The invention relates to a magneto-resistance effect element and a magnetic memory device. Lowering the magnetic domain wall movement current and drive at room temperature in a current induction single magnetic domain wall movement phenomenon are achieved. A magneto-resistance effect element is formed by including at least: a magnet wire 1 for forming magnetic domain wall potential 7 binding a single magnetic domain wall 2; a magnetic field applying means for generating a magnetic field for introducing the single magnetic domain wall 2 into the magnet wire 1; and a drive current applying means for applying the current 3 including a resonance frequency component determined on the basis of the magnetic domain wall potential 7.