Magneto-optical properties of neodymium-doped LiYF4

Journal of Alloys and Compounds 291 (1999) 300–311

L

Magneto-optical properties of neodymium-doped LiYF 4 ¨ H. De Leebeeck, K. Binnemans*, C. Gorller-Walrand K.U.Leuven, Department of Chemistry, Coordination Chemistry Division, Celestijnenlaan 200 F, B-3001 Heverlee, Belgium Received 15 May 1999; received in revised form 5 June 1999; accepted 19 June 1999

Abstract In this paper we demonstrate the validity of a semi-empirical approach to describe the magneto-optical properties of lanthanide complexes. The polarised absorption (IR–VIS–UV), magnetic circular dichroism (MCD) and magnetic susceptibilities of a LiYF 4 :Nd 31 (1.5%) single crystal were recorded and analysed in a temperature region of 4.2 K up to room temperature. The crystal structure is obtained by means of X-ray analysis. Starting values of the free ion, crystal field and intensity parameter sets were obtained by using an additive crystal-field model based on the coordinates of the eight F - ions in the first coordination sphere (S4 symmetry). After several iterations the parameter values are optimised and checked by simulations of the optical and magneto-optical spectra and by the simulation of the magnetic susceptibilities.  1999 Elsevier Science S.A. All rights reserved. Keywords: Crystal and ligand fields; Optical properties; Light absorption and reflection; Magnetic measurements; Electronic states (localized)

1. Introduction The LiYF 4 single crystal, doped with trivalent neodymium is known as a very good laser host [1–4]. In ˚ and 10471 solid state laser optics the emission at 10530 A ˚ are commonly used laser lines [5]. In view of these A applications the energy diagram of the neodymium ion in LiYF 4 is extensively studied using the approximating D2d point group as site symmetry of the Nd 31 [6–9]. More recently we started the optical considerations in the exact S4 site symmetry and we did not limit our interpretations to the crystal field energy level diagram but included a preliminary intensity analysis of the transitions [10,11] where the LiYF 4 :Nd 31 complex was also investigated with the magnetic circular dichroism technique. Furthermore the temperature-dependence of the magnetic susceptibilities was probed [12]. In this paper we combine spectroscopic and magnetic properties and evaluate the optimisation of the corresponding parameter sets. The labelling of the crystal field energy levels by the irreducible representations of the S4 point group is based on the polarised absorption spectra and is used for the optimisation of the free ion and crystal

*Corresponding author. Tel.: 132-16-327-446; fax: 132-16-327-992. E-mail address: [email protected] (K. Binnemans)

field parameters. The dipole strength of these transitions is used in the intensity calculations where intensity parameters are optimised. The fitting procedures are started with parameters values as we calculated them using the results of our X-ray analysis on the 1.5% doped LiYF 4 :Nd 31 single crystal. The obtained parameter sets are evaluated in a graphical simulation of another spectroscopic phenomenon, magnetic circular dichroism (MCD), and in a nonspectroscopic property, namely the magnetic susceptibility.

2. Structural considerations LiYF 4 crystals are isomorphous with the mineral scheelite (CaWO 4 ). The Y 31 ion is equivalent with Ca 21 in the CaWO 4 lattice, the Li 1 ion replaces W 61 and the F 2 ion takes the O 22 position. The scheelites are tetragonal and 6 belong to the I4 1 / a (C 4h ) (no 88 of the International Tables for X-ray Crystallography) space group with four formula units in the unit cell (Z 5 4). In the lanthanide doped LiYF 4 compounds the lanthanide takes the place of the Y 31 ion [13]. The cell parameters of the 1.5% neodymium doped LiYF 4 unit cell are determined using an Enraf Nonius ˚ and c5 CAD-4F diffractometer a 5 b55.1706(2) A ˚ These values do not differ much from the 10.7557(11) A. pure LiYF 4 parameter values [13] and this is due to the

0925-8388 / 99 / $ – see front matter  1999 Elsevier Science S.A. All rights reserved. PII: S0925-8388( 99 )00284-4

H. De Leebeeck et al. / Journal of Alloys and Compounds 291 (1999) 300 – 311

low percentage of doping. The concentration of neodymium ions in the LiYF 4 :Nd 31 (1.5%) single crystal is calculated at 0.3465 mol 1 21 . The positions of the atoms are also derived from the refractions registered on the Enraf Nonius CAD-4F diffrac¯ tometer. The origin of the unit cell is placed in the 4-axis and the atoms are found at: Li Y or Nd F

0, 0, 0 0, 0, ]12 0.2818(4), 0.1640(4), 0.0812(2)

The unit cell of LiYF 4 :Nd 31 (1.5%) is given in Fig. 1. The first coordination sphere of an Y 31 / Nd 31 ion is also completely drawn. The Y 31 / Nd 31 ion is surrounded by eight fluoride ions which form the edges of a slight distorted dodecahedron [14]. The symmetry of this polyhedron is found to be S4 , a slight distortion of the D2d point group. In Table 1 the axial coordinates of the eight fluoride ions with an indication of the distortion of the f -coordinate are given. The slightly distorted dodecahedron is shown in Fig. 2. In this figure the choice of the coordinate axes is indicated [15]. The choice of the coordinate axes is determining the number and the values of the crystal field and intensity

