- Email: [email protected]
The valence transition in SmSe
492
Physica B 158 (1989) 492-494 North-Holland. Amsterdam
The Valence Transition in SmSe K.R. BauchspieB,
l
E.D. Crazier* and R. lngallst
*Physics Dept., Simon Fraser University, Burnaby, B. C., Canada, V5A 1S6 tPhysics Dept., University of Washington, Seattle, WA 98195, U.S.A. Introduction The Sm monochalcogenides, which crystallize in the NaCl crystal structure, undergo pressure-induced mixed valence transitions. These isostructural phase transitions are of first order in SmS and continuous in SmSe and SmTe. It has been suggested’ that these transitions may all be of first order at low enough temperature. Thus we investigated the valence transition at 77K in order to observe a possible sharpening. Another reason for the low-temperature work was the reduction of the temperature-dependent part of the EXAFS DebyeWailer factor in order to observe better a possible structural disorder. For maximum resolution in R-space we measured the Se K-edge EXAFS up to 24 A-1. While previous work2 already indicated an anomaly in the DebyeWaller factor in the region of the phase transition we now try to determine whether this anomaly can be interpreted as being due to a splitting of the nn Se-Sm distance into two Se-Sm distances according to the different ionic radii of the rare earth ion.
Results The polycrystalline SmSe sample was pressurized up to 75 kbar. The pressure was obtained from the EXAFS of a Cu foil, placed in the gasket together with the sample, and from a table relating the reduced volume of Cu with pressure. 3 From a fit to the nn Cu shell we obtain conservative error bars of *8 kbar. The Sm valence was determined from the Ltj edge4 and the reduced volume V/V, was obtained from a one shell fit to our Se K-edge EXAFS data. The E, correction was fixed at 6.3 eV and the number of nearest neighbours was set to 4.3 (instead of 6, due to the So2 term and uncertainty in the contribution of inelastic effects). This was done in order to suppress the correlation of E, with R and the correlation between 02 and N. For the analysis we employed theoretical amplitudes and phases which we calculated from first principles. First, atomic charge densities were calculated relativistically. Then for a Sm atom in the SmSe matrix the total charge density was calculated according to the Mattheiss prescription as the sum of the atomic Sm charge density plus the spherical average of the charge densities of its first 15 coordination shells. Slater-type pi/s exchange was included. The potential, which is of the muffin-tin form and real, was obtained by solving Poisson’s equation. The interstitial potential outside the muffin tins was adjusted such that the unit cell became electrically neutral. 5 Partial-wave phase shifts up to I = 30 0921-4526/89/$03.50 @ El sevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
K. R. BauchspieS
et al. / Valence transition
in SmSe
493
were obtained from the logarithmic derivatives which were determined by solving the Schrodinger equation. To obtain the backscattering amplitude and phase the phase shifts were combined employing a curved-wave formalism.6 We found that there is no significant difference between the backscattering of Sm2+ and Sms+. Central-atom phase shifts were taken from Teo and Lee’s calculation.7 Fig. 1 shows the l. results. We see that at 77K the transition has not yet sharpened 0.90 significantly. We also that the ? notice valence transition ’ 0.85 does not begin at the valence 2 but rather 0.80 at -2.1. This may be -++++ attributed to deviations from exact 10 20 30 40 50 60 70 stoichiometry. At the P (kbar) high-pressure end we notice that the transition is not complete at 75 kbar. This was also observed at room temperature. The one-shell fits can be improved by including a second Sm coordination shell. We did this by requiring that the sum of the two Sm coordination numbers be equal to 4.3 as before for the one-shell fit. E, was set to 1.6 eV for both shells and five parameters were now varied: the two distances, EXAFS Debye-Waller factors, and one of the two Pair DistributionFunctions coordination numbers. The goodness of fit, which Fig.2 P=75kbar was corrected for the increased number of variable parameters, was thus improved by a factor of -2.5. We therefore think that the addition of a second Sm shell to the fit is significant. From these fits the difference between the two Sm distances is approximately 0.1 I A. Since the harmonic
P=45kbar
P=28kbar P=42kbar
r
\
t c---l
0.4A
I
494
K.R. BauchspieB et al. / Valence transition in SmSe
approximation is employed for each shell, we obtain pair distribution functions which are sums of two Gaussian distributions, shown in Fig. 2 for several pressures. We see that at the beginning and at the end of the mixed valence transition the pair distribution functions exhibit merely a shoulder while in the transition region two peaks are resolved. This may indicate that SmSe is in fact not homogeneously mixed valent like e.g. some Sm alloys.8 Conversely, it could mean that the Sm atoms may indeed relax with a time constant like that of the valence fluctuations (-10-13 s). For SmS this possibility was ruled out because of a large electronic hybridization energy.9 In order to obtain more confidence in the results of our fits we performed a beating analysis. The empirical EXAFS phase shift was extracted from the first peak of the Fourier transform. If there are indeed two distances present this should show as a peak or valley in the first derivative of the empirical phase shift at the corresponding k-value. We did indeed observe a structure at -14 A-1. The fact that this feature occurs at a large value of k makes it less likely that it originated from a theoretical phase shift because backscattering amplitudes and phases are rather structureless above, say, 10 A-1. The feature near 8 A-1, that we observed earlier*, is due to the backscattering phase shift. Acknowledgements This work was supported by the Natural Sciences and Engineering Research Council, Canada and the U.S. Department of Energy. The experiments were performed at the Stanford Synchrotron Radiation Laboratory, Beamline IV-l.
