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Self-consistent mean field methods based on phenomenological Skyrme effectiveinteractions are known to exhibit spurious spin and spin-isospin instabilitiesboth at zero and finite temperatures when applied to homogeneous nuclear matterat the densities encountered in neutron stars and in supernova cores. Theorigin of these instabilities is revisited in the framework of the nuclearenergy density functional theory and a simple prescription is proposed toremove them. The stability of several Skyrme parametrizations is reexamined.

Spin and spin-isospin instabilities in asymmetric nuclear matter at zero and finite temperatures using Skyrme functionals