301

Table 1 Polar coordinates of the eight F 2 ions which form the site symmetry of Nd 31 in LiYF 4 a Atom

r

u

w

F(1) F(2) F(3) F(4) Nd F(6) F(7) F(8) F(9)

rB rB rA rA 0 rB rB rA rA

uB uB uA uA 0 180 2 uB 180 2 uB 180 2 uA 180 2 uA

270 1 55.04 1 Dw 90 1 55.04 1 Dw 180 1 55.04 2 Dw 55.04 2 Dw 0 180 1 55.04 1 Dw 55.04 1 Dw 90 1 55.04 2 Dw 270 1 55.04 2 Dw

a

˚ rB 52.2996 A; ˚ uA 567.148; uB 537.868; Dw 51.968. rA 52.2481 A;

parameter sets appearing in the simulations of the optical properties.

3. Experimental details The polarised absorption spectra were recorded on an AVIV 17 DS spectrophotometer, in the spectral region between 245 and 2500 nm (40500–4000 cm 21 ) at 4.2 K, 150 K and room temperature. Cooling was done in an OXFORD 1204 continuous flow cryostat. Light polarisa-

Fig. 1. Unit cell of LiYF 4 :Nd 31 with a complete polyhedron surrounding one neodymium ion.

H. De Leebeeck et al. / Journal of Alloys and Compounds 291 (1999) 300 – 311

302

Table 2 Selection rules for electric dipole (ED) and magnetic dipole (MD) transitions in the S4 symmetry

Fig. 2. The site symmetry of Nd 31 in LiYF 4 as a slightly distorted dodecahedron (S4 point group).

tion was achieved by a Glan-Thompson polariser. The so-called a, p and s spectra are determined as follows:

a

→

→

E optic axis H optic axis →

→

→

→

p E optic axis H optic axis s

E optic axis H optic axis

The magnetic circular dichroism (MCD) is registered by means of an AVIV 62DS CD spectrometer at 4.2 K using the same cryostat. The optical region of 285–800 nm (35 000–12 500 cm 21 ) is investigated on a LiYF 4 :Nd 31 (1.5%) single crystal positioned with its optical c-axis along the magnetic field lines of a 0.9T OXFORD N177 electromagnet. The light beam passes through the single crystal parallel to the c-axis (optic axis). The evolution of the magnetic susceptibility versus temperature (1.7–300 K) are recorded using a MPMS-5S Quantum Design SQUID with a sensitivity of 10 210 cgsemu g 21 . The measurements were taken with the magnetic field parallel and perpendicular to the optic axis of the crystal. The signals were corrected for the diamagnetism of the constituent atoms, using Pascal’s constants [16].

4. Analysis of the spectra The polarised absorption spectra of trivalent neodymium in the LiYF 4 host show a large number of peaks. In identifying these transitions the selection rules for polarised absorption are very useful. In Table 2 the theoretically allowed transitions for a lanthanide ion surrounded by a S4 site symmetry and containing an odd number of electrons are given. In addition, the a polarised measurements on LiYF 4 :Nd 31 are found to be similar to the s polarisation,

ED

G5,6

G7,8

MD

G5,6

G7,8

G5,6 G7,8

as aps

aps as

G5,6 G7,8

aps ap

ap aps

indicating the predominantly electric dipole character of the transitions. The spectra at higher temperatures are more complicated compared with the ones at 4.2 K. This is partly due to the broadening of the bands what results in an overlap of transitions. Another reason is the population of the crystal field levels of the 4 I 9 / 2 ground state (Table 3). The identification of these levels is deduced from the simple 2 P1 / 2 ← 4 I 9 / 2 transition at different temperatures (see Figs. 3–5). The determination of the experimental energy diagram of LiYF 4 :Nd 31 is mainly based on the identification of 155 very narrow transitions which occur in the spectra at 4.2 K. As indicated by Couto dos Santos et al. [9] a more complete experimental energy level scheme (they used 137 experimental energy levels) will lead to a more adequate set of free ion and crystal field parameters and consequently produce a better simulation of the energy diagram. Not only the energy position but also the intensity of the transitions is analysed. This is done by integrating the area under the peaks by means of a Gauss curve [17,18]. The values are expressed as dipole strengths in Debye 2 . The optimisation of the intensity parameters is based on 365 experimental dipole strengths of spectra in the a, p and s polarisation at 4.2 K. The magnetic circular dichroism (MCD) spectra of LiYF 4 :Nd 31 are composed of a great number of overlapping transitions even at 4.2 K. This is due to the Zeeman effect on the Kramers’ degeneration of crystal field levels of an odd electron system. For this reason it is not possible to determine the experimental Zeeman energy levels. The interpretation will be limited to a comparison of the simulated MCD spectra with the experimental data and this concerning the position, the sign as well as the intensity of the MCD terms. Table 3 Fractional Boltzmann population of the crystal field levels in the 4 I 9 / 2 ground state of LiYF 4 :Nd 31 Crystal field level (cm 21 )

Population at 4.2 K

Population at 150 K

Population at 293 K

G7,8 G7,8 G5,6 G5,6 G7,8

1.000 0.000 0.000 0.000 0.000

0.639 0.184 0.114 0.060 0.004

0.432 0.228 0.178 0.128 0.033

0 130 180 247 523

H. De Leebeeck et al. / Journal of Alloys and Compounds 291 (1999) 300 – 311

Fig. 3. Polarised absorption spectra of the LiYF 4 :Nd 31 at 4.2 K.

