Interaction Induced Special Temperatures in Magnets and Gases

The magnetic bulk susceptibility can be used to classify magnets as ferromagnets (chi T/C >1) or antiferromagnets (chi T/C <1). In this study we identify a new class of ``inverting'' magnets that exhibit a maximum in chi T/C as a function of temperature. In strong analogy with van der Waals theory of classical gases we identify the peak temperature with a magnetic Joule temperature, where the system is quasi-ideal, dU/dM=0, and the onset of antiferromagnetic correlations. In addition, we find a magnetic Boyle temperature, where chi T/C=1, and the incipient ferromagnet turns to an antiferromagnet at low temperature. We provide a phenomenological model of the susceptibility which reveals the mechanism that induces the special temperatures and elevates the effects of minute frustrated exchange interactions to surprisingly high temperature. By explicitly decomposing the dipolar Hamiltonian we demonstrate that these special temperatures and eventual antiferromagnetic ordering are caused by the quadrupolar corrections to a monopolar (dumbbell) Hamiltonian. Our study establishes chi T/C as a direct measure of interaction parameters which are otherwise difficult to access experimentally, and we find that the spin ice materials Dy/Ho2Ti2O7 and the spinel GeCo2O4 belong to this group.