1D.I. Khomskii, Sov. Phys. Usp. 22(1 l), 879 (1979) *K.R Bauchspiess, E.D. Crozier, Ft. Ingalls, J. Phys. (Paris) Colloq. 47, C8-975 (1986) 3American Institute of Physics Handbook, 3rd edition, McGraw-Hill 1972, p. 4-100 4K.R. BauchspieB, Diplomarbeit, Universitat zu Kbln, 1982 5L.F. Mattheiss, J.H. Wood, AC. Switendick in: Methods in Computational Physics, Vol. 8, Academic Press 1968 6A.G. McKale, S.K. Chan, B.W. Veal, A.P. Paulikas, G.S. Knapp, J. Phys. (Paris) Colloq. 47, C8-55 (1986) 7B.K. Teo, P.A. Lee, J. Am. Chem. Sot. 101,2815 (1979) 8E. Beaurepaire, J.P. Kappler, D. Malterre, G. Krill, Europhys. Lett. 5, 369 (1988) 9W. Kohn, T.K. Lee, Y.R. Lin-Liu, Phys. Rev. B 25, 3557 (1982)
Physica B 158 (1989) 492-494 North-Holland. Amsterdam
The Valence Transition in SmSe K.R. BauchspieB,
l
E.D. Crazier* and R. lngallst
*Physics Dept., Simon Fraser University, Burnaby, B. C., Canada, V5A 1S6 tPhysics Dept., University of Washington, Seattle, WA 98195, U.S.A. Introduction The Sm monochalcogenides, which crystallize in the NaCl crystal structure, undergo pressure-induced mixed valence transitions. These isostructural phase transitions are of first order in SmS and continuous in SmSe and SmTe. It has been suggested’ that these transitions may all be of first order at low enough temperature. Thus we investigated the valence transition at 77K in order to observe a possible sharpening. Another reason for the low-temperature work was the reduction of the temperature-dependent part of the EXAFS DebyeWailer factor in order to observe better a possible structural disorder. For maximum resolution in R-space we measured the Se K-edge EXAFS up to 24 A-1. While previous work2 already indicated an anomaly in the DebyeWaller factor in the region of the phase transition we now try to determine whether this anomaly can be interpreted as being due to a splitting of the nn Se-Sm distance into two Se-Sm distances according to the different ionic radii of the rare earth ion.
