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Neutron scattering study of crystal-field excitations in TmTe
ELSEVIER
Physica B 230-232 (1997) 735-737
Neutron scattering study of crystal-field excitations in TmTe E. Clementyev a'b, R. K6hler ~, M. Braden a'c, J.-M. Mignot a'*, C. Vettier d, T. Matsumura e, T. Suzuki e aLaboratoire Lbon Brillouin, CEA-CNRS, CEA/Saclay, 91191 Gif sur Yvette, France bRussian Research Centre "'Kurchatov Institute", Moscow, Russian Federation CForschungszentrum Karlsruhe, INFP, 76021 Karlsruhe, Germany d European Synchrotron Radiation Facility, BP 220, 38043 Grenoble Cedex, France ~Department of Physics, Tohoku University, Sendai 980, Japan
Abstract
Inelastic neutron scattering measurements have been carried out on TmTe to settle the controversial issue of the crystal-field level scheme in this compound. By comparing data obtained with different energy resolutions, it is shown that the total splitting cannot exceed 2 meV. The energies and intensities of the excitations are consistent with a F 8 quartet ground-state, but their width is appreciably larger than the resolution. This broadening may be due to spin fluctuations and/or a weak quadrupolar splitting of the quartet state.
Keywords: Crystal electric field; TmTe; Neutron scattering; Quadrupolar interactions
The thulium monochalcogenide family displays unique examples of valence instabilities of Tm [1, 2]. TmSe is already mixed-valent under normal conditions whereas an external pressure of about 2 G P a is required to destabilize the divalent state in TmTe [3,4]. At P = 0 , this compound is a semiconductor with the Tm 2 + ground-state 4f 13, 2F7/2, and a small energy gap of 0.2-0.3 eV [1, 2]. Besides providing a valuable integral-valence reference for the exotic physical properties of TmSe, TmTe is interesting in its own right, especially since it was recently reported [5] to undergo a phase transition at TQ = 1.7 K, far above the magneticordering temperature (TN ,~ 0.2-0.4 K depending on the specimens). This transition was ascribed to the onset of long-range ordering among the Tm
* Corresponding author.
quadrupolar moments, but the exact mechanism is still controversial [5, 6]. One problem is the lack of experimental consensus regarding the crystal-field (CF) level scheme of this compound. In a cubic point symmetry, the ground-state multiplet 2F7/2 of Tm 2÷ splits into one quartet state F8 and two doublets F6 and FT. In the early work of Ott et al. [7], the thermal properties TmTe (elastic constants, thermal expansion and specific heat) were interpreted consistently in terms of the following level scheme: Fs(0), Fv(10K), F6(16 K). On the other hand, subsequent attempts to measure CF transitions by inelastic neutron scattering (INS) yielded conflicting results: Fs(0)-FT(100 K)-F 6 (200 K) on a polycrystalline sample [8], /'8(0)-/'6(8 K)F7(15 K) on a small single crystal [9], and no detectable excitation in Ref. [10] (single-crystal). Obviously, the experimental situation requires some clarification. In particular, a reliable determination of the CF parameters is essential for
0921-4526/97/$17.00 Copyright © 1997 Elsevier Science B.V. All rights reserved Pll S092 1 - 4 5 2 6 ( 9 6 ) 0 0 8 2 2 - 8
E Clementyev et al. / Physica B 230-232 (1997) 735-737
736
assessing the role of quadrupolar effects in the lowtemperature transition. This report describes new INS measurements carried out at the Laboratoire L6on Brillouin in Saclay on two different triple-axis spectrometers. In comparison with the previous studies, better conditions were achieved by (i) using a large, highquality, single-crystal, (ii) varying the experimental resolution (0.9 meV on the thermal beam at cono 1 stant kf = 2.662A- ~ and 0.2meV on the cold source at kf = 1.55 A-l), and (iii)checking the consistency of the data obtained at different temperatures. Let us first discuss the thermal-beam results. Low-temperature spectra were measured at T = 4.6 K, i.e. sufficiently above the transition temperature TQ, for energy transfers of up to 25 meV. Representative scans are plotted in Fig. 1. One sees that no sizeable peak is detected above 2 meV. On the other hand, a large contribution exists at lower energies, in agreement with previous studies I-8, 10]. The momentum-transfer dependence of its intensity is in agreement with the form factor of Tm 2+, clearly indicating that this signal is magnetic. If it originated merely from quasielastic scattering within the CF-split ground-state, it follows from simple examination of the transition matrix elements of J l (Table 1) that at least one other strong peak, due to an excitation from the ground-state to an excited state, should occur at higher energy, which is obviously not the case. The possibility of a low-lying
1.6
i
i
TmTe 0--(0,0,1.8) ~ T = ' 4 " 6 K ----o-- T~120K ~d 1.2
0.4
0.0 -5
5 10 Energy (meV)
15
Fig. 1. Inelastic neutron spectra (background-corrected) of T m T e measured at fixed E r = 1 4 . 7 m e V for Q = (0,0,1.8); T = 4.6 K (closed circles) and 120 K (open circles). Inset: lowenergy part of the spectrum at T = 4.6 K.
