The Jahn-Teller system Ag2+: NaF, an electron paramagnetic resonance and optical absorption study

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1 The Jahn-Teller system Ag2+: NaF, an electron paramagnetic resonance and optical absorption study A. Monnier, A. Gerber, and H. Bill Departement de Chimie Physique, Universite de Geneve, Sciences //, 1211 Geneve 4, Switzerland (Received 20 November 1990; accepted 17 January 1991) The ion Ag2 + introduced into NaF shows a tetragonal electron paramagnetic resonance spectrum at 4.2 K which dynamically averages above ~40 K. Uniaxial stress is used to show that the ground state is a strongly coupled E E Jahn-Teller state. The well-resolved superhyperfine structure due to the F - neighbors is analyzed with a linear combination of atomic orbitals picture. Optical absorption of as-grown and treated crystals is further presented. The former ones show peaks at 202, 213, 219 nm due to Ag +. The latter ones present complex absorption spectra related to silver. INTRODUCTION A continuing investigation of the properties of d 9 ions introduced into cubic fluoride host crystals prompted us to prepare and to study the Ag2 + (4d 9) ion in NaF single crystals. The octahedral first neighbor ligand field of this host imposes a 2Eg ground state of the silver ion. On the contrary, in the alkaline earth fluorides the first neighbors form a cube yielding a ground state which transforms as 2T 2g 1 Both levels are Jahn-Teller (J-T) active. Published electron paramagnetic resonance (EPR) results exist on the Ag2 + ion in several alkali halide crystals, e.g., in KCI, NaCl, LiCP These centers all present a strong E e J-T effect. But the present one has a low local transition temperature in comparison to these systems. It further exhibits very well resolved superhyperfine (shf) interaction with the F - neighbors. This paper reports results of an EPR study and of preliminary optical absorption experiments. EXPERIMENT Crystals were grown from Optran grade NaF powder and AgF (98% pure, typically 0.5 to 1 % added to the melt) which were molten in a graphite crucible under high vacuum in our Bridgman type furnace. The EPR experiments were performed on a laboratory assembled X-band spectrometer with a E 114 E line bridge. The K-band spectrometer is fully laboratory assembled and uses a Gunn diode source. Absorption measurements were realized on a Cary 2300 spectrometer. EXPERIMENTAL RESULTS In order to observe any EPR signals one has to irradiate the as-grown samples with x-rays. At 4.2 K sample temperature a tetragonal EPR signal is observed. Spectra obtained with B along the principal crystal axes C 4, C 3, and C2 are shown in Figs. 1 (a) and 1 (b). A detailed study of their angular dependence was realized with B being rotated in {( 1(0) } and {( 11O)} planes, respectively. The results are in agreement with a g tensor and a silver hyperfine structure tensor which both have tetragonal symmetry. Superhyperfine (shf) splitting due to two different sets of mutually equivalent fiuorine neighbors (Fl, F2, F4, FS and F3, F6, respectively) is resolved in the spectra. This is seen by inspecting Fig. I spectrum B II C2 [110] and spectrum B II C 4 [100]. The parallel component of this latter one further shows that, for this direction of B, the silver nucleus (two isotopes 107 Ag: 49%, 109 Ag: 51%, not resolved) produces a hyperfine splitting which is nearly commensurate to the one due to the set FI, F2, F4, F5. Incidentally, only this spectrum, and the perpendicular component of the one with B IIC4' exhibit a clearly resolved triplet superhyperfine structure arising from the neighbors F3 and F6. The X-band spectra were recorded, with 15 db attenuation (0 db = 200 mw microwave power), in a cavity with Q = They saturate only at the highest microwave power available to us. Our relaxation measurements with pulsed EPR (in progress) show that the dynamical effects