Ground States of Magnetorheological Fluids

Through energy minimization and stability argument, we find the ground states of the magnetorheological fluids to consist of magnetic particles arranged in a body centered tetragonal structure inside spheroidal clusters. The width $D$ of the clusters varies with the length $L$ as $D\sim L^n$, where $n=0.62\mathrm{}$ for magnetically saturated particles. In the case of magnetically unsaturated particles, the power law variation is divided into two segments, with $n=0.4\mathrm{}$ in the first segment and $n=0.62\mathrm{}$ in the large $L$ limit. Our results offer a theoretical framework for the resolution of conflicting experimental observations, with the demagnetization field being the crucial physical consideration.