High Field Magnetism

M. Date, M. Date

• Publisher: North Holland
• Year: 2012
• ISBN:
  9780444599193
• Topic: Tecnología e ingeniería
• Subtopic: Ciencias de los materiales

High Field Magnetism presents the proceedings of the International Symposium on High Field Magnetism held at the Osaka University and Hotel Plaza in Osaka on September 13-14, 1982 as a satellite symposium of the International Conference on Magnetism-1982-Kyoto. The symposium tackled a wide variety of high field generation methods and material systems, with magnetism orientation as the main objective. A special Technical Exposition was held in the poster session where representatives from MIT, Grenoble, and other high field facilities were invited to give a descriptive review of each laboratory. This book is divided into eight parts, beginning with an introductory chapter into the subject of high field magnetism. The succeeding parts focus on magnetic interactions and phase transitions in high magnetic fields; metals and alloys in high magnetic fields; high field superconductivity; spin and charge fluctuations in high magnetic fields; high field magneto-optics; high field magnetic resonance; and high magnetic field facilities and techniques. This book will be of interest to practitioners in the fields of cryogenic engineering and applied physics.

Part 1

INTRODUCTION TO HIGH FIELD MAGNETISM

ON THE PHYSICS OF HIGH MAGNETIC FIELDS

R. Orbach^*, Ecole Supérieure de Physique et de Chimie Industrielles de la Ville de Paris, 10, rue Vauquelin, 75005 Paris, France

A brief list of current areas of research in high field physics is presented covering most of the presentations at this Symposium. More detailed description is given for three topics for which high magnetic fields are required, and which possess unusual interest. These are: 1) Density of states for vibrational states on fractals “Fractons”, 2) Thermodynamic properties of exchange enhanced systems, and 3) p-state pairing in thin film or layered superconductors.

1 INTRODUCTION

This Symposium follows at least two others in the rapid development of high magnetic field physics.^1,2 In addition, a survey, now rather aging, of opportunities for research in high magnetic fields has been prepared.³ The purpose of the present paper is to briefly classify the character of those papers to be presented at this Symposium, and then to describe in outline form three areas which are of particular interest to the author.

The general areas of research in high magnetic fields to be discussed at this Symposium can very roughly be titled as:

1) Collective phenomena (e.g., p-wave superconductivity)

2) Magnetic structures (e.g., phase transitions, magnetic saturation)

3) Atomic-like states (e.g., exciton structure and dynamics)

4) Diamagnetism (e.g., orientational ordering of large molecules)

5) Thermodynamic properties (e.g., field dependent susceptibilities)

6) Transport properties (e.g., quantum oscillations)

7) High energy density of states (e.g., vibrations on a fractal)

No list is complete, but this can serve as a rough outline of topics unique to high magnetic field research.

This paper will explore three of the seven areas listed above, The remaining four will be well covered by others at this Symposium. Only one of these three represents original work by this author. However, the significance of the other two warrants some attention.

Each of the three topics is described below in terms of the physical ideas which have been developed, and the possible experimental probes. Space limitations require that the reader be referred to the original treatments for the complete details.

2 DENSITY OF VIBRATIONAL STATES ON A FRACTAL, “FRACTONS”

Fractals are open, self similar structures, with interesting properties as a function of the length scale.⁴ A specific example would be a percolation arrangement where the number of sites on the infinite cluster (p > p_c, where p_c is the percolation threshold concentration) increases not as

where r is the distance and d the Euclidean dimensionality, but rather as

where

is an effective dimensionality, equal to d − (β/ν) in terms of the usual percolation exponents.⁵ This behavior occurs for short length scales in comparison to the coherence length for percolation, ξ_p. For larger lengths one finds usual Euclidean^p properties. If now one examines diffusion along the infinite cluster, the “dead ends” cause a length dependence for the diffusion constant:

where again for percolation

, t being the conductivity exponent.

The diffusion problem along a fractal can be solved, leading to the ensemble averaged autocorrelation function⁶

(1)

where the particle has assumed to have been localized at the origin at time t = 0.

One now notes that the form of the diffusion equation (Master Equation) is the same as, for example, the harmonic vibrational problem, with a simple replacement of the first time derivative by the second. This mapping allows us to regard the inverse Laplace transform of Eq. (1) as the lattice vibrational density of states (with ω² replacing the Laplace transform spectral parameter ε) for a fractal arrangement of masses and springs. One finds

(2)

For Euclidean systems, p = d-1, so we are led to define, for mode counting purposes, a reciprocal space of effective dimensionality

(3)

We refer to these states, when quantized, as “fractons.” Their properties are most interesting. Before we outline them in more detail, some experimental examples are of interest.

Our attention to this problem was aroused by the work of Stapleton et al.⁷ who measured the spin-lattice relaxation time for low-spin Fe(3+) in three hemoproteins. These large molecules were shown by x-ray measurements (counting the increase of the number of alpha carbons with dista...