Phase diagram of electron gas (Ceperley 1999).

While it may at first seem counterintuitive, magnetic behavior and even magnetic order is possible even in compounds which have no magnetic components. The reason for this is that at low densities, a free electron gas undergoes a series of many-body instabilities which include the formation of an ordered electron lattice (the Wigner lattice) and then ferromagnetic order. The phase diagram at the right shows the regimes of stability for these phenomena in three dimensional electron systems, as functions of temperature and electron density.

Recently ferromagnetism was found in single crystals of semiconducting CaB₆, in which small amounts of La were introduced to create mobile electrons at densities of about 10¹⁹cm³, or with electronic separations of ~50 Bohr radii. Since this density is comparable to those expected to yield magnetically ordered Wigner lattices,

Fig. 1 a) The saturation moment Ms at 250 K as a function of the electron concentration n. Filled circles are from a previous La doping study (Young 1999). b) The same data, plotted as moment per electron Ms/n.

there was much excitement about this result, especially the Curie temperatures which were found to be as large as 900 K in this system. We carried out a detailed study of the relationship between the spontaneous moment, determined by low temperature magnetization measurements and the electron concentration, taken from Hall effect measurements. As the figure at the left shows, there is no clear relationship between the moment and the density of electrons.

Fig. 2 (a) Electron backscattering image of an unetched crystal, demonstrating contaminant decoration of the facets. (b) - (d) Electron microprobe maps of the same region for Ca, Fe, and Ni.

The reason for this was revealed in an electron microscopy study of the crystal surfaces, as shown in the figure at the right. Microprobe measurements show that macroscopic amounts of Fe and Ni are deposited on the crystal facets and surfaces during the synthesis of the crystals. Unfortunately, it now appears that the ferromagnetic order found in doped alkali earth hexaborides is at least partially extrinsic and due to accidental contamination by ferromagnetic elements.

Fig. 5 The temperature dependence of the electrical sensitivity for several RXN samples.

The properties of magnetic moments, whether introduced intentionally or not, are subtle and interesting. We have explored several families of intermetallic compounds, which as small gap insulators or low carrier density semimetals, might have the potential to be driven magnetic at low carrier concentrations. One example is the half-Heusler compounds, RXN, where R and X are transition metal atoms and N is a pnictogen. Electronic structure calculations suggested that if the total number of valence electrons per formula unit is 17 or more, and if the d-electrons from the R and X elements total 10 that semiconducting behavior should be found, and that only the defect states could lead to weak magnetic behavior. We have confirmed this prediction by synthesizing and studying the transport and magnetic properties of high quality single crystal and polycrystalline specimens of HfNiSn, TiNiSN, and TiPtSn. The figure at left demonstrates the intrinsically semiconducting behavior of the undoped hosts.

Perhaps the most striking attribute of these low carrier density systems is their linear magnetoresistance, found only at the lowest temperatures and only in samples – both single crystal and polycrystalline - with substantial doping levels. An example is shown at the right for a collection of different single crystals. On general grounds, the magnetoresistance is not expected to be linear, or any odd function of field, since the magnetoresistance should not depend on the sign of the field. It is in principle possible that orbital or magnetic order occurs in these materials, introducing an internal symmetry breaking field. However, we believe that the linear magnetoresistance results from phase separation on small length scales into conducting regions superposed on an insulating matrix. To read more about linear magnetoresistance, please see Parish and Littlewood, Nature 426, 162 (2003). A linear and nonsaturating magnetoresistance might serve as the basis for a magnetic field sensor device, especially for large magnetic fields such as those produced at the National High Magnetic Field Laboratory. For more about this type of application see Xu, et al, Nature 417, 421 (2002).