Nuclear Magnetic Resonance In Metals Research Articles

Microscopic model of the Knight shift in anisotropic and correlated metals

We present a microscopic model of nuclear magnetic resonance in metals. The spin-1/2 local nucleus and its surrounding orbital electrons interact with the arbitrary constant and perpendicular time-oscillatory magnetic inductions and with each other via an anisotropic hyperfine interaction. An Anderson-like Hamiltonian describes the excitations of the relevant occupied local orbital electrons into the conduction bands, each band described by an anisotropic effective mass with corresponding Landau orbits and an anisotropic spin tensor. Local orbital electron correlation effects are included using the mean-field decoupling procedure of Lacroix. The Knight resonance frequency and corresponding linewidth shifts are evaluated to leading orders in the hyperfine and Anderson excitation interactions. While respectively proportional to and a constant for weak , both highly anisotropic shifts depend strongly upon when a Landau level is near the Fermi energy. Electron correlations affect the anisotropy of the linewidth shift. The model is easily generalizable to arbitrary nuclear spin I.

Vertex corrections and the Korringa ratio in strongly correlated electron materials

We show that the Korringa ratio, associated with nuclear magnetic resonance in metals, isunity if vertex corrections to the dynamic spin susceptibility are negligible, the hyperfinecoupling is momentum independent, and there exists an energy scale below which the densityof states is constant. In the absence of vertex corrections we also find a Korringa behaviour forT1, the nuclear spin relaxation rate, i.e., , and a temperature independent Knight shift. These results are independent of the formand magnitude of the self-energy (so far as is consistent with neglecting vertex corrections)and of the dimensionality of the system.

Dipolar coupling and saturation effects in acoustic nuclear magnetic resonance

The observed signal for dipolar coupled acoustic nuclear magnetic resonance in metals is explained and the saturation behavior is predicted.

Nuclear magnetic resonance in metals

AbstractThe method of nuclear magnetic resonance (N.M.R.) was first successfully demonstrated by Bloch, Hansen, and Packard and Purcell, Torrey, and Pound in 1946. Although the initial interest was concerned with the determination of nuclear magnetic moments, it was soon realised that the nuclei were excellent probes for the investigation of magnetic and electric fields in bulk materials. Application to a wide range of chemical and physical problems has been possible. The greatest impact has probably been in the field of organic chemistry, where the method provides a powerful tool for the identification and structure determination of complex molecules. This success is largely due to the favourable magnetic properties and frequent occurrence of the hydrogen nucleus or proton and the extremely high resolution attainable in diamagnetic liquid samples.

Nuclear magnetic resonance in metals

Nuclear magnetic resonance in metals

Nuclear magnetic resonance in metals

Nuclear magnetic resonance in metals

The Physical Principles of Magnetism

The Physical Principles of Magnetism

核磁気共鳴の金属への応用

核磁気共鳴の金属への応用

Nuclear Magnetic Resonance in Metals under Anomalous Skin Effect Conditions

Nuclear magnetic resonance in metals is complicated by eddy current effects when the specimen dimensions are not small compared with the penetration depth of the radiofrequency field. Deviations from the form of the resonance absorption predicted by the theory based on the classical skin effect have been observed for some pure metals at low temperatures. It is suggested that these deviations are due to the partial onset of anomalous skin effect conditions. Theoretical expressions, applicable to a semi-infinite plane specimen, are derived for the parameters a and b in the expression aχ + bχ which determines the resonance absorption, as functions of the ratio of the electron mean free path to the classical skin depth. The theoretical results go some way towards explaining both the deviations referred to and some new measurements made on thick aluminium foils at helium temperatures.

Nuclear magnetic resonance in metals

A review is given of the experimental resuits and theory of nuclear magnetic resonance as they pertain to metals. There are 217 references from which information was obtained. Sections give such information as features of experimental techniques; quantities measured in or derived from resonance experiments; mechanisms responsible for the position, width, shape, and intensity of observed nuclear resonance absorption lines; and where and when the nuclear magnetic resonance method can be used. (N.W.R.)

