Effect Of Paramagnetic Impurities Research Articles

On the BCS theory of paramagnetic impurities in anisotropic superconductors

We develop a theory based on BCS theory which treats the effect of paramagnetic impurities in an anisotropic superconductor. It is found that in a separable model for the order parameter its anisotropy is expected to increase with increasing concentration of paramagnetic impurities. The critical temperature, the order parameter, and the quasiparticle density of states are computed numerically from our theoretical results. We find that there exists a regime which is superconducting by virtue of the fact that the paramagnetic impurities make the material highly anisotropic. In this regime the critical temperature can be reduced rapidly to zero by adding dilute concentrations of normal scattering impurities.

The effect of paramagnetic impurities on EPR linewidth in KMnF3. Experimental and theoretical studies

The EPR linewidth dependence on temperature and impurities concentration in KMn1-xMexF3 single crystals (where Me is Ni2+, Co2+, Fe2+) is investigated both experimentally and theoretically. The theoretical investigation is performed with the use of a nonequilibrium statistical operator method proposed by Zubarev (1971). The microscopic kinetic equations of motion for the magnetisation of the host and impurities subsystems are derived and the width of the resonance line is calculated. The theoretical results and compared with the experimental data.

Paramagnetic impurities in strong coupling superconductors

We have calculated the effect of paramagnetic impurities on strong coupling superconductors. Imaginary axis solutions of the Eliashberg gap equations with a spin-flip term form the basis of our work. We compute the variation of the critical temperature (T/sub c/) with increasing impurity concentration, the functional derivatives of T/sub c/, the specific-heat jump, the critical-field deviation function, and the tunneling characteristics which we compare with the results of Abrikosov-Gorkov theory. In all cases important strong coupling corrections are obtained.

Properties of an itinerant antiferromagnet with paramagnetic impurities

The effect of paramagnetic impurities on the Néel temperature of an intinerant antiferromagnet is described. Numerical calculations show that a low concentration minimum, qualitatively similar to that observed in Cr Co, is obtained in this model only when the coupling of the impurity to the spin-density-wave is included.

Self-diffusion studies in solids using nuclear magnetic resonance techniques

N.m.r. measurements of spin–lattice relaxation time, T1, and spin–spin relaxation time, T2, give valuable information on diffusive motion in a wide variety of solids when self-diffusion provides the dominant relaxation mechanism. These measurements however have a limited useful range. As the mean time, τ, between jumps increases, the effects of paramagnetic impurities can dominate T1 and T2 reaches a constant rigid lattice value. These limitations can be overcome by measuring the spin–lattice relaxation time in the presence of an r.f.field, T1ρ, or the spin–lattice relaxation time in the dipolar field, T1D. Recent theoretical developments often allow τ to be evaluated with reasonable accuracy and if the jump distance is known then the self-diffusion coefficient, D, can be calculated. Paramagneticimpurity effects can also cause anomalous results in the solid in the fast diffusion range. The technique and its limitations will be illustrated by recent work on 19F– diffusion studies in fluorite lattices. Measurements of these relaxation times provide information at the microscopic level on the atomic motion and thus can indicate the dominant diffusion mechanism.

Natural abundance nitrogen‐15 n.m.r. spectroscopy. Spin–lattice relaxation in organic compounds

AbstractThe small negative magnetogyric ratio (γ) of the 15N nucleus decreases the efficiency of 15N1H dipole‐dipole relaxation to about 25% of that for an analogous 13C nucleus. This may lead to greater competition from other relaxation mechanisms in 15N n.m.r. and consequent partial or total quenching of the negative nuclear Overhauser effect (NOE). In unfavorable circumstances nulling of the 15N resonance can occur. Previous 15N relaxation studies have examined isotopically enriched, low molecular weight compounds. The present study examines several small to intermediate size organic compounds containing nitrogen at natural isotopic abundance. In contrast to some of the earlier studies, 15N1H dipolar relaxation was found to be dominant for protonated nitrogen atoms, even for two tertiary nitrogens (the tertiary amine nitrogen in 1,2,3,4,6,7,12,12b‐octahydroindolo[2,3‐a] quinolizine and the oxime nitrogen in 3‐methyl‐2‐pentanone ketoxime). The magnitude of the NOE and the moderate value of T1 indicate effective dipolar relaxation from neighboring but not directly bonded protons in these cases. Nitro groups were found, as expected, to have predominant contributions from non‐dipolar mechanisms, and in one case (2‐methyl‐2‐nitro‐1, 3‐propanediol) signal nulling (NOE of η = −1) was observed. The effect of paramagnetic impurities was demonstrated for ethanolamine, which contains a basic nitrogen. In this case T1DD(15N1H) = 4·3 s; added Ni(acac)2 at 1 × 10−4 Molar reduced the 15N T1 to 0·065 s and consequently the NOE to η = 0.

