I think it can be much simpler than this. You can use a digital output to create a pulse. The pulse will drive a high power transistor or fet which is connected to the coil. This transistor is powered from some external power source because we need a strong pulse. After the pulse is switched off, we wait a while and amplify the resulting signal with an opamp. This signal is digitized and connected to a digital input.
I came across the chance metal detector
, it is a russian design and uses an ATMEGA8. Circuit diagram attached.