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Low energy excitations in CeNiSn
Journal of Magnetism and Magnetic Materials 190 (1998) 245—250
Low energy excitations in CeNiSn S. Raymond *, A.P. Murani, B. Fa k , L.P. Regnault , G. Lapertot , P.A. Alekseev, J. Flouquet CEA-Grenoble, De& partement de Recherche Fondamentale sur la Matie% re Condense& e/SPSMS/MDN, 38 054 Grenoble Cedex 9, France Institut Laue Langevin, BP 156, 38 042 Grenoble Cedex 9, France ISSS, Kurchatov Institute, 12 3182 Moscow, Russia Received 14 April 1998; received in revised form 15 June 1998
Abstract We have studied the magnetic excitation spectrum of CeNiSn at low energies both on a polycrystalline sample using time-of-flight technique and on a single crystal with a triple axis spectrometer. The energy gap in the excitation spectrum is clearly observed in the polycrystalline sample reconciling the earlier discrepancies between the two kinds of measurements. The experimental results are consistent with the occurrence of a quasielastic signal within the gap without any significant wave vector dependence and characterized by an energy scale C+0.2 meV. 1998 Elsevier Science B.V. All rights reserved. PACS: 75.20.H; 75.30.M; 78.70.N Keywords: CeNiSn; Kondo insulator; Neutron scattering
1. Introduction CeNiSn has attracted considerable attention in recent years as a novel system among Ce-based intermetallic compounds because of its non-conventional ground state. While most Ce-based intermetallic compounds are good metals (for example, a Fermi liquid state is realized in the so-called heavy fermion (HF) compounds), CeNiSn is classified as a ‘Kondo insulator’ [1,2]. It is now well
* Corresponding author. Tel.: #33-4-76-883738; fax: #334-76-885109; e-mail: [email protected].
established that this behavior was partly due to impurity effects [3] and it is believed that the compound is a semimetal with a partially closed gap. A metallic behavior is indeed observed when the measurements are performed along the a-axis. The spin dynamics probed by NMR also reveals the pseudogap behavior which was interpreted with a V-shaped density of states [4]. The first inelastic neutron scattering (INS) experiments performed on time-of-flight (TOF) spectrometers using powder samples exhibited a quasielastic linewidth of the order of 3—4 meV at 10 K [5]. At the lowest temperature of 3 K, a broad inelastic contribution was observed at about 4 meV superposed to a quasielastic contribution [6]. Measurements performed
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S. Raymond et al. / Journal of Magnetism and Magnetic Materials 190 (1998) 245—250
on triple-axis spectrometers (TAS) using single crystal samples reveal the existence of two excitations below 10 K. The first one is peaked at the Brillouin zone center and is inelastic with a characteristic energy gap of 2 meV [7]. The second excitation is centered at the zone boundary along the b-axis and is also inelastic with a characteristic energy of 4 meV [8,20]. Macroscopic measurements show that the heavy fermion-like behavior is restored by applying a magnetic field or on alloying [2]. From the point of view of the spin dynamics this effect is linked to the appearance of a quasielastic signal which is clearly observed on alloying with Cu [9]. On the other hand the effect is less pronounced when a magnetic field (limited to 12 T for neutron scattering experiments) is applied, although some additional scattering appears at lower energy due to the broadening of the excitation [9,10]. The effect of an applied external pressure is quite puzzling, since bulk measurements indicate a decrease of the gap [2] whereas INS measurements are consistent with an increase in the gap energy [11]. The aim of the present work is to search and characterize the quasielastic signal in the pure CeNiSn compound at low temperatures, expected because of the semimetallic behavior of the compound. A quasielastic signal due to local Kondo-like fluctuations is in fact frequently observed in metallic heavy fermion compounds. In addition, the apparent discrepancy between TOF and TAS measurements which exhibit either a strong quasielastic line (down to 3 K) or a sharp gapped signal centered at u"2 meV and u" 4 meV has motivated us to reinvestigate the spin dynamics in this compound in the low-energy range with improved instrumental resolution.
