Spin and energy coupling in the Ising model with a transverse field: One dimension,T=∞

The dynamics of the one dimensional Ising model with a transverse field is studied in the limit T = ∞. Numerical studies of the classical chain and exact calculations for the spin $\text{1}\text{2}$ chain indicate the presence of an energy density term in the dynamic spin susceptibility along the direction of the field.     

Oscillations of local magnetization in the semi-infinite antiferromagnet

The presence of the boundary in the semi-infinite antiferromagnetic chain is shown to produce spatial oscillations of the local magnetization. A Green function technique is used to obtain the exact form of these Friedel-type oscillations within the spin $\text{1}\text{2}$XY model. It is shown that a non-zero external magnetic field is the necessary condition for the oscillating behavior of the local magnetization. Comparison is made with an earlier treatment of the infinite chain with a weak perturbation potential     

Absence of the second-order phase transitions in the dimerized Ising chains with spin larger than 12

A general spin S Ising chain interacting with a single phonon mode of the harmonic lattice is studied. The thermodynamics of the spin system is calculated exactly for S = 1, $\text{1}\text{2}$ and $\text{3}\text{2}$, while self-consistent equations for the induced lattice distortions are derived. It is demonstrated that for S >$\text{1}\text{2}$ there is no second-order phase transition, in contrast to the case S = $\text{1}\text{2}$ which was proved to have a tricritical point. This is found to cohere with the previous studies of the dimerized magnetic model chains.     

Excitations in the antiferromagnetic Heisenberg chain

Non-singlet excitations of the antiferromagnetic Heisenberg chain of N atoms with spin $\text{1}\text{2}$ are examined. It is found that the energy of the lowest lying excitations for total spin S and wave number q converges to $\text{(}\text{π}\text{2}\text{)|}\text{sin}\text{q |}\text{as}\text{N → ∞,}\text{if only}\text{S?}\text{ln}\text{N}$.     

Measurement of the spin-depairing interaction in Sn0.75Eu0.25Mo6S8

Mössbauer effect measurements of the ¹⁵¹ Eu resonance in the Chevrel phase superconductor Sn_0.75Eu_0.25Mo₆S₈ have been used to obtain the temperature dependence of the Eu paramagnetic relaxation rate. This consists of a temperature independent part arising from spin-spin interactions and a part linear in T due to the Korringa process. From the slope we obtain $\text{I}$ = 0.0033/Eu atom-spin, where $\text{I}$ is the exchange coupling between the rare-earth spin and the conduction electron spin, and N(E_F) is the local density of states. This value is roughly one order of magnetude lower than that measured in binary superconductors, and accounts for the very weak dependence of the transition temperature on magnetic impurity concentration.     

Temperature-induced local magnetic moments in CoSe2-59Co NMR

From the temperature dependences of the ⁵⁹Co Knight shift and the nuclear spin-lattice relaxation rate in the exchange-enhanced paramagnetic metal CoSe₂, it is shown that the amplitudes of the temperature-dependent spin density fluctuations are saturated at $\text{T}{}^1\text{= 130 K}$. This fact indicates that there exist local moment type fluctuations above T¹. The results obtained from the present NMR investigation are in general accord with the predictions based on the general theory of spin fluctuations in itinerant electron systems developed recently by Moriya and Takahashi.     

Field dependence of the ESR “g-shift” in superconductors

Electron spin resonance (ESR) measurements at 36 GHz (Q-band) in $\text{Gd:}\text{CeRu}{}_2$ show a different g-value in the superconducting phase than previously published data measured at 9 GHz (X-band). This frequency dependent “g-shift” is attributed to the spatial change in local field in the vortex state for different external fields.     

Spin alternation in one-dimensional exchange-coupled systems: Magnetic behaviour of the (12−1)N chain

We report on the magnetic behaviour of exchange-coupled closed chains (rings) of increasing length made of two alternating spin sublattices $\text{S}{}_{\mathrm{<mtext>a</mtext>}}\text{=}\text{1}\text{2}\text{, S}{}_{\mathrm{<mtext>b</mtext>}}\text{= 1}$. Taking into account the geometrical and spin space symmetries of such syste the problem is shown to be tractable up to 10 spins for distinct values of the g_a/g_b ratio between Landé factors; the results are discussed for an antiferromagnetic coupling. The limiting behaviour for the infinite chain is determined by extrapolation of the data obtained for finite rings. At very low temperatures, the analogy with the regular $\text{S =}\text{1}\text{2}$ ferromagnetic chain is underlined.     