Results The polycrystalline SmSe sample was pressurized up to 75 kbar. The pressure was obtained from the EXAFS of a Cu foil, placed in the gasket together with the sample, and from a table relating the reduced volume of Cu with pressure. 3 From a fit to the nn Cu shell we obtain conservative error bars of *8 kbar. The Sm valence was determined from the Ltj edge4 and the reduced volume V/V, was obtained from a one shell fit to our Se K-edge EXAFS data. The E, correction was fixed at 6.3 eV and the number of nearest neighbours was set to 4.3 (instead of 6, due to the So2 term and uncertainty in the contribution of inelastic effects). This was done in order to suppress the correlation of E, with R and the correlation between 02 and N. For the analysis we employed theoretical amplitudes and phases which we calculated from first principles. First, atomic charge densities were calculated relativistically. Then for a Sm atom in the SmSe matrix the total charge density was calculated according to the Mattheiss prescription as the sum of the atomic Sm charge density plus the spherical average of the charge densities of its first 15 coordination shells. Slater-type pi/s exchange was included. The potential, which is of the muffin-tin form and real, was obtained by solving Poisson’s equation. The interstitial potential outside the muffin tins was adjusted such that the unit cell became electrically neutral. 5 Partial-wave phase shifts up to I = 30 0921-4526/89/$03.50 @ El sevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
K. R. BauchspieS
et al. / Valence transition
in SmSe
493
were obtained from the logarithmic derivatives which were determined by solving the Schrodinger equation. To obtain the backscattering amplitude and phase the phase shifts were combined employing a curved-wave formalism.6 We found that there is no significant difference between the backscattering of Sm2+ and Sms+. Central-atom phase shifts were taken from Teo and Lee’s calculation.7 Fig. 1 shows the l. results. We see that at 77K the transition has not yet sharpened 0.90 significantly. We also that the ? notice valence transition ’ 0.85 does not begin at the valence 2 but rather 0.80 at -2.1. This may be -++++ attributed to deviations from exact 10 20 30 40 50 60 70 stoichiometry. At the P (kbar) high-pressure end we notice that the transition is not complete at 75 kbar. This was also observed at room temperature. The one-shell fits can be improved by including a second Sm coordination shell. We did this by requiring that the sum of the two Sm coordination numbers be equal to 4.3 as before for the one-shell fit. E, was set to 1.6 eV for both shells and five parameters were now varied: the two distances, EXAFS Debye-Waller factors, and one of the two Pair DistributionFunctions coordination numbers. The goodness of fit, which Fig.2 P=75kbar was corrected for the increased number of variable parameters, was thus improved by a factor of -2.5. We therefore think that the addition of a second Sm shell to the fit is significant. From these fits the difference between the two Sm distances is approximately 0.1 I A. Since the harmonic
P=45kbar
P=28kbar P=42kbar
r
\
t c---l
0.4A
I
494
K.R. BauchspieB et al. / Valence transition in SmSe
approximation is employed for each shell, we obtain pair distribution functions which are sums of two Gaussian distributions, shown in Fig. 2 for several pressures. We see that at the beginning and at the end of the mixed valence transition the pair distribution functions exhibit merely a shoulder while in the transition region two peaks are resolved. This may indicate that SmSe is in fact not homogeneously mixed valent like e.g. some Sm alloys.8 Conversely, it could mean that the Sm atoms may indeed relax with a time constant like that of the valence fluctuations (-10-13 s). For SmS this possibility was ruled out because of a large electronic hybridization energy.9 In order to obtain more confidence in the results of our fits we performed a beating analysis. The empirical EXAFS phase shift was extracted from the first peak of the Fourier transform. If there are indeed two distances present this should show as a peak or valley in the first derivative of the empirical phase shift at the corresponding k-value. We did indeed observe a structure at -14 A-1. The fact that this feature occurs at a large value of k makes it less likely that it originated from a theoretical phase shift because backscattering amplitudes and phases are rather structureless above, say, 10 A-1. The feature near 8 A-1, that we observed earlier*, is due to the backscattering phase shift. Acknowledgements This work was supported by the Natural Sciences and Engineering Research Council, Canada and the U.S. Department of Energy. The experiments were performed at the Stanford Synchrotron Radiation Laboratory, Beamline IV-l.
1D.I. Khomskii, Sov. Phys. Usp. 22(1 l), 879 (1979) *K.R Bauchspiess, E.D. Crozier, Ft. Ingalls, J. Phys. (Paris) Colloq. 47, C8-975 (1986) 3American Institute of Physics Handbook, 3rd edition, McGraw-Hill 1972, p. 4-100 4K.R. BauchspieB, Diplomarbeit, Universitat zu Kbln, 1982 5L.F. Mattheiss, J.H. Wood, AC. Switendick in: Methods in Computational Physics, Vol. 8, Academic Press 1968 6A.G. McKale, S.K. Chan, B.W. Veal, A.P. Paulikas, G.S. Knapp, J. Phys. (Paris) Colloq. 47, C8-55 (1986) 7B.K. Teo, P.A. Lee, J. Am. Chem. Sot. 101,2815 (1979) 8E. Beaurepaire, J.P. Kappler, D. Malterre, G. Krill, Europhys. Lett. 5, 369 (1988) 9W. Kohn, T.K. Lee, Y.R. Lin-Liu, Phys. Rev. B 25, 3557 (1982)