Showing papers on "Spin-½ published in 1978"

Dynamic effects of pair correlation functions on spin relaxation by translational diffusion in liquids. II. Finite jumps and independent T1 processes

Abstract: Hwang and Freed have previously given solutions for the relative diffusion of molecules that include the proper boundary condition (i.e., an excluded volume due to a distance of minimum approach) which has usually been neglected in spin relaxation theories. In this work their results are extended to include effects of (1) one type of spin that is rapidly relaxing, (2) diffusion by jumps of finite size, and (3) frequency‐dependent diffusion coefficients in the theory of spin relaxation by intermolecular dipolar interactions. These results are mathematically simpler and sounder than those commonly employed. In particular, it is shown that for case (2) measurements of J (O), the zero‐frequency spectral density cannot solely be used to determine the jump size, in constrast to the Torrey theory, which did not consider the boundary‐value problem.

Critical Indices from Perturbation Analysis of the Callan-Symanzik Equation

Abstract: Recent results giving both the asymptotic behavior and the explicit values of the leading-order perturbation-expansion terms in fixed dimension for the coefficients of the Callan-Symanzik equation are analyzed by the the Borel-Leroy, Pade-approximant method for the n-component φ^4 model. Estimates of the critical exponents for these models are obtained for n=0, 1, 2, and 3 in three dimensions with a typical accuracy of a few one thousandths. In two dimensions less accurate results are obtained.

Spin-flop multicritical points in systems with random fields and in spin glasses

Abstract: Mean-field theory and renormalization-group arguments are used to study the phase diagram of an anisotropic $n$-component $d$-dimensional magnetic system with a uniaxially random magnetic field. The resulting phase diagram is shown to be very similar to that of anisotropic antiferromagnets in a uniform field: For small random fields, the system orders along the direction of uniaxial anisotropy, with exponents which are related to those of nonrandom Ising systems in $d\ensuremath{-}2$ dimensions. For larger random fields, parallel to the direction of uniaxial anisotropy, the transverse $n\ensuremath{-}1$ spin components order, with exponents which are unaffected by the random field. The two regions are separated by a spin-flop first-order line, by an intermediate "mixed" phase, and by a tetracritical (or bicritical) point. The exponents at this multicritical point are shown to coincide, near $d=6$, with those of the random-field Ising model. This phase diagram is shown to describe the behavior of random-site spin glasses in a uniform magnetic field. Other types of anisotropic random fields, related experimental realizations and other generalizations are also mentioned. Although some of the quantitative results are found only near $d=6$, qualitative results are believed to apply at $d=3$ as well.

Cluster expansion of the wavefunction. Pseudo‐orbital theory based on the SAC expansion and its application to the spin density of open‐shell systems

Abstract: We have studied the pseudo‐orbital theory, which is based on the symmetry‐adapted‐cluster (SAC) expansion of an exact wavefunction proposed previously, in comparison with the conventional open‐shell orbital theories, and applied it to the calculations of the spin densities of the first‐row atoms, Li(2S), Li(2P), Be+(2S), B2+(2S), B(2P), C(3P), N(4S), O(3P), and F(2P). We have started from the RHF reference wavefunction and considered mainly the spin‐polarization excitation operator and its self‐consistency effect. This pseudo‐orbital theory corresponds to an extension of the UHF and spin‐extended HF (SEHF) theories, and yet it is free from the theoretical defects found previously for these theories. The relative magnitudes of the calculated spin densities are predicted to be in the order of the UHF or SEHF, present, and first‐order (FO) CI in the decreasing order. This sequence has been confirmed in the calculated spin densities for the first‐row atoms. For the three‐electron atoms the present theory give...