related to the J-T effect are at the origin of these very short relaxation times. With increasing temperature the EPR spectrum evolves into a motionally averaged pattern. Figure 2 presents the spectra recorded at 78 K, with B parallel to the principal crystal axes. The respective g value are B IIC 4 g = 2.240, B iic 3 g = 2.236, B IIC 2 g = The transition is not yet complete at this temperature. One still observes remains of the tetragonal spectrum. The one with B II C 3 is particularly interesting. On thoroughly oriented samples the motionally averaged spectrum appears at 45 K. But complete averaging is reached only at approximately 120 K. The reorientation dynamics depends strongly on M[ ( == M[ 1 + M12 + M[4 + M 15 ), the projection of the total nuclear spin of the fluorine neighbors (see Fig. 2). No detailed investigation was undertaken. Additionally, EPR experiments were performed (Xband, 4.2 K) with uniaxial stress being applied to the sample, along {[ loo]}. This perturbation produces strong and "instantaneous" modification of the relative intensities of the spectral components, such that the elongations perpendicular to the stress orientation are favored. Parametrization of the results yielded a stress coupling constant with a= +6.8xlO- 23 [JPa-'] In(nll/n 1 ) = (ap/kt) and showed linear behavior for p..;,10 7 r Pa J. J. Chem. Phys. 94 (9),1 May /91/ $ American Institute of Physics 5891

2 5892 Monnier, Gerber, and Bill: Jahn-Teller system Ag2+: NaF Ir:l. ter:l.si t B//[1.1.1] o (8) Magr:l.etic Field [rn.t] a.. u.. ] B//[100J 500 o B//[110J -500 (b) l\!iagn..etic Field [TJ FIG. I. EPR spectra of the Ag2 + ion obtained with B oriented along the principal crystal axes. T= 4.2 K. (a) X band-v = 9.26 GHz, (b) Ka bandv = 36.3 GHz. The insert defines our labeling of the F neighbors. Stress applied along an [111] axis produced no measurable effects. Stress experiments were published previously on the system NaCI:Ag Effects were only observed at 78 K sample temperature. These were, necessarily, very small. Optical absorption spectra The optical absorption of the samples used for EPR was further studied. This paragraph reports preliminary results obtained from as-grown samples, which subsequently underwent a series of treatments. The spectrum shown in Fig. 3 was obtained from an as-grown crystal. No other absorption bands were found in the visible and UV. We assign the transitions to the Ag + ion. Indeed, none of the samples showed any EPR signals prior to x-irradiation though silver was certainly present in the as-grown samples. This excludes the presence of Ag2 + or of AgO. Each sample presented a strong Ag2 + EPR spectrum after x-irradiation and simultaneously the optical absorption bands had their intensity reduced in proportion. The irradiated samples exhibit a considerably modified absorption spectrum which extends into the visible. Subsequently they were cycled several times through the following J. Chem. Phys., Vol. 94, No.9, 1 May 1991

3 Monnier, Gerber, and Bill: Jahn-Teller system Ag2+: NaF 5893 a."'u..] B/ /[ 111 J o B//[110J 260D 2BOD 300D Magnetic Field [rrl.tj FIG. 2. EPR spectrum observed at 78 K sample temperature. v = 9.3 GHz. The motionally averaged one and the remnants of the low temperature spectrum are observed in the three spectra. 0.4 NaF:Ag+l ' I O.2>f " () () m :100 2lO :140 16O 210 loo -e CI) ,.. ) :( ' ~--~----~----~----~----~--~~--~----~----~--~ wavelength [run] FIG. 3. Absorption spectrum of the Ag + ion in NaF. T = 290 K. The insert presents, for comparison, the absorption spectrum of Ag + :SrF2. Sample thickness approximately 2 mm. J. Chem. Phys., Vol. 94, No.9, 1 May 1991

