Introduction

Coppens, P.; Su, Z.; Becker, P. J.

doi:10.1107/97809553602060000615

International
Tables for
Crystallography
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

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International Tables for Crystallography (2006). Vol. C. ch. 8.7, p. 725

Section 8.7.4.1. Introduction

P. Coppens,^a Z. Su^b and P. J. Becker^c

^a 732 NSM Building, Department of Chemistry, State University of New York at Buffalo, Buffalo, NY 14260-3000, USA,^bDigital Equipment Co., 129 Parker Street, PKO1/C22, Maynard, MA 01754-2122, USA, and ^cEcole Centrale Paris, Centre de Recherche, Grand Voie des Vignes, F-92295 Châtenay Malabry CEDEX, France

8.7.4.1. Introduction

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Magnetism and magnetic ordering are among the central problems in condensed-matter research. One of the main issues in macroscopic studies of magnetism is a description of the magnetization density $[\boldmu]$ as a function of temperature and applied field: phase diagrams can be explained from such studies.

Diffraction techniques allow determination of the same information, but at a microscopic level. Let m(r) be the microscopic magnetization density, a function of the position r in the unit cell (for crystalline materials). Macroscopic and microscopic magnetization densities are related by the simple expression $[{\boldmu}={1\over V}\int_{\rm cell}\,{\bf m}({\bf r})\,{\rm d}{\bf r}, \eqno (8.7.4.1)]$ where V is the volume of the unit cell, $[{\bf m}({\bf r})]$ is the sum of two contributions: $[{\bf m}_s({\bf r})]$ originating from the spins of the electrons, and $[{\bf m}_L({\bf r})]$ originating from their orbital motion. $[{\bf m}({\bf r}) = {\bf m}_s({\bf r})+{\bf m}_L({\bf r}). \eqno (8.7.4.2)]$

References

International Tables for Crystallography (2006). Vol. C. ch. 8.7, p. 725