- Email: [email protected]
Study of the hybridization gap in a heavy fermion compound: CeRu4Sb12
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 272–276 (2004) e21–e22
Study of the hybridization gap in a heavy fermion compound: CeRu4Sb12 D.T. Adrojaa,*, J.-G. Parkb,c, K.A. McEwend, N. Takedae, M. Ishikawae, J.-Y. Sof a
ISIS Facility, Rutherford Appleton Laboratory, Room UG8 Building R3, Chilton, Didcot, Oxon OX11 0QX, UK Department of Physics and Institute of Basic Science, SungKyunKwan University, Suwon 440-746, South Korea c Center for Strongly Correlated Materials Research, Seoul National University, Seoul 151-742, South Korea d Department of Physics and Astronomy, University College London, London WC1E 6BT, UK e Institute for Solid State Physics, University of Tokyo, 5-1-5 Kashiwa, Chiba 277-8581, Japan f School of Physics and Center for Strongly Correlated Materials Research, Seoul National University, Seoul 151-742, South Korea b
Abstract We have investigated the temperature and momentum dependence of the inelastic neutron scattering response of CeRu4Sb12. Our neutron scattering study shows the opening of a Q-independent spin gap of 30 meV in the excitation spectrum, which is smaller than the charge gap of 47 meV observed in optical studies. The spin gap is nearly temperature independent below 100 K, while above this temperature the gap starts to fill up and at higher temperatures the magnetic response becomes purely quasielastic. We discuss the origin of the spin gap and consider the difference between the magnitude of the spin and charge gaps on the basis of theoretical models. r 2004 Elsevier B.V. All rights reserved. PACS: 75.30.mb; 71.27.+a; 75.20.hr; 72.15 Keywords: Hybridization gap; Spin gap; CeRu4Sb12; Kondo lattice
Among the filled skutterudite compounds, YbFe4Sb12 and CeRu4S12 are of particular interest as they exhibit a large electronic contribution to the heat capacity, g ¼ 140 and 380 mJ/mol K2, respectively [1,2]. Furthermore, optical studies revealed that both compounds exhibit a charge gap feature in the AC conductivity below 70 K, with a gap energy of Dcharge=11.2 meV for YbFe4Sb12 and 47.1 meV for CeRu4Sb12 [3]. One of the key questions is whether there is also a gap in the spin excitation spectrum, analogous to the charge counterpart. If the spin gap exists, then the second question is what is its Q and temperature dependence. The answers to these questions are important to understand the underlying microscopic mechanism of the gap formation: inter-site coupling or on-site single-ion coupling as well as the role of the coherence phenomenon. The *Corresponding author. Tel.: +44-1235-445797; fax: +441235-445720. E-mail address: [email protected] (D.T. Adroja).
earlier optical study cannot tell us anything about the Q-dependence, because of the intrinsic limitations of the technique itself, i.e. it is a Q ¼ 0 probe. Inelastic neutron scattering (INS) is the best technique to answer the above questions. Therefore, we have investigated CeRu4Sb12 and LaRu4Sb12 using INS between 5 and 250 K. The data of LaRu4Sb12 were used to estimate the phonon contribution in CeRu4Sb12. The INS measurements were carried out using the HET spectrometer at the ISIS Facility, Rutherford Appleton Laboratory, UK, with an incident neutron energy of Ei ¼ 100 meV. Fig. 1 shows the magnetic response of CeRu4Sb12, after subtracting the phonon and elastic nuclear scattering estimated from LaRu4Sb12, allowing for a difference in the total scattering cross section, for several temperatures. As can be seen in Fig. 1(a) for 5 K, the magnetic scattering is almost absent for energy transfers below 10–15 meV: it starts to develop with increasing energies and exhibits a broad peak at 30 meV. We have taken the peak position as an estimate of the magnitude
0304-8853/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2003.11.126
ARTICLE IN PRESS D.T. Adroja et al. / Journal of Magnetism and Magnetic Materials 272–276 (2004) e21–e22
e22
6 (a)
4
CeRu4Sb12 5K
2 0 (b)
4
60K
S (Q, ω) (mb/sr meV)
2 0 (c)
4
100K
2 0 (d)
4
150K
2 0 (e)
4
250K
2 0 0
20
40
60
80
Energy Transfer (meV) Fig. 1. (a–e) The magnetic response from CeRu4Sb12 at low scattering angles (19 ) after subtracting off the nonmagnetic scattering using LaRu4Sb12 data (see the text) at several temperatures. The arrow shows the position of the spin gap.
