A 2006 supercell density-functional study by Gopal and Spaldin (using LSDA+U, the local spin density approximation augmented by an on-site Hubbard repulsion on the transition-metal 3d orbitals) surveyed magnetic interactions between substitutional 3d transition-metal ions (Cr, Mn, Fe, Co, Ni, Cu) in wurtzite ZnO, combined with Cu, Li, oxygen vacancies, other native defects, and second transition-metal species. It concluded that antiferromagnetic ordering is generally favored, that neutral oxygen vacancies do not mediate ferromagnetism, that Li and Zn vacancies favor ferromagnetism but yield metallic states incompatible with ferroelectricity, and that ferrimagnetic orderings in mixed (Co,Fe) and (Co,Mn) systems are lowest in energy only within constrained geometries requiring heterogeneous clustering. The study explicitly left open whether charged oxygen vacancies (in particular the singly positively charged state), more accurate correlation treatments, realistic defect concentrations and distributions, controlled insulating multiferroic co-doping, or synthetically achievable heterogeneous clustering could change these conclusions. Twenty years of subsequent work has produced mutually incompatible models (charged-vacancy exchange, carrier-mediated double exchange, bound magnetic polarons, zinc-vacancy and grain-boundary mechanisms) without consensus, so the microscopic origin and control of magnetic order in transition-metal-doped ZnO remain open.

Background

Dilute magnetic semiconductors (DMSs) are semiconductors in which a few percent of the host cations are replaced by magnetic ions, with the goal of combining charge transport and magnetism in one material for spintronics. A widely cited mean-field prediction (Dietl et al., Science 2000) estimated that p-type Mn-doped ZnO could order ferromagnetically above room temperature, and numerous experiments subsequently reported room-temperature ferromagnetism in ZnO doped with Co, Mn, Fe and other 3d transition metals (TM), while other experiments on nominally identical materials found antiferromagnetism, spin-glass behavior, or no magnetism at all. To explain the positive reports, Coey, Venkatesan and Fitzgerald (Nat. Mater. 2005) proposed a donor-impurity-band exchange model in which an extended donor-derived impurity band, for example from oxygen vacancies, hybridizes with spin-polarized TM 3d states; if the Fermi level lies inside this hybridized spin-split band, the carriers mediate ferromagnetic coupling between the TM moments.

Gopal and Spaldin (Phys. Rev. B 74, 094418 (2006)) tested this picture with periodic-supercell density functional theory. In a supercell calculation one substitutes or removes atoms in a periodically repeated block of the crystal and compares total energies of different magnetic arrangements; the local spin density approximation (LSDA) was augmented by LSDA+U, i.e. by an on-site Hubbard repulsion U and exchange J on the TM 3d states, which corrects the LSDA self-interaction error for these localized orbitals. Their findings: (1) for single TM species substituted at Zn sites, antiferromagnetic (AFM) coupling is generally favored within LSDA+U, whereas LSDA sometimes favors ferromagnetism (FM) - the sign of the answer depends on the exchange-correlation functional, on the k-point mesh (the Brillouin-zone sampling grid) and plane-wave energy cutoff (the two standard numerical-convergence parameters of a plane-wave DFT calculation), and on the degree of lattice relaxation, with better convergence and better correlation treatment disfavoring FM; (2) co-doping with Cu does not help, but substitutional and interstitial Li, as well as Zn vacancies, do stabilize FM; (3) a neutral oxygen vacancy leaves the TM moments antiferromagnetically coupled and does not create a hybridized spin-split impurity band at the Fermi level, contradicting the donor-impurity-band picture; (4) in mixed (Co,Fe) and (Co,Mn) systems, ferrimagnetic (FiM) orderings - antiparallel moments of unequal magnitude giving a net magnetization - are lowest in energy within constrained pair geometries; and (5) Li co-doping produces metallic, not insulating, electronic structures, whereas ferroelectricity (a switchable spontaneous electric polarization) requires an insulator.

Independent of magnetism, the point-defect physics of ZnO was being consolidated at the same time: standard defect-theory calculations (Janotti and Van de Walle, Phys. Rev. B 76, 165202 (2007)) and later GW calculations (Lany and Zunger, Phys. Rev. B 81, 113201 (2010); GW is a many-body perturbation-theory approximation for quasiparticle energies that goes beyond density-functional theory) established that the oxygen vacancy in ZnO is a deep donor (an electron-donating defect whose occupied level lies deep in the band gap rather than near the conduction-band edge) whose charge states obey negative-U behavior (the 2+ and 0 states are stable and the 1+ state is metastable, with the (2+/0) transition level deep in the gap), not a shallow donor that could populate an impurity band. The bound magnetic polaron (BMP) picture - in which carriers trapped at defects align the surrounding TM moments within a localization volume, and overlapping polarons couple ferromagnetically - became the main competing explanation for the observed magnetism. Which defect species, in which charge state, actually controls magnetic ordering in TM-doped ZnO has remained disputed.

Problem Statement

Determine quantitatively whether native point defects - above all oxygen vacancies in their positive charge states - can mediate or stabilize long-range magnetic ordering between substitutional 3d transition-metal ions (Cr, Mn, Fe, Co, Ni, Cu) in ZnO, and whether that ordering can be controlled synthetically. Concretely, the unresolved questions left open by Gopal and Spaldin (Phys. Rev. B 74, 094418 (2006)) are: (i) does the singly positively charged oxygen vacancy (or any other defect charge state) change the magnetic coupling between TM ions, given that neutral oxygen vacancies leave them antiferromagnetically coupled? (ii) is the computed AFM-versus-FM stability robust to the correlation treatment - the choice of Hubbard U and J on the TM 3d states, hybrid functionals, or methods beyond density functional theory - given that the sign of the energy difference changes between LSDA and LSDA+U? (iii) how do realistic defect and dopant concentrations, statistical distributions, clustering, and growth-dependent kinetics, as opposed to fixed 12.5% TM pair arrangements in small supercells, change the magnetic ground state of experimentally relevant samples? (iv) can controlled co-doping (for example with Li, or with Zn vacancies) produce an insulating, simultaneously ferromagnetic and ferroelectric (multiferroic) state of ZnO, given that the calculated Li-co-doped ferromagnetic states are metallic? and (v) can the heterogeneous clustering needed for the predicted ferrimagnetic (Co,Fe)/(Co,Mn) orderings - unlike species adjacent, like species distant - be achieved experimentally by a thermodynamic or kinetic route? These five sub-questions are jointly the concrete content of the general objective above; resolving the task requires addressing all five, and each is independently refutable, so a well-supported negative result on any one of them resolves that sub-question while the others remain open. Resolving the question requires determining the defect species and charge states responsible for any observed ordering, the exchange mechanism (carrier-mediated exchange via delocalized or impurity-band carriers; double exchange, in which carriers hopping between neighboring magnetic ions align their moments; bound-magnetic-polaron coupling; or superexchange, the short-range exchange transmitted through intervening oxygen ions), and the quantitative conditions (Fermi level, defect density, dopant distribution) under which ferromagnetic or ferrimagnetic order appears, is absent, or is destroyed.

References

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