If the magnetic moments or "spins" on the atoms are in opposite directions on the atomic scale, they also cancel, and the material is called an ¶anti-ferromagnet. Manganese flouride (MnF2) is a simple example. The moments on the Mn atoms at the corners of the cube point in one direction, and at the centre of the cube they point in the opposite direction. Since there are equal numbers of each (when many of these unit cells are stacked together), they cancel exactly.

The most famous anti-ferromagnetic, ¶manganese oxide (MnO) helped earn the Nobel prize for C. Shull, who showed how such magnetic structures could be obtained by neutron diffraction (but not with the more common X-ray diffraction). This material also has the simple BCC ¶rock salt structure, but here the basic unit is doubled in all three directions; the Mn moments in one plane point in one direction, and in the opposite direction in the adjacent plane.

¶Magnetite or "loadstone" has been known as a magnet from antiquity. It is one of the common oxides of iron (Fe3O4) and is also cubic, with iron in two valence states. The formula might be simplistically written FeO.Fe2O3 with Fe++ as FeO and Fe+++ as Fe2O3. The Fe+++ occupy the tetrahedral holes, and half the octahedral holes, with the Fe++ occupying the other half. (The charge-ordering of Fe++ and Fe+++ at low temperature (110K) produces the famous Verwey transition). The magnetic moments on the octahedral sites are antiferro-magnetic and cancel (not shown), while on the tetrahedral sites they are ferro-magnetically aligned. Such a mixture of anti- and ferro-magnets is called a ferr-i-magnet.

Many magnetic structures are much more complex. Neutron diffraction, and especially the Rietveld method for powder diffraction, has been used to solve these more complex magnetic structures, such as that of ¶MnTa4S8. Single crystal techniques using polarized neutrons and strong magnetic fields are needed however, to understand the most complex magnetic structures.

The discovery of new types of magnets has had great industrial importance - try counting how many small electric motors are used in a modern automobile - most made from synthetic magnets. Or consider the importance of magnets in communications and other electronic equipment. The so-called ¶hard magnets, whose structure was again found using neutron diffraction, are examples of these important new materials. This material (Nd2Fe14B) consists of layers of iron (orange) with interleaved neodinium (purple) and boron (blue): neutrons show that hydrogen (white) can also be accommodated

Some of the most exiting recent results are being obtained with Giant Magneto-Resistive (GMR) oxides such as ¶(La,Ca)MnO3. Already such materials are being used by IBM to make computer hard drives of much higher capacity. This GMR material has a familiar perovskite-type structure, which is subtly distorted with temperature. The complex magnetic structure is not shown, but this, together with the structural distortions, are important for understanding the unique properties of these materials. The details of the valence and spin ordering in this material is the ILL Grenoble's most most cited current work.

More unusual structures can be formed when the magnetic moments are aligned at different angles to each other; for example ¶Er6Mn23 has a particularly interesting magnetic structure with moments on both types of atom. Even more complex structures are produced when the moments form a spiral structure extending over many unit cells. Such difficult structures can only be obtained with neutron diffraction from single crystals; they help us understand better the subtle balance of forces in these materials.

We have concentrated on the structures of relatively simple materials that are of interest for physical applications. Now let's look at some structures that start off being simple, but end up being complicated ! The first of these are the layered structures, important examples of which we already saw with the oxide superconductors. There are many more, ranging from the moly-disulphide lubricant in your car's engine oil, to the treacherous clay montmorillonite !