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We study a bilayer consisting of an ordinary superconductor and a magnet witha spiral magnetic structure of the {\rm Ho} type. We use a self consistentsolution of the Bogolioubov-de Gennes equations to evaluate the pair amplitude,the transition temperature, and the thermodynamic functions, namely, the freeenergy and entropy. We find that for a range of thicknesses of the magneticlayer the superconductivity is reentrant with {\it temperature} $T$: as onelowers $T$ the system turns superconducting, and when $T$ is further lowered itturns normal again. This behavior is reflected in the condensation free energyand the pair potential, which vanish both above the upper transition and belowthe lower one. The transition is strictly reentrant: the low and hightemperature phases are the same. The entropy further reveals a range oftemperatures where the superconducting state is {\it less ordered} than thenormal one.

Reentrant superconductivity in conical-ferromagnet/superconductor nanostructures