Effect of paramagnetic impurities on relaxation of nuclear spins in the superconductors

The ratio of nuclear spin relaxations rates R s/ R n in the superconductors is calculated for different temperatures and concentrations of paramagnetic impurities, on the base of exact formulae for the density of electronic states and the factor of coherence.

Effect of Paramagnetic Impurities on Nuclear Spin-Lattice Relaxation: A Numerical Study

The effect of paramagnetic impurities on the nuclear spin-lattice relaxation time in metals is investigated by applying the theory of Blume and Hubbard in an appropriately generalized form. The calculations are carried out at finite temperature and magnetic field strength assuming that the Ruderman-Kittel-Kasuya-Yosida interaction couples the impurity spins. The effect of approximating this interaction by $\frac{1}{{r}^{3}}$ is examined as is the temperature, magnetic field, and impurity-concentration dependence of the relaxation time. Quantitative results are obtained using parameters appropriate to the rare-earth alloy ${\mathrm{La}}_{1\ensuremath{-}c}{\mathrm{Gd}}_{c}{\mathrm{Al}}_{2}$ and a comparison is made with experiment; agreement is generally good.

Absorption lineshape of highly polarized nuclear spin systems

We have studied both theoretically and experimentally the variation of NMR absorption lineshape as a function of nuclear polarization in systems with one spin species. General expressions are given for the first and second moments M 1 and M 1, as well as the values of M 3 and M 4 in the special case of spherical samples of spins 1 2 forming a simple cubic lattice. The influence of paramagnetic impurities on the line shape is analyzed, in detail. Measurements of M 3 in spherical samples of CaF 2 polarized up to 90% by the solid effect confirm the theory. In such samples the second moment, corrected from the effect of paramagnetic impurities, follows the simple law: M 2( p) = M 2(0) (1− p 2). This has been used to perform an absolute calibration of fluorine polarization with an accuracy between 3 and 5%.

Theoretical Study of Nuclear-Spin-Lattice Relaxation via Paramagnetic Centers

The effect of paramagnetic impurities with local moments on the nuclear-spin-lattice relaxation is studied by using the method of Blume and Hubbard. An average over random impurities is taken on the equations of motion for nuclear and electron spins in the low-concentration limit. An integral equation for the electron-spin correlation function is obtained and solved self-consistently. The correlation function behaves like $\mathrm{exp}[\ensuremath{-}{(\frac{t}{{\ensuremath{\Gamma}}_{1}})}^{2}]$ for small $t$, $\mathrm{exp}[\ensuremath{-}(\frac{t}{{\ensuremath{\Gamma}}_{2}})]$ for intermediate $t$, and $\mathrm{exp}[\ensuremath{-}{(\frac{t}{{\ensuremath{\Gamma}}_{3}})}^{\frac{1}{2}}]$ for large $t$. The nuclear-spin correlation function is calculated from the electron-spin correlation function. The dependence of the spin-lattice relaxation time on the concentration of impurities, magnetic field; and temperature is obtained. Our calculations are discussed in terms of results obtained from the phenomenological approach.

Effect of Paramagnetic Impurities on Josephson Currents through Junctions with Normal-Metal Barriers

The present paper deals with a study of the effect of paramagnetic impurities on zero-bias Josephson currents through junctions with normal-metal barriers at $T=0\ifmmode^\circ\else\textdegree\fi{}$K. The ratio of the barrier supercurrent of the impure-SNS (superconductor-normal-metal-superconductor) junction to that of the pure-SNS junction is found to be equal to $1\ensuremath{-}\ensuremath{\zeta}$, where $\ensuremath{\zeta}$ is a measure of the impurity concentration. For $\ensuremath{\zeta}<1$, the Josephson current is nonzero and decreases with increase of impurity concentration, but in the gapless region (${\ensuremath{\omega}}_{g}=0$) when $\ensuremath{\zeta}>~1$, the current is zero for $\ensuremath{\zeta}=1$ and then becomes negative for $\ensuremath{\zeta}>1$. At $\ensuremath{\zeta}=0$, the result is in exact agreement with that of Ishii for the pure case.

