A method of manufacturing a plurality of magnetoresistive memory element having a dielectric thermal buffer layer between a thin top electrode of the magnetic tunnel junction (MTJ) element and a bit line, and a bit-line VIA electrically connecting the top electrode and the bit line having a vertical distance away from the location of the MTJ stack. In a laser thermal annealing, a short wavelength of a laser has a shallow thermal penetration depth and a high thermal resistance from the bit line to the MTJ stack only causes a temperature rise of the MTJ stack being much smaller than that of the bit line. As the temperature of the MTJ element during the laser thermal annealing of bit line copper layer is controlled under 300-degree C., possible damages on MTJ and magnetic property can be avoided.