Theory of localized magnetic moments in metals I finite cluster approach

The origin of localized magnetic moments formation in metals is investigated theoretically using a self-consistent local spin density molecular cluster approach. Clusters with up to 55 atoms are employed to describe isolated impurity local moment behavior in the cases of Fe$\text{Ag}$ and Fe$\text{Pd}$. Densities of states and spin magnetic moments were determined and compared with results of spectroscopic (notably photoemission) and magnetization measurements, respectively. In the case of a noble metal host, the spin magnetization density is found to be highly localized around the Fe site; the iron moment is ≈ 3.9μ_B and the polarization of the host Ag atoms is small. In the case of a transition metal host, the iron moment is ≈ 3.2 μ_B but here the strong hybridization of the Fe-3d and Pd-4d states results in a large induced magnetic moment in the host PD metal — in essential agreement with experiment for this giant moment system.     

Equivalence between a spin 12 dimerized XY chain and two independent Ising chains in transverse fields

It is shown that the hamiltonian representing a 1-D spin $\text{1}\text{2}$ dimerized XY chain with an even number of sites can be transformed into a sum of two hamiltonians representing two orthogonal and non coupled Ising chains in transverse fields. Special cases are discussed.     

A new representation for the density matrix: (II). Equations of motion

The equations of motion for the new SU(n) parameters representing the density matrix for arbitrary spin are derived. It is shown that for a class of hamiltonians which are diagonal, the equations are exactly solvable by using the device of combining the SU(n) parameters in pairs using the Pauli spin matrix σ_y. It is also shown that using the correspondence relations between the SU(n) parameters and the spherical tensor moments, it is possible to picture the time evolution of the tensor parameters using the explicit solutions for the SU(n) parameters. This procedure has been illustrated by discussing in detail the problem of spin-1 and $\text{spin}\text{-}\text{3}\text{2}$ systems interacting with an external magnetic field and subjected to quadrupole interactions.     

Intermolecular spin-spin interactions in liquids

Kinetic equations for the one-particle spin density matrix for a system of magnetic molecules in a liquid interacting with one another through intermolecular spin-spin forces are derived under the following assumptions: a) “internal” relaxation processes are ignored: b) at t = 0 the entire density matrix is factorized,$\text{σ}\text{(0) = Π}{}_1\text{σ}{}_1\text{(0),}\text{σ}\text{(0)}$ being the spin density matrix of the matrix of the with molecule; c) random motions of particles in the liquid are considered as a classical markovian process. The finite set of integrodifferential equations, with rank equal to the number of different kinds of the molecules, is obtained for the matrices $\text{〈}\text{σ}{}_1\text{(t)〉}$ averaged over all the possible trajectories of the molecules in the liquid.The equation of motion for the magnetic moment, nonlinear in magnetization, is written for a system of identical molecules with $\text{S =}\text{1}\text{2}$ in the low-concentration limit. This equation is used to investigate the form of the equilibrium magnetization-recovery curve.     

Non-string two-magnon configurations in the isotropic Heisenberg magnet

By means of the $\text{1}\text{N}$ expansion we study the Bethe-ansatz equations for two-magnon states in the one-dimensional isotropic Heisenberg spin chain of N spins $\text{1}\text{2}$. A qualitative picture of complex solutions for N → ∞ is obtained which substantially disagrees with the string hypothesis. For example, the solutions $\text{λ}{}_{\mathrm{<mtext>1,2</mtext>}}\text{= x ±}\text{i}\text{y, x ～ N,y ～}\text{N}$ are found, whereas according to the string hypothesis $\text{y →}\text{1}\text{2}$ if N → ∞.     

Spin relaxation in metals at very low temperatures

A general theory of spin relaxation in metals is developed from a statistical mechanical point of view. The theory is valid for all temperature domain and the multiple-time characteristics of the relaxation process are completely determined: The relaxation times are strongly dependent on the temperature and magnetic field. At very low temperatures, behaviours of the relaxation times are quite different from the usual ones showing a saturation effect. Temperature varations of the relaxation times for I ? 1 (I the magnitude of spin) are qualitatively different from those for $\text{I =}\text{1}\text{2}$. Namely, in the former case, the largest relaxation time has a maximum as a function of inverse temperature.     