Table 1 Squared matrix elements IG]IJ±Ir j> 12 for the crystal-field eigenstates of T m 2 ÷ in cubic symmetry
F6 /'7 Fs
1
0
I'6
F7
1"8
5.44
0 9.00
15.56 12.00 14.44
~
~ ~ r 6 ilk 3
217 4'6K
g -0.5
0.0
0.5 1.0 1.5 Energy (meV)
2.0
2.5
Fig. 2. Inelastic neutron spectrum of TmTe at T = 2.2 K measured at Ef = 5.0 meV for Q = (0, 0, 2.4); the solid lines represent the fit discussed in the text; labels 0, 1, and 2, 3 denote incoherent, quasielastic and inelastic contributions, respectively.
F8 excited state, partially depopulated at T = 4.6 K, can also be ruled out because it should give rise to a sizeable peak when temperature increases, whereas no such feature was actually observed in the spectra at T = 12, 40, 120 and 293 K. It can thus be concluded that all the magnetic spectral weight is concentrated in the narrow energy range 0 ~< E ~< 2 meV, in agreement with the conclusions of Ref. [7]. The magnetic signal cannot be fitted by a single quasielastic Lorentzian, and at least one excitation centered at about he) = 1 meV has to be included. However, the resolution is not sufficient to properly separate quasielastic and inelastic intensities. To be more specific, we now need to analyse the low-energy data measured with a higher energy resolution. Fig. 2 shows a spectrum measured at T -- 2.2 K for energy transfers of up to 2.5 meV. The data confirm the existence of a magnetic signal responsible for the rather flat intensity between 0.4 and 1.1 meV. As in the above measurements, no extra peak appears at energies E > 2 meV when
E. Clementyev et aL / Physica B 230-232 (1997) 735-737
temperature is increased (here, measurements were extended only up to 70 K). To fit the low-temperature signal with Lorentzian lines, one is forced to use two peaks, one of which at least has to be inelastic, with ho9 ~ 1 meV. If one of the CF doublets (denoted F6/7) is assumed to be the groundstate, and the excitation at 1 meV is then ascribed to the F6/7 ~ Fs transition, it is impossible to account for the intensity found around 0.4 meV because the diagonal matrix elements of J± for the doublets are too small. On the other hand, a very good fit can be obtained with a F8 ground-state and two low-lying excited doublets. The fit shown as a solid line in Fig. 2 corresponds to the sequence Fa(0)-F7(4.6 K)-F6(10.7 K), but a nearly as good solution is given by Fs(0)-F6(4.9 K)-Fv(II.1 K). In conclusion, the results of our INS study on a stoichiometric specimen of T m T e clearly indicate that the level scheme proposed in Ref. [8] has to be rejected. More generally, any solution implying a large total CF splitting of the multiplet seems very unlikely. Furthermore, if one analyses the data in terms of the eigenstates of a single-site CF hamiltonian with cubic symmetry, the 1"8 quartet is found to be the only possible ground-state, with the higher levels lying at energies of about 4 K and 10.5 K. The order in which F6 and F 7 appear is, however, difficult to ascertain from the neutron data alone. This picture agrees qualitatively with the CF parameters deduced from the elastic constant measurements [5, 7]. However, it should be noted that the quasielastic and inelastic Lorentzian line widths ( F W H M ) derived from Fig. 2 (Fq~ ,-~ Fin ~ 0.9 meV) are considerably larger than the instrumental resolution (0.2 meV in the present case). Possible reasons for this anomalous broadening are mag-
737
netic fluctuations (proximity of the valence instability) or a weak splitting of the F8 level due to quadrupolar interactions. The latter mechanism seems quite plausible in view of the pronounced deviations from a single-ion CF calculation observed in the elastic constants below 5 K [5]. It was previously hypothesized in Ref. [6], albeit for a completely different CF level scheme. This point will be discussed at greater length in a forthcoming publication [11].