2

P1 / 2 ← 4 I 9 / 2 transition in

5. Discussion

5.1. Energy diagram In a semi-empirical approach the energy diagram of a trivalent lanthanide ion is determined using a parametric scheme: free ion parameters take the free ion perturbations into account; crystal field (CF) parameters incorporate the site symmetry of the first coordination sphere. No additional parameters are required for the Zeeman perturbation. In Eq. (1) the parametric expression for the energy levels of the Nd 31 ion in an S4 environment is given.

O O

E 5 EAV 1

fk F k 1 znl A SO 1 a L(L 1 1) 1 b G(G2 ) 1 g G(R 7 )

k 52,4,6

1

i 52,3,4,6,7,8

T iti 1

O

k 52,4,6

P k pk 1

O

M kmk

k 50,2,4

1 B 20 C 20 1 B 40 C 40 1 B 60 C 60 1 B 44 (C 44 1 C 424 ) 1 iB 44 (C 44 1 C 424 ) 1 B 64 (C 64 1 C 624 ) 1 iB 64 (C 64 1 C 624 ) 1 b (L 1 2S)H

(1)

The significance of the parameters can be found in Table 4. Fk and A SO represent the angular part of the electrostatic and spin–orbit interaction respectively; L and S are the total angular and spin momenta; G(G2 ) and G(R 7 ) are the

Fig. 4. Polarised absorption spectra of the LiYF 4 :Nd 31 at 150 K.

303

2

P1 / 2 ← 4 I 9 / 2 transition in

Casimir operators for the groups G2 and R 7 ; t i are the three body operators; pk and m k represent the operators for the magnetic corrections; C kq is a spherical operator of rank k with components q; b is the Bohr magneton and H is the applied magnetic field. The optimisation of the free ion and crystal field parameters is performed by a linear least squares fitting of the calculated versus the 155 experimental CF energy levels in the absence of a magnetic field (H50 Tesla). In order to obtain realistic parameter values it is important to perform the first diagonalisation with physically acceptable values. The free ion parameters of Ref. [11] are used as starting values for the free ionic part but the crystal field starting parameters are calculated by means of the coordinates of the fluoride ions on the edges of the slightly distorted dodecahedron with S 4 symmetry (see Table 1). These coordinates are inserted in Eq. (10) of Ref. [19] and the results are given in Table 4. The fitting procedure comprises several iterations with consecutively more parameters to vary. The optimisation is completed by a diagonalisation incorporating all the free ion and crystal field perturbations together and the resulting parameter values are compared with the starting values in Table 4. The labelled crystal field energy levels (experimental and

304

H. De Leebeeck et al. / Journal of Alloys and Compounds 291 (1999) 300 – 311 Table 4 Free-ion and crystal field parameters for LiYF 4 :Nd 31 using the S4 point group

Fig. 5. Polarised absorption spectra of the LiYF 4 :Nd 31 at room temperature.

2

Parameter

Starting value (cm 21 )

Optimised value (cm 21 )

EAV F2 F4 F6 z4f a b g T2 T3 T4 T6 T7 T8 M0 M2 M4 P2 P4 P6 B 20 B 40 B 60 B 44 iB 44 B 64 iB 64

24413 72911 52471 35486 872 21 2575 1488 226 43 87 2285 320 212 0.7 0.56 0.38 195 0.75 0.50 926 21523 2103 21440 1475 2819 654

24411 72939 52491 35489 873 21 2572 1478 217 44 86 2285 318 205 0.7 0.56 0.38 186 0.75 0.50 372 2974 220 21116 598 21020 200

M0 M0 P2 P2

M0 M0 P2 P2

P1 / 2 ← 4 I 9 / 2 transition in

calculated) of LiYF 4 :Nd 31 according to the S4 symmetry are given in Table 5. In contrast with the conclusions of Ref. [9], the simulation of the CF energy diagram is more adequate using the S4 point group. Although the distortion from D2d to S4 is 4 6 rather small, the additional imaginary iB 4 and iB 4 parameter values are of a significant magnitude as predicted by the calculation of the starting values based on the structure of the complex. In addition no arbitrary choice of the azimuthal angle in spherical coordinates is possible here l because the B kq and A tp parameter sets have to be consistent. This implies the use of all the B kq parameters including both the imaginary iB 44 and iB 64 parts. The Zeeman energy diagram is calculated using the optimised parameter values and the diagonalisation is performed introducing free ion, crystal field and Zeeman (H50.9 Tesla) perturbations at the same time. The double Kramers’ degeneration of the CF levels is lifted and all the Zeeman levels are non degenerate, separated by a few cm 21 . It is between these levels that the transitions of circularly polarised light in the MCD spectra occur.

