EPR and optical properties of LiNbO 3 :Yb, Pr single crystals

EPR and optical properties of LiNbO 3 :Yb, Pr single crystals T. Bodziony 1, S.M. Kaczmarek 1, J. Hanuza 2 1 Institute of Physics, Technical University of Szczecin, 48 Al. Piastow Str., 70-310 Szczecin, Poland 2 Institute of Low Temperatures and Structure Research PAS, 2 Okolna Str., Wroclaw, Poland ABSTRACT Electron paramagnetic resonance (EPR) measurements of LiNbO 3 : Yb, Pr (0.8wt.%, 0.1 wt.%) single crystals were analyzed for lattice sites of Yb in the crystal and also for the Yb 3+ pairs arising. Parameters of the spin Hamiltonian were calculated using EPRNMR program. From the angular variations of the EPR spectra it results Yb 3+ ions of C 1 symmetry arise in the crystal. Pr 3+ ions change parameters of spin hamiltonian for Yb 3+ ion. Some results of the absorption measurements were also analyzed for UV-VIS and IR giving evidence, together with EPR results, on Yb 3+ location at Li + sites and Pr 3+ location at Nb 5+ sites. For comparison absorption spectra of the LiNbO 3 doped with 0.5 wt. % Pr 3+, 0.8 wt. % Yb 3+ were analyzed. Low temperature absorption measurements have shown the presence of low energy phonons responsible for the intensity of the main Yb 3+ absorption line in IR as a function of the temperature. Raman spectra confirmed the observation. Keywords: ytterbium, praseodymium, EPR, optical spectroscopy, Raman spectra, photoluminescence 1. INTRODUCTION High-power InGaAs laser diodes emitting in the 910-980 nm spectral range are commercially available, so it makes possible the diode-pumped solid state 1060 nm lasers using Yb 3+ - doped crystals because Yb 3+ has a broad absorption band in such a range. Spectral properties have been studied of various crystals doped with Yb 3+ and favourable hosts for laser action have been suggested 1. Among many kinds of oxide crystals, Ca 5 (PO 4 ) 3 F and Sr 5 (PO 4 ) 3 F are selected as the favourable hosts, while LiNbO 3 (LN) is suggested as the most unfavourable one. The evaluation is based on the emission cross-section and minimum pump intensity. LiNbO 3 is one of the useful optical materials because of its nonlinearity. If Yb 3+ - doped LiNbO 3 (LN) could be realized as the efficient laser crystal, it becomes a useful 1060 nm laser which exchange Nd: Y 3 Al 5 O 12 laser. Montoya et al. 2 obtained not only the 1060 nm laser action with high efficiency of about 47 % but also self-frequency doubled laser action using Yb 3+ /Mg 2+ -codoped LN. Jones et al. 3 achieved lasing with a slope efficiency of about 16 % using Yb 3+ /Ticodoped LN waveguide. Co-doping is one of the methods to improve the laser efficiency of Yb 3+ - doped LN since the presence of additional impurity ions changes the ligand field of Yb 3+ in LN lattice and changes the electronic states of Yb 3+ 4. Optical spectroscopy of LN:Yb crystals was described by E. Montoya et al. in 5. They have found, using site selective spectroscopy method, the existence of non-equivalent positions of the Yb 3+ which can be related to the presence of Yb 3+ in the Li + octahedral site with slightly different shifts from the regular site. The Rutherford back-scattering (RBS) study has suggested that both Yb 3+ and Pr 3+ usually enter Li + sites 6. Site selective spectroscopy performed for LiNbO 3 :Pr 3+ crystal by Lorenzo et al. 6 detected the presence of at least four non-equivalent Pr 3+ centres. Lorenzo et al. 7 and Kaczmarek et al. 8, 9 have found Pr 3+ ions are substituted also for Nb 5+ sites. EPR spectroscopy of Yb 3+ in LiNbO 3 was examined by Burns et al. 10 and by Bonardi et al. but the only C 3 symmetry of Yb 3+ centres was found 11. Malovichko et al. 12, 13 have shown that octahedral sites where rare-earth ions can substitute in LiNbO 3 single crystal can generally have C 3 and C 1 symmetry. From our investigations of the Yb singly doped LiNbO 3 crystals it results the C 1 symmetry sites are clearly observed when the EPR measurements are performed at 30 K. Therefore we are going to study the spectral and EPR properties of Yb 3+ :LN co-doped with Pr 3+ ions ones more.

