Session L3: How to Predict Localized Hole-States in Oxides and Wide-Gap Semiconductors?

Exotic magnetism in the alkali sesquioxides Rb$_4$O$_6$ and Cs$_4$O$_6$

Among the various alkali oxides the sesquioxides Rb$_4$O$_6$ and Cs$_4$O$_6$ are of special interest. They comprise two different types of dioxygen anions, the hyperoxide and the peroxide anions. The nonmagnetic peroxide anions do not contain unpaired electrons while the hyperoxide anions contain unpaired electrons in antibonding $\pi^*$-orbitals. Electronic structure calculations using the local spin-density approximation reveal strong electron correlations and charge ordering that is due to the mixed valency. The experimental investigation of the temperature dependent magnetization reveals a low-temperature magnetic transition. The mixed valency of both compounds is confirmed using Raman spectroscopy. The time- and temperature-dependent magnetization experiments indicate that both compounds follow a behavior being known from spin glasses and frustrated systems The frustration is explained by first principle calculations that incorporate the correlation between the oxygen $2p$-electrons and deal with the mixed-valent oxygen. This leads to a physical picture where the symmetry is reduced because one third of the oxygen anions in the oxides is nonmagnetic while the remaining anions are antiferromagnetically arranged. A degenerate, insulating ground state with a large number of frustrated non-collinear magnetic configurations is confidently deduced from the theoretical point of view. Further it is shown that the compounds exhibit a variety of interesting physical phenomena under high pressure. Around 75~GPa a transition from the insulating antiferromagnetic frustrated phase to a half-metallic ferromagnetic state takes place. At a pressure of 75~GPa all anionic oxygen molecules (peroxide and hyperoxide) carry magnetic moments. Finally, above 160~GPa a metallic phase appears, where all oxygen molecules become equivalent. It is demonstrated that the bond length differences of O$_{2}^{2-}$ and O$_{2}^{-}$ have a vital effect on magnetism and conductivity of the sesquioxides.   

Polarons and excitons in insulators: insight from computer simulations

Localization of electrons and holes as well as excitons in insulators is a ubiquitous phenomenon which controls carrier mobility, luminescence and radiation damage of many materials. When such localization takes place in a perfect lattice it is called self-trapping, however in many cases it is facilitated by perturbation induced by intrinsic defects and impurities. Whatever the mechanism, it is hard to prove experimentally and especially theoretically. I will first review briefly the established models of self-trapped polarons and excitons (STE) in alkali halides and cubic oxides and will demonstrate how they are linked to the mechanisms of photo-induced desorption of these materials [1]. I will then discuss the results of our modeling, which extend these models further to more complex oxides forming so called electrides -- materials where electrons serve as anions [2], and to a qualitatively new type of electron trapping at grain boundaries in polycrystalline materials with negative electron affinity [3]. Combining periodic and embedded cluster methods we can explain and sometimes predict the properties of polarons and excitons in a range of insulators, such as amorphous SiO$_{2}$ [4], and polycrystalline HfO$_{2 }$[5] and HfSiO$_{4}$. I will discuss the applicability of different techniques to studying localization problems in insulators and will compare the predictions of periodic plane wave and embedded cluster DFT calculations. \\[4pt] [1] W. P. Hess, et al. J. Phys. Chem. B, 109, 19563 (2005) \\[0pt] [2] P. V. Sushko et al. J. Amer. Chem. Soc., 129, 942 (2007) \\[0pt] [3] K. P. McKenna and A. L. Shluger, Nature Materials, 7, 859 (2008) \\[0pt] [4] A. V. Kimmel, et al. J. Non-Cryst. Sol., 353, 599 (2007) \\[0pt] [5] D. Munoz Ramo, et al. Phys. Rev. Lett. 99, 155504 (2007)   

Localization, lattice distortion, charge transition levels, and magnetism of small-polaronic hole- and electron-states in wide-gap semiconductors