of the spin gap, which is consistent with the theoretical studies [4]. For energy transfers higher than 30 meV, the magnetic scattering falls off gradually, and there is still a visible sign of magnetic scattering even at the energy transfer of 95 meV. On increasing the temperature to 60 K, there is very little change in the data regarding the intensity, position and width of the magnetic scattering (see Fig. 1(b)). A first visible temperature dependence was observed when the sample was heated through the coherence temperature of Tcoh ¼ 80 K (estimated from the peak position of the magnetic contribution to the resistivity). As shown in Fig. 1(c), the spin gap feature starts to fill up at 100 K, while the peak position hardly moves compared with the data taken at lower temperatures. We recall that the static magnetic susceptibility also exhibits a maximum at 100 K, which implies TK ¼ 300 K according to the single-impurity Anderson model. A further rise in temperature to 150 K destroys the gap in the magnetic response completely, and now the magnetic response can be described by a broad quasielastic peak. At 250 K, some intensity of the magnetic scattering at high energy transfers shifts
towards lower energies and its shape becomes purely quasielastic. We note that the peak-like structure seen near B10 meV at 250 K is an artefact arising from the difficulties of making a precise subtraction of the elastic line. The overall drastic change in the magnetic response between 60 and 250 K again suggests that the temperature dependence of the spin gap is quite different from that of a conventional band structure gap. The collapse of the inelastic gap-like response and the appearance of the quasielastic scattering at higher temperatures observed in CeRu4Sb12 are similar to that observed in Ce3Bi4Pt3 and YbAl3 [5,6], and also in agreement with the predictions of theoretical models [7,8]. We now discuss the wave vector (Q) dependence of the magnetic response. We have analysed the magnetic response at three different values of jQj; between 0.75 ( 1 at 5 K, which clearly indicates that the spin and 3.25 A gap is independent of Q: Further, the Q dependence of the peak intensity agrees well with the Q dependence of the square of the Ce3+ magnetic form factor. The observed Q-independent response in CeRu4Sb12 demonstrates that the gap arises from single-ion Kondo interactions. On the other hand, the temperature evolution of the response suggests that the coherence of the Kondo lattice also plays an important role in the gap formation. This is consistent with the theoretical models, which show that the gap in the strongly correlated bands starts to open at Tcoh [8], in agreement with the present experimental observation of CeRu4Sb12. A further interesting observation for CeRu4Sb12 is that the magnitude of the spin gap (B30 meV) estimated from the present neutron scattering study is smaller than that of the charge gap (B47 meV) deduced from the optical study. A very similar difference between the spin gap and the charge gap has been previously observed for many heavy fermion systems [8]. This difference has been explained by a few theoretical models, which predict that the spin gap is smaller than the charge gap [8,9]. Further details of this work may be found in [10].
References [1] [2] [3] [4]
[5] [6] [7] [8] [9] [10]
N.R. Dilley, et al., Phys. Rev. B 61 (2002) 4608. N. Takeda, et al., J. Phys. Cond. Matt. 13 (2001) 5971. S.V. Dordevic, et al., Phys. Rev. Lett. 86 (2001) 684. A.J. Fedro, et al., in: L.M. Falicov, et al. (Eds.), Valence Fluctuations in Solids, North-Holland, Amsterdam, 1981, p. 329. A. Severing, et al., Phys. Rev. B 44 (1991) 6832. A.P. Murani, Phys. Rev. Lett. 54 (1985) 1444. P. Riseborough, Adv. Phys. 49 (2000) 257. M.J. Rozenberg, et al., Phys. Rev. B. 54 (1996) 8452. T. Mutou, et al., Phys. Rev. Lett. 81 (1998) 4939. D.J. Adroja, et al., Phys. Rev. B 68 (2003) 94425.