2. EXPERIMENTAL LiNbO 3 :Yb 3+ (0.8 wt. %), Pr 3+ (0.1 wt. %) single crystals were grown by the Czochralski method from a congruent melt (Li/Nb = 0.94) in the Institute of Electronic Materials Technology. The conditions of growth were: growth rate: 1-2 mm/h, rotation rate: 5-20 rpm, axial temperature gradient over melt: 10-30 deg/cm, atmosphere air. The as grown crystals were regular and free of macroscopic defects [8]. The samples were cut out from the crystals parallel to the Y growth direction, and perpendicularly to Z and than polished to the thickness of about 1 mm. Room temperature (RT) transmission measurements were performed in the Institute of Optoelectronics, MUT, Poland, using Lambda-900 and FTIR-3025 spectrophotometers. Unpolarized absorption spectra were measured with a Cary-5E spectrophotometer in a spectral range of 190-3100 nm at temperatures range of 16-300 K at the Kyoto Sangyo University. The spectral resolution was set at 0.2 nm. Photoluminescence (PL) measurements were carried out using a SS-900 Edinburgh Inc. spectrophotometer at the Institute of Optoelectronics, MUT, Poland. Samples of 4*4*2 mm were measured using BRUKER ESP-300 (X band) spectrometer. It was equipped with helium cryostat ESR-900 Oxford Instruments. EPR lines were observed in the temperature range 5 to 15 K, microwave power was changed between 0,002 and 200 mw. 3. RESULTS AND DISCUSSION 3.1. Optical absorption measurements Fig. 1 presents the absorption coefficient at room temperature of Yb 3+ (0.8 wt. %), Pr 3+ (0.1 wt. %), and, Yb 3+ (0.8 wt. %) and Pr 3+ (0.5 wt. %) co-doped LiNbO 3 (LN) single crystals. Reach spectrum one can observe with the absorption bands characteristic of Yb 3+ (850-1100 nm band, 2 F 7/2-2 F 5/2 transition) and Pr 3+ ions. The intensity of the Pr 3+ related absorption bands strongly depend on the Pr 3+ concentration. Moreover, distinct OH - absorption band is observed cantered at about 2871 nm due to the necessity of charge compensation of trivalent rare-earth ions introduced for Li + and/or Nb 5+. The band is twice higher than usually detected for rare-earth doped LN crystals. It is suggested that Yb 3+ ion is substituted for Li + ion with small ionic radius of 0.74 nm, while Pr 3+ ion with large ionic radius of 1.013 nm is substituted for Nb 5+ ion with much smaller ionic radius of 0.64 nm 7, 8. The latter substitution leads to the deformed octahedrons and creation of positively charged defects which demand compensation with negatively charged OH - ions. 5 Absorption coefficient [1/cm] 4 3 2 1 2 F 5/2 3 P 2 3 P 1 3 P 0 1 - LiNbO 3 :Yb, Pr (0.8wt.%, 0.1wt.%) FAE=320 nm 2 - LiNbO 3 :Yb, Pr (0.8wt.%, 0.5wt.%) FAE=355 nm 2 3 F 4 3 F 3 3 F 2 + 3 H 6 OH - 1 D 2 1 G 4 1 0 500 1000 1500 2000 2500 3000 Wavelength [nm] Fig. 1. The absorption coefficient of Yb (0.8 wt. %) and Pr (0.1 wt. % - 1, 0.5 wt. % -2) doped LiNbO 3 single crystal at room temperature

Fig. 2 shows the absorption spectra of the LN: Yb (0.8 wt. %), Pr (0.1 wt. %) crystal measured in a temperature range of 15-292 K. The spectra consist of intense and sharp absorption bands due to the 2 F 7/2-2 F 5/2 electronic transition of Yb 3+ and weak bands due to vibronic transitions. The intense bands arise at 918.5, 955 and 980.3 nm due to 2 F 7/2-2 F 5/2 of Yb 3+, while very weak bands are observed at 987.8, 1019, 1030 and 1057 nm, which are due to 4 H 4-4 G 4 of Pr 3+. Optical density [a.u.] 0,8 0,6 0,4 0,2 0,0 LiNbO 3 :Pr, Yb (0.1wt.%, 0.8wt.%) 15 K 29 K 80 K 109 K 143 K 168 K 197 K 226 K 252 K 276 K 288 K 292 K -0,2 860 880 900 920 940 960 980 1000 1020 1040 Wavelength [nm] Fig. 2. The absorption spectra of LiNbO 3 :Yb (0.8wt.%, Pr (0.1wt. %) single crystal in the temperature range from 15 K to 292 K LiNbO 3 :Pr, Yb 0.1wt.% 0.8wt.% 1,2 Optical density [a.u.] 1,0 0,8 0,6 0,4 918 955,5 980 0,2 0,0 0 50 100 150 200 250 300 Temperature [ o C] Fig. 3. Temperature dependence of 918, 955.5 and 980 nm absorption peaks for LiNbO 3 :Yb (0.8 wt. %), Pr (0.1 wt. %). The peak position of the sharp line cantered at 980 nm is different among LN crystals doped with rare-earths 9, moreover the intensity of the line strongly depend on the temperature. This is clearly observed in Fig. 3. The shape of the curve attributed to 980 nm one can explain taking into account the possibility of the arising of rare-earth ion pairs in the crystal. In the co-doped crystals or crystals with large dopant concentration, two kinds of Yb 3+ ions may be present, one

