Context :

Aims : In order to analyze the importance of the star formation rate in generating and amplifying magnetic fields in the interstellar medium we perform a deep continuum polarization study of three angularly large , late type spiral galaxies .

Methods : We obtained deep total power and polarization maps at 4.85 GHz of NGC 4236 , NGC 4656 and IC 2574 using the 100-m Effelsberg radio telescope .
This was accompanied by imaging in the H \alpha line .
We also observed these objects at 1.4 GHz to obtain their integrated fluxes at this frequency and to determine their radio spectra .

Results : All galaxies were found to possess weak but detectable total power emission at 4.85 GHz , coincident with regions of recent star formation as traced by bright H \alpha regions .
The surface brightness of the radio-strongest object of our sample ( NGC 4656 ) is comparable to the radio-weakest objects in a sample of more than 50 normally star-forming spiral galaxies for which measurements at 4.8 GHz with the Effelsberg radio telescope are available .
The surface brightness of the two other objects is even three times smaller .
The fractional polarization of the 2 galaxies of our sample is less than 2 % , significantly lower than for spiral galaxies of intermediate types , suggesting that the magnetic fields are not only weaker , but also less ordered than in spiral galaxies .
The radio spectra of galaxies in our small sample are indicative of a substantial fraction of thermal emission , with a higher thermal fraction than in spirals with high star formation rates ( SFR ) , while the nonthermal emission in our sample is relatively weak compared to spiral galaxies .
We propose an equipartition model where the nonthermal emission increases \propto SFR ^ { ~ { } \approx 1.4 } and the ratio of nonthermal to thermal emission increases \propto SFR ^ { ~ { } \approx 0.4 } .
The objects of our sample still follow the radio-FIR correlation of surface brightness of the total emission , extending it towards the lowest values measured so far .

Conclusions :