LI Jufen, SU Juan, YI Xuebin, TANG Bin, WU Xinhui, ZHONG Shuirong

(1. School of Science, Southwest Petroleum University, Chengdu 610065, China; 2. Southwest Institute of Technical Physics,Chengdu 610065, China)

Abstract: The electron paramagnetic spectra of trigonal Mn2+ centers in [Co(H2O)6]SiF6, [Co(H2O)6]SnF6, and [Co(H2O)6]PtCl6 crystals were studied on the basis of the complete energy matrices for a d5 configuration ion in a trigonal ligand field. When Mn2+ is doped in the [Co(H2O)6]SiF6, [Co(H2O)6]SnF6, and[Co(H2O)6]PtCl6 crystals crystals, there is a similar local distortion. The experimental results show that the local lattice structure around a trigonal Mn2+ center has an elongation distortion along the crystalline C3 axis. From the EPR calculation, the local lattice structure parameters R=2.278A, θ=52.6406° for [Co(H2O)6]SiF6, R=2.280,θ=52.4936° for [Co(H2O)6]SnF6 and R=2.244A, θ=53.0616° for [Co(H2O)6]PtCl6 were determined.

Key words: [Co(H2O)6]SiF6; [Co(H2O)6]SnF6 and [Co(H2O)6]PtCl6; local lattice structure distortion;EPR spectrum; ligand-fields theory

1 Introduction

Since the electron paramagnetic resonance (EPR)zero-field splitting of paramagnetic impurity ions in crystals is very sensitive to the local structures of impurity, electron paramagnetic resonance is regarded as an effective method to study the local geometry and local properties in the vicinity of impurity[1-4]. As for the compounds of general formula [M(H2O)6]XY6(M=Mg, Mn , Fe, Co, Ni, Zn, and Cd, X is a quadrivalent element typically Si, Sn, Ti, Pt, Zr, and Ge, and Y may be F or Cl) series, the EPR spectra are extensively used in studying the structural phase transition and the local structural parameters of impurity centers in these crystals[5-11]. For example, the local lattice structure of Mn2+, Fe2+, Co2+, Ni2+ion in [Zn(H2O)6]SiF6has been investigated by WAN KL[5], Misra SK[6], Wen-Chen Z[7]and Rubins RS[8]. The Crystal structural phase transitions of Mn2+ion in [Mn(H2O)6]SiF6, [Zn(H2O)6]TiF6, [Mg(H2O)6]SiF6, [Co(H2O)6]SiF6, and [Zn(H2O)6]ZrF6had been studied by hattopadhyay T[9], Zapart W[10], Roy SKD[11]. The EPR spectra of Mn2+is doped into [Co(H2O)6]SiF6, [Co(H2O)6]SnF6, and [Co(H2O)6]PtCl6have been experimentally studied at different temperatures using X-band microwave frequency by R HRABAŃSKI[12]. He found that at room temperature the EPR spectra transition metal Mn2+in single crystals of three cobalt salts, crystals belong to the trigonal distortion. In addition, he discovered that Mn2+ion was doped into [Co(H2O)6] PtCl6single crystal would replace Co2+ion exhibiting a unique magnetic complex[13]. Thereafter, JAIN VKet al[14]have studied the EPR spectra for Mn2+in [Co(H2O)6]SiF6single crystal using the Newman superposition model. However, their studies all are based on the second-order EPR parameterb20.

It is well known that for ad5configuration ion in a trigonal ligand-field, the high-spin ground state is the6A1state. To describe the6A1ground-state splitting of the Mn2+ions in [Co(H2O)6]SiF6, [Co(H2O)6]SnF6, and[Co(H2O)6]PtCl6crystals, the spin Hamiltonian should include three different zero-field splitting parametersandb43, which are quite sensitive to distortion of the local environment around the paramagnetic ion.The parameterb43relates to a fourth-order spin operator and represents a cubic component of the crystalline electric field. The parametersb20andb40are, respectively, associated with the second-order and fourth-order spin operators and represent an axial component of the crystalline electric field that is axially symmetric about theC3axis. To explain more reasonable distortion structure, herein, we suggest that the two zero-field splitting parametersb20andb40should be simultaneously considered in the determination of the local structure distortion for Mn2+in [Co(H2O)6]SiF6, [Co(H2O)6]SnF6,and [Co(H2O)6]PtCl6crystals.