5.2. Transition intensity Transitions in optical spectra occur according to the magnetic and / or electric dipole mechanism. The calcula-

tion of the dipole strength depends on the character of the transition and as mentioned above the transitions of the neodymium ion in LiYF 4 are predominantly electric dipole transitions. However due to J-mixing it is not correct to exclude the magnetic dipole contributions and the global dipole strength is calculated as given in Eq. (2) [18]. 1

2

D 5 xMDukc u 2 b (L 1 2S)r uc 9lu 1 xED e

2

FO a A G l tp

l tp

2

l ,t, p

(2) In this equation x represents the local field corrections and for the electric dipole part intensity parameters A ltp with their coefficients a ltp are introduced. In the S4 point group the ( l, t, p) combinations (2, 3, 62), (4, 3, 62), (4, 5, 62), (6, 5, 62), (6, 7, 62) and (6, 7, 66) have to be considered, each consisting of a real and imaginary part. The intensity parameters are optimised by a non-linear least squares fitting of the calculated versus the 365 experimental dipole strengths of the a, p and s spectra at 4.2 K. The fitting procedure is started with physically determined values as Reid et al. [19] developed in their Eq. (4). The coordinates of the F 2 ligands (Table 1) are introduced in the equation and the resulting starting values can be found in Table 6. The a ltp coefficients are calculated by means of the crystal field wavefunctions and the A ltp parameters are optimised after several interactions where all parameters

H. De Leebeeck et al. / Journal of Alloys and Compounds 291 (1999) 300 – 311

305

Table 5 Labelled experimental and calculated crystal field energy levels and dipole strengths for transitions from the G7,8 crystal field ground state of LiYF 4 :Nd 31 according to the S4 point group Label 4

I9 / 2 I9 / 2 4 I9 / 2 4 I9 / 2 4 I9 / 2 4 I 11 / 2 4 I 11 / 2 4 I 11 / 2 4 I 11 / 2 4 I 11 / 2 4 I 11 / 2 4 I 13 / 2 4 I 13 / 2 4 I 13 / 2 4 I 13 / 2 4 I 13 / 2 4 I 13 / 2 4 I 13 / 2 4 I 15 / 2 4 I 15 / 2 4 I 15 / 2 4 I 15 / 2 4 I 15 / 2 4 I 15 / 2 4 I 15 / 2 4 I 15 / 2 4 F3 / 2 4 F3 / 2 4 F5 / 2 4 F5 / 2 2 H(2) 9 / 2 4 F5 / 2 2 H(2) 9 / 2 2 H(2) 9 / 2 2 H(2) 9 / 2 2 H(2) 9 / 2 4 F7 / 2 4 F7 / 2 4 S3 / 2 4 S3 / 2 4 F7 / 2 4 F7 / 2 4 F9 / 2 4 F9 / 2 4 F9 / 2 4 F9 / 2 4 F9 / 2 2 H(2) 11 / 2 2 H(2) 11 / 2 2 H(2) 11 / 2 2 H(2) 11 / 2 2 H(2) 11 / 2 2 H(2) 11 / 2 4 G5 / 2 4 G5 / 2 4 G5 / 2 4 G7 / 2 4 G7 / 2 4 G7 / 2 4 G5 / 2 4 G7 / 2 4 G7 / 2 4

G7,8 G7,8 G5,6 G5,6 G7,8 G7,8 G5,6 G7,8 G5,6 G5,6 G7,8 G5,6 G7,8 G5,6 G7,8 G5,6 G5,6 G7,8 G5,6 G5,6 G7,8 G7,8 G7,8 G5,6 G7,8 G5,6 G7,8 G5,6 G7,8 G5,6 G7,8 G5,6 G5,6 G7,8 G5,6 G7,8 G7,8 G5,6 G7,8 G5,6 G7,8 G5,6 G5,6 G7,8 G7,8 G5,6 G7,8 G5,6 G7,8 G7,8 G5,6 G7,8 G5,6 G5,6 G7,8 G5,6 G7,8 G5,6 G7,8 G5,6 G7,8 G5,6

Ecalc (cm 21 )

Eexp (cm 21 )

Dcalc (a ) (10 26 D 2 )

Dexp (a ) (10 26 D 2 )

Dcalc (p ) (10 26 D 2 )

0 144 178 255 533 1985 2024 2026 2070 2228 2260 3940 3964 3988 4015 4203 4241 4244 5864 5922 5960 6033 6325 6364 6399 6440 11535 11574 12525 12560 12631 12669 12685 12787 12802 12877 13510 13527 13639 13645 13654 13656 14759 14781 14877 14897 14945 16005 16006 16025 16038 16064 16094 17180 17274 17328 17390 17399 17473 17663 19037 19076

