By direct magnetization measurements, performed employing a new detection scheme, we demonstrate an electrical control of magnetization in wurtzite (Ga,Mn)N. In this dilute magnetic insulator the Fermi energy is pinned by Mn ions in the mid-gap region, and the Mn3+ ions show strong single-ion anisotropy. We establish that (Ga,Mn)N sustains an electric field up to at least 5 MV/cm, indicating that Mn doping turns GaN into a worthwhile semi-insulating material. Under these conditions, the magnetoelectric coupling may be driven by the inverse piezoelectric effect that stretches the elementary cell along the c axis and, thus, affects the magnitude of magnetic anisotropy. We develop a corresponding theory and show that it describes the experimentally determined dependence of magnetization on the electric field quantitatively with no adjustable parameters as a function of the magnetic field and temperature. In this way, our work bridges two research domains developed so far independently: piezoelectricity of wurtzite semiconductors and electrical control of magnetization in hybrid and composite magnetic structures containing piezoelectric components.
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