Spin ice and demagnetising theory

Abstract: Frustration, or the inability to simultaneously minimise all local interactions is, a phenomenon occurring in a broad number of physical systems. We will in this thesis focus on a class of frustrated ferromagnetic materials called spin ices and how both numerical and experimental techniques can be used to understand their properties. Spin ices show a number of peculiar properties such as low temperature residual entropy and magnetic monopole excitations. Considering a dipolar Hamiltonian model with exchange interactions we verify a qualitative and previously established agreement with experimental data of the quantity χT/C , where χ is the magnetic susceptibility, T  the temperature and C the Curie parameter. We find a quantitative agreement by identifying that further near-neighbour interactions are sensitive probes of χT/C and the neutron structure factor, in particular its zone boundary scattering and relative peak intensities. In systems passing from being governed by ferromagnetic interactions into potentially ordered anti-ferromagnets at low temperature we define special temperatures in close relation with real gases. These temperatures enable a new classication of "inverting" magnets of which spin ice is a member. Due to rich complex long-range interactions in spin ice and a high sensitivity of the quantity χT/C, we identify demagnetising corrections to be crucial in extracting the correct physics. Apart from previously reported results we find the demagnetising factor to be clearly temperature and lattice structure dependent and not just shape dependent. The large moment of the Dy ions in Dy2Ti2O7  thus implies that an incorrect demagnetising treatment can shift the important features in χT/C  outside of the relevant temperature range considered. Employing our refined demagnetising theory we obtain good agreement with experiments down to sub-kelvin temperatures. The magnetic ions in spin ice enable neutron scattering as an excellent tool to study spin ice. A massively parallel computer code is developed in order to obtain high resolution neutron scattering factors in Fourier space. These high resolution charts are in good agreement with carefully verified experimental data down to 350 mK.