Superconducting phase transitions in rare-earth compounds

Abstract: The superconducting transition temperature ${T}_{c}$ and the upper critical field ${H}_{c2}$ in the rare-earth ($R$) compounds ${R}_{x}{\mathrm{Mo}}_{6}{\mathrm{S}}_{8}$, ${R}_{x}{\mathrm{Mo}}_{6}{\mathrm{Se}}_{8}$, and $R{\mathrm{Rh}}_{4}{\mathrm{B}}_{4}$, are theoretically studied within a model in which the superelectrons mainly originate from the $4d$ electrons of Mo and Rh atoms. The fluctuation of local spins inside a Cooper pair weakens the BCS coupling. Thus, the quantitites ${T}_{c}$ and ${H}_{c2}$ are strongly influenced by the fluctuation. These quantities are obtained as functions of the intra- and interatomic exchange interactions and the concentration of the spins. The theoretical results explain the existence of the upper and lower superconducting transition temperatures ${T}_{c1}$ and ${T}_{c2}$ in Er${\mathrm{Rh}}_{4}$${\mathrm{B}}_{4}$ and ${\mathrm{Ho}}_{1.2}$${\mathrm{Mo}}_{6}$${\mathrm{S}}_{8}$, and the concentration dependence of ${T}_{c}$ in ${\mathrm{La}}_{1\ensuremath{-}x}{\mathrm{Gd}}_{x}{\mathrm{Mo}}_{6}{\mathrm{Se}}_{8}$ and ${\mathrm{Sn}}_{1.2(1\ensuremath{-}x)}{\mathrm{Eu}}_{x}{\mathrm{Mo}}_{6.35}{\mathrm{S}}_{8}$. The suppression of the spin fluctuation by application of a magnetic field causes an increase of the BCS coupling. In calculating ${H}_{c2}$, this fact is taken into account as well as the spin splitting of conduction bands and spin-orbit scattering. Our theory explains the anomalous behavior of the temperature dependence of ${H}_{c2}$ observed in ${\mathrm{Sn}}_{1.2(1\ensuremath{-}x)}{\mathrm{Eu}}_{x}{\mathrm{Mo}}_{6.35}{\mathrm{S}}_{8}$. It is proposed that in certain compounds a superconducting state may appear only in the presence of a magnetic field.

Spin Correlations in Actinide Materials: A Neutron Study of USb

Abstract: Measurements have been made of the short-range spin correlations in USb, a metallic compound that orders antiferromagnetically. The system has no transverse fluctuations, and the longitudinal spin correlations are anisotropic, showing stronger interactions within the ferromagnetic sheets than between them. The results of this and other expeiments can be understood with simple concepts involving the bonding of 5f electrons.

1H‐15N Spin–spin couplings in alumichrome

Abstract: We report the determination of two- and three-bond 1H-15N spin–spin couplings in the nmr spectra of a polypeptide. The 1H- and 15N-nmr spectra of 99.2% 15N-enriched alumichrome have been studied at 360 MHz and 10.1 MHz, repectively. While some 2J and 3J coupling are of the order of 5 Hz, most splitting resulting from the heteronuclear interaction are ≲2 Hz, which introduces strigent requirements of spectral resolution. In the 1H spectra these requirements were met by digital deconvolution with a sine bell routine combined with positive exponential filtering. Although the 15N spectra clearly exhibit features of fine structure, mainly because of the intrinsic higher nmir sensitivity of protons, observation of 1H-15N spin–spin couplings was found to be more practical in the 1H than in the 15N spectra. We find that the alumichrome data do not satisfy a simple cyclic relationship linking the heteronuclear couplings to the crystallographic ψ dihedral angles. It is suggested that a formal treatment of the ψ-related interresidue 1H-15N coupling might have to take into account a more complex dependence of the intervening 3J on the overall local electronic structure, which is dependent on ϕ,ψ, and ω simultaneoulsy. In contrast, our analysis indicates that χ1 can be readily determined from the measurement of the corresponding heteronuclear 3J coupling in the 1Hβ or in the amide 15N resonances. Karplus relationships are proposed that relate this heteronuclear 3J to the corresponding dihedral angle θ and which, on average, yield

Gauge models for spin-glasses

Abstract: A Landau-Ginzburg description of a spin-glass which incorporates naturally the concept of "frustration," or the incompatibility of different local stable spin configurations in neighboring regions, is presented. For a planar spin, the effective Hamiltonian has a form analogous to that of the Landau-Ginzburg functional for a superconductor in a magnetic field, except that the role of the vector potential is taken by a quenched random variable $Q(x)$ which represents the wave vector of the spin-density wave of minimum local free energy. The model is thus a simple transcription to a Landau-Ginzburg picture of the basic notion of a spin-glass as a material whose properties are determined by competition between ferromagnetic and antiferromagnetic interactions. The probability distribution of $Q(x)$ is chosen not to depend on $Q(x)$ directly (in order not to favor any particular value of $Q$), but to be Gaussian in the curl of $Q(x)$. The variance $f$ of this distribution, the mean-square vorticity in $Q(x)$, is a measure of the degree of frustration. [Any longitudinal part of $Q(x)$ is gauged away by rotating the local spin axes appropriately.] For a classical vector (Heisenberg) spin system, the analogous description is a Hamiltonian of $O(3)$ Yang-Mills form, again with the gauge random variable. Two calculations are presented. The first tests the stability of the $f=0$ theory (thermodynamically identical to an ordinary ferromagnet) against the introduction of a small amount of frustration. The result is that the $f=0$ fixed point is unstable, and no new fixed point (of order $4\ensuremath{-}d$) appears. Thus the spin-glass transition does not appear to be related to any normal sort of critical point with a particular local-spin-density configuration as a "hidden" order parameter. The second is a mean-field analysis of a transition to a state characterized by an Edwards-Anderson order parameter; its qualitative features are similar to those of mean-field theories for other models for spin-glasses. The conditions for the thermodynamic stability of such a state remain unknown.

