Nuclear Acoustic Resonance Absorption and Dispersion in Vanadium via Coupling to the Magnetic Dipole Moment

Abstract

The first observation of both NAR absorption and NAR dispersion in a single crystal vanadium due to the coupling of longitudinal acoustic waves to the magnetic dipole moment of the V5* nuclei is reported. The experiment is performed in the temperature range of 5 to 294 K. The obRerved angular dependence and NAR line shapes are in good agreement with the formvlas derived in this paper.Es wird uber den ersten erfolgreichen Nachweis von NAR-Absorptions-und NAR-Dispersionssignalen in einem Vanadiumeinkristall mit longitudinalem Schall berichtet. Die Kopplung des Schallfeldes mit den VSl-Kernen erfolgt iiber die Wechselwirkung mit dem magnetischen Kerndipolmoment. Die Messungen werden im Temperaturbereich von 5 bis 294 K durchgefuhrt. Die beobachtete Winkelabhangigkeit und NAR-Linienform sind in guter ubereinstimmung mit den in dieser Arbeit abgeleiteten Formeln. IntrodudionI n conducting materials in the presence of a dc magnetic field B,, a sound wave produces a n electric current which results in an internal electromagnetic field oscillating coherently with the sound wave [l]. I n metals an acoustic wave therefore may induce nuclear magnetic dipole transitions which are detected through a change in ultrasonic phase velocity and attenuation. This coupling mechanism has been observed in several pure metals [2 to 81 and generally the resulting NAR signals are found to be asymmetric. This asymmetry has been expressed by several authors in terms of the real and imaginary part of the complex nuclear magnetic spin susceptibility x. The actual expressions [9 to 181, however, differ markedly in their dependencies on x' and f ' and the final result of a comprehensive theory [ 161 is not in agreement with experiment if x is interpreted as conventional nuclear magnetic spin susceptibility observed in NMR. Furthermore we feel that most of the actual derivations of the given formulas do not reveal the physics. To elucidate the physical origin of the terms causing the observed asymmetry of the NAR lines, we choose a model [19] where the real metal is substituted by a gas of conduction electrons embedded in a background of positive ions and the interaction between the charged particles is replaced by the interaction with a self-consistent electromagnetic field derived from Maxwell's equations. When an acoustic wave propagates in the metal, the ions will experience oscillatory motions which are screened by the condution electrons. I n the presence of an external magnetic field, however, the screening is not quite complete so that there is a small resultant current density j. Hence, in addition to the ordinary elastic force density, the Lorentz force density