2. Experimental conditions Experiments using a TAS were performed on IN12 spectrometer, installed at the high flux reactor of ILL, Grenoble. The single crystal sample of mass +6 g, obtained by the Czochralsky method, is the same crystal as previously used in the investigation reported in Ref. [12]. Although two orthorhombic space groups are reported for CeNiSn, a description with the centrosymmetric Pnma
space group seems as good a description as that obtained with the non-centrosymmetric space group Pn2 a [13] and yields the lattice parameters a"7.542 As , b"4.601 As and c"7.617 As at room temperature. For the TAS measurements the single crystal sample was mounted in a variable temperature cryostat with the (a, b)-plane forming the scattering plane and the c-axis vertical. Measurements were performed with a constant final wave vector of k "1.55 As \ (j"4 As ). Use of open col limations 60 —60 resulted in an energy resolution at u"0 of 0.16 meV, as measured on a vanadium sample. Prior to the TOF inelastic scattering measurements, neutron and X-ray powder diffraction spectra were taken in order to check the structure and single phase character of the polycrystalline samples. Due to the strong texture, the neutron diffraction measurements performed on the bulk sample allowed us to check the position of the Bragg peaks only. Concerning inelastic neutron scattering, this texture is not penalyzing for the low wave vector measurements, the advantage being of working on a larger amount of matter. However, X-ray diffraction measurements performed on several small pieces were successfully analyzed and confirmed the CeNiSn structure, except for three small unaccountable Bragg peaks which were observed over a wide range of scattering angles but which did not correspond to the well known impurity phases found in CeNiSn samples (e.g. Ce O , CeNi Sn , CeNi Sn [3]). The measure ments were performed on the IN6 spectrometer at ILL on a powdered sample of 48 g of CeNiSn. A non-magnetic reference sample consisting of 47 g of LaNiSn was also measured under identical conditions in order to determine and subtract out the phonon contribution. The powdered samples were mounted in a flat rectangular aluminium foil which was placed inside a variable temperature cryostat. The wavelength used was j"5.1 As (k "1.23 As \) which gave an elastic energy resolution of 0.11 meV. The measurements were corrected for background including sample holder and cryostat scattering taking due account of the sample transmission. The data were corrected for detector efficiency and normalized with respect to scattering from a vanadium plate.
S. Raymond et al. / Journal of Magnetism and Magnetic Materials 190 (1998) 245—250
3. Experimental results The magnetic excitation spectrum obtained at low temperatures on IN6 reproduced in Fig. 1a for ¹"1.6 K shows clearly an inelastic excitation even for a polycrystalline sample, exhibiting a plateau in the range 0.75—1.25 meV followed by a hump at 1.5 meV. In order to increase the statistical accuracy the observed scattering was summed over the angular range 37.2°(2h(57.4° corresponding to the Q-range 0.71 As \(Q(1.18 As \ (at zero energy transfer), which covers slightly more
Fig. 1. (a) Inelastic magnetic scattering from CeNiSn measured on IN6 at ¹"1.6 K using neutrons of incident energy 3.24 meV. The data are integrated over the scattering angular range 37.2°(2h(57.4°. (b) Spectrum at ¹"20 K. The solid line is a fit as described in the text performed in the energy range outside the vertical dashed lines.