is Yb 3+ accompanied by nearby rare-earth ion perturbed Yb 3+, the other is Yb 3+ located far from the rare-earth ion isolated. In Fig. 4 Raman spectra are presented for two different LN crystals. As one can see localized phonons are clearly observed. a). b). 7500 7000 6500 6000 18000 16000 14000 LiNbO 3 :Er Intensity [a.u.] 5500 5000 4500 4000 3500 LiNbO 3 :Nd,Yb Intensity [a.u.] 12000 10000 8000 6000 3000 2500 2000 1500 4000 2000 0 60 80 100 120 140 160 180 200 220 0 200 400 600 800 1000 Wavenumber [cm -1 ] Wavenumber [cm -1 ] Fig. 4. The Raman spectra of LiNbO 3 :Nd, Yb (0.5 wt. %, 0.8 wt.%) and LiNbO 3 :Er (1 wt. %) Fig. 5 reveal photoluminescence (PL) spectra of the Yb 3+ (0.8 wt. %), Pr 3+ (0.1 wt. %) compared to Yb 3+ (1 wt. %) doped LN single crystals excited with 980 nm of laser diode. As one can see the presence of Pr 3+ ions leads to the shift of the position of each hot emission peak (1004, 1024 and 1060 nm) present in the range 1000-1100 nm of the PL spectrum, moreover the peak at 1032 arises due to localized phonon (pairs of rare-earth ions). 7000 6000 1 1 - LiNbO 3 :Yb (1at.%) 2 - LiNbO 3 :Yb,Pr (0.8at.%,0.1at.%) 5000 PL [a.u.] 4000 3000 2 λ ex =980 nm (laser) 2000 1000 0 1000 1020 1040 1060 1080 1100 Wavelength [nm] Fig. 5. Photoluminescence spectrum of the Yb 3+ (0.8 wt. %), Pr 3+ (0.1 wt. %) compared to Yb 3+ (1 wt. %) doped LN single crystals excited with 980 nm of laser diode

3.3. EPR measurements The second of the impurities in LN:Yb, Pr single crystal is Pr 3+ ion having 2 electrons in the 4f shell, so we have a non-kramers ion whose ground state is 3 H 4 (J=4). Magnetic resonance of the Pr 3+ ion is observed only through distortions of the crystal field which admix the two conjugated states, giving an asymmetrical line whose intensity is greatest when the oscillatory magnetic field is also along the crystal axis 14. We don t observe similar behaviour in our spectra, so we concluded that in the EPR spectra we could only directly observe a resonance line originating from Yb 3+ ions. Pr 3+ ions may influence resonance behaviour of Yb 3+ ones. The configuration of the Yb 3+ consists of a single hole in the 4f shell (4f 13 ) and therefore is equivalent to a single hole in the 4f shell. The EPR spectra of Yb 3+ -doped host crystal at helium temperature should reveal a single central line corresponding to the fine structure transition (effective spin S=1/2) for the even 170 Yb isotope with no nuclear magnetic moments (I=0, natural abundance 69.6 %) and/or two hyperfine transitions distributed (for odd isotopes) about the central transitions corresponding to nuclear spin I=1/2 for 171 Yb isotope (natural abundance 14.3 %) and/or six hyperfine transitions distributed about the central transitions corresponding to nuclear spin I=5/2 for 173 Yb isotope (natural abundance 16.1 %) 14,15. The spin Hamiltonian characterizing the EPR spectra of the rare-earth Kramers ions (Yb 3+ ) can be written as a sum of the electron Zeeman and hyperfine terms: H = µ B S g B + S A I (1) where µ B is the Bohr magneton, S is electron spin, I is nuclear spin and B is external magnetic field, g and A are anisotropic and non-coincident tensors characterizing Zeeman and hyperfine interactions, respectively. Fig. 6. Angular dependence of the EPR lines for the Yb 3+, Pr 3+ doped LiNbO 3 single crystal at a temperature of 8 K measured in a plane that contains the crystal c-axis (ZY).