Tunneling into Superconducting Films in a Magnetic Field

Tunneling experiments were performed on thin superconducting films in the presence of a magnetic field. The experiments were done at ${\mathrm{He}}^{3}$ temperatures on tin and tin-indium alloy films with thicknesses between 600 and 2000 \AA{}. As expected theoretically, the effect of the field on the density of states is, for dirty films, similar to the effect of paramagnetic impurities with the square of the magnetic field playing a role analogous to the paramagnetic impurity concentration. The data are compared with the theoretical results of Maki for the limit of zero mean free path, and agreement is fair. The difference between these results and those of this experiment is attributed to the finite mean free path. Str\"assler and Wyder have calculated the field dependence of the density of states for small particles with arbitrary mean free path. We find that their calculations are in good agreement with experiment.

Spatial Variation of the Order Parameter in the Vicinity of a Paramagnetic Impurity

In view of the strong effects of paramagnetic impurities on the properties of a superconductor it is interesting to study how the order parameter varies spatially in the vicinity of a paramagnetic impurity. Near the transition temperature one can derive an integral equation which describes the spatial variation of the order parameter Δ(r). It is shown that the variation extends over the distance of the order of the coherence length ξ0 ∼vF/Tc from the impurity and that Δ(r) is approximately given by Δ(∞) [1 - {3π/ 7 ζ(3)} (xC / ln xC) (a2 / r2) exp {-(2πT / vF) r }, where a is the scattering length of the exchange potential and xC is a constant related to a. Abrikosov and Gor'kov calculated the effect of paramagnetic impurities on the transition temperature using the average value of Δ. A small correction to their result due to the spatial variation of Δ(r) is calculated in the limit of low impurity concentration.

Effect of Paramagnetic Impurities on the Superconducting Behavior of Cubic Molybdenum Carbide

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Effect of Paramagnetic Impurities on Proton Spin—Lattice Relaxation Time in Methane

Measurements of the proton spin—lattice relaxation time T1 were carried out in samples of CH4 from 110°—90°K having an oxygen concentration of 1.08% and 2.54%, respectively. The results verify the inverse proportionality of T1 and oxygen concentration.

Tunneling Density of States for a Superconductor Carrying a Current

A current flowing in a superconducting film has a tendency to break pairs similar to the effect of paramagnetic impurities in a superconductor. The effect of the current on the tunneling density of states for a normal-superconducting tunneling junction has been computed by the Green's-function method of Abrikosov, Gorkov, and Maki, and found to be identical (for a short mean free path) to that of paramagnetic impurities. A simple relationship between the current parallel to the junction and the equivalent paramagnetic-impurity concentration is derived. Passing various amounts of current through the sample in the one experiment gives the same information as is obtainable in the other experiment only by preparing different samples with various impurity concentrations.

Properties of Superconducting Alloys Containing Paramagnetic Impurities

We have made some additional calculations on the effects of paramagnetic impurities in superconductors, using the Abrikosov-Gor'kov theory as our starting point and taking full advantage of the information contained in the Green's function of the system. The density of states in energy has been computed for different values of the inverse collision time for exchange scattering $\ensuremath{\Gamma}$. The (half) excitation energy gap ${\ensuremath{\Omega}}_{G}$ (as distinguished from the order parameter $\ensuremath{\Delta}$) is defined to be the energy at which the density of states vanishes. The temperature-dependent order parameter has been computed for different values of $\ensuremath{\Gamma}$, and from this, the behavior of ${\ensuremath{\Omega}}_{G}$ ($T$) is determined. A comparison with tunneling experiments shows a disagreement of about 30%. The thermodynamic properties of the system follow from the density of states; the critical field and the discontinuity in the specific heat at the critical temperature are calculated in considerable detail. Expressions for the penetration depth and complex conductivity are obtained, and numerical results are presented for the case $T=0\ifmmode^\circ\else\textdegree\fi{}$. The real part of the conductivity at $T=0\ifmmode^\circ\else\textdegree\fi{}$ is shown to be zero for frequencies less than $2{\ensuremath{\Omega}}_{G}$ and proportional to the square of the density of states for vanishingly small frequencies in the gapless region of impurity concentrations.

Magnetic behavior of very small superconducting particles

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.

Effect of Paramagnetic Atoms on the Energy Gap of Superconductors

The effects of paramagnetic impurities in superconductin films, and of paramagnetic films superimposed on superconducting films, on the transition properties and superconducting energy gaps of these superconducting films are examined. The effects are studied by measuring the d-c resistivity (to determine the transition temperature) and the tunneling supercurrent (to determine the energy gap or density of states). (T.F.H.)