  We study the spin thermalization, i.e., the inter-spin energy relaxation
mediated by electron-electron scattering in small spin valves. When one or two
of the dimensions of the spin valve spacer are smaller than the thermal
coherence length, the direct spin energy exchange rate diverges and needs to be
regularized by the sample dimensions. Here we consider two model systems: a
long quasi-1D wire and a thin quasi-2D sheet.