Journal of Magnetism and Magnetic Materials 272–276 (2004) e21–e22
Study of the hybridization gap in a heavy fermion compound: CeRu4Sb12 D.T. Adrojaa,*, J.-G. Parkb,c, K.A. McEwend, N. Takedae, M. Ishikawae, J.-Y. Sof a
ISIS Facility, Rutherford Appleton Laboratory, Room UG8 Building R3, Chilton, Didcot, Oxon OX11 0QX, UK Department of Physics and Institute of Basic Science, SungKyunKwan University, Suwon 440-746, South Korea c Center for Strongly Correlated Materials Research, Seoul National University, Seoul 151-742, South Korea d Department of Physics and Astronomy, University College London, London WC1E 6BT, UK e Institute for Solid State Physics, University of Tokyo, 5-1-5 Kashiwa, Chiba 277-8581, Japan f School of Physics and Center for Strongly Correlated Materials Research, Seoul National University, Seoul 151-742, South Korea b
Abstract We have investigated the temperature and momentum dependence of the inelastic neutron scattering response of CeRu4Sb12. Our neutron scattering study shows the opening of a Q-independent spin gap of 30 meV in the excitation spectrum, which is smaller than the charge gap of 47 meV observed in optical studies. The spin gap is nearly temperature independent below 100 K, while above this temperature the gap starts to fill up and at higher temperatures the magnetic response becomes purely quasielastic. We discuss the origin of the spin gap and consider the difference between the magnitude of the spin and charge gaps on the basis of theoretical models. r 2004 Elsevier B.V. All rights reserved. PACS: 75.30.mb; 71.27.+a; 75.20.hr; 72.15 Keywords: Hybridization gap; Spin gap; CeRu4Sb12; Kondo lattice
Among the filled skutterudite compounds, YbFe4Sb12 and CeRu4S12 are of particular interest as they exhibit a large electronic contribution to the heat capacity, g ¼ 140 and 380 mJ/mol K2, respectively [1,2]. Furthermore, optical studies revealed that both compounds exhibit a charge gap feature in the AC conductivity below 70 K, with a gap energy of Dcharge=11.2 meV for YbFe4Sb12 and 47.1 meV for CeRu4Sb12 [3]. One of the key questions is whether there is also a gap in the spin excitation spectrum, analogous to the charge counterpart. If the spin gap exists, then the second question is what is its Q and temperature dependence. The answers to these questions are important to understand the underlying microscopic mechanism of the gap formation: inter-site coupling or on-site single-ion coupling as well as the role of the coherence phenomenon. The *Corresponding author. Tel.: +44-1235-445797; fax: +441235-445720. E-mail address: [email protected] (D.T. Adroja).
earlier optical study cannot tell us anything about the Q-dependence, because of the intrinsic limitations of the technique itself, i.e. it is a Q ¼ 0 probe. Inelastic neutron scattering (INS) is the best technique to answer the above questions. Therefore, we have investigated CeRu4Sb12 and LaRu4Sb12 using INS between 5 and 250 K. The data of LaRu4Sb12 were used to estimate the phonon contribution in CeRu4Sb12. The INS measurements were carried out using the HET spectrometer at the ISIS Facility, Rutherford Appleton Laboratory, UK, with an incident neutron energy of Ei ¼ 100 meV. Fig. 1 shows the magnetic response of CeRu4Sb12, after subtracting the phonon and elastic nuclear scattering estimated from LaRu4Sb12, allowing for a difference in the total scattering cross section, for several temperatures. As can be seen in Fig. 1(a) for 5 K, the magnetic scattering is almost absent for energy transfers below 10–15 meV: it starts to develop with increasing energies and exhibits a broad peak at 30 meV. We have taken the peak position as an estimate of the magnitude
0304-8853/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2003.11.126
ARTICLE IN PRESS D.T. Adroja et al. / Journal of Magnetism and Magnetic Materials 272–276 (2004) e21–e22
e22
6 (a)
4
CeRu4Sb12 5K
2 0 (b)
4
60K
S (Q, ω) (mb/sr meV)
2 0 (c)
4
100K
2 0 (d)
4
150K
2 0 (e)
4
250K
2 0 0
20
40
60
80
Energy Transfer (meV) Fig. 1. (a–e) The magnetic response from CeRu4Sb12 at low scattering angles (19 ) after subtracting off the nonmagnetic scattering using LaRu4Sb12 data (see the text) at several temperatures. The arrow shows the position of the spin gap.
