Coherent Spin Control by Electrical Manipulation of the Magnetic Anisotropy

Abstract

High-spin paramagnetic manganese defects in polar piezoelectric zinc oxide exhibit a simple, almost axial anisotropy and phase coherence times of the order of a millisecond at low temperatures. The anisotropy energy is tunable using an externally applied electric field. This can be used to control electrically the phase of spin superpositions and to drive spin transitions with resonant microwave electric fields. DOI: 10.1103/PhysRevLett.110.027601 PACS numbers: 76.30.Fc, 76.60.Lz, 77.65.Àj Couplings between magnetic and electric degrees of freedom give rise to such fundamental phenomena in condensed matter as multiferroelectricity [1,2], unconventional superconductivity [3], and spin-density waves [4], and are key to proposed future technologies such as high sensitivity metrology [5] and quantum-dot-based quantum information processing [6]. The control of spin states using electric fields rather than magnetic fields is particularly valuable for quantum information processing [7], because electric fields can be applied on short length scales, and down to the scale of qubit separations in a device [8][9][10]. In this Letter, we identify a class of electrically controllable spin qubits: high-spin magnetic defects in polar semiconductor hosts. In one member of this class, the manganese substitutional defect in a crystalline zinc oxide host, we demonstrate coherent oscillations of the spin state driven by dc electric field pulses and spin transitions driven by resonant microwave electric fields.Electrical control has been considered in various candidate physical systems for spin qubits, both experimentally and theoretically. In lithographically defined GaAs quantum dots, spin-orbit coupling permits coherent control of an electron spin by applying a resonant high frequency voltage to one of the confining gates [11]. Stark shifts in spin splittings, originating from hybridization with excited state orbitals, have been observed in self-assembled quantum dots [12] and in bound donors in semiconductors [13,14] and in defects in diamond [15], while frustrated spin triangles exhibit spin-electric couplings via modulation of exchange interactions [16,17]. Here, our approach is to manipulate the electrostatic environment of a high-spin paramagnetic defect, manganese, in a polar piezoelectric host material, zinc oxide, thereby controlling electrically the spin Hamiltonian of the defect [18].The spin Hamiltonian of manganese defects in zinc oxide (ZnO:Mn) is well known from continuous-wave ESR [19]. The polar environment lifts the spin degeneracy of the S ¼ 5=2 Mn 2þ ions which are substitutional on Zn 2þ sites, while the I ¼ 5=2 nuclear spin of 55 Mn is coupled to the electron spin by the hyperfine interaction.The Hamiltonian, including a magnetic field which lifts the remaining Kramer's degeneracies, iswhere the axial anisotropy, or zero-field splitting (ZFS), termHigher order effects, such as fourth order electron spin anisotropy and nuclear quadrupole terms, have been detected [19], but they are small and not relevant f...

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