0 130 180 247 523 1997 2040 2042 2077 2227 2262 3933 3949 3993 4026 4208 4221 4241 5854 5913 5946 6026 6314 6348 6392 6434 11542 11602 12540 12550 12647 12632 12670 12736 12809 12843 13499 13524 13630 13650 13640 13662 14753 14783 14882 14896 14954 15976 15928 16002 16063 16136 16147 17163 17274 17301 17423 17412 17479 17653 19072 19082

152.56 2.62 126.15 40.76 19.49 32.13 79.70 1.50 9.11 16.21 4.15 19.20 9.29 0.70 16.43 120.02 52.70 184.39 357.10 18.06 21.75 6.38 78.96 9.92 2.31 32.45 28.23 186.91 15.61 12.74 150.66 4.45 1.65 12.21 5.87 9.13 4.13 0.37 0.84 0.55 0.80 1.55 90.90 15.26 104.96 4.82 70.37 98.86 47.76 5.78 26.86

/ / / 41.36 13.51 11.01 91.06 6.93 16.81 16.19 4.31 15.89 1.68 0.65 16.99 12.89 33.03 25.29 34.52 1.12 84.22 10.59 108.02 10.30 2.98 11.19 6.16 19.49 122.90 185.99 19.19 4.31 1.78 20.80 5.51 3.96 3.42 0.29 0.75 1.31 0.25 1.48 26.51 77.97 116.06 22.11 2.14 102.96 102.96 13.00 12.80

78.67 0.11 595.40 0.02 89.62 25.36 0.16 70.89 8.87 0.03 0.01 0.02 72.83 0.00 19.54 0.00 240.47 0.03 1325.14 0.03 49.37 151.08 0.12 72.40 0.69 0.22 167.95 0.02 203.35 0.00 554.37 21.46 0.18 0.00 17.95 0.00 3.22 0.00 0.00 3.16 0.00 1.32 64.62 0.02 108.89 0.01 6.53 0.00 254.08 0.00 7.06

Dexp (p ) (10 26 D 2 )

/ / / 8.78 79.75 16.19 33.33 16.69 10.30 3.24 0.00 0.00 44.04 0.00 20.21 4.26 98.50 13.51 41.66 24.49 250.86 74.10 8.81 26.19 0.00 3.84 30.35 19.61 288.95 11.49 72.02 9.52 0.45 0.98 15.30 0.30 2.52 0.00 0.07 3.51 0.00 2.62 12.50 13.00 71.42 5.12 6.78 11.01 100.88 5.42 12.29

H. De Leebeeck et al. / Journal of Alloys and Compounds 291 (1999) 300 – 311

306 Table 5. Continued Label 4

G7 / 2 G7 / 2 4 G9 / 2 4 G9 / 2 4 G9 / 2 2 K 13 / 2 2 K 13 / 2 2 K 13 / 2 4 G9 / 2 4 G9 / 2 4 G9 / 2 2 K 13 / 2 2 K 13 / 2 2 K 13 / 2 2 G(1) 9 / 2 2 G(1) 9 / 2 2 G(1) 9 / 2 2 G(1) 9 / 2 2 G(1) 9 / 2 2 D(1) 3 / 2 2 D(1) 3 / 2 4 G 11 / 2 4 G 11 / 2 4 G 11 / 2 2 K 15 / 2 2 K 15 / 2 2 K 15 / 2 2 K 15 / 2 2 K 15 / 2 4 G 11 / 2 2 K 15 / 2 4 G 11 / 2 2 K 15 / 2 4 G 11 / 2 2 K 15 / 2 2 P1 / 2 2 D(1) 5 / 2 2 D(1) 5 / 2 2 D(1) 5 / 2 2 P3 / 2 2 P3 / 2 4 D3 / 2 4 D3 / 2 4 D5 / 2 4 D5 / 2 4 D5 / 2 4 D1 / 2 2 I 11 / 2 2 I 11 / 2 2 I 11 / 2 2 I 11 / 2 2 I 11 / 2 2 I 11 / 2 2 L 15 / 2 2 L 15 / 2 2 L 15 / 2 2 L 15 / 2 2 L 15 / 2 2 L 15 / 2 4 D7 / 2 4

Ecalc (cm 21 )

G5,6 G7,8 G7,8 G5,6 G7,8 G5,6 G7,8 G5,6 G7,8 G5,6 G7,8 G5,6 G7,8 G5,6 G5,6 G7,8 G5,6 G7,8 G7,8 G7,8 G5,6 G5,6 G7,8 G5,6 G5,6 G7,8 G5,6 G7,8 G7,8 G7,8 G5,6 G7,8 G5,6 G5,6 G7,8 G7,8 G7,8 G5,6 G5,6 G7,8 G5,6 G5,6 G7,8 G5,6 G5,6 G7,8 G7,8 G5,6 G7,8 G5,6 G7,8 G5,6 G7,8 G7,8 G5,6 G5,6 G7,8 G5,6 G7,8 G7,8

