Spin Dynamics and Spectroscopy

Lecture Notes, J-Ph Ansermet, 1998

1. Introductory lecture

What training in physics ?

The status of physics in the US and in Europe is questionned by several public institutions. Consequently, a recent article in Physics Today raised the question : "What future will we choose for Physics ?" The authors pointed out that "conceptual tools, more than anything else, differentiate the physicist from other scientists. The physics is most cogently identified, not by the subject studied, but by the way in which a subject is studied and by the nature of the information being sought. " They recommanded that " at least a few topics be taught in enough depth that students learn what it really means to solve problems."

I am trying to create a set of lectures in the spirit of these recommandations. The objectives of this course are to develop skills in the quantum mechanical description of experimental techniques and phenomena. Spin dynamics, as it is often referred to in standard textbooks of quantum mechanics, is a great way to reveal some key aspects of quantum mechanics, and lends itself to tracktable calculations. I chose as a guideline for the development of my course nuclear magnetic resonance. Then I exploit the formalism put in place to describe aspects of magnetism : the indirect coupling of localized magnetic moments and spin dependent effects in electronic transport.

Nuclear magnetic resonance is an amazing field of study. It makes possible with simple means the direct observation of purely quantum mechanical phenomena. Theoretical tinkering with hamiltonians can be illustrated with spectroscopic experiments. Great carriers and Nobel prizes are linked with research activity in this field.

A personal anecdote

The desire to teach a course based on NMR dtaes back to a time long ago when I could not suspect I would be in the postion to do so. I was then working with my collegue Po Kang Wang in Prof. Slichter's group. We had worked out litterlally on the back of an envelope the effect of a frequency offset on a double quantum coherence, a notion to be introduce in this course. Having adjusted some settings on the NMR spectrometer, we were able to verify our prediction of this purely quantum mechanical effect within minutes. I was thrilled to experience such closeness of theory and experiment! I felt that some day, I ought to teach about it. This was long before I suspected I would be in the position to do so.

The importance of magnetic resonance

In many ways, magnetic resonance has played a conspicuous role in condensed matter physics. I do not think it a coincidence that the October issue of Physics Today 1993, which celebrated the 100th birthday of the Physical Review, had three of the eight papers refer to historical developments of magnetic resonance. The papers were written by Bloombergen, Ramsey, and Pake, some major pionneers of magnetic resoance. Nowadays, everybody has heard of NMR or MRI, magnetic resonance imaging. Every large hospital is equipped with MRI and research activity is still fierce in this field. In 1994, functional MRI came to the fore. It is a technique which images the parts of the brain which are activated during well defined intellectual activities. In 1995, sharp images of the lungs were produced by inhaling highly polarized xenon nuclei. In chemistry, NMR is such an important tool that manufacturers are now offering spectrometers with automatic sample changers which make possible the analysis of 20000 samples a year ! Furthermore, advanced techniques in high resloution NMR spectroscopy have become a major tool in biochemistry. Magnetic resonance is also joining the club of near field probe techniques. The possibility of detecting magnetic resonance with a force microscope cantilever was suggested in 1993 (PRL 70(22), 3506 (1993)). The APS 1995 Digest related several successes in this area.

At Lausanne, professor Zuppiroli uses electron paramagnetic resonance. The Institut de Physique Experimentale has a long tradition in magnetic resonance. The chemistry department of course has NMR facilities. At UNIL, Prof. Mehrbach is active in the field. Until a year ago when he left for a position in the US, Prof. Bodenhausen was developping advanced NMR techniques at UNIL also. In Switzerland, Prof. Ernst of ETHZ received in 1991 the Nobel prize for his develoments of Fourier techniques in NMR. Looking up the Science Citation Index as a means of estimating the activity in NMR in Switzerland, I found 54 papers on imaging, 44 on the determination of the molecular structure of biomolecules, 24 papers of chemistry, 10 in physics, were the spin was treated as a spectator of a condensed matter phenomenon, and 15 papers were the spins were actors, Abragam's expression for experiments where spins are used to verify a theoretical prediction.

This course focuses on spin dynamics. First the quantum mechanical description of spin precession will be given, so as to develop a concrete image of the basic phenomena to be described in the rest of the course. Then the linear response of an ensemble of interacting spins will be presented in quantum mechanical terms. Thus, basic notions of spectroscopy will be presented. Then we will consider the effect of the coupling of this ensemble of spins to a thermal bath. Relaxation measurements can provide unique information about a system. They constitute a major advantage of MRI over say, X-ray scanners. Relaxation phenomena play an ever increasing role in many spectroscopic techniques, well beyond the scope of magnetic resonance. Otpical studies use time resolved techniques for example. Magnetic studies of mesoscopic systems also require careful consideration of the effect of a thermal bath. At the end of the course, the formalism which was developped to describe relaxation phenomena will be used to address two important issues in magnetism : the coupling of localized moments via the bath of conduction electrons and spin relaxation effects in electron transport in magnetic structures.

The content of the course can be more concretely described the following synopsis.

more should be said on ....

- the approach chosen (see the science filter) :

- the exercices....going to Mathematica

- the projects : why projects, my experience, what I expect

.....