The effective electron spin S = 1/2 is valid for all isotopes of the Yb 3+. The components of the g and A tensors were computed using the least-square fitting method, where all allowed electronic or hyperfine line positions observed for the orientation of B in three planes (XY, ZX, YZ) were fitted simultaneously (EPR-NMR program, 6.51 version). In Figs 6 and 7 we have shown representative EPR spectra of the LiNbO 3 doped with Yb 3+ and Pr 3+ crystal sample taken at various angels in a plane that contains the crystal c-axis (ZY) and a plane perpendicular to the crystal c-axis (XY), respectively. Depending on the angles we can observe one or two strong and broad lines and additionally several weak lines, which partially could not to be visible on these figures because of low resolution of the pictures. In the (YZ) plane we can distinctly observe the moving of the all lines. In case of XY plane behaviour of the lines is more complex. The strong and broad central line splits into several lines. Certain of them move in the range between 180 and 350 mt. The spectra taken at third (XZ) plane are similar to those at (ZY) plane (see Fig. 6) and its angular variation for the orientation of the external magnetic field along the crystallographic YZ plane is presented in Fig. 8. On the basis of the full anisotropy we can deduced that the observed spectrum is a result of superposition of various lines arising from magnetically non-equivalent paramagnetic centres with axial and lower than axial point group symmetry. It should be noticed that the position of the central line that is visible in Fig 7, is not constant. The line is moving slightly. It may be caused by the fact that the line is a superposition of several lines, some of which are moving during rotation of the sample. Fig. 7. Angular dependence of the EPR lines for the Yb 3+, Pr 3+ doped LiNbO 3 single crystal at a temperature of 8 K measured in a plane perpendicular to the crystal c-axis (XY).

It is obviously that the most intense line is originating from the non magnetic 170 Yb isotope (nuclear spin I=0), which can occupy slightly different sites. The case of weak lines is more complicated. The full anisotropy of EPR spectrum in three perpendicular planes shows two line pattern characteristic of EPR spectra for 171 Yb isotope (I=1/2), so we concluded that these weak lines originate from this isotope. The resonance line originating from the above identified 170 Yb and 171 Yb isotopes are clearly marked in Fig 6. The full analysis of the anisotropy is very complex one. We can observe (see Fig. 8) several lines which can originate, e.g. from 173 Yb (nuclear spin I=5/2). One can not expect the presence of the Yb 3+ - Yb 3+ dimers. Moreover, accurate deconvolution of the spectra could not be achieved due to the low resolution. G. Malovochko and V. Grachev were made a full analysis and classification of clusters, consisting of impurity (extrinsic) and intrinsic defects in lithium niobate crystals 12, 13. They concluded there are two possible structures of impurity centres in lithium niobate lattice. One of them - the sites located along the Z (optical c) axis of the crystal, including the sites of Li, Nb and structural vacancy has got the symmetry of the C 3 point group (axial symmetry). All other ions take positions of the lowest possible C 1 symmetry 12. Because we observed the lines which are moving in angular variation at all three planes, we concluded we are dealing with the centres of C 1 point group symmetry. We decide to focus in the present work on the sites having lowest C 1 symmetry. On the basis of a given position of the resonance lines we made a computation to evaluate the components of g and A tensors. The results are presented in Tables 1 and 2. The principal values of the A and g matrices