Oblique incidence infrared reflectance spectroscopy of phonons in cubic MgO, MnO, and NiO

Abstract

The infrared (IR) reflectivity of the cubic metal oxides MgO, MnO, and NiO has been measured at room temperature using the technique of oblique incidence. The use of this technique at three angles of incidence provides multiple sets of spectra (including both s- and p-polarizations) to analyze when compared to the standard normal incidence case, which has been used extensively in the past for these compounds. It is shown that the transverse optic (TO) and longitudinal optic (LO) mode phonon parameters can be determined with greater accuracy by using the factorized model for the fits, as compared with the popular classical model used previously, and by fitting the derivative of the reflectivity. Our results for the phonon mode parameters are similar to those found earlier, as could be expected, but are generally more precise. An analysis of the difference in frequency of the TO mode in antiferromagnetic NiO at room temperature for the two polarizations of reflected light revealed a TO mode splitting of about 4 cm⁻¹, with the p-polarized light TO mode having the higher frequency: This small splitting is in agreement with theoretical predictions. This more precise IR method for revealing the phonon mode behavior in such magnetically ordered cubic metal oxides, which are prototypes of strongly correlated electronic systems and have been found to be Mott-Hubbard insulators, may be readily applied to any similar antiferromagnetic system.

Introduction

Simple metal oxides such as MgO, MnO, and NiO that possess the cubic rock-salt crystal structure have long been of interest for their optical and, in many cases, magnetic properties. At room temperature, MgO is diamagnetic, MnO is paramagnetic (Néel temperature T_N = 118 K) [1], and NiO is antiferromagnetic (T_N = 523 K) [2], which makes for interesting comparisons of their properties. Extensive theoretical calculations have been performed of the phonons in these materials including the phonon dispersion [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13]. Interestingly, the magnetic ordering in MnO and NiO is predicted to give rise to a splitting of the degenerate transverse-optic (TO) branches that increases with lowering the temperature below T_N [6], [8], [9], [14]. More recently, MgO has been of interest because of its wide bandgap (7.8 eV) [15] and studies of MgO alloys (such as Mg_xZn_1-xO) [16] and nanostructures (see, for example, Ref. [17]) have been carried out for potential optical and optoelectronic applications such as light emitters or detectors operating in the ultraviolet [18]. On the other hand, MnO and NiO, which are prototypes of strongly correlated electronic systems and have been found to be Mott-Hubbard insulators, have attracted substantial theoretical interest (see, for example, Refs. [9], [10]). A good knowledge of the optical phonon energies is of importance for these calculations.

Crystals with the rock salt structure have space group symmetry $O_h^1$ ($\mathit{Fm}\overline{3}m$), with both types of atoms having a coordination number of six and occupying octahedral symmetry sites, and there are two atoms per primitive unit cell. A factor group analysis of the lattice modes of vibration at zero wave vector reveals two triply degenerate modes – three acoustic modes and three optic modes. The optic modes are split into two degenerate transverse modes and one longitudinal mode. Because the rock salt structure possesses inversion symmetry, the optic modes have odd symmetry and thus these modes can be observed directly in infrared (IR) spectroscopy but not in Raman spectroscopy. The case of NiO oxide is more complicated than that of MnO, because of a very small structural distortion that occurs even in the paramagnetic state [19], but this distortion is too small to produce observable effects in our reflectivity study [20], [21].

Despite decades of research using IR spectroscopy and also inelastic neutron scattering (INS), the frequencies (and line widths) of the zone-center TO and longitudinal-optic (LO) modes are not known that accurately, as can be seen from the widespread range of mode frequencies obtained in these earlier studies (see Table 1). Magnesium oxide (magnesia), for example, has been investigated in detail by IR spectroscopy since the measurements performed by Tolksdorf in 1928 [22]. Soon thereafter, three further optical absorption studies on MgO powders were reported [23], [24], [25]. However, as discussed in detail by Willmott [26], there was no general agreement between the results obtained. More complete studies by absorption and reflectivity had to await the availability of single crystals of MgO [25], [26] and further advances in the optical techniques employed for measuring their properties. All of these early (and also subsequent) measurements on MgO, as well as for the other oxides, were performed at near normal incidence in optical reflectance and/or absorption geometries. For the absorption case the results are not accurate due to difficulties in preparing sufficiently thin single-crystal samples, while the reflectance spectra have proved difficult to model using the traditional Kramers-Kronig and classical formalisms due to the appearance of an unanticipated additional feature in the spectrum in the vicinity of the LO and TO phonon modes.

In this paper we report on IR reflectivity measurements at oblique incidence for three angles of incidence, which is an experimental geometry that improves the ability to determine the optical mode frequencies [31]; the analysis of the spectra with factorized model [32]; and lastly fits to the derivative of the spectra for improved accuracy and interpretation of the weaker features. The results obtained are then compared with earlier measurements. A detailed analysis of the results obtained for the TO modes reveals evidence for the splitting of the TO mode degeneracy in antiferromagnetic NiO, and the splitting obtained at room temperature of 3.6 ± 1.0 cm⁻¹ agrees well with theoretical predictions.