The formation of a small polaron, i.e. of a localized (electron or hole) quasi-particle state that is stabilized by a lattice distortion, is a problem in solid state physics that has eluded a quantitative description by first principles Hamiltonians for a long time. Specifically, conventional density functional theory calculations typically predict a much too delocalized state and usually fail to correctly predict the lattice distortions of localized hole-states in semiconductors and insulators. While this problem has been studied in detail for some prototypical cases like the Al impurity in SiO$_{2}$, it has at the same time precluded an extensive theoretical literature on the phenomenology of systems with localized hole states, despite the potentially dramatic effect of hole localization on such timely research topics as $p$-type doping of oxides or that of diluted magnetic semiconductors. Indeed, many predictions for hole-introducing defects and impurities that were based on local density approximations have led to a qualitatively wrong physical picture about the lattice distortion, the energies of the hole-bearing acceptor levels in the gap, and about ferro-magnetic interactions between defects. In order to stabilize the polaronic localized states in the gap, we define a parameterized hole- (or electron-) state potential which increases the energy splitting between occupied and unoccupied orbitals, where we further require that a fundamental physical condition is satisfied, i.e., the piecewise linearity of the energy as a function of the occupation number. This requirement takes the form of a generalized Koopmans conditions, which uniquely determines the one free parameter of the hole- (electron-) state potential. Applying this method to the anion-$p$ orbitals within the II-VI series of ZnO, ZnS, ZnSe, and ZnTe, we demonstrate electronic correlation effects remove the partial band occupation and the metallic band-structure character that is predicted by local density calculations for$^{ }$cation vacancies in II-VI semiconductors. This transition dramatically changes the structural, electronic and magnetic$^{ }$properties along the entire series and impedes strongly the ferromagnetic coupling between vacancies. Thus, our results demonstrate that important correlation effects due to open$^{ }p$ shells exist not only for first-row (2$p)$ elements, but$^{ }$also for much heavier anions like Te (5$p)$. We further employ our method to determine the charge transition states caused by acceptors in wide gap semiconductors (ZnO, In$_{2}$O$_{3}$, SnO$_{2}$, GaN), as well as the self-trapped electrons and holes in TiO$_{2}$.   

Prediction of d$^0$ magnetism in self-interaction corrected density functional theory

Over the past couple of years, the phenomenon of ``d$^0$ magnetism'' has greatly intrigued the magnetism community~[1]. Unlike conventional magnetic materials, ``d$^0$ magnets'' lack any magnetic ions with open $d$ or $f$ shells but surprisingly, exhibit signatures of ferromagnetism often with a Curie temperature exceeding 300 K. Current research in the field is geared towards trying to understand the mechanism underlying this observed ferromagnetism which is difficult to explain within the conventional m-J paradigm~[1]. The most widely studied class of d$^0$ materials are un-doped and light element doped wide gap Oxides~such as HfO2, MgO, ZnO, TiO2 all of which have been put forward as possible d0 ferromagnets. General experimental trends suggest that the magnetism is a feature of highly defective samples leading to the expectation that the phenomenon must be defect related. In particular, based on density functional theory (DFT) calculations acceptor defects formed from the O-2p states in these Oxides have been proposed as being responsible for the ferromagnetism~[2,3]. However. predicting magnetism originating from 2p orbitals is a delicate problem, which depends on the subtle interplay between covalency and Hund's coupling. DFT calculations based on semi-local functionals such as the local spin-density approximation (LSDA) can lead to qualitative failures on several fronts. On one hand the excessive delocalization of spin-polarized holes leads to half-metallic ground states and the expectation of room-temperature ferromagnetism. On the other hand, in some cases a magnetic ground state may not be predicted at all as the Hund's coupling might be under estimated. Furthermore, polaronic distortions which are often a feature of acceptor defects in Oxides are not predicted~[4,5]. In this presentation, we argue that the self interaction error (SIE) inherent to semi-local functionals is responsible for the failures of LSDA and demonstrate through various examples that beyond-LSDA approaches that are either self-interaction free or effectively correct for it overcome such failures to produce a more accurate description of acceptor defects in Oxides. Typically, correcting for the SIE, leads to an enhanced localization of the holes responsible for the magnetism. Additionally, the ground state becomes insulating driven by polaronic distortions around the defect site and the magnetic coupling between the impurities becomes weak~[4,5,6].\\[4pt] [1]~J.M.D.~Coey, Solid State Sci., \textbf{7}, 660 (2005). \\[0pt] [2]~I.S. Elfimov et al, PRL~\textbf{89}, 216403 (2002).\\[0pt] [3]~C.~D.~Pemmaraju and S.~Sanvito, PRL~{\bf 94},217205 (2005)\\[0pt] [4]~A.~Droghetti et al, PRB~{\bf 78}, 140404(R) (2008)\\[0pt] [5]~J.A.~Chan et al, PRL~{\bf 103}, 016404, (2009).\\[0pt] [6]~V. Pardo et al, PRB~\textbf{78}, 134427 (2008)