4 5894 Monnier, Gerber, and Bill: Jahn-Teller system Ag2+: NaF thermal treatment: the sample was heated in argon within ca. 90 s to the given temperature and kept under these conditions for 15 min. Then, it was cooled within ca. 60 s to room temperature with forced air. After each cycle the absorption spectrum was recorded. The crystal always remained in situ. The low heat capacity furnace with the monitoring thermocouple and a serpentine connected through a valve to the air compressor were directly placed around the sample holder into the sample compartment of the Cary 2300 spectrometer. The observed evolution of the absorption as a function of the cycle temperature is shown in Fig. 4. DISCUSSION Optical absorption The spectrum of the as-grown crystals is clearly due to the Ag + ion. In addition to the arguments given above we might add that we observed a similar spectrum in untreated CaF2 and SrF2 doped with AgF (Fig. 3 insert). It has maxima at 227 and 200 nm. There too no EPR signal has been observed prior to x-irradiation of the samples. The ion Ag + has a ground state (4d to) ISo and the first excited configuration is (4d 9 5s). Including spin-orbit coupling, one obtains in cubic symmetry from this latter configuration the terms leg, IT 2g, 3E g (T Ig, T 2g ) and 3T 2g (A 2g, E g, T Ig, T 2g ). The superficial similarity of the absorption with the spectra of Cu + in NaF reported by Mc Clure et al. 4 suggests an assignment IA Ig -+ leg, and IA Ig -+ IT 2g. But, the spin-orbit coupling is strong (1840 cm - I in the ground states). Detailed assignment probably needs the use of two-photon spectroscopy. The absorption spectrum of the x-irradiated samples is complex and not of one unique origin. We established by cross correlation of the spectra that at least four different centers are involved. In particular the line at 496 nm, probably due to the M center, is practically always present. A detailed study is in progress. J-TModel Our EPR results are in agreement with local D4h symmetry of the cluster. The stress experiments together with the finding that a dynamically averaged spectrum is seen, - IfIorX ray... 1fIor160C~ demonstrate that the center reorients between the three possible tetragonal deformations, which are energetically equivalent. This is clear evidence for a cubic E E Jahn-Teller effect being involved. The tetragonal symmetry of the observed EPR spectrum shows that the coupling is rather strong and that the three-state model (Ham 2, O'Brien 6 ) applies to describe the vibronic ground state of the Ag2 +. This model works within a lowest vibronic doublet E g, and aa 2g singlet, 3r above the former level. Transformation to localized vibronic states into each of the three minima of the warped adiabatic potential yields (we follow Ref. 7 where details and the necessary equations are given) (a) the relation r + yl2q=0 between the two Ham reduction factors under strong coupling conditions, (b) eigenvalues of the external tetragonal strain, the Zeeman, the hyperfine structure (hfs) terms (the left column gives the axis of the tetragonal elongation) z E~ = r + {fjob(gll nzsz + gl (nxsx + nysy» X,Y +A"I~Sz +A~(l~Sx +I~Sy)} + (2/3 )ap + shf terms, E~.3 = r + {permutation of above} r = tunnel splitting, gl =gl -qlg2\' - (1/3) ap + shf terms, gil = gl + 2qlg21, A II =A I + 2q1A21, A I =AI - q1a21, a = (q + yl2r) Vs (SI I - S12) = stress coupling coefficient, see below for the superhyperfine structure term. The nondiagonal terms between the localized states are small and were neglected. By fitting these equations to the observed spectra we obtained the parameters given in Table I. Superhyperfine structure The validity of the crystal field approximation of the ligand field model is questionable for this system because the superhyperfine interaction with the direct fluorine neighbors ofthe silver ion is important. The electronic states forming the partners of the IREP of Eg symmetry are obtained as the antibonding part in a Hartree-Fock type treatment of the 3eg subshell of Ag(4d 9 ) and F(2s,2p) orbitals. Within (1) otw230c~.... otw300c~ _1fIor480C~ TABLE I. Experimental EPR parameters, model (1),4.2 K. Wavelength [nm] FIG. 4. Absorption spectrum of the NaF:Ag system, after the treatments described in the text have been applied. T= 300 K. gil = (5) gl = (15) shfs F3 a shffl a silver IA» I = 85(1) IA~I =62(1) IA3111,;" IA3zzi = 18 IA311 = IA3xxi = IA3yyl < 8 IA,xxl = 581 IA,yyl = 63 IA,zzl = 83 Stress coupling coefficient a = 6.8 X [J Pa - '] at 4.2 K Hyperfine structure constants in MHz. J. Chern. Phys., Vol. 94, No.9, 1 May 1991

