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Unusual phonon softening in the Kondo lattice CeCu2
Physica B 312–313 (2002) 181–183
Unusual phonon softening in the Kondo lattice CeCu2 Michael Loewenhaupta,*, Ulrike Wittea,b, Sirko Krampa, Markus Bradenc, Pavel Svobodad a
Technische Universita¨t Dresden, Inst. fu¨r Angewandte Physik, 01062 Dresden, Germany b Hahn-Meitner-Institut Berlin, Glienicker Str. 100, 14109 Berlin, Germany c LLB Saclay, 91191 Gif-Sur-Yvette Cedex, France d Department of Electronic Structures, Charles University, Ke Karlovu 5, 121 16 Praha, Czech Republic
Abstract CeCu2 is a Kondo lattice with antiferromagnetic order below 3.5 K and a Kondo temperature of about 6 K. Earlier neutron scattering experiments lead to the assumption of a coupling between a crystal field transition and some phonons with energies around 14 meV. With the results from our newly performed inelastic neutron measurements on a single crystal we found these assumptions confirmed. We observed an unusual softening of certain phonons with increasing temperature. This softening of up to 15% is much stronger than the normal thermal behavior of phonons. Additionally, the line width of these phonons is increasing. At the same time the magnetic response is strongly broadened by the coupling to the phonons. The findings for CeCu2 are discussed in relation with similar observation of a coupling between electronic and lattice degrees of freedom in CeAl2 and YbPO4. r 2002 Elsevier Science B.V. All rights reserved. PACS: 75.20.Hr; 63.20.Ls; 61.12.-q Keywords: Crystal field-phonon coupling; Kondo lattice; Inelastic neutron scattering
1. Introduction
2. Inelastic neutron scattering experiment
Earlier neutron scattering experiments on CeCu2 (temperature dependent time-of-flight measurements on polycrystalline samples) have shown an anomaly in the inelastic neutron spectra at about 14 meV and temperatures of 100–150 K [1]. These findings have led to the assumption of a coupling between a crystal field transition and phonons [2]. The first excited crystal field level becomes thermally populated in the temperature region where the anomalies have been observed. From this, it was concluded that there is a coupling between phonons with energies around 14 meV and the crystal field transition from the first (9 meV) to the second (23 meV) excited level.
The present experiment was performed at the thermal three-axis spectrometer T1 of the LLB in Saclay. We used a CeCu2 single crystal of high quality grown at the Charles University in Prague. We measured inelastic neutron spectra at different temperatures in the magnetically disordered state between 26 and 300 K with a fixed final neutron energy of 14.7 meV and an experimental resolution in energy between 0.2 and 0.6 meV for energy transfers between 5 and 25 meV, respectively. The measured spectra consist of two parts: intensity of magnetic origin (crystal field transitions) and intensity due to scattering by phonons. For the identification of both contributions we refer to the earlier low-Q and high-Q measurements [1]. The magnetic part of the observed spectra at T ¼ 26 K shows one broad peak at 23 meV, which arises from the crystal field transition from the ground
*Corresponding author. Tel.: +49-351-463-36055; fax: +49351-463-33199. E-mail address: [email protected] (M. Loewenhaupt).
0921-4526/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 0 1 ) 0 1 3 1 3 - 8
M. Loewenhaupt et al. / Physica B 312–313 (2002) 181–183
182 400
26 K 100 K 200 K 300 K
Q = (0.7 4 0)
Intensity in counts/mon
350 300 250
was for a phonon peak at around 7 meV measured at Q ¼ ð0 4 0Þ: Its energy at 300 K is lower by around 15% with respect to its position at low temperature (26 K). Additionally, the line widths of the shifted phonons are strongly increasing with temperature.