In this paper, the local structure of the Mn2+in-[Co(H2O)6]SiF6, [Co(H2O)6]SnF6, and [Co(H2O)6]PtCl6crystals will be studied by diagonalizing the complete energy matrices and analyzing the two low-symmetry EPR parametersb20andb40. The local structure parametersR=2.278A,θ=52.6406° for CFSiH,R=2.280,θ=52.4936° for CFSnH andR=2.244A,θ=53.0616° for CCPtH have been determined by simulating the calculated EPR parameters, respectively. [Co(H2O)6]SiF6,[Co(H2O)6]SnF6, and [Co(H2O)6]PtCl6crystals, hereafter to be referred to as CFSiH, CFSnH and CCPtH,respectively.

2 Theoretical analysis

The EPR spectra of Mn2+ion in a trigonal symmetry field can be described in terms of spin Hamiltonian as follows[15]:

where, the first term corresponds to the Zeeman interaction and the following terms represent the zero-field interaction.uBis the Bohr magneton,is the spin angular momentum operator,gis the splitting factor,is the external magnetic field,are the zero-field splitting parameters, andOkqare the standard Stevens spin operators[16].

From the spin Hamiltonian the explicit expressions of the energy levels in the ground state6A1for a zero magnetic field are given as follows:

Then, the zero-field splitting energies ΔE1and ΔE2in the ground state6A1may be expressed as a function of the zero-field splitting parametersb20,b40, andb43.

where, the positive and negative signs in Eq.(3) correspond tob20≥0 andb20＜0, respectively. It is noteworthy to mention that the parametersbkqare related to the parametersa,Dand (a-F). a is the cubic field splitting parameter,Dand (a-F) correspond to axial component of the second-order and the fourth-order zero-field splitting parameter, respectively. The relationships are given by[15]:

The perturbation Hamiltonian for a paramagnetic Mn2+ion in a trigonal ligand field may be written as[17]:

where, the first term is the electron-electron interactions, the second term is the spin-orbit coupling interactions, and the third is the ligand-field potentials, which can be expressed as:

According to the perturbation Hamiltonian (5),for ad5configuration ion, two 84×84 energy matrices have been constructed in terms of the irreducible representations Γ4(Γ5) and Γ6ofC3point symmetry[17]. The matrix elements are as functions of the Racah parametersBandC, the Trees correction α，the spin-orbit coupling coefficientζ，and the crystal field parametersB20,B40,B43C,B43S[18], which are generally defined as:

The crystals of CFSiH, CFSnH, and CCPtH, supposedly isomorphous with [Ni(H2O)6]SnCl6, with space groupR3[12,13], crystallizes in trigonal symmetry. By analogy with the isomorphous lattices, it is expected that the divalent metal ion is surrounded by a trigonally distorted octahedron of six water molecules. In order to describe the distortion, theZaxis is chosen along threefold axis, as shown in Fig.1.

Fig.1 The local structure of octahedral (CoO6)2+ cluster in CFSiH,CFSnH, and CCPtH crystals

Then, the ligand-field parameterB43Swill vanish. From the point-charge-dipole model, the trigonal ligand-field parametersB20,B40, andB43Ccan be expressed as:

with

where,θdenotes the angle between the Mn-O bond andC3axis,Ris the Mn-O distance. According to the Van Vleck approximation forGk(τ) integral[19], we have the relationships:

where,A4=-eqτ＜r4＞ andA2=-eqτ＜r2＞,A2/A4=＜r2＞/＜r4＞, the ＜r2＞/＜r4＞ =0.119328 for Mn2+may be obtained from the parametric radial wave function[20].A4is a constant for an octahedral [MnO6]2-cluster, and its value can be determined from the optical spectra and the Mn-O band length of the MnCO3crystal[21]. By the way, we deriveA4=26.7375 au andA2=3.1905 au for the octahedral [MnO6]2-cluster. Taking these values into account, the relationship between the EPR parametersb20andb40, as well as the molecular structure parametersRand Δθcan be obtained for the complete energy matrices.