5 Monnier, Gerber, and Bill: Jahn-Teller system Ag2+: NaF 5895 an electronic Eg doublet any operator connecting this space with other degrees of liberty can be represented as a sum: au I + bu 2 + CU9 + due> where U I is the 2X2 unit matrix and u 2 = O'y, U9 = - O'z, U, = ax (ax, O'y' O'z are the Pauli spin matrices). Application of this decomposition by using the hf operator given by Abragam and Price 9 yields the following equivalent operator (keeping the presently important contributions): Hshf = haul + heue + h,u, (2). 1 6 With ha = - 2: hi(/;,s), 6 i= I he = - M2(h 3 +h6) -hi -h2 -h4 -hs}, 1 h, = - r,;:; {hi + h4 - h2 - hs} 2,,12 These expressions are defined in the appendix. By assuming the adiabatic approximation to hold, one evaluates Eg. (2) within the vibronic triplet introduced before and transforms to the local vibronic basis. The following expression is obtained in the potential minimum corresponding to Q. = 0 (tetragonal elongation along z) : H? shf = ha + ~he (q + V2r). (3) The contribution in the other wells are obtained by applying rotations C 3, C ~ along [Ill]. One interesting aspect of Eq. (3) is that the nuclei F and F6 contribute nonzero shf interaction, as long a~ (q + v2r) # 3/2. Therefore, even within the adiabatic approximation, at least two contributions provide for nonzero shf interaction with these nuclei: the one just described and configuration interaction, which is a more conventional contribution. Unfortunately this latter part is difficult to estimate without a detailed ab initio investigation. We have studied experimentally the influence of temperature and external stress on the EPR spectrum in order to search for possible deviations from the assumed adiabatic picture. Uniaxial stress applied along an [001] crystal axis produces deformations which transform as A + E Both, they affect the Ag-F bonds axially. Therefore, expressing Qo, Q. by p cos q:;, p sin q:;, this stress geometry should produce effects on p. A very thorough experimental investigation of an eventual influence of stress onto the observed shf splitting gave negative results. Thus, the radial force constant is large and one has P=Po = (radius of the minimum in the adiabatic potential sheet). Additionally, as both, the numerator and the denominator, respectively, in the expressions of the shf constants depend on Q9 and Q their effects compensate, at least in part. ENDOR experi~ ments under uniaxial stress would be needed. The temperature dependence of the observed EPR spectra implies on the other hand a dependence on q:;. In particular the orientation with B IIC 3 is useful for this study. Based on the 4.2 K spectrum, under the assumption of equivalent wells one obtains Ig g0' The high temperature spectrum yields the experimental value A(C 3 ) = 7.41(0.15) mt. The difference is clearly outside the experimental errors and a deformation coordiate dependent part has to be included into Eq. (3). Taylor expansion ofeq. (2) gives to first order in QA' Q., Qe (retaining only the important terms) H:hf:;;r.HshfO +h~qaua +h~qeue"', where the prime indicates the derivative with respect to the variable. H shfo is independent of the QA'... Then, one changes to vibronic states and subsequently transforms to the localized ones. After introducing polar coordinates for Q9' Q. one obtains H :hf :;;r.hshfo + h ~ QA + ~h ~ ('I'I I cos q:; 1'1' 1 )Po' (4) The totally symmetrical mode yields by its own the usual small temperature dependence of the shf constants as is for instance found for