200 150
3. Conclusions and comparison with other substances
100 50 0 5
10
15
20
25
Energy in meV
Fig. 1. Inelastic neutron spectra of CeCu2 at different temperatures for scattering vector Q ¼ ð0:7 4 0Þ (data corrected for background). The phonon at 14 meV belongs to the irreducible representation A1g : It becomes unusually soft (shifted to lower energies) with increasing temperatures. The phonon at 8 meV belongs to another irreducible representation and is not shifted. The dotted lines perpendicular to the x-axis show the phonon positions measured at 26 K, the full lines those at 300 K. Between the phonon peaks an increase of intensity with temperature is visible, which arises from the broadened 14 meV crystal field transition from the first to the second excited level. At 23 meV the crystal field transition from the ground state to the second excited state is observed.
state to the second excited level (see Fig. 1). The other crystal field transition from the ground state to the first excited state at 9 meV is not visible because of its negligible matrix element. Its position was deduced from the temperature dependence of the intensity of the strong 23 meV transition [1]. As expected, the intensity of the 23 meV peak diminishes with increasing temperature because of the decreasing probability of that transition with rising temperature. However, the expected strong transition at 14 meV between the two excited levels is not observed at elevated temperatures. Instead, we find a strong rise of intensity in the whole energy region below 20 meV reminiscent of the 14 meV crystal field transition, which is strongly broadened by the coupling to the phonons. In the phononic part of the spectra we observe some phonon branches becoming unusually soft (shifting to lower energies) with increasing temperature and other phonons with normal behavior. The phonon shown in Fig. 1 at 14 meV is shifting to lower energies much stronger than expected for the normal temperature dependence of the phonon energy. In contrast, the phonon at 8 meV shows normal behavior with temperature. We found the unusual softening for only the three phonon branches of one single irreducible representation (A1g symmetry). The strongest shift, we observed
In general, elementary excitations like phonons and crystal field transitions are considered decoupled. But some examples are known, where an observation of an unusual behavior (line width effects, line splittingy) in both subsystems has to be interpreted as a signature of a strong coupling between both phenomena. In the literature a coupling between electronic (crystal field transitions) and lattice degrees of freedom is reported for CeAl2 and YbPO4 as evidenced by inelastic neutron scattering experiments. YbPO4 crystallizes in zircon structure and has 36 phonon modes. Strong temperature effects on crystal field spectra and damping of phonons lead to the assumption of an underlying mechanism involving monopolar fluctuations of the Yb 4f orbital [3]. CeAl2 with cubic Laves phase structure is yielding 18 phonon modes. One crystal field transition is expected, two were observed [4] in combination with an unusual phonon shift and line width at low temperatures [5]. A theoretical model was developed by Thalmeier and Fulde [6] considering a ‘‘bound state’’ between a certain phonon and the crystal field transition. CeCu2 has the orthorhombic CeCu2 structure and 18 phonon modes. The assumption of a coupling between a crystal field transition and phonons was confirmed by the present investigation. As in CeAl2 we found unusual phonon energy shifts and line widths, in addition to a strong broadening of the 14 meV crystal field excitation. The differences between CeCu2 on the one hand, and CeAl2 and YbPO4 on the other hand, are that the crystal field transitions involved in the coupling to the phonons is connecting two excited crystal field states in the former case, while it is between the ground state and excited states in the latter case.
Acknowledgements The experiment at the LLB was supported by the European Commission by Access to Research Infrastructures of the Improving Human Potential Program (HPRI-CT-1999-00032). The project is partly supported by the BMBF (LO04.02P ‘‘Kristallfeld-Phonon-Kopplung in 4f-Verbindungen’’) and by the Sonderforschungsbereich 463 (funded by the Deutsche Forschungsgemein schaft).
M. Loewenhaupt et al. / Physica B 312–313 (2002) 181–183
References [1] M. Loewenhaupt, M. Prager, E. Gratz, B. Frick, J. Magn. Magn. Mater. 76 & 77 (1988) 415–416. . [2] M. Loewenhaupt, E. Gratz, N. Pillmayr, H. Muller, Physica B 163 (1990) 427–430.
183
[3] C.-K. Loong, M. Loewenhaupt, J.C. Nipko, M. Braden, L.A. Boatner, Phys. Rev. B 60 (1999) R12 549. [4] M. Loewenhaupt, B.D. Rainford, F. Steglich, Phys. Rev. Lett. 42 (1979) 1709. [5] W. Reichardt, N. Nucker, . J. Phys. F 14 (1984) L135. [6] P. Thalmeier, P. Fulde, Phys. Rev. Lett. 49 (1982) 1588.
