We study the phase transition in a helimagnetic film with Heisenberg spins under an applied magnetic field in the c direction perpendicular to the film. The helical structure is due to the an-tiferromagnetic interaction between next-nearest neighbors in the c direction. Helimagnetic films in zero field are known to have a strong modification of the in-plane helical angle near the film surfaces. We show that spins react to a moderate applied magnetic field by creating a particular spin configuration along the c axis. With increasing temperature (T), using Monte Carlo simulations we show that the system undergoes a phase transition triggered by the destruction of the ordering of a number of layers. This partial phase transition is shown to be intimately related to the ground-state spin structure. We show why some layers undergo a phase transition while others do not. The Greens function method for non collinear magnets is also carried out to investigate effects of quantum fluctuations. Non-uniform zero-point spin contractions and a crossover of layer magnetizations at low T are shown and discussed.
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