Selecting a MOSFET to Drive a coil with square wave
There are plenty of N-Channel FETs that might suffice for your task.

You are searching for a FET with low RDS(on) but also low C(gate).
You can search on Digikey or the like for low C(gate) ... &lt;50 pf, and low RDS(on) (though this can be part of your 2.5 Ohm resistor in reality) and Low VGS(threshold)

Here's one that might fit your need, the PMZ390UN
This has under 50 pf gate capacitance and is able to support your ID needs of 1.4 A at 3 V drive.
The RDS(on) is under 500 mOhm, so you could drop your 2.5 Ohm resistor to 2 Ohms to allow for it.
Turn on/off times would easily meet you 3 Mhz requirement, but remember that delay will impact any phase relationship you might want to maintain. 

Since you are driving an inductive load, there will be no problem with turn on characteristics, but you might want to add a very fast Schottcky diode across the inductor.