Unusual phonon softening in the Kondo lattice CeCu2 Michael Loewenhaupta,*, Ulrike Wittea,b, Sirko Krampa, Markus Bradenc, Pavel Svobodad a
Technische Universita¨t Dresden, Inst. fu¨r Angewandte Physik, 01062 Dresden, Germany b Hahn-Meitner-Institut Berlin, Glienicker Str. 100, 14109 Berlin, Germany c LLB Saclay, 91191 Gif-Sur-Yvette Cedex, France d Department of Electronic Structures, Charles University, Ke Karlovu 5, 121 16 Praha, Czech Republic
Abstract CeCu2 is a Kondo lattice with antiferromagnetic order below 3.5 K and a Kondo temperature of about 6 K. Earlier neutron scattering experiments lead to the assumption of a coupling between a crystal field transition and some phonons with energies around 14 meV. With the results from our newly performed inelastic neutron measurements on a single crystal we found these assumptions confirmed. We observed an unusual softening of certain phonons with increasing temperature. This softening of up to 15% is much stronger than the normal thermal behavior of phonons. Additionally, the line width of these phonons is increasing. At the same time the magnetic response is strongly broadened by the coupling to the phonons. The findings for CeCu2 are discussed in relation with similar observation of a coupling between electronic and lattice degrees of freedom in CeAl2 and YbPO4. r 2002 Elsevier Science B.V. All rights reserved. PACS: 75.20.Hr; 63.20.Ls; 61.12.-q Keywords: Crystal field-phonon coupling; Kondo lattice; Inelastic neutron scattering
1. Introduction
2. Inelastic neutron scattering experiment
Earlier neutron scattering experiments on CeCu2 (temperature dependent time-of-flight measurements on polycrystalline samples) have shown an anomaly in the inelastic neutron spectra at about 14 meV and temperatures of 100–150 K [1]. These findings have led to the assumption of a coupling between a crystal field transition and phonons [2]. The first excited crystal field level becomes thermally populated in the temperature region where the anomalies have been observed. From this, it was concluded that there is a coupling between phonons with energies around 14 meV and the crystal field transition from the first (9 meV) to the second (23 meV) excited level.
The present experiment was performed at the thermal three-axis spectrometer T1 of the LLB in Saclay. We used a CeCu2 single crystal of high quality grown at the Charles University in Prague. We measured inelastic neutron spectra at different temperatures in the magnetically disordered state between 26 and 300 K with a fixed final neutron energy of 14.7 meV and an experimental resolution in energy between 0.2 and 0.6 meV for energy transfers between 5 and 25 meV, respectively. The measured spectra consist of two parts: intensity of magnetic origin (crystal field transitions) and intensity due to scattering by phonons. For the identification of both contributions we refer to the earlier low-Q and high-Q measurements [1]. The magnetic part of the observed spectra at T ¼ 26 K shows one broad peak at 23 meV, which arises from the crystal field transition from the ground
*Corresponding author. Tel.: +49-351-463-36055; fax: +49351-463-33199. E-mail address: [email protected] (M. Loewenhaupt).
0921-4526/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 0 1 ) 0 1 3 1 3 - 8
M. Loewenhaupt et al. / Physica B 312–313 (2002) 181–183
182 400
26 K 100 K 200 K 300 K
Q = (0.7 4 0)
Intensity in counts/mon
350 300 250
was for a phonon peak at around 7 meV measured at Q ¼ ð0 4 0Þ: Its energy at 300 K is lower by around 15% with respect to its position at low temperature (26 K). Additionally, the line widths of the shifted phonons are strongly increasing with temperature.