References [1] E. Bucher, K. Andres, F.J. di Salvo, J.P. Maita, A.C. Gossard, A.S. Cooper and G.W. Hull Jr., Phys. Rev. B 11 (1975) 500. [2] P. Wachter, in: Handbook of the Physicsand Chemistry of Rare Earths, Lanthanides-Actinides: Physics - II, Vol. 19, eds. K.A. GschneiderJr., L. Eyring, G.H. Lander and G.R. Choppin (Elsevier,Amsterdam, 1994)p. 177 and references therein. I3] A. Jayaraman, in: Handbook of the Physics and Chemistry of Rare Earths, Vol. 2, eds. K.A. Gschneider Jr. and L. Eyring (North-Holland, Amsterdam, 1979) p. 575. 1'4] T. Matsumura et al., to be published. [51 T. Matsumura, Y. Haga, Y. Nemoto, S. Nakamura, T. Goto and T. Suzuki, Physica B 206&207 (1995) 380. 16] T. Kasuya, J. Phys. Soc. Japan 63 (1994) 3936. [7] H.R. Ott, B. L/ithi and P.S. Wang, in: Valence Instabilities and Related Narrow-Band Phenomena, ed. R.D. Parks (Plenum, New York, 1977) p. 289. 18] A. Furrer, W. Biihrer and P. Wachter, in: Valence Instabilities, eds. P. Wachter and H. Boppart (North-Holland, Amsterdam, 1982) p. 319. 1-9] H. Boppart, P. Wachter and A. Furrer, Internal Report, E.T.H. Ziirich, 1983, unpublished. 1-10"1Y. Lassailly, C. Vettier, F. Holtzberg, A. Benoit and J. Flouquet, Solid State Commun. 52 (1984) 717. 1'11] E. Clementyevet al., to be published.
Physica B 230-232 (1997) 735-737
Neutron scattering study of crystal-field excitations in TmTe E. Clementyev a'b, R. K6hler ~, M. Braden a'c, J.-M. Mignot a'*, C. Vettier d, T. Matsumura e, T. Suzuki e aLaboratoire Lbon Brillouin, CEA-CNRS, CEA/Saclay, 91191 Gif sur Yvette, France bRussian Research Centre "'Kurchatov Institute", Moscow, Russian Federation CForschungszentrum Karlsruhe, INFP, 76021 Karlsruhe, Germany d European Synchrotron Radiation Facility, BP 220, 38043 Grenoble Cedex, France ~Department of Physics, Tohoku University, Sendai 980, Japan
Abstract
Inelastic neutron scattering measurements have been carried out on TmTe to settle the controversial issue of the crystal-field level scheme in this compound. By comparing data obtained with different energy resolutions, it is shown that the total splitting cannot exceed 2 meV. The energies and intensities of the excitations are consistent with a F 8 quartet ground-state, but their width is appreciably larger than the resolution. This broadening may be due to spin fluctuations and/or a weak quadrupolar splitting of the quartet state.
Keywords: Crystal electric field; TmTe; Neutron scattering; Quadrupolar interactions
The thulium monochalcogenide family displays unique examples of valence instabilities of Tm [1, 2]. TmSe is already mixed-valent under normal conditions whereas an external pressure of about 2 G P a is required to destabilize the divalent state in TmTe [3,4]. At P = 0 , this compound is a semiconductor with the Tm 2 + ground-state 4f 13, 2F7/2, and a small energy gap of 0.2-0.3 eV [1, 2]. Besides providing a valuable integral-valence reference for the exotic physical properties of TmSe, TmTe is interesting in its own right, especially since it was recently reported [5] to undergo a phase transition at TQ = 1.7 K, far above the magneticordering temperature (TN ,~ 0.2-0.4 K depending on the specimens). This transition was ascribed to the onset of long-range ordering among the Tm
* Corresponding author.
