A circular coil carrying current has a magnetic moment associated with it and it produces magnetic field. A electron spin also has magnetic moment associated with it. Hence it should also produce magnetic field. (I seen papers where they measure Magnetic field created by a collection of spin). Can i just plug in electron magnetic moment into the equation for magnetic field produced by a magnetic dipole.
Yes. You're right. Depending on what you'll use it for. If you want to know how it affects energy levels of atoms, you need to use real quantum mechanics. But if you want to know the magnetic field produced by a lump of iron, treating each electron in the iron as a tiny dipole, you will get exactly the right answer. That's exactly what the electron magnetic moment is for - for you to use it to calculate magnetic fields it produces (and how it responds to magnetic fields)