Dilute magnetic semiconductors (DMSs) based on wide-bandgap ZnO were proposed as room-temperature spintronic materials, but the experimental and computational study of Risbud, Spaldin, Chen, Stemmer, and Seshadri [Phys. Rev. B 68, 205202 (2003)] on bulk polycrystalline Zn1−xCoxO\mathrm{Zn}_{1-x}\mathrm{Co}_x\mathrm{O} (x=0.05x=0.05–0.150.15) found nearest-neighbor antiferromagnetic interactions in stoichiometric material, and local-spin-density-approximation (LSDA) supercell calculations suggesting that robust ferromagnetism requires additional p-type (hole) doping — modeled in the calculations by Zn vacancies, a device unfeasible experimentally since p-type ZnO is notoriously difficult to realize. This left an open problem: achieving chemically and thermally stable, high-density p-type (hole) doping in bulk Zn1−xCoxO\mathrm{Zn}_{1-x}\mathrm{Co}_x\mathrm{O} and quantifying the resulting hole concentrations; demonstrating experimentally that such hole doping stabilizes robust ferromagnetism in phase-pure bulk samples; obtaining a converged beyond-LSDA account of magnetic interactions and of how the choice of doping model affects them; and delineating the role of native defects, unintentional impurities, and inhomogeneities in magnetic ordering.

Background

A dilute magnetic semiconductor (DMS) is a semiconductor in which a few percent of the host cations are replaced by magnetic transition-metal ions, with the aim of combining semiconductor device functionality with ferromagnetic order. Room-temperature ferromagnetism in carrier-mediated DMSs — where itinerant or loosely bound carriers align the localized transition-metal spins — was predicted for magnetically doped, p-type (hole-doped) oxide and nitride semiconductors, making ZnO doped with Co2+\mathrm{Co}^{2+} on the Zn site (Zn1−xCoxO\mathrm{Zn}_{1-x}\mathrm{Co}_x\mathrm{O}, wurtzite structure, wide gap of about 3.3 eV) a leading candidate. Divalent Co2+\mathrm{Co}^{2+} substitutes isovalently for Zn2+\mathrm{Zn}^{2+} and is soluble to at least x≈0.15x\approx0.15–0.4 without forming secondary phases, which made it a particularly clean test system compared with heterovalent dopants.

In this context, Risbud, Spaldin, Chen, Stemmer, and Seshadri prepared phase-pure bulk polycrystalline Zn1−xCoxO\mathrm{Zn}_{1-x}\mathrm{Co}_x\mathrm{O} (x=0.05x=0.05, 0.10, 0.15) by precursor decomposition, characterized it by x-ray diffraction, transmission electron microscopy, and dc magnetization, and studied it computationally with density-functional theory in the local spin density approximation (LSDA, the spin-polarized form of the local-density approximation) with pseudopotentials and supercells. Two results defined the problem. First, the well-characterized stoichiometric bulk phases showed dominant nearest-neighbor antiferromagnetic coupling between Co2+\mathrm{Co}^{2+} ions (superexchange, the short-range antiferromagnetic interaction transmitted through the intervening oxygen ligand), consistent with the small Curie–Weiss temperatures measured. Second, the total-energy calculations suggested that robust ferromagnetism would occur only if additional hole (p-type) carriers were introduced: supercells from which a Zn atom was removed — creating a Zn vacancy, the computational stand-in for hole doping — favored the ferromagnetic over the antiferromagnetic spin alignment, while undoped and oxygen-vacancy-doped supercells did not.

The authors flagged three difficulties that they could not resolve. (i) The ferromagnetic–antiferromagnetic total-energy differences were only a few meV per cell, at the expected accuracy limit of the LSDA pseudopotential approach, so small splittings (roughly below 10 meV) should not be overinterpreted, and treatments of the localized Co 3d3d states such as LDA+UU (an extension adding an on-site Hubbard repulsion UU to the local-density treatment of correlated dd electrons) or self-interaction corrections (methods that remove the spurious interaction of an electron with its own exchange-correlation potential, improving the description of localized states) could change quantitative conclusions such as band-gap size and dd-level positions; the way different authors model carrier doping (Zn vacancies, explicit acceptor impurities, or uniform background charge) also differed without an established equivalence. (ii) Although the calculations required substantial p-type (hole) doping, the paper gave no experimental route to stable, high-density p-type bulk Zn1−xCoxO\mathrm{Zn}_{1-x}\mathrm{Co}_x\mathrm{O}: Zn vacancies were a model device, not a demonstrated dopant, and achievable hole concentrations, their thermal and chemical stability, and their effect on magnetic order were not quantified. (iii) The roles of nonstoichiometric defects, unintentional donors/acceptors, and small-scale inhomogeneities in real samples remained to be delineated experimentally and theoretically. These issues generalize to the whole field of ZnO-based DMSs, where reported room-temperature ferromagnetism varies widely with preparation method and has frequently been attributed to defects, secondary phases, or measurement artifacts rather than to intrinsic carrier-mediated order.

Problem Statement

The source problem, in the general form raised by the experimental and computational findings of Risbud et al. (2003): determine whether robust ferromagnetism in Zn1−xCoxO\mathrm{Zn}_{1-x}\mathrm{Co}_x\mathrm{O} — intrinsic ferromagnetic order of the doped phase that persists at and above room temperature — can be stabilized and controlled by p-type (hole) doping, and understand its microscopic origin. Concretely, the requested results are: (1) the experimental determination, for a candidate acceptor scheme in bulk Zn1−xCoxO\mathrm{Zn}_{1-x}\mathrm{Co}_x\mathrm{O}, of whether and how the substantial p-type (hole) doping that the first-principles calculations indicate is required can be achieved and controlled, i.e., the achievable hole concentrations and the chemical and thermal stability of the scheme, going beyond the Zn-vacancy computational stand-in; (2) the experimental determination, in phase-pure, well-characterized samples, of whether such hole doping converts the nearest-neighbor antiferromagnetic interaction of stoichiometric bulk Zn1−xCoxO\mathrm{Zn}_{1-x}\mathrm{Co}_x\mathrm{O} into robust ferromagnetic order or not, including the dependence of the ordering temperature and magnetization on hole density; (3) a reliable theoretical account, using beyond-LSDA methodology (LDA+UU, self-interaction corrections, or successors), of the ferromagnetic versus antiferromagnetic total-energy differences in neutral and doped supercells, resolving how the answer depends on the way carrier doping is modeled (Zn vacancies versus explicit acceptors versus uniform background charge) and on the accuracy limits that make few-meV splittings untrustworthy at the LSDA level; and (4) a delineation, experimental and theoretical, of the roles of nonstoichiometric defects, unintentional donors and acceptors, and small-scale inhomogeneities in real samples in producing or suppressing magnetic ordering. These four results jointly serve one objective — establishing whether and how hole doping stabilizes ferromagnetism in Zn1−xCoxO\mathrm{Zn}_{1-x}\mathrm{Co}_x\mathrm{O} — and that objective turns on whether they are mutually consistent, in particular whether the measured carrier type and density correspond to the theoretically modeled hole population whose predicted exchange the measured magnetic order tracks. The task is resolved whether the outcome is affirmative or negative: a well-supported finding that p-type hole doping does not stabilize ferromagnetism — or that the magnetic order arises by a mechanism other than hole mediation — resolves it as fully as an affirmative demonstration, provided the conclusion is supported by results (1)–(4) rather than by absence of evidence.

References

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