200 150
3. Conclusions and comparison with other substances
100 50 0 5
10
15
20
25
Energy in meV
Fig. 1. Inelastic neutron spectra of CeCu2 at different temperatures for scattering vector Q ¼ ð0:7 4 0Þ (data corrected for background). The phonon at 14 meV belongs to the irreducible representation A1g : It becomes unusually soft (shifted to lower energies) with increasing temperatures. The phonon at 8 meV belongs to another irreducible representation and is not shifted. The dotted lines perpendicular to the x-axis show the phonon positions measured at 26 K, the full lines those at 300 K. Between the phonon peaks an increase of intensity with temperature is visible, which arises from the broadened 14 meV crystal field transition from the first to the second excited level. At 23 meV the crystal field transition from the ground state to the second excited state is observed.
state to the second excited level (see Fig. 1). The other crystal field transition from the ground state to the first excited state at 9 meV is not visible because of its negligible matrix element. Its position was deduced from the temperature dependence of the intensity of the strong 23 meV transition [1]. As expected, the intensity of the 23 meV peak diminishes with increasing temperature because of the decreasing probability of that transition with rising temperature. However, the expected strong transition at 14 meV between the two excited levels is not observed at elevated temperatures. Instead, we find a strong rise of intensity in the whole energy region below 20 meV reminiscent of the 14 meV crystal field transition, which is strongly broadened by the coupling to the phonons. In the phononic part of the spectra we observe some phonon branches becoming unusually soft (shifting to lower energies) with increasing temperature and other phonons with normal behavior. The phonon shown in Fig. 1 at 14 meV is shifting to lower energies much stronger than expected for the normal temperature dependence of the phonon energy. In contrast, the phonon at 8 meV shows normal behavior with temperature. We found the unusual softening for only the three phonon branches of one single irreducible representation (A1g symmetry). The strongest shift, we observed
In general, elementary excitations like phonons and crystal field transitions are considered decoupled. But some examples are known, where an observation of an unusual behavior (line width effects, line splittingy) in both subsystems has to be interpreted as a signature of a strong coupling between both phenomena. In the literature a coupling between electronic (crystal field transitions) and lattice degrees of freedom is reported for CeAl2 and YbPO4 as evidenced by inelastic neutron scattering experiments. YbPO4 crystallizes in zircon structure and has 36 phonon modes. Strong temperature effects on crystal field spectra and damping of phonons lead to the assumption of an underlying mechanism involving monopolar fluctuations of the Yb 4f orbital [3]. CeAl2 with cubic Laves phase structure is yielding 18 phonon modes. One crystal field transition is expected, two were observed [4] in combination with an unusual phonon shift and line width at low temperatures [5]. A theoretical model was developed by Thalmeier and Fulde [6] considering a ‘‘bound state’’ between a certain phonon and the crystal field transition. CeCu2 has the orthorhombic CeCu2 structure and 18 phonon modes. The assumption of a coupling between a crystal field transition and phonons was confirmed by the present investigation. As in CeAl2 we found unusual phonon energy shifts and line widths, in addition to a strong broadening of the 14 meV crystal field excitation. The differences between CeCu2 on the one hand, and CeAl2 and YbPO4 on the other hand, are that the crystal field transitions involved in the coupling to the phonons is connecting two excited crystal field states in the former case, while it is between the ground state and excited states in the latter case.
Acknowledgements The experiment at the LLB was supported by the European Commission by Access to Research Infrastructures of the Improving Human Potential Program (HPRI-CT-1999-00032). The project is partly supported by the BMBF (LO04.02P ‘‘Kristallfeld-Phonon-Kopplung in 4f-Verbindungen’’) and by the Sonderforschungsbereich 463 (funded by the Deutsche Forschungsgemein schaft).
M. Loewenhaupt et al. / Physica B 312–313 (2002) 181–183
References [1] M. Loewenhaupt, M. Prager, E. Gratz, B. Frick, J. Magn. Magn. Mater. 76 & 77 (1988) 415–416. . [2] M. Loewenhaupt, E. Gratz, N. Pillmayr, H. Muller, Physica B 163 (1990) 427–430.
183
[3] C.-K. Loong, M. Loewenhaupt, J.C. Nipko, M. Braden, L.A. Boatner, Phys. Rev. B 60 (1999) R12 549. [4] M. Loewenhaupt, B.D. Rainford, F. Steglich, Phys. Rev. Lett. 42 (1979) 1709. [5] W. Reichardt, N. Nucker, . J. Phys. F 14 (1984) L135. [6] P. Thalmeier, P. Fulde, Phys. Rev. Lett. 49 (1982) 1588.