Electron Spin Correlation Research Articles

Nuclear Spin-Lattice Relaxation Study in Spin Glass CoxGa1-xIntermetallic Compounds

The spin echo decay of 59 Co associated with nonmagnetic Co atom in CoGa compounds was measured at 9, 5 and 2.5 MHz in wide temperature range through the spin glass transition temperature, T g . At T ≫ T g , nuclear spin-lattice relaxation time, T 1 , was also measured. Analyzing the spin echo decay and T 1 , we have deduced the average nuclear spin-lattice relaxation rate, , to the system of localized moments, which shows a progressive peak like the case of the critical slowing down near T g . The temperature at the peak is somewhat lower than T g measured by magnetic susceptibility in zero field. increases rapidly with decreasing the resonance field near the temperature at the peak. Following Chen and Slichter, the electron spin correlation time, τ m was estimated from and the integrated intensity. τ m - shows a slowing down of orders three at the transition.

Critical fluctuations in a 2D Ising system

RbFeCl3·2H2O consists of layers of weakly coupled linear chains with an interlayer exchange which is another order of magnitude smaller. The low-temperature magnetic behaviour is well described with the 2D S′ = 12 rectangular Ising model. Mössbauer spectra are presented from a broad region around the Néel temperature, which is 12.08 K. Towards the ordering temperature an increasing line broadening is evident. Above the ordering temperature a paramagnetic and a magnetic phase apparently coexist. It will be shown that a model for a distribution of ordering temperatures does not describe the observed spectra well. The possible occurrence of superparamagnetic effects is discussed. Although this mechanism cannot be excluded, an even better explanation can be found within the relaxation model of Blume for a fluctuating hyperfine field, arising from an effective S′ = 12 doublet. The general features of the observed relaxation phenomena are well reproduced by this model. We attribute the decrease in the fluctuation rate of this effective field to critical slowing down of the electron spin correlations.

The angular dependence of the proton relaxation rate in CuSO 4[rad]5H 2O: Deviations from the point-dipolar model

The electron-proton interaction has been determined experimentally for a proton in CuSO 4 5H 2O. Deviations from a simple point-dipolar interaction are found. These deviations are attributed to the spatial extension of the copper ion and partially covalent bonds with the surrounding ligands. The experimentally determined interaction tensors are used in the analysis of the angular dependence of the proton relaxation rate T −1 ln. It is found that this approach gives a better description of the relaxation results in terms of electron spin correlation functions, and therefore permits more reliable conclusions with respect to the dynamics of the S = 1 2 antiferromagnetic chain system in CuSO 4 5H 2O.

Nmr in Liquid Semiconducting Sex Te1-x

ABSTRACTFor x > 0.2, liquid SexTel-x alloys are semiconducting near the liquidus and have strongly temperature–dependent magnetic susceptibilities. We have studied the electronic paramagnetic centers by measuring their influence on the nuclear magnetic resonance shift and relaxation times of 77 Se and 125 Te in liquid Se .5Te.5. We find that the electronic centers are highly localized, their average hyperfine contact interaction with 125Te is three times that with 77Se, and the electronic spin correlation time is of order 1 psec at 350°C and decreases with rising T.

Magnetic field effect on the hyperfine-induced electron spin motion in radicals undergoing diamagnetic–paramagnetic exchange

A semiclassical description of the hyperfine-induced spin motion of radical pairs suggested recently [K. Schulten and P. G. Wolynes, J. Chem. Phys. 68, 3292 (1978)] has been generalized to arbitrary magnetic field situations. Analytical expressions for the elements of the electron spin correlation tensor <S(o) S (t) ≳ averaged over all nuclear spin configurations are derived and applied to calculate the time evolution of the electron spin state of radical pairs initially prepared in a singlet state. The treatment includes the possibility that the radicals undergo a diamagnetic–paramagnetic exchange reaction. The effect of such exchange on the magnetic field dependence of the radical pair (triplet) recombination is predicted.