In CFSiH, CFSnH, and CCPtH crystals, Co2+ion is surrounded by six water molecules forming almost regular octahedral structures (Co·6H2O)2+[12,13]. When Mn2+is doped in CFSiH, CFSnH, and CCPtH crystals,Mn2+will replace the host Co2+ion located at the octahedral site (Mn·6H2O)2+. The local lattice structure around the Mn2+displays a trigonal distortion, as plotted in Fig.2.

Fig.2 The local lattice structure distortion of trigonal Mn2+ center in CFSiH, CFSnH, and CCPtH from the cubic configuration

The trigonal distortion can be described by parametersRand Δθ. We may approximately regard the water as the oxygen ligand in the following calculation.The local structure parameterθfor Mn2+replacing Co2+in the crystals can be written as:

where,B0=918 cm-1,C0=3 273 cm-1,ζ0=347cm-1,α0=65 cm-1, andβ0=-131 cm-1are given for the freeion parameters of Mn2+ions[24]. N is the covalent factor, we may take the typical average covalent factorN=0.965 as found in the MgO:Mn2+system for Mn2+inthe CFSiH, CFSnH, and CCPtH crystals[12,24]. Thus, the trigonal ligand-field parametersB20,B40, andB43Care only functions ofRand Δθ. For the trigonal Mn2+centers in CFSiH, CFSnH and CCPtH crystals, the EPR parameters can be simulated with the use of parameters R and Δθ by diagonalizing the complete energy matrices. The comparison between the theoretical value and the experimental findings are listed in Table 1.The comparison between the theoretical value and the experimental findings are listed in Table 1. Subsequently, we obtain the local crystal structure parameter,i e,θ=52.641° for CFSiH;θ=52.496° for CFSnH;θ=53.062° for CCPtH. The bond lengths and angles between Mn-O and C3-axis are listed in Table 2.

Table 1 The ground-state splittings ΔE1, ΔE2 and the EPR parameters D and(a-F) for the octahedral Mn2+ center in CFSiH,CFSnH, and CCPtH crystals as a function of R and Δθ at the room temperature,

Table 2 The local structure parameters R and θ for the CFSiH,CFSnH, and CCPtH crystals as following

3 Discussion

From the table1, the calculated EPR parameters of Mn2+in CFSiH, CFSnH, and CCPtH crystals are all in good agreement with the corresponding experimental findings, respectively. The results show that when Mn2+is doped in CFSiH, CFSnH, and CCPtH crystals,there is a similar local distortion. The results ofθ＜θcindicates that the local structure around the Mn2+ion in CFSiH, CFSnH, and CCPtH exhibits an elongation distortion. In addition, the bond lengths of Co-H2O isR=2.092 A for CFSiH[25],R=2.077 A[26]for CFSnH, respectively. The comparison between the bond lengths of Co-H2O in CFSiH, CFSnH and the bond lengths of Mn-H2O in (Mn·6H2O)2+, we find the bond lengths is indeed elongated. This may be due to the fact that the radius of Mn2+(rMn2+=0.80 A) ion is larger than that of the host Co2+(rCo2+=0.72 A) ion. Of course, careful experimental investigations especially optical absorption experiment are required to clarify the local structure of Mn2+doped in those crystals in detail.

4 Summary

The EPR spectrum of Mn2+in CFSiH, CFSnH,and CCPtH crystals have been studied on the basis of the complete energy matrices for ad5configuration ion in a trigonal ligand field. The calculated EPR parameters of Mn2+in CFSiH, CFSnH, and CCPtH crystals are all in good agreement with the corresponding experimental data, and the local structure parametersR=2.278 A,θ=52.6406° for CFSiH,R=2.280,θ=52.4936° for CFSnH andR=2.244 A,θ=53.0616° for CCPtH have been determined. The results show that when Mn2+is doped in CFSiH, CFSnH, and CCPtH crystals there is a similar local distortion. The results ofθ＜θcindicates that the local structure around the Mn2+ion in CFSiH,CFSnH, and CCPtH crystals exhibits elongation distortion.