Bound Small Polaron Optical Absorption in V⁻‐Type Centres in MgO

Abstract

A theory, based on the method of moments, is described which predicts exact lineshapes for the optical absorption of bound small polarons. This theory explains the position, large width, and high oscillator strength of the optical absorption of the Vxl centre in MgO and the polarisation of V-in MgO, which has been observed under uniaxial stress.Eine Theorie, beruhend auf der Methode der Momente, wird beschrieben, die exakt die Linienform der optischen Absorption gebundener kleiner Polaronen herleitet. Diese Theorie erklart die Lage, grode Breite und hohe Oszillatorenstarke der optischen Absorption von Vgl Zentren in MgO und die Polarisation von V-in MgO, welche unter einachsigem Druck beobachtet wurden. Theory V-type centres in alkaline earth oxides (a hole trapped a t one of the 02-ions neighboring various negative defects [l])show broad absorption bands [ 2 to 51 in the visible, the origin of which has so far not been understood [ 3 ] . With V-[6] andVi1 [7] in MgO as examples (negative charge represented by a vacancy, isolated or associated with A13+, respectively), we will show that these bands can be explained if the distortion of the centres is taken into account.Even in V-, where the six 02-ions surrounding the vacancy are equivalent, the hole is localised at one ion a t low teperatures and the centre shows tetragonal symmetry. This can be attributed to a distortion of the centre by a coupling of the hole to a TI, phonon (coordinates Q,, Qy, Qz), competing with the tunneling of the hole. This exchange ( J > 0) between neighbouring 02-pz functions (Fig. l a ) respectively. If hole-T1,-phonon interaction is introduced in a manner analogous to that described by Ham [9, 101, it can be shown that to each af the six 02-p, functions there belongs a spherically symmetric oscillator, displaced in Q-space (Fig. lb), with the potential energies (in the limit J +-0)for the wells centred on the &,-axis and similarly for the four equivalent ones.EJT is an abbreviation for V2/(2pmE), where hm,, is the oscillator energy and V , the reduced matrix elementl) describing the strength of hole-phonon coupling.

Optical absorption in lithiated tungsten oxide thin films: Experiment and theory

“…22 Theories for optical absorption due to transitions between localized states have been proposed based on various theoretical frameworks. In the present context, the most relevant ones appear to be intervalence transfer absorption 23 and small polaron absorption, [24][25][26] which have both been used for tungsten oxide films. 7,19,27 These theories lead to quite similar expressions and appear to be difficult to distinguish from one another.…”

O−holes associated with alkali acceptors inBaTiO3Varnhorst1, Schirmer2, Kröse3 et al. 1996Phys. Rev. BSelf Cite674360View full textAdd to dashboardCite

“…The features of the absorption band-large width, high intensity, peak in the visible or near infrared, correlation with O Ϫ ESR-are characteristic for light-induced hole transfer between O 2Ϫ ions equivalent with respect to the acceptor core, Na ϩ in the present case. In the past this model 20,21,18 has successfully explained O Ϫ -related absorptions in many materials ͓e.g., MgO:V Ϫ and similar defects, 21 …”

“…Since the intensity of the optical transfer transition depends on the square of the energy overlap integral, 20 J, which is a function exponentially decreasing with distance, only the nearest neighbors of an initial O Ϫ ion are eligible as final sites. Among these there are the four O 2Ϫ ions indicated in Fig.…”

O– bound polarons in oxide materials

“…This simple approach allows to explain the typical features of those objects -wide absorption bands, high oscillator strengths, excited state tunnelling splittings -under a common guideline. This method was developed rather early [1]. New manifestations of O -bound small polarons have been found in many materials.…”