Heisenberg model. The resulting diagrammatic-perturbational approach (Green's functions) is carried out in both the high- and low-temperature domains, where the expansion criteria of Stinchcombe et al. are closely followed. The present work effectively reexpresses the semi-invariant analysis of these authors in a much simpler manner, and many of their results are straight-forwardly reproduced. The use of standard quantum-field-theory techniques enables renormalization to be undertaken in a simple, systematic manner. At low temperatures the present fermion analysis gives Dyson's ${T}^{4}$ contribution to the free energy from the first Born approximation to spin-wave scattering. Higher-order spin-wave contributions give a damping term, which, upon evaluation in the lowest approximation, is identical to that found by ter Haar and Tahir-Kheli.
TL;DR: In this paper, it was shown that the zeros of the partition function for the Ising model with higher spin values lie on the unit circle in the fugacity plane (or complex magnetic field plane).
Abstract: The theorem of Lee and Yang has been extended to the ferromagnetic Ising model with arbitrarily mixed spin values of Sj = ½, 1, and 32, including the case of equal spin values as a special one. Namely, it has been proved that the zeros of the partition function for the above Ising model with higher spin values lie on the unit circle in the fugacity plane (or complex magnetic‐field plane). Expressions for general correlation functions in Ising ferromagnets with higher spin values have been derived in terms of the above generalized theorem. By the use of these expressions, the relations among the critical indices are discussed and the same results are obtained as those predicted by the scaling‐law approach.