Nuclear Spin Lattice Relaxation in Paramagnetic Fluorosilicates

Nuclear spin lattice relaxation time T1 of 19F have been studied in MSiF6 · 6H2O with M2+ = Fe2+, Co2+, Ni2+ and Cu2+ from 150 to 300 K The derived electron spin correlation times are mostly determined by rapid electron spin lattice relaxation and not by exchange spin flips. The electron spin lattice relaxation in CoSiF6 · 6H2O seems to follow an Orbach process with excited state at 625 cm-1. Relaxation times T1ρ in the rotating frame give information on molecular motion and on the structural phase transition in CoSiF6 · 6H2O.

Semiclassical description of electron spin motion in radicals including the effect of electron hopping

The coherent electron spin motion in radicals induced by the hyperfine coupling to nuclear spins is described semiclassically. The nuclear spins are treated as constant classical vectors around which the electron spin precesses. The ensemble average over all nuclear spin configurations is taken yielding the electron spin correlation tensor <S(0)S(t) ≳. Borrowing from the theory of rotational diffusion the effect of electron hopping between molecules on the spin correlation tensor is described. The treatment is applied to the time evolution of the electron spin state of a radical pair initially prepared in a singlet state.

Effect of pair correlation on the NMR of powdered paramagnets

Temperature and field variation studies of the $^{31}\mathrm{P}$ NMR linewidths in the polycrystalline paramagnets SmP${\mathrm{O}}_{4}$ and PrP${\mathrm{O}}_{4}$ indicate that in the former the linewidth decreases with lowering of temperature and is virtually field independent, whereas in the latter, the width increases with decrease of temperature and varies directly as the field. This behavior of PrP${\mathrm{O}}_{4}$ is typical of a powdered paramagnet, whereas the behavior of SmP${\mathrm{O}}_{4}$ is anomalous and has been shown to arise from the unusual magnetic properties of ${\mathrm{Sm}}^{3+}$. The effective diamagnetic character of SmP${\mathrm{O}}_{4}$ provided a unique situation wherein anisotropic broadening effects resulting from powdered structure could be avoided and line narrowing arising from the electron-spin pair correlation effect could be observed. Though PrP${\mathrm{O}}_{4}$ apparently behave behave differently with respect to shifts and linewidths, the exchange interaction has been shown to be antiferromagnetic in nature for both.

Electron spin distribution and molecular dynamics of aromatic hydrocarbon radical anions studied by1H and2D N.M.R.

The 1H N.M.R. spectra of the anions of anthracene, pyrene and triphenylene and the 2D N.M.R. spectra of the anions of anthracene-d10 and partly, randomly deuterated triphenylene have been measured in ethereal solutions. The hyperfine splitting constants derived from the measured Fermi contact shifts are presented and compared with E.S.R. data and predictions from theory. From the measured 1H and 2D linewidths the electron spin and rotational correlation times have been calculated. It is shown that the derived rotational correlation times are not very sensitive to anisotropic rotation.

Alkali N.M.R. experiments on the radical ion pairs of biphenyl and fluorenone

Line widths in the 6Li, 7Li, 23Na, 39K, 85Rb, 87Rb and 133Cs N.M.R. spectra of solutions of the alkali salts of biphenyl and fluorenone are reported as a function of solvent and temperature. From a numerical analysis of the room temperature data the contribution of the various relaxation mechanisms to the line widths are established. It is shown that the results are consistent with the observed solvent and temperature dependence of the line widths. Values of the electron spin correlation time are obtained and a value of 1·6 ± 0·4 A is found for the ‘Van der Waals radius’ of the biphenyl anion. Line width expressions for the static and the dynamic ion pair model are presented. It is demonstrated that the static ion pair model applies to solutions of caesium biphenylide. Semi-empirical rules are presented concerning the importance of various relaxation mechanisms for the different alkali nuclei in the type of solution studied here.

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.

