Magnetic Order in Clifford Geometric Algebra

Abstract

The observation of magnetic Bragg peaks, by both neutron and x-ray diffraction, which cannot be explained in terms of a single ordering wave vector has stimulated the suggestion of the coexistence of multiple magnetic-order-parameters. The peaks are empirically classified into distinct sets on the basis of their symmetry and relative intensities, and each set is allocated a distinct order parameter. In the present example, certain uranium rock-salts exhibit three, independent, sets of peaks whilst maintaining cubic symmetry, suggesting the coexistence of three, orthogonal, order parameters. Recently, in this cubic 3- k phase, we have found a fourth set of peaks, also indicative of long-range order which, however, lie outside both the conventional neutron and x-ray cross sections. This paper develops a formalism of extended quantum correlations via Clifford geometric algebra as a microscopic basis for the existence of multiple order parameters and hence an understanding of the enigmatic fourth set of peaks. This work exploits these physically accessible magnetic systems as a route to unfolding more general states of multiple electronic order.