and direction cosines for the 171 Yb 3+ (I=1/2, S=1/2) ions in the congruent LN:Yb, Pr crystal are presented in the Table 1. The principal values and direction cosines of the g matrix for the 170 Yb 3+ (I=0, S=1/2) ions in the two magnetically in-equivalent sites in the congruent LN:Yb, Pr crystal are listed in the Table 2. Fig. 8. Angular dependence of the EPR lines for the Yb 3+, Pr 3+ doped LiNbO 3 crystal at a temperature of 8 K measured in a plane that contains the crystal c-axis (ZX). The solid and dashed curve means fitted positions of the lines for 170 Yb and 171 Yb isotopes, respectively

Table 1. The principal values of the A and g matrices for the odd 171 Yb 3+ (S=1/2, I=1/2) ions in the congruent LN:Yb, Pr crystal at helium temperatures (8 K). All values are estimated using the least-squares-fitting technique (program EPR- NMR, ver. 6.51). Principal values of g-matrice Direction cosines /X /Y /Z Principal values of A-matrice [GHz] Direction cosines /X /Y /Z g x = 3.3260 0.0349-0.7195 0.6936 A x = 13.178-0.6752-0.7376-0.0051 g y = 2.4455 0.0801-0.6898-0.7196 A y = 2.952 0.7364-0.6746 0.0515 g z = 0.0471 0.9962 0.0807 0.0336 A z = -2.089-0.0414 0.0310 0.9987 RMSD [GHZ] 0.066 The RMSD value is root mean sum of squares of weighted differences between observed and calculated transition frequencies, in MHz. The sum is taken over all data points provided with non-zero weighted observed data. (X, Y, Z ) are the principal axes of the g-matrix as expressed in the (X, Y, Z) frame, whereas (X, Y, Z ) is the principal axes of the A-matrix as expressed in the principal axes system of the g-matrix. Table 2. The principal values of the g matrices for the even 170 Yb 3+ (I=0, S=1/2) ions in the magnetically in-equivalent sites in the congruent LN:Yb, Pr crystal at helium temperatures (8 K). All values are estimated using the least-squaresfitting technique (program EPR-NMR, ver. 6.51). Site I Site II Principal values of g - matrice Direction cosines /X /Y /Z g x = 4.6075 0.0073-0.6930 0.7209 g y = 3.5945-0.0310-0.7207-0.6926 g z = 1.3980 0.9995-0.0173-0.0268 g x = 4.7311 0.1561 0.6639-0.7313 g y = 3.8323 0.2814 0.6798 0.6773 g z = 0.5587 0.9468-0.3115-0.0807 RMSD [GHZ] 0.139 0. 186 In Fig. 8 there are marked fitted resonance line positions computed on the basis of evaluated g and A matrices, where solid lines mean resonance lines originating from 170 Yb ion while dashed line means resonance line originating from 171 Yb ion. The position in the lattice and local environment of rare-earth (RE) and transition metal (TM) ions in congruent LiNbO 3 crystals have been widely studied in recent years. Particular emphasis has been given to lanthanide trivalent rareearth ions like Pr 3+, Nd 3+, Eu 3+, Dy 3+, Ho 3+, Er 3+, Tm 3+, Yb 3+ and to the transition metal Cr 3+ ion 6, 15-19. There are reported only axial symmetry centres of the trivalent RE impurities in the LiNbO 3 crystal. G. Malovichko et al., reported both axial (C 3 ) and (C 1 ) centres in the lithium niobate crystal doped with Cr 3+ ions 12, 13. C. Bonardi et al., observed low symmetry Yb 3+ centres but they wasn t able to analyse the EPR spectra of the centres due to low resolution 11. In our unpublicized paper on the LN crystal doped with Yb 3+, we reported on low symmetry centres (C 1 ) arising from both even and odd Yb isotopes 20. In case of our crystal we obtained spectra with enough good resolution to investigate, analyse and evaluate spinhamiltonian parameters of the centres with low symmetry. The results are similar for symmetry determining to those obtained for LN crystal doped with Yb 3+ 20. Another problem is answering the question: which site Li + or Nb 5+ or may be vacancy site is occupied by Yb 3+ with low C 1 symmetry. Basing on the EPR and optical results the question stay open.