The concept of frustration in spin glasses

Abstract: This paper gives a precise definition of those spin systems which have the property of “frustration” which is thought to be essential to the canonical spin-glass behavior. The definition is that the coupling energy across a generalized plane boundary between large blocks of spins grows only as the square root of the area of that boundary.

High spin states and neutron multiplicities after pion capture in181Ta and209Bi

Abstract: The absorption of stoppedπ− in181Ta and209Bi has been investigated by studying prompt and delayedγ-ray spectra. Absolute cross-sections for the yield of isotopes per capturedπ− in (π−, xn) reactions, as well as the relative probability of populating nuclear states of different spins have been measured for the hafnium and lead isotopes, respectively. A spin as high as 20 has been observed in the production of204Pb. The ground-state rotational bands of the hafnium isotopes are excited to spin values up to 16. Neutron multiplicities as large as 15 have been observed for both targets. A neutron multiplicity of ≃8 is most probable for both tantalum and bismuth targets.

Vanishing of the Edwards-Anderson order parameter in two- and three-dimensional Ising spin glasses

Abstract: The nature of the freezing process in two- and three-dimensional Ising spin glasses with bonds Jij=+or-J has been investigated. Monte Carlo simulations indicate that the characteristic cusp in the susceptibility chi is a non-equilibrium phenomenon resulting from the finite observation times available for the computation of chi (or its experimental measurement). This picture of the freezing process, which is illustrated by explicit calculation for the one-dimensional Ising spin glass, implies chi =1/kBT for all temperatures, or that the Edwards-Anderson order parameter q vanishes. Investigation of the ground states of certain periodic models in two and three dimensions show that every spin belongs to a finite cluster which may be turned over with no cost of energy, so that q is rigorously zero for such models. It is argued that this result holds also for the fully random models.

Spin fluctuations in metals: Application to the actinides

Abstract: We present here a review of the spin fluctuation theory and of its applications to transition and actinide systems, with a particular emphasis to the latter where some very anomalous properties find an explanation in terms of spin fluctuation effects. Firstly, we summarize the development of the spin fluctuation model which had been initially applied to transition metals and alloys such as palladium or Pd–Ni alloys. Then, we present the extension of the paramagnon model to nearly magnetic actinide systems by taking into account explicitly the temperature dependence of the Stoner susceptibility, because the 5f-band of actinides is much narrower than the d-band of transition metals. As a result the paramagnon contribution to the resistivity departs from the usual T 2 and T power laws at temperatures higher than the spin fluctuation one and saturates at high temperatures, with eventually the presence of a maximum at intermediate temperatures. We present also the calculation of the other properties o...

Test of equivalence principle for particles with spin

Abstract: We consider a simple modification of the Dirac equation, such that spin-1/2 particles violate the equivalence principle, but the latter is restored by averaging over spins. An experiment is suggested to test the existence of such an effect.

Positive-muon spin depolarization in solids

Abstract: A theory of positive-muon spin depolarization in solids is presented. Treating the interaction of the muon spin with the solid perturbatively, the depolarization rate is related to the temporal correlations of the local magnetic fields at the position of the muon. This general result encompasses both transverse and longitudinal spin depolarization. For some situations it is shown that the local-field correlations can be expressed in terms of two quantities, a muon self-diffusion function which contains the information regarding muon motion, and a function describing the spin dynamics of the solid. When applicable, this separation precisely identifies the aspects of muon motion that are studied by muon-spin-rotation experiments. The consequences of some simple models for muon motion are examined. The effect of the finite spread of the muon wave function when centered on a particular interstitial site is also included. The possible importance of this effect is suggested by calculations which account for the applied-magnetic-field dependence of the depolarization rate in copper.

