Rui-Peng Chai(柴瑞鵬), Dan-Hui Hao(郝丹輝), Dang-Li Gao(高當(dāng)麗), and Qing Pang(龐慶)

1College of Science,Xi’an University of Architecture and Technology,Xi’an 710055,China

2Xi’an University of Architecture and Technology Huaqing College,Xi’an 710043,China

Keywords: EPR parameters,distorted local structure,covalent effect,optical properties

1. Introduction

The metal difluorides with the formula MF2(M = Ca,Cd,Sr,Ba)can be used as ideal laser media,scintillators,and other optoelectronic materials,due to the excellent optical and electronic properties when activated with trivalent rare-earth ions.[1-13]Weakly interacting dopants with rare-earth ions are favourable for the possibility of production of the compact laser.[10-13]In particular, the case of Er3+is of considerable interest,[14-21]since it has been found that the visible and infrared photoluminescence spectra of Er3+ions with low concentration in MF2-type fluorides are closely related to the different charge compensation centers,mainly resulting from the modification of local site symmetry and local lattice distortion.

2. Theoretical methods

In general, the perturbation Hamiltonian for a 4f11configuration ion Er3+in a trigonal crystal-field can be expressed as[42-44]

where the preceding eight terms on the right-hand side indicate the spherically symmetric free ion parts,and the last term represents the crystal-field potential function. The operators and parameters of Eq.(1)are written and defined according to traditional practice.[27-30]The crystal-field Hamiltonian with the C3vsite symmetry may be expanded as

where

where the sum i runs over all the unfilled electrons. The reduced matrix elements of the generalized tensor on the extreme right side of Eq.(7)can be further reduced to

For the sake of saving space,the abbreviation[Y]=2Y+1 is used and valid only when there is a single symbol enclosed within the square brackets in Eq.(8). With simple manipulation of transformation, the relations between the components of these vector operators in the Cartesian coordinates systems and the components of the corresponding tensor operators may be written as follows:

where effective S = 1/2 is taken. The constants required for following calculations are 〈r?3〉 = 10.6 a.u. and μN(yùn)=?0.5647 for the167Er3+isotope.[29]The correlation between the EPR parameters and the actual Hamiltonian is established by completing the energy matrices.

3. Calculations and discussion

Table 1. The crystal-field parameters for Er3+ ions in CdF2 and CaF2 crystals,in units of cm?1.

Table 2. The calculated and experimental Stark energy levels of 4I15/2 states for C3v (II)centers of Er3+ ions in CdF2 and CaF2 crystals. All values are in units of cm?1.

Table 3. The calculated and observed EPR parameters for C3v (II)centers of Er3+ ions in CdF2 and CaF2 crystals, the hyperfine parameters are in units of 10?4 cm?1.