Mn 2 + in NaF. The last term contributes to the observed difference because the matrix element < tpl I cos q:; I tpl ) is reduced 6 due to the spread of the angular vibration in the well, with increasing temperature. CONCLUSIONS This preliminary communication shows that the Ag2 + ion identified by EPR is a Jahn-Teller system, but that the associated optical absorption spectra are only indirectly related. EPR results are presented and, by applying an idea of O'Brien 6 the influence of the Jahn-Teller effect onto the shf interaction is qualitatively analyzed. ACKNOWLEDGMENTS The authors acknowledge the help of F. Rouge who made the necessary mechanical constructions, of J. B. Pluss who realized several electronics devices, and of Renata Da Costa who typed the manuscript. Work supported by the Swiss National Sciences Foundation. APPENDIX Here are determined the superhyperfine structure terms ofeq. (2). By assuming adiabatic electronic states, only the antibonding Eg ground state and T2 excited state were con- 'd g Sl ered. The other states are quite higher in energy. A standard LCAO method 8 was chosen to represent them, including covalent contributions from the two stets of fluorine neighbors. Application of the Abragam-Price hyperfine operator 9 to the fluorine ions yields in the one nucleus approximation contributions from the two sets of neighbors. The results are A (C 3 ) = j{2 U (A ~yy + A ~zz + A ~xx ) ] 1/2 + U(A 3 1\ + 2A31 ) ] 1I2} = 6.95 mt. J. Chern. Phys., Vol. 94, No.9, 1 May 1991

6 5896 Monnier, Gerber, and Bill: Jahn-Teller system Ag2+: NaF A-A- ~ ( 10 1 )] [ ---K (S I ) 5 20 Nt 3~1 ~2 Y y, + [-l:...-k _~ A-A-; (~+_I )] 5 20 Nt 3a 2 a 1 X (Szlz,)} K_81T la-sl2 (r s- 3 ) I R.12-3 la-al 2 (r - 3 ) Xs(,), p A- = spin-orbit coupling constant of the F -, A-s> A-a, A-t are the mixing coefficients of the fluorine s,p orbitals in the Eg states and of the p orbitals in the T 2g one. The other shf operators are obtained by permutation, i.e., (1... l x1 Sx' 2... l y2 Sy, 4... l x4 Sx ) Both, the ground state and the T 2g state are J-T states. The presently relevant interaction of this latter one is the T case. Its splitting of the adiabatic potential sheets at the equilibrium ground state deformation (at QII = QIIO and QE = QED ) produces orthorhombic shf structure tensors for FI, F2, F4, F5 and an axial one for F3, F6. Treating the excited T 2g e g J-T problem within the strong coupling limit one obtains the following energy differences to the excited states: al::;;dodq - 2VTE Qll0 + (m'u)t/2)(q~0 + Q:o), ~2~ lodq + VTEQllo + (m'u)t/2)(q~0 + Q:o), the first term is the cubic field splitting, then follows the J-T term and finally the elastic energy (m': effective mass, U)T: effective vibrational frequency). Within this model, and the likely assumption that V TE is negative, one obtains that a 2 is smaller than ai' and thata zz - Ayy = 20 MHz. The secondorder contribution to the hi is thus of the order of 6-8 %. A full analysis needs to know the relative signs of the different shf interaction constants. This has not yet been performed. I H. Bill, D. Lovy, and H. Hagemann, Solid State Commun. 70, 511 (1989). 2 F. S. Ham, in Electron Paramagnetic Resonance, edited by S. Geschwind, (Plenum, New York, 1972). 3R. H. Borcherts, H. Kanzaki, and H. Abe, Phys. Rev. 2, 23 (1970). S. C. Weaver and D. S. Mc Clure, J. Chern. Phys. 92, 3994 (1990), and references therein., A. E. Moore, Atomic Energy Levels, Vol. III, Circular of the National Bureau of Standards 467 (1958). 6 M. c. M. O'Brien, Proc. R. Soc. A 281, 323 (1964). 7 H. Bill, The Dynamical Jahn-Teller Effect in Loc. Systems, edited by Yu. E. Perlin and M. Wagner (Elsevier, Amsterdam, 1984), Chap. XIII. 8 S. Sugano, Y. Tanabe, and H. Kamimura, Multiplets 0/ Transition-Metal Ions in Crystals (Academic, New York, 1970). 9 A. Abragam and H. M. Pryce, Proc. R. Soc. A 205, 135 (1951). J. Chem. Phys., Vol. 94, No.9, 1 May 1991