19190 19208 19456 19550 19615 19664 19697 19706 19733 19737 19752 19803 19972 19987 21013 21057 21084 21092 21175 21311 21329 21450 21464 21580 21682 21715 21749 21780 21812 21820 21821 21915 21952 21997 22010 23409 23919 23952 24019 26282 26333 28093 28213 28366 28565 28578 28810 29233 29292 29394 29517 29689 29711 30161 30202 30275 30319 30360 30367 30404

Eexp (cm 21 ) 19185 19215 19464 19564 19618 19668 19700 19691 19719 19762 19727 19823 19950 19973 / 21063 21072 21083 21111 21283 21335 21440 21462 21555 21713 21730 21750 21776 21806 21812 21830 21902 21948 21985 21994 23404 23898 23942 24038 26264 26344 28110 28217 28372 28529 28584 28803 29206 29296 29377 29467 929719 29734 / / 30235 30292 30375 / 30450

Dcalc (a ) (10 26 D 2 )

Dexp (a ) (10 26 D 2 )

Dcalc (p ) (10 26 D 2 )

Dexp (p ) (10 26 D 2 )

57.74 122.98 6.35 3.27 2.20 0.49 4.91 4.47 10.05 12.16 0.55 5.80 4.32 9.35 3.08 4.59 4.66 8.60 0.84 3.97 3.61 0.39 0.59 2.18 3.01 3.24 1.85 0.78 1.64 0.71 0.41 3.16 5.37 0.99 5.33 7.36 0.73 0.96 0.22 0.57 0.52 15.67 31.38 11.98 68.43 17.04 35.52 1.73 2.54 1.31 1.56 0.36 0.10 5.56 0.86 2.09 0.31 2.42 2.18 8.96

49.10 127.96 0.32 0.35 2.35 / 2.87 / 15.80 9.08 13.30 / / / / 5.59 4.40 5.65 0.90 1.50 7.95 0.38 0.67 3.54 1.85 0.40 1.61 0.73 0.83 0.49 0.56 2.66 9.91 0.52 9.49 7.02 0.53 0.90 0.13 1.18 0.57 16.31 27.70 3.81 65.17 44.04 24.40 2.34 0.63 1.41 0.37 / / / / 1.72 2.07 0.84 / 9.11

126.99 0.00 0.01 5.07 0.00 23.74 0.00 1.27 0.00 9.32 0.00 0.31 0.00 17.73 2.21 0.00 11.63 0.00 0.00 0.00 4.16 11.83 0.00 0.76 6.34 0.00 3.03 0.00 0.00 0.00 0.43 0.00 9.05 18.53 0.00 0.00 0.00 3.66 0.80 0.00 0.11 2.90 0.01 83.73 5.29 0.00 0.00 3.46 0.00 10.31 0.00 0.48 0.01 0.00 10.84 34.52 0.00 1.49 0.00 0.00

79.75 24.31 0.00 8.57 0.12 26.69 0.00 2.08 5.95 9.25 8.69 0.32 / / / 2.62 11.10 1.80 0.12 0.12 14.70 22.79 0.00 1.44 8.33 0.00 3.27 0.00 0.00 0.02 0.29 0.00 5.83 20.89 0.00 1.64 0.09 2.59 0.00 0.14 0.62 9.46 3.93 50.59 10.30 6.01 3.99 1.71 0.00 9.64 0.00 / / / / 0.21 0.09 2.47 / 1.22

H. De Leebeeck et al. / Journal of Alloys and Compounds 291 (1999) 300 – 311

307

Table 5. Continued Label 4

D7 / 2 L 15 / 2 4 D7 / 2 2 L 15 / 2 4 D7 / 2 2 I 13 / 2 2 I 13 / 2 2 I 13 / 2 2 I 13 / 2 2 I 13 / 2 2 I 13 / 2 2 I 13 / 2 2 L 17 / 2 2 L 17 / 2 2 L 17 / 2 2 L 17 / 2 2 L 17 / 2 2 L 17 / 2 2 L 17 / 2 2 L 17 / 2 2 L 17 / 2 2 H(1) 9 / 2 2 H(1) 9 / 2 2 H(1) 9 / 2 2 H(1) 9 / 2 2 H(1) 9 / 2 2 D(2) 3 / 2 2 D(2) 3 / 2 2 H(1) 11 / 2 2 D(2) 5 / 2 2 H(1) 11 / 2 2 H(1) 11 / 2 2 H(1) 11 / 2 2 H(1) 11 / 2 2 H(1) 11 / 2 2 H(1) 11 / 2 2 H(1) 11 / 2 2 F(2) 5 / 2 2 F(2) 5 / 2 2 F(2) 5 / 2 2 F(2) 7 / 2 2 F(2) 7 / 2 2 F(2) 7 / 2 2 F(2) 7 / 2 2 G(2) 9 / 2 2 G(2) 9 / 2 2 G(2) 9 / 2 2 G(2) 9 / 2 2 G(2) 9 / 2 2 G(2) 7 / 2 2 G(2) 7 / 2 2 G(2) 7 / 2 2 G(2) 7 / 2 2 F(1) 7 / 2 2 F(1) 7 / 2 2 F(1) 7 / 2 2 F(1) 7 / 2 2 F(1) 5 / 2 2 F(1) 5 / 2 2 F(1) 5 / 2 2