quadrupolar moments, but the exact mechanism is still controversial [5, 6]. One problem is the lack of experimental consensus regarding the crystal-field (CF) level scheme of this compound. In a cubic point symmetry, the ground-state multiplet 2F7/2 of Tm 2÷ splits into one quartet state F8 and two doublets F6 and FT. In the early work of Ott et al. [7], the thermal properties TmTe (elastic constants, thermal expansion and specific heat) were interpreted consistently in terms of the following level scheme: Fs(0), Fv(10K), F6(16 K). On the other hand, subsequent attempts to measure CF transitions by inelastic neutron scattering (INS) yielded conflicting results: Fs(0)-FT(100 K)-F 6 (200 K) on a polycrystalline sample [8], /'8(0)-/'6(8 K)F7(15 K) on a small single crystal [9], and no detectable excitation in Ref. [10] (single-crystal). Obviously, the experimental situation requires some clarification. In particular, a reliable determination of the CF parameters is essential for
0921-4526/97/$17.00 Copyright © 1997 Elsevier Science B.V. All rights reserved Pll S092 1 - 4 5 2 6 ( 9 6 ) 0 0 8 2 2 - 8
E Clementyev et al. / Physica B 230-232 (1997) 735-737
736
assessing the role of quadrupolar effects in the lowtemperature transition. This report describes new INS measurements carried out at the Laboratoire L6on Brillouin in Saclay on two different triple-axis spectrometers. In comparison with the previous studies, better conditions were achieved by (i) using a large, highquality, single-crystal, (ii) varying the experimental resolution (0.9 meV on the thermal beam at cono 1 stant kf = 2.662A- ~ and 0.2meV on the cold source at kf = 1.55 A-l), and (iii)checking the consistency of the data obtained at different temperatures. Let us first discuss the thermal-beam results. Low-temperature spectra were measured at T = 4.6 K, i.e. sufficiently above the transition temperature TQ, for energy transfers of up to 25 meV. Representative scans are plotted in Fig. 1. One sees that no sizeable peak is detected above 2 meV. On the other hand, a large contribution exists at lower energies, in agreement with previous studies I-8, 10]. The momentum-transfer dependence of its intensity is in agreement with the form factor of Tm 2+, clearly indicating that this signal is magnetic. If it originated merely from quasielastic scattering within the CF-split ground-state, it follows from simple examination of the transition matrix elements of J l (Table 1) that at least one other strong peak, due to an excitation from the ground-state to an excited state, should occur at higher energy, which is obviously not the case. The possibility of a low-lying
1.6
i
i
TmTe 0--(0,0,1.8) ~ T = ' 4 " 6 K ----o-- T~120K ~d 1.2
0.4
0.0 -5
5 10 Energy (meV)
15
Fig. 1. Inelastic neutron spectra (background-corrected) of T m T e measured at fixed E r = 1 4 . 7 m e V for Q = (0,0,1.8); T = 4.6 K (closed circles) and 120 K (open circles). Inset: lowenergy part of the spectrum at T = 4.6 K.
Table 1 Squared matrix elements IG]IJ±Ir j> 12 for the crystal-field eigenstates of T m 2 ÷ in cubic symmetry
F6 /'7 Fs
1
0
I'6
F7
1"8
5.44
0 9.00
15.56 12.00 14.44
~
~ ~ r 6 ilk 3
217 4'6K
g -0.5
0.0
0.5 1.0 1.5 Energy (meV)
2.0
2.5
Fig. 2. Inelastic neutron spectrum of TmTe at T = 2.2 K measured at Ef = 5.0 meV for Q = (0, 0, 2.4); the solid lines represent the fit discussed in the text; labels 0, 1, and 2, 3 denote incoherent, quasielastic and inelastic contributions, respectively.
