Looks like an IRL530N will do the job just fine. "Logic level" (at 3A at least) and generously rated. Mind you I prefer the English datasheets! 
Note you are going to use use PWM. You should have a 220 ohm series resistor to the gate in order not to overload the MCU pin when it has to charge and discharge the gate; otherwise I did not look at your code. You also need a 47k resistor from the gate to ground to keep the FET switched off if the MCU is in reset or otherwise not functioning.
PWM to a solenoid eh? I don't recall; are you the guy playing with ferrofluids, or doing a "levitation" trick?