G5,6 G7,8 G7,8 G5,6 G5,6 G5,6 G7,8 G5,6 G7,8 G5,6 G7,8 G5,6 G7,8 G7,8 G5,6 G5,6 G7,8 G5,6 G7,8 G7,8 G5,6 G7,8 G7,8 G5,6 G5,6 G7,8 G5,6 G7,8 G5,6 G5,6 G7,8 G5,6 G7,8 G7,8 G5,6 G7,8 G5,6 G5,6 G5,6 G7,8 G7,8 G5,6 G5,6 G7,8 G7,8 G5,6 G7,8 G7,8 G5,6 G7,8 G5,6 G7,8 G5,6 G7,8 G5,6 G7,8 G5,6 G5,6 G7,8 G5,6

Ecalc (cm 21 )

Eexp (cm 21 )

Dcalc (a ) (10 26 D 2 )

Dexp (a ) (10 26 D 2 )

Dcalc (p ) (10 26 D 2 )

Dexp (p ) (10 26 D 2 )

30517 30577 30587 30601 30649 30676 30723 30760 30888 30934 31043 31054 31666 31736 31783 31852 31880 31923 31941 32065 32074 32949 33034 33047 33104 33148 33439 33522 34245 34298 34305 34431 34432 34496 34503 34636 34639 38533 38628 38693 39969 39984 40051 40145 47789 47869 47882 47961 47993 48689 48746 48858 48935 66381 66622 66807 66879 67631 67957 68051

/ 30548 / 30574 30599 30720 30672 30758 30898 30925 31062 / 31645 31743 31800 31858 31890 31934 31940 32048 32096 32920 / 33019 33104 33155 33433 33516 34232 34289 34338 34429 34460 / 34523 / / 38458 38672 38704 39970 39924 40070 40179 / / / / / / / / / / / / / / / /

0.29 3.70 5.34 2.39 3.15 0.37 0.02 0.53 0.29 0.92 0.25 0.12 0.08 0.41 0.31 0.14 0.03 0.01 0.22 0.03 0.40 0.26 2.03 0.07 0.57 0.05 2.32 1.15 0.98 0.03 0.71 0.87 0.21 0.20 2.19 0.40 0.05 0.30 0.70 0.03 0.12 0.15 0.33 0.12 0.07 0.11 0.25 0.08 0.00 0.05 0.73 0.21 0.05 0.24 0.06 0.12 0.25 0.59 0.20 0.14

/ 0.98 / 1.04 1.35 / 3.54 1.04 1.21 2.73 0.63 / 0.07 0.69 0.56 0.54 0.16 / 0.08 0.01 0.34 0.18 / / 0.57 1.02 5.03 1.76 1.46 0.03 1.24 0.41 0.46 / 6.40 / / 1.00 0.70 0.22 0.19 0.89 0.41 / / / / / / / / / / / / / / / / /

5.43 0.00 0.00 10.79 5.21 1.14 0.00 0.12 0.00 3.19 0.00 0.02 0.00 0.00 1.27 0.10 0.00 0.83 0.00 0.00 0.65 0.00 0.00 1.52 0.73 0.00 1.15 0.00 0.85 2.77 0.00 1.36 0.00 0.00 2.78 0.00 0.08 2.47 0.73 0.00 0.00 1.06 0.29 0.00 0.00 0.26 0.00 0.00 0.07 0.00 0.32 0.00 0.28 0.00 0.18 0.00 0.44 0.02 0.00 0.98

/ 0.00 / 8.51 3.27 4.79 1.99 1.10 0.00 9.58 / / / 0.08 3.66 0.71 / 0.85 / / 1.04 / / 2.57 0.79 / 5.92 0.37 3.01 3.45 0.07 0.25 / / 6.49 / / 4.29 6.73 / / 4.20 0.39 / / / / / / / / / / / / / / / / /

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H. De Leebeeck et al. / Journal of Alloys and Compounds 291 (1999) 300 – 311

Table 6 Starting and optimised intensity parameters for LiYF 4 :Nd 31 in S4 symmetry Parameter

Starting value (10 212 cm)

Optimised value (10 212 cm)

A 232 A 432 A 452 A 652 A 672 A 676

248233i 289261i 2612170i 21872523i 2120.4i 242211i

35278i 2178118i 2281214i 22631532i 57115i 74280i

are free to vary. The optimised intensity parameter set is compared with the starting values in Table 6. The calculated and experimental dipole strengths are included in Table 5. These optimised parameter set is also used to calculate the dipole strength of the MCD transitions. The calculations are performed by means of the Zeeman energy diagram and the corresponding Zeeman wavefunctions.