X-ray photoelectron spectra of iron complexes: Correlation of iron 2p satellite intensity with complex spin state

Metal and ligand core-level spectra have been obtained for 36 iron complexes which possess a variety of ligands including carbonyl, nitrosyl, triphenylphosphine,o-phenylenebis(dimethylarsine), halides and pseudohalides. Formal metal oxidation states range from ? 1 to + 3, and complex spin states represented in the series include 0, $\text{1}\text{2}$, $\text{3}\text{2}$, 2 and $\text{5}\text{2}$. A clear correlation between complex spin state and satellite intensity in the Fe 2p spectra is found. The satellite intensities observed experimentally are in approximate quantitative accord with those predicted by a “spin flipping” model. Although the present analysis does not provide a definitive choice between the “sudden approximation” and “spin flipping” models, the agreement between experimental satellite intensities and the intensities predicted by the “spin flipping” model suggests that such a mechanism can be important in the satellite process.     

Variation of the local field through the liquid-vapour interface

We derive an integral equation for the self-consistent local field E^loc(z) within an inhomogeneous non-polar fluid, with particular application to the liquid-vapour interface. Approximate solutions are given for the cases of induced atomic dipoles oriented perpendicular and parallel to the interface. For the perpendicular case we relate the average field to the local field and thus obtain an equation for the static dielectric constant ?(z) in terms of the density profile n(z). The departures of the local field from Lorentz form $\text{E}{}^{\mathrm{<mtext>ext</mtext>}}\text{/(1 + (}\text{8}\text{3}\text{)παn(z))}$ and of the dielectric constant from the Clausius-Mossotti form ($\text{1 + (}\text{8}\text{3}\text{)πan(z))/(1 ? (}\text{4}\text{3}\text{)παn(z))}$ are shown to be small. For the parallel case we discuss fringing of the external field and show that the dipoles align themselves with the average field, not the external field. The departure of the local field from $\text{E}{}^{\mathrm{<mtext>ave</mtext>}}\text{/(1 ? (}\text{4}\text{3}\text{παn(z))}$ is shown to be small.     

Implications of the τ and b spins for theories of quarks and leptons

We argue that the present evidence that the spin of the τ is $\text{1}\text{2}$ is circumstantial, and that a spin of $\text{3}\text{2}$ is not excluded. If the τ spin were $\text{3}\text{2}$, it would have important implications for the idea that leptons and quarks were composite states, perhaps allowing an explanation of the existence of three generations. Supergravity ideas could also be affected. Similar ideas suggest the b-quark could have spin-$\text{3}\text{2}$; we give several ways to test this.     

NMR relaxation at low temperature in one dimensional antiferromagnets: Comparison between S = 12 and S = 52

The proton spin-lattice relaxation time T₁ has been measured at low temperatures in spin $\text{5}\text{2}$ (CH₃)₄NMnCl₃ (TMMC) and spin $\text{1}\text{2}$ CuCl₂2NC₅H₅ (CuPC). The two systems have very different temperature dependences which we attribute to the different spin values.     

Semi-microscopic calculation of the level density in spherical nuclei

The level density at the neutron binding energy for 90 spherical nuclei in the interval 50 < A < 205 is calculated by a method of direct counting of the number of states taking into account collective vibrational excitations. The results of calculations are in satisfactory agreement with the experimental data. The difference in the level density of doubly even and odd-A nuclei is correctly described. The effect of nuclear vibrations on the level density is studied, and it is shown that the account of them leads to an increase in the density by a factor of 1.5–10 and to a decrease in the density fluctuations. It is also studied how the level density depends on excitation energy. With increasing excitation energy, our results come nearer the corresponding values obtained by the statistical model. It is found that the density fluctuations decrease with increasing excitation energy but remain still strong at the neutron binding energy for nuclei with A = 50–70 and for nuclei around closed shells. The density ρ(I^π) is studied as a function of spin and parity. It is shown that at the neutron binding energy the ratio $\text{ρ(I}{}^{\mathrm{+}}\text{)}\text{ρ(I}{}^{\mathrm{?}}\text{)}$ is different from unity for the majority of nuclei. This difference is especially striking for ⁵⁷Fe and ⁵⁸Fe nuclei.