Academic Staff - Dr Andrew S. Wills - Physical/Inorganic

Magnetic Properties of Solid State Systems Frustrated Magnetism Application of Symmetry to Magnetic Structure Determination Development of Polarised Neutron Scattering Techniques for Chemistry

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Magnetic Structures and Magnetic Symmetry

Downloads (SARAh and SARAh-Refine)

Tutorials and Notes on Representational Analysis

Some Thoughts on Magnetic Structures

Learning the language of representations and the basis vectors is a major difficulty for researches new to magnetism, or those who are trying to improve on their techniques. It is important to realise that all representations do is provide symmetry classifications, that can be visualised in terms of basis vectors. We are actually very familar with this formalism as it is used thoughout chemistry and physics: the splitting of d-orbitals in an octahdral coordination, the vibrations of a molecule, the classification of phonons of a crystal and the electronic states of a metal are all described using the labels of representational theory, e.g. E_g and T_2g. SARAh and all the notes in these pages are about the appliation of these symmetry calculations to magnetic strutures.

When we do this, we begin to appreciate the language of basis functions and how they naturally reflect the symmetry of the problem being examined. In this way, they help us understand what the different magnetic structures are. Once this is understood we can look at how they occur and start to make use of the reference point that is Landau Theory.

When the symmetry of magnetic structures were first examined, there was a srong desire to build it from the unit cell formalism well known in crystallography, and this resulted in the Shubnikov space groups. This is a lower symmetry formalism than that of represenations and is fully contained within the more general symmetry types of representation theory, note that the black and white space groups correspond directly to representations of order 1 but representations up to order 6 occur in crystalline solids. Many symmetries cannot usefully be described by Shubnivok groups.

By using the language of representations, our description can be linked directly with Landau Theory, bringing us closer to an understanding of the drive for magnetic ordering. The reasons for it, and the couplings that make it will become apparent.

The presentations and notes below, together with the efforts that go into SARAh, and the workshops that we hold on magnetic structures, are designed to help make magnetic structures better understood, better analysed, and better appreciated. Of course, this means that the physics of your sample, i.e. that which interest you, will become clearer too.

-I wish you the best of luck with your refinements and analyses. Feel free to email me with any questions or ideas.

ASW

This page last modified 26 January, 2008

University College London
Department of Chemistry
United Kingdom
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