Experimental and Theoretical Study of Perturbed Angular Correlations for a Rare-Earth Localized Moment in Iron

In order to study the static and dynamic properties of a localized moment in a ferromagnet, the temperature-dependent hyperfine interaction of dilute thulium in iron was measured between 4.2 and 450\ifmmode^\circ\else\textdegree\fi{}K. Time-integral perturbed-angular-correlation (IPAC) experiments were performed simultaneously on two cascades in $^{169}\mathrm{Tm}$, using a sum-coincidence technique. Samples were prepared by implantation of radioactive $^{169}\mathrm{Yb}$ with an isotope separator. To analyze the results, the $\ensuremath{-}{J}_{\mathrm{sf}}\stackrel{\ensuremath{\rightarrow}}{\mathrm{s}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}$ interaction is approximated by a molecular field model, in which the exchange field ${H}_{\mathrm{exch}}$ between Tm and Fe is proportional to the host magnetization. The electronic Larmor frequency is then proportional to the Brillouin function representing the rare-earth susceptibility $〈{J}_{z}〉$. Above \ensuremath{\sim}200\ifmmode^\circ\else\textdegree\fi{}K, the IPAC data may be interpreted in terms of the generalized Abragam-Pound theory. Below \ensuremath{\sim}200\ifmmode^\circ\else\textdegree\fi{}K, however, the electron-spin correlation time ${\ensuremath{\tau}}_{c}$ is of the order of the nuclear lifetime ${\ensuremath{\tau}}_{N}$, and the Abragam-Pound theory is not appropriate. We describe the application of a more general theory of perturbed angular correlations (Ref. 7), whose validity does not depend on the condition $\frac{{\ensuremath{\tau}}_{c}}{{\ensuremath{\tau}}_{N}}\ensuremath{\ll}1$. Exact analytical expressions are obtained assuming negligible quadrupole interaction, an axially symmetric magnetic hyperfine interaction, and exponential decay of the electron-spin correlation functions (whose amplitude is defined by the molecular field model). Experimental results above \ensuremath{\sim}20\ifmmode^\circ\else\textdegree\fi{}K are in good over-all agreement with this analysis. A strong temperature dependence of the hyperfine field is observed (about 600% variation over the temperature range). The deduced exchange field between Tm and Fe at 0\ifmmode^\circ\else\textdegree\fi{}K is 2.5\ifmmode\pm\else\textpm\fi{}0.5 MOe. It is found that ${\ensuremath{\tau}}_{c}(300\ifmmode^\circ\else\textdegree\fi{}\mathrm{K})\ensuremath{\sim}5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$ sec, in agreement with the Korringa limit, and results are consistent with a $\frac{1}{T}$ dependence of the electron correlation time. Below \ensuremath{\sim}20\ifmmode^\circ\else\textdegree\fi{}K, results of the calculation are insensitive to the value of ${\ensuremath{\tau}}_{c}$; hyperfine field values are then deduced by assuming a static magnetic interaction. The hyperfine field at 0\ifmmode^\circ\else\textdegree\fi{}K is 5.60\ifmmode\pm\else\textpm\fi{}0.15 MOe. The discrepancy between this value and the sum of the free-ion field and the contact term (\ensuremath{\sim}7.5 MOe) may be ascribed to ion-implantation problems or to crystalline electric field effects.

Electron spin correlations in copper

Values of the dipolar spin-lattice relaxation times, T 1dd, of the nuclei in copper metal between 4.2°K and 170°K are reported. The results are discussed in terms of the presence of perturbing quadrupole effects associated with defects in the lattice structure of the metal and a temperature independent value of T 1dd T is deduced.

Range and Spatial Variation of the Kondo Spin-Compensated State

Spin compensated state of localized magnetic impurity moment in space, calculating size range of magnetic impurity spin/conduction electron spin correlation function

Mössbauer-Effect Study of Erbium Spin Relaxation in Magnetically Ordered Compounds

The 166Er hyperfine fields, Er3+ magnetic moments, and electronic spin correlation times in ferromagnetic erbium-aluminum intermetallic structures have been studied between 1.5° and 80°K using the Mössbauer effect of the 80.6 keV gamma rays of 166Er. The spin correlation times deduced from both the rate equation model and the Wegener formula follow approximately a T−1 temperature dependence below TC. Above TC the spin correlation times of about 5 × 10−11 sec decrease by nearly an order of magnitude and are found to be rather sensitive to the distinct assumptions made on the electronic ground-state multiplet and attributed Sz distribution function in the different theoretical approaches.

