Defect-trapped electrons and ferromagnetic exchange in ZnO

Abstract

A model for ferromagnetism observed at ambient temperature in films of oxides such as ZnO is proposed and evaluated. The ferromagnetic moment in the model arises from electrons trapped at negatively charged vacancies in an n-type oxide. These vacancies are capable of trapping either one or two electrons. Trapped electrons are described by a one-band Hubbard Hamiltonian where the Hubbard U is the effective electron-electron repulsion for a pair of electrons in a vacancy. Ferromagnetism is known to exist in the Hubbard model applied to periodic three-dimensional (3D) lattices, provided the Hubbard U parameter exceeds the defect bandwidth W and the filling is away from half or complete filling. Hybrid and local-density approximation density-functional theory calculations are used to evaluate Hubbard model parameters for electrons trapped in defects in ZnO. They are also used to calculate magnetic exchange couplings of well-separated, singly negatively charged defects, which are induced by a conduction band electron. Strong ferromagnetic coupling between defects is found in these total-energy calculations over a range exceeding 10Å when the defects have a large, positive Hubbard U value. Hubbard U values for oxygen (V O ), zinc (V Zn ), and zinc-oxygen complex (V ZnO ) vacancies in various charge states are estimated from defect transition levels. V

Structural, optical, XPS and magnetic properties of Zn particles capped by ZnO nanoparticles

“…It can be interpreted as an evidence that the magnetic order development is related to the presence of vacancies, such as V Zn , in the crystal lattice of the Zn nanoparticles, whose role in RTFM was reported earlier for undoped ZnO [80,81]. ܸ For magnetization to reach a value comparable to those observed in the our experiments, the defect density in the order of 1 at % was necessary in ZnO [25]. This was found comparable to the decrease in V observed in our NPs.…”

“…For the Zn-O system, also known as a pristine oxide, it was shown that defects, such as Zn and O vacancies [16][17][18][19][20][21], Zn interstitials [22], grain boundaries [23] and lattice distortions [24], might contribute to the development of RTFM. If all these defects are indeed responsible for the ferromagnetism in thin films and nanoparticles, they should be thermodynamically stable at least to room temperature, and magnetic exchange interaction between them should be strong enough for the existence of ferromagnetism to be feasible [25].…”

“…However, there remain a number of unanswered questions regarding the magnetic properties of such material [25]. Exactly which defect species or group of defects are responsible for the development of magnetic moments?…”

Transition levels of defects in ZnO: Total energy and Janak's theorem methods

“…For ease of comparison of TL for both acceptor and donor defects, we refer acceptor levels to the VBM rather than the CBM using the band gap energy, E g , obtained from the ionization potential and electron affinity of the bulk supercell. 7 A TL is denoted (q /q), where q and q are two different charge states of the defect, and is obtained from the difference in formation energies of a defect in two distinct charge states using Eq. (1),…”

“…The values of IP and EA for ZnO are 7.14 eV and 11.06 eV (Ref. 7) from differences in total energies of charged and neutral bulk 3 × 3 × 3 supercells. The absolute IP and EA values have no meaning since they are obtained using charged unit cells.…”