of the spin gap, which is consistent with the theoretical studies [4]. For energy transfers higher than 30 meV, the magnetic scattering falls off gradually, and there is still a visible sign of magnetic scattering even at the energy transfer of 95 meV. On increasing the temperature to 60 K, there is very little change in the data regarding the intensity, position and width of the magnetic scattering (see Fig. 1(b)). A first visible temperature dependence was observed when the sample was heated through the coherence temperature of Tcoh ¼ 80 K (estimated from the peak position of the magnetic contribution to the resistivity). As shown in Fig. 1(c), the spin gap feature starts to fill up at 100 K, while the peak position hardly moves compared with the data taken at lower temperatures. We recall that the static magnetic susceptibility also exhibits a maximum at 100 K, which implies TK ¼ 300 K according to the single-impurity Anderson model. A further rise in temperature to 150 K destroys the gap in the magnetic response completely, and now the magnetic response can be described by a broad quasielastic peak. At 250 K, some intensity of the magnetic scattering at high energy transfers shifts
towards lower energies and its shape becomes purely quasielastic. We note that the peak-like structure seen near B10 meV at 250 K is an artefact arising from the difficulties of making a precise subtraction of the elastic line. The overall drastic change in the magnetic response between 60 and 250 K again suggests that the temperature dependence of the spin gap is quite different from that of a conventional band structure gap. The collapse of the inelastic gap-like response and the appearance of the quasielastic scattering at higher temperatures observed in CeRu4Sb12 are similar to that observed in Ce3Bi4Pt3 and YbAl3 [5,6], and also in agreement with the predictions of theoretical models [7,8]. We now discuss the wave vector (Q) dependence of the magnetic response. We have analysed the magnetic response at three different values of jQj; between 0.75 ( 1 at 5 K, which clearly indicates that the spin and 3.25 A gap is independent of Q: Further, the Q dependence of the peak intensity agrees well with the Q dependence of the square of the Ce3+ magnetic form factor. The observed Q-independent response in CeRu4Sb12 demonstrates that the gap arises from single-ion Kondo interactions. On the other hand, the temperature evolution of the response suggests that the coherence of the Kondo lattice also plays an important role in the gap formation. This is consistent with the theoretical models, which show that the gap in the strongly correlated bands starts to open at Tcoh [8], in agreement with the present experimental observation of CeRu4Sb12. A further interesting observation for CeRu4Sb12 is that the magnitude of the spin gap (B30 meV) estimated from the present neutron scattering study is smaller than that of the charge gap (B47 meV) deduced from the optical study. A very similar difference between the spin gap and the charge gap has been previously observed for many heavy fermion systems [8]. This difference has been explained by a few theoretical models, which predict that the spin gap is smaller than the charge gap [8,9]. Further details of this work may be found in [10].
References [1] [2] [3] [4]
[5] [6] [7] [8] [9] [10]
N.R. Dilley, et al., Phys. Rev. B 61 (2002) 4608. N. Takeda, et al., J. Phys. Cond. Matt. 13 (2001) 5971. S.V. Dordevic, et al., Phys. Rev. Lett. 86 (2001) 684. A.J. Fedro, et al., in: L.M. Falicov, et al. (Eds.), Valence Fluctuations in Solids, North-Holland, Amsterdam, 1981, p. 329. A. Severing, et al., Phys. Rev. B 44 (1991) 6832. A.P. Murani, Phys. Rev. Lett. 54 (1985) 1444. P. Riseborough, Adv. Phys. 49 (2000) 257. M.J. Rozenberg, et al., Phys. Rev. B. 54 (1996) 8452. T. Mutou, et al., Phys. Rev. Lett. 81 (1998) 4939. D.J. Adroja, et al., Phys. Rev. B 68 (2003) 94425.