Variational study on the ground state of the spin XY magnet

Abstract: An approximate wave function of the ground state of the spin XY magnet is derived using a variational method. This wave function yields estimates of the ground state energy and long-range order which agree very well with the results obtained by Betts and Oitmaa by a finite lattice method.

Stochastic theory of spin depolarization of muons diffusing in the presence of traps

Abstract: We have made a model calculation for the decay of phase coherence of muon spin rotation in the case of muon diffusion in the presence of traps. First we have developed a random-walk theory of the decay functionP(t), for diffusion in homogeneous systems, and obtained an explicit expression in the frequency domain previously found by Kubo. We have derivedP(t) in the time domain by numerical inversion of the Laplace transform applying the recently developed Korrektur method. The result coincides with the usual Gaussian-Markovian theory for slow and fast modulation, and deviates at most by 8% in the intermediate region. We have extended our theory to a two-state description for capture and release processes on traps and found an analytic expression equivalent to the NMR lineshapeI(ω). The results for the decay function agree with experimental results for muon diffusion in metals with traps. Finally we have compared our theory with approximate calculations of the decay function and the damping rate.

Generalized Phase-Space Method in the Langevin-Equation Approach

Abstract: In this article is proposed a method of constructing the quantal Boltzmann-Langevin equation, i.e. the stochastic kinetic equation for a suitably chosen statistical operator with a fluctuating force term. This method is based on the use of the generalized phase-space method, which makes calculations very simple. As an example, the method of spin coherent states is applied to a model of a localized single spin placed under actions of its magnetic environment, and the Bloch-Langevin equation, i.e. the well-known Bloch equation for a spin magnetic moment with a fluctuating force term, is derived. The drift and the relaxation terms contained in the Boltzmann-Langevin and the Bloch-Langevin equations are completely in agreement with those previously obtained. An expression of the fluctuation-dissipation theorem generalized so as to include non-linear dissipation terms is given.

Quantum mechanics of electromagnetically bounded spin-1/2 particles in expanding universes: II. Energy spectrum of the hydrogen atom

Abstract: Completing the preceding paper, the energy spectrum of the hydrogen atom in expanding Robertson-Walker universes is studied in detail using rigorous methods of functional analysis. Thereby, for closed universes (spherical case,e=1), the corresponding electromagnetic field needs special considerations. For the hyperbolic case (e=−1) it is shown (a) that the Hamilton operator is uniquely self-adjoint, (b) that the continuous energy spectrum agrees with the one in 4-flat space-time and that the energy eigenvalues are bounded by±m 0 , (c) that they approach Minkowski space spectrum for increasing curvature radius, and (d) that the hydrogen atom cannot be used as an atomic clock showing proper time. For the spherical case (e=1) it is shown (a) that the Hamilton operator is uniquely self-adjoint and (b) that the energy spectrum is solely discrete.

On the nature of the ordering in Ising spin glasses

Abstract: Monte Carlo studies of the Ising square lattice and simple cubic lattice with a random (symmetric Gaussian) nearest-neighbor exchange are extended, with emphasis on the behavior at zero temperature and at very long “observation” times. Characterizing a ground-state spin configuration by a vector we found that projections of two ground states on each other are typically of order zero. We observe that the order parameterΨ decreases under the action of a homogeneous magnetic field and vanishes at a critical field. The zero-field susceptibility at zero temperature is found to be finite for both two and three dimensions. The anomalous slow relaxation observed in simulations of spin glasses is traced back to the high ground-state degeneracy. Two sources of anomalous relaxation are identified: (i) disappearance of large domains with (on the average) wrong orientation of the order parameter; and (ii) diffusion of order parameter orientation in a finite system with continuous symmetry of the order parameter. Case (i) is exemplified by computations on a two-dimensional Mattis spin glass model. We find that the observations of Bray and More cannot be maintained asfirm evidence against a phase transition, althoughfirm evidence in favor of a transition is also lacking. With the hypothesis that a transition occurs, a cluster description is used to derive some relations characterizing its singularities. Our Monte Carlo simulations give the field-dependence of the Edwards-Anderson order parameterq atTf and give Chalupa's exponentδq as about 5 in two dimensions. Our scaling theory shows that a spin-glass transition may occur with finite susceptibilityχq, which offers a possible interpretation of the series-expansion results of Fisch and Harris.