F8 excited state, partially depopulated at T = 4.6 K, can also be ruled out because it should give rise to a sizeable peak when temperature increases, whereas no such feature was actually observed in the spectra at T = 12, 40, 120 and 293 K. It can thus be concluded that all the magnetic spectral weight is concentrated in the narrow energy range 0 ~< E ~< 2 meV, in agreement with the conclusions of Ref. [7]. The magnetic signal cannot be fitted by a single quasielastic Lorentzian, and at least one excitation centered at about he) = 1 meV has to be included. However, the resolution is not sufficient to properly separate quasielastic and inelastic intensities. To be more specific, we now need to analyse the low-energy data measured with a higher energy resolution. Fig. 2 shows a spectrum measured at T -- 2.2 K for energy transfers of up to 2.5 meV. The data confirm the existence of a magnetic signal responsible for the rather flat intensity between 0.4 and 1.1 meV. As in the above measurements, no extra peak appears at energies E > 2 meV when
E. Clementyev et aL / Physica B 230-232 (1997) 735-737
temperature is increased (here, measurements were extended only up to 70 K). To fit the low-temperature signal with Lorentzian lines, one is forced to use two peaks, one of which at least has to be inelastic, with ho9 ~ 1 meV. If one of the CF doublets (denoted F6/7) is assumed to be the groundstate, and the excitation at 1 meV is then ascribed to the F6/7 ~ Fs transition, it is impossible to account for the intensity found around 0.4 meV because the diagonal matrix elements of J± for the doublets are too small. On the other hand, a very good fit can be obtained with a F8 ground-state and two low-lying excited doublets. The fit shown as a solid line in Fig. 2 corresponds to the sequence Fa(0)-F7(4.6 K)-F6(10.7 K), but a nearly as good solution is given by Fs(0)-F6(4.9 K)-Fv(II.1 K). In conclusion, the results of our INS study on a stoichiometric specimen of T m T e clearly indicate that the level scheme proposed in Ref. [8] has to be rejected. More generally, any solution implying a large total CF splitting of the multiplet seems very unlikely. Furthermore, if one analyses the data in terms of the eigenstates of a single-site CF hamiltonian with cubic symmetry, the 1"8 quartet is found to be the only possible ground-state, with the higher levels lying at energies of about 4 K and 10.5 K. The order in which F6 and F 7 appear is, however, difficult to ascertain from the neutron data alone. This picture agrees qualitatively with the CF parameters deduced from the elastic constant measurements [5, 7]. However, it should be noted that the quasielastic and inelastic Lorentzian line widths ( F W H M ) derived from Fig. 2 (Fq~ ,-~ Fin ~ 0.9 meV) are considerably larger than the instrumental resolution (0.2 meV in the present case). Possible reasons for this anomalous broadening are mag-
737
netic fluctuations (proximity of the valence instability) or a weak splitting of the F8 level due to quadrupolar interactions. The latter mechanism seems quite plausible in view of the pronounced deviations from a single-ion CF calculation observed in the elastic constants below 5 K [5]. It was previously hypothesized in Ref. [6], albeit for a completely different CF level scheme. This point will be discussed at greater length in a forthcoming publication [11].
References [1] E. Bucher, K. Andres, F.J. di Salvo, J.P. Maita, A.C. Gossard, A.S. Cooper and G.W. Hull Jr., Phys. Rev. B 11 (1975) 500. [2] P. Wachter, in: Handbook of the Physicsand Chemistry of Rare Earths, Lanthanides-Actinides: Physics - II, Vol. 19, eds. K.A. GschneiderJr., L. Eyring, G.H. Lander and G.R. Choppin (Elsevier,Amsterdam, 1994)p. 177 and references therein. I3] A. Jayaraman, in: Handbook of the Physics and Chemistry of Rare Earths, Vol. 2, eds. K.A. Gschneider Jr. and L. Eyring (North-Holland, Amsterdam, 1979) p. 575. 1'4] T. Matsumura et al., to be published. [51 T. Matsumura, Y. Haga, Y. Nemoto, S. Nakamura, T. Goto and T. Suzuki, Physica B 206&207 (1995) 380. 16] T. Kasuya, J. Phys. Soc. Japan 63 (1994) 3936. [7] H.R. Ott, B. L/ithi and P.S. Wang, in: Valence Instabilities and Related Narrow-Band Phenomena, ed. R.D. Parks (Plenum, New York, 1977) p. 289. 18] A. Furrer, W. Biihrer and P. Wachter, in: Valence Instabilities, eds. P. Wachter and H. Boppart (North-Holland, Amsterdam, 1982) p. 319. 1-9] H. Boppart, P. Wachter and A. Furrer, Internal Report, E.T.H. Ziirich, 1983, unpublished. 1-10"1Y. Lassailly, C. Vettier, F. Holtzberg, A. Benoit and J. Flouquet, Solid State Commun. 52 (1984) 717. 1'11] E. Clementyevet al., to be published.