4. CONCLUSIONS Reach absorption spectrum we observed for LN:Yb, Pr single crystal with the absorption bands characteristic of Yb 3+ (850-1100 nm band, 2 F 7/2-2 F 5/2 transition) and Pr 3+ ions. The intensity of the Pr 3+ related absorption bands strongly depend on the Pr 3+ concentration. Distinct OH - absorption band is observed cantered at about 2871 nm due to the necessity of charge compensation of trivalent rare-earth ions introduced for Li + and/or Nb 5+. The band is twice higher than usually detected for rare-earth doped LN crystals. It is suggested that Yb 3+ ion is located at Li + ion with small ionic radius of 0.74 nm, while Pr 3+ ion with large ionic radius of 1.013 nm is located at Nb 5+ ion with much smaller ionic radius of 0.64 nm. The intensity of the 980 nm absorption line strongly depends on the temperature. The shape of the curve attributed to 980 nm one can explain taking into account the possibility of the arising of rare-earth ion pairs in the crystal. The conclusion is confirmed by the presence of localized phonons in the Raman spectrum of LN:Yb, Pr single crystal. The presence of the Pr 3+ ions leads to the shift of the position of each hot emission peak (1004, 1024 and 1060 nm) present in the range 1000-1100 nm of the PL spectrum, moreover the peak at 1032 arises due to localized phonon (pairs of rare-earth ions). Fine and hyperfine EPR transitions were observed in the EPR spectra of LN:Yb, Pr for different isotopes of Yb 3+. The spectra indicate the presence of a few magnetically in-equivalent Yb 3+ sites in unit cell of the LiNbO 3 :Yb, Pr. A new ytterbium centers are detected with a lowest C 1 point group symmetry. The values of the components of the g and A tensors are estimated. Pr 3+ ions in significant manner change g and A matrices of Yb 3+ ion. 4. ACKNOWLEDGMENTS The authors deeply acknowledge to MSc Izabella Pracka from the Institute of Electronic Materials Technology, Warsaw for crystals to the investigations, prof. T. Tsuboi from Kyoto Sangyo University for low temperature absorption measurements and Maksymilian Wlodarski from the Institute of Optoelectronics MUT, Warsaw for transmission and photoluminescence measurements at RT. References 1 G. Boulon, Opt. Materials 22, 85-87, 2003 2 E. Montoya, J. Capmany, L.E. Bausa, T. Kellner, A. Diening and G. Huber, Appl. Phys. Lett. 74, 3113, 1999 3 J.K. Jones, J.P. de Sandro, H. Hempstead, A.C. Large, A.C. Tropper and J.S. Wilkinson, Opt. Lett. 20, 1477, 1995 4 L. Sokólska, I. Pracka, Phys. Stat. Sol. (a) 170, 159-166, 1998 5 E. Montoya, A. Lorenzo, L. E. Bausa, Optical characterization of LiNbO 3 :Yb 3+ crystals, J. Phys.: Condens. Matter 11, 311-320, 1999 6 A. Lorenzo, H. Joffrezic, B. Roux, G. Boulon, L.E. Bausa, J. Garcia-Sole, Lattice location of Pr 3+ ions in LiNbO 3, Phys. Rev. B 52, 6278-6284, 1995 7 A. Lorenzo, H. Joffresic, B. Roux, G. Boulon, J. Garcia-Sole, Appl. Phys. Lett. 67, 3735-3737, 1995 8 S.M. Kaczmarek, I. Pracka, Z. Mierczyk, K. Kopczyński, R. Piramidowicz, M. Malinowski, J. Kisielewski, A.O. Matkovskii, D. Yu. Sugak, Acta Phys. Pol. A, 90, 411-418, 1996 9 T. Tsuboi, S.M. Kaczmarek, G. Boulon, Spectral properties of Yb 3+ ions in LiNbO 3 single crystals: influences of other rare-earth ions, OH - ions, and γ-irradiation, J. All. Comp. 380, 196-200, 2004 10 G. Burns, D.F. O Kane, R.S. Title, Optical and Electron-Spin-Resonance Spectra of Yb 3+, Nd 3+ and Cr 3+ in LiNbO 3 and LiTaO 3, Phys. Rev. 167, 314-319, 1968 11 C. Bonardi, C.J. Magon, E.A. Vidoto, M.C. Terrile, L.E. Bausa, E. Montoya, D. Bravo, A. Martin, F.J. Lopez, EPR spectroscopy of Yb 3+ in LiNbO 3 and Mg:LiNbO 3, J. All. Comp. 323-324, 340-343, 2001 12 G. Malovichko et al, Phys. Rev. B 59, 9113, 1999 13 G. Malovichko and V. Grachev, Phys. Rev. B 62, 7779, 2000 14 A. Abragam, B. Bleaney, Electron Paramgnetic Resonance of Transitions Ions, Dover, New York, 1986 15 S. K. Misra, S. Isber, Physica B, 253, 111-122, 1998 16 C. Bonardi, C. J. Magnon, E. A. Vidoto, M. C..Terrile, L. E. Bausa, E. Montoya, D. Bravo, A. Martin, F. J. Lopez, J. All. Comp. 323-324, 340-343, 2001

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