Nuclear Zeeman splitting measured through the Mössbauer effect

From the Zeeman hyperfine splitting in 57Fe, the effective magnetic field acting on the nucleus can be derived. It is shown that the Mössbauer technique is particularly suited to study the sublattice magnetization in rather complicated magnetic systemst An important parameter for the observation of the Zeeman splitting is the product of the nuclear Larmor frequency and the electron-spin correlation time. The apparens collapse of the hyperfine splitting observed in a few cases can be interpreted in term. of very rapid relaxation.

Nuclear Relaxation as a Probe of Electron Spin Correlation

Adiabatic demagnetization of a nuclear spin system produces a state in which there is considerable correlation between neighboring spins. This correlation affects the nuclear relaxation rate and, in metals, where nuclei relax via interaction with conduction electrons, can be used as a probe of spin correlation in the electronic system. For a given lattice temperature the ratio $\ensuremath{\delta}$ of low- to high-field relaxation rates can be written in the form $\ensuremath{\delta}=2+\ensuremath{\eta}$, where $\ensuremath{\eta}$ is essentially the electron spin correlation function at the nearest neighbor distance. $\ensuremath{\eta}$ can also be related to the nonlocal electron spin susceptibility.For noninteracting electrons, calculated values of $\ensuremath{\eta}$ are more than an order of magnitude too small to explain the observations ($\ensuremath{\eta}\ensuremath{\sim}0.2$ in the alkalis). The electronic spin correlation is considerably enhanced by exchange. Calculations which include this effect yield the value 0.1 for $\ensuremath{\eta}$.

Valence-Bond Studies of the Dependence upon Substituents of C13–H and Si29–H Coupling

An interpretation is presented for the additivity of substituent effects on the C13–H coupling constant, which has been observed previously in the high-resolution NMR spectra of substituted methanes. Each atom or group X is assigned a characteristic ``affinity'' for s character in the carbon hybrid orbital of the C—X bond. Distribution of s character among the carbon orbitals in accord with the relative s affinities of the four substituents leads to the observed additivity relation provided that the total s character is conserved. The valence-bond approach used with this model gives a linear relation between the s character of the carbon hybrid orbital involved in the C–H bond (αH2) and the observed C13–H coupling constant (JCH=500 αH2). Also, it allows the determination of the s character of the other carbon orbitals. The dependence of the s character of the C—X bond on the electronegativity of X is discussed in terms of electron spin and charge correlation. It is noted that the hybridization changes should affect not only JCH but also JHH, which is consistent with the observed proportionality between JCH(CH3X) and the cis and trans H–H coupling constants in CH2=C13HX. The treatment developed for methanes has been extended to JCH in substituted ethylenes and to the Si29–H coupling in silanes. For the former, introduction of the s-electron affinities, obtained from the values of JCH(CH3X) observed for the substituted methanes, leads to the result that JCH(CH2=C13HX) = JCH(CH2=CH2)+43 [JCH(CH3 X) – JCH(CH4)]. Values predicted in this manner are systematically larger than those observed, which implies that there is a small, negative π-electron contribution of 5 to 10 cps to JCH(CH2=C13HX). Such a contribution is compatible with current theories for proton and C13 hyperfine splittings in ESR spectra of free radicals. The Si29–H coupling constants observed in substituted silanes exhibit large, systematic deviations from the simple additivity found in the methanes. These deviations are explicable qualitatively in terms of changes in the Si–H-bond polarity.

Electron spin correlation and the ethane barrier

The barrier to rotation in ethane is discussed in terms of hydrogen-hydrogen exchange integrals properly weighted by experimentally determined bond orders. Such bond orders are proportional to the spin correlation of delocalized electrons as determined from nuclear magnetic resonance spin-spin coupling constants. The calculated value of 2·3 kcal per mole determined for the rotational barrier in ethane in this study is in good agreement with the experimentally determined value of 2·7–3·0 kcal per mole.