5.3. Simulations of the optical spectra The validity of the parameter optimisations can be evaluated by means of a numerical comparison of the

results. This is done here in Table 5 for the crystal field energy diagram and the dipole strengths of the transitions in the polarised absorption spectra. Another way to confront the calculated with the experimental quantities is a graphical simulation of the optical spectra. In particular for the MCD spectra of Nd 31 the graphical comparison is the only way to compare the calculation and the experiment. This is due to the complexity of several overlapping bands [12]. The graphical simulations are performed using Eqs. (3) and (4) for the polarised absorption spectra and the magnetic circular dichroism spectra respectively [20]. Xa (T ) ´( n¯ CF , T ) 5 327n¯ CF ]] Dcalc fCF ( n¯ ) ga

(3)

D´( n¯ Zeeman , T ) 327n¯ Zeeman Xa (T )(D 1calc 2 D rcalc )fZeeman ( n¯ ) ]]]] 5 ]]]]]]]]]]] H H (4) with ´, extinction coefficient (1 mol 21 cm 21 ); n¯ , position of the crystal field (CF) or Zeeman transition (cm 21 ); T, temperature (K); H, magnetic field (G); Xa , population of the ground field level; ga , degeneration of the ground field

Fig. 6. Experimental and simulated axial absorption (a) and magnetic circular dichroism (MCD) spectrum of the 2 P1 / 2 ← 4 I 9 / 2 transition of LiYF 4 :Nd 31 at 4.2 K.

H. De Leebeeck et al. / Journal of Alloys and Compounds 291 (1999) 300 – 311

level; Dcalc , calculated dipole strength (Debye 2 ); f( n¯ ), form function (Lorentz or Gauss). These graphical simulations are carried out for the complete optical region. We present here the transitions which illustrate the neodymium spectra in a single crystalline state. The very simple 2 P1 / 2 ← 4 I 9 / 2 transition (Fig. 2 2 4 2 4 6) and the G(1) 9 / 2 , D(1) 3 / 2 , G(1) 1 / 2 , K 15 / 2 ← I 9 / 2 transitions (Fig. 7) demonstrate the very narrow bands and the small separation of the Zeeman levels resulting in an overlap of the bands.

5.4. Simulation of the magnetic susceptibilities versus temperature The evolution of the magnetic susceptibility x A versus temperature is given by the Van Vleck formalism [21]. The calculations are performed with the crystal field wavefunctions of the 18 lowest crystal field energy levels ( 4 I 9 / 2 , 4 I 11 / 2 , 4 I 13 / 2 ). This is sufficient to cover the thermal population effect up to 1000 K. The crystal field wavefunctions are determined by the set parameters (Table 4) optimised in the spectroscopic part of this project. A more detailed discussion on the magnetic susceptibilities of LiYF 4 / Nd 31 can be found in Ref. [12]. The results of the calculations are shown in Fig. 8.

309

6. Conclusion The physical behaviour of the trivalent neodymium ion in a LiYF 4 host is determined by the S4 symmetry of the coordination polyhedron. This is due to the shielding of the 3 4f valency electrons by the completely filled 5s and 5p orbitals. Based on an accurate structural analysis, the coordinates of the eight fluoride ions of the site are derived. These coordinates are used to calculate starting values for the optimisation of semi empirical parameter sets. The free ion and crystal field parameters are optimised based on the crystal field energy diagram and the intensity parameters are optimised based on the dipole strengths of the crystal field transitions in the polarised absorption spectra at 4.2 K. A comparison of the starting parameters and the optimised values clearly shows a dependency on the polyhedron around the central ion. The agreement between the calculated and experimental energy diagram and dipole strengths of the crystal field analysis is deduced in a numerical as well as in a graphical way and is very satisfying. The obtained parameter sets are also used to simulate graphically the magnetic circular dichroism spectra. Despite the small separation of the Zeeman energy levels and the overlapping of the bands in a neodymium spectrum, the

Fig. 7. Experimental and simulated axial absorption (a ) and magnetic circular dichroism (MCD) spectrum of the 2 G(1) 9 / 2 , 2 D(1) 3 / 2 , 4 G(1) 1 / 2 , 2 K 15 / 2 ← 4 I 9 / 2 transition of LiYF 4 :Nd 31 at 4.2 K.

H. De Leebeeck et al. / Journal of Alloys and Compounds 291 (1999) 300 – 311

310

Fig. 8. Experimental and calculated temperature dependence of the magnetic susceptibilities of LiYF 4 :Nd 31 .

simulations are a sound prediction of the experimental spectra. In addition the parameters allow the calculation of a non spectroscopic phenomenon: the temperature variation of the magnetic susceptibility. The experimental and calculated curves are in good agreement especially in the lower temperature region. This extensive study on the LiYF 4 :Nd 31 single crystal results in a free ion, crystal field and intensity parameter set which can be used to predict other physical properties of this compound.

Acknowledgements We would like to thank Laursen I., Jensen G.B. and Søtofte I. for the experiments and the discussions concerning the structural considerations. We also wish to acknowledge Reid M.F. for the disposition of the computer

programs used in the optimisation procedures. Porcher P. and Saez–Puche R. are gratefully acknowledged for the advise on the magnetic susceptibility part. This work was financially supported through a grant from the IWONL and through the FWO. KB is Postdoctoral Fellow of the FWOFlanders (Belgium).

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