The Effect of Eddy Currents on Nuclear Magnetic Resonance in Metals

A theoretical and experimental investigation of this effect is described. The theoretical treatment is developed for specimens in the form of (i) a flat plate, (ii) a long cylinder and (iii) a sphere; and is applicable to foils, wires and powders with spherical particles. In each case the power absorption per unit volume W is expressed as W = W0 + W1, where W1 determines the nuclear resonance absorption and is of the form W1 ∝ aχ' + bχ'', where (χ' - iχ'') is the complex susceptibility. Explicit expressions are derived for W0, a and b as functions of p = 2t/δ, where δ is the skin depth, and 2t is (i) the thickness of the plate, (ii) the diameter of the cylinder, (iii) the diameter of the sphere. These results indicate that both the dependence on reduced specimen dimension and the magnitude of the effect differ considerably from those previously supposed. Measurements of the nuclear magnetic resonance absorption in aluminium foils, in the temperature range 20°K, to 300°K, are described, and it is shown that the results are in satisfactory agreement with the theoretical treatment. The effect of eddy currents on the position of the centre, the shape and the amplitude of the absorption line are discussed, and methods of correcting observed lines to obtain the undistorted line are indicated. Extensions of the treatment to methods of observing nuclear resonance other than by absorption measurements are also outlined.

Nuclear Magnetic Resonance in Metals. II. Temperature Dependence of the Resonance Shifts

The temperature dependence of the nuclear resonance shift in metals has been investigated in lithium, sodium, rubidium, cesium, and gallium. The resonance shifts were found to change by no more than 5 to 6 percent over temperature ranges of 200°, including the melting point. For sodium, the observed temperature dependence of the resonance shift is correlated directly with the volume dependence predicted theoretically for the mass magnetic susceptibility due to the conduction electrons. In the other metals, effects appear which are related apparently to the volume dependence of the wave functions for electrons at the top of the conduction band. The room temperature resonance shifts of Sn117 and Sn119 and the temperature dependence of the Rb87 line width are also reported for the metals. The resonance shift of tin is 0.705×10−2. The estimation of activation energies for self-diffusion from the temperature dependence of the line widths is discussed.

On the nuclear magnetic resonance in metals and alloys

The shift of the nuclear resonance and the line width has been measured in α- and β-tin, thallium, lead and several alloys. While gray tin has no shift relative to the resonance in insulating compounds, white tin has an anisotropic shift of 0.79 per cent along the tetragonal axis and 0.74 per cent perpendicular to it. A theory for the anisotropy and asymmetry of the observed line is given. Thallium has an anomalously broad resonance line with a shift of 1.54 per cent. In thallium alloys the shift varies continuously with composition in each phase and has discontinuities when phase transitions occur. A maximum shift of 2.1 per cent has been found in a TlMg-alloy, while the NaTl structure exhibits a negative shift of −1.0 per cent. Quadrupolar effects are important when the nuclear spin I > 1 2 . The intensity of the copper resonance in pure copper can be increased by annealing and decreased by cold work. In alloys like α-brass and copper-silver the intensity decreases rapidly with increasing zinc or silver content. At 25 per cent zinc the copper resonance becomes unobservable. These effects are explained in terms of quadrupole interaction and can give information about the state of order or disorder on an atomic scale in the alloy.

Nuclear Magnetic Resonance in Metals. I. Broadening of Absorption Lines by Spin-Lattice Interactions

Magnetic resonance line shapes and widths, their temperature dependence, and the conduction electron shifts in resonance frequency are reported for the metals Li7, Na23, Al27, Cu63, Cu65, Ga69, Ga71, Rb85, Rb87, and Cs133. The absorption lines in most of these metals are broader than predicted for nuclear magnetic dipolar broadening alone. We propose that the mechanism responsible for most, if not all, of this additional broadening is the interaction between the nuclear spins and the conduction electrons, which also determines the spin-lattice relaxation time. Spin-lattice relaxation times T1 are estimated from the nondipolar broadening of the experimental absorption lines. These T1 values compare favorably with available directly measured values and with approximate T1 values obtained by Korringa's theory from the measured resonance shifts. In the case of lithium, a dipolar line-width transition was observed at 255°K; this transition results from self-diffusion, for which we determine an activation energy of 9.8±1 kcal/mole.

Nuclear Magnetic Resonance in Metals: Temperature Effects forNa23

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