how do the composition and phases of earth's inner layers generate a magnetic filed
In a sense, yes. You probably know that the Earth is stratified. In radius it is composed of layers having different chemical composition and different physical properties. The crust of the Earth has some permanent magnetization, and the core of the Earth, the outer part of which is liquid iron and the inner of which is solid iron, generates its own magnetic field, sustaining the main part of the field we measure at the surface. So we could say that the Earth is, therefore, a "magnet."
But there is no giant bar magnet near the Earth's center, despite the depictions you may have seen in elementary textbooks on geology and geophysics. Permanent magnetization cannot occur at temperatures above about 650 degrees Celsius, when the thermal motion of atoms becomes sufficiently vigorous to destroy the ordered orientations needed to establish permanent magnetization. The core of the Earth has a temperature of several thousand degrees Celsius, and therefore it is not permanently magnetized.