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than the first Brillouin zone. The measurements presented in Fig. 1 are phonon corrected with reference to the LaNiSn data normalized to their total scattering cross sections. In this approximation, we neglect the spectral dependence of the partial density of states. Since the spectral region around u"0 meV is overshadowed by the elastic incoherent scattering, broadened by the instrumental energy resolution, as well as a high angle Bragg peak from the sample backscattered from the cryostat walls which appeared in the region around 0.3—0.4 meV, the data inside the interval !0.5( u(0.5 meV were considered unreliable and hence ignored. The appearance below 10 K of the shallow valley followed by the hump at &1.5 meV does not strictly imply the formation of a gap, but suggests that only a single quasielastic line cannot describe the data at all temperatures. The main feature of these measurements is the relatively high intensity remaining inside the gap region compared to the background determined from the scattering at negative energy transfers at the lowest temperature. In the range of energies studied, the maximum intensity inside the gap represents of the magnetic signal and the hump at 1.5 meV represents of the signal. The solid line is a fit to the data using a quasielastic Lorentzian lineshape and a damped harmonic oscillator to represent the hump. This description is not unique and may not even be physically justified. Its only purpose is to take one step beyond a qualitative analysis of the data. Within the limitations of this analysis the quasielastic line is found to have a half-width at half-maximum C+0.2 meV and the harmonic oscillator is characterized by a centroid at u +1.7 meV and a damping constant of K+0.5 meV. The data obtained at 20 K are shown in Fig. 1b. The signal in the region 0.75—2 meV is almost flat and the hump as well as the dip, which are the signature of the gap, have disappeared. More likely the two contributions to the scattering have merged in a single quasielastic line characterized with C+2.7 meV. An almost symmetric spectral shape, as expected due to the detailed balance condition, is re-established at 100 K, with a C of less than 10 meV. The temperature dependence of the magnetic excitation spectrum of CeNiSn is shown in Fig. 2 over the extended energy range available on the energy gain
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Fig. 2. Inelastic scattering from CeNiSn for different temperatures measured on IN6. The lines are best fits to a Lorentzian lineshape. The peak appearing at 12 meV at 150 K is due to inadequate phonon subtraction as explained in the text. The inset shows the temperature dependence of the half-width at half-maximum C of the Lorentzian. The solid line is a fit to a square root law; the dashed line indicates a linear temperature dependence C"k¹.
side, since we are limited to energies less than 2 meV on the energy loss side. The lines are best fits using a Lorentzian lineshape with a single energy scale represented by its half width C. Once again the phonon contribution is subtracted out with reference to the LaNiSn spectra measured at the same temperatures, except for the 150 K spectrum where the subtraction is performed using the 100 K LaNiSn data. This inadequacy is reflected by the observed hump related to phonon scattering [5] around 12 meV. The temperature dependence of C is shown in the inset of Fig. 2. It follows roughly a square root behavior as observed in CeAl and several other HF compounds [14,21]. A line representing the linear temperature dependence C"k ¹, expected from a purely thermally driven relaxation phenomenon, is shown in the figure as well as the best fit to the form C"a(¹, which yields a"0.7 meV K\ . In order to better understand these data, we have studied the Q-dependence of the signal within the
Fig. 3. Constant-Q scan performed at Q"(0 1 0) at T"1.5 K on IN12 using k "1.55 As \. The line is the best fit to the signal using a Gaussian for the incoherent signal, a Lorentzian for the quasielastic signal and an oscillator for the inelastic signal.
range 0.75—1.25 meV inside the gap using the TAS technique on a single crystal sample. Both constant-Q scans and constant energy scans were performed. A typical constant-Q scan is shown in Fig. 3 at Q"(0 1 0) (center of the ‘second’ Brillouin zone) at ¹"1.5 K. The corresponding value of the momentum transfer is Q"1.37 As \ at u"0 meV. The magnetic excitation spectrum exhibits the 2 meV excitation [7,8,20] (in fact, the centroid is situated at 2.3 meV with a half width at half height of the order of 0.5 meV) and a quasielastic signal with a half-width at half-maximum of the order of 0.2 meV. Various constant-u scans were performed in different directions with u"0.6 meV i.e. within the gap. One such scan is shown in Fig. 4 at ¹"1.5 K. It shows no Q-dependence of the signal. Guided by some new theoretical insight [15], we studied carefully the magnetic excitation spectrum at each high symmetry point of the Brillouin zone. The same weak quasielastic signal is observed at 1.5 K for Q"(0 0.5 0), Q"(0.5 0.5 0), Q" (1 0.5 0), Q"(0.5 1 0), and Q"(1 0 0). It appears that the quasielastic signal as measured on a TAS has no Q-dependence and is relatively weak all over the Brillouin zone.
S. Raymond et al. / Journal of Magnetism and Magnetic Materials 190 (1998) 245—250
Fig. 4. Constant energy scan performed at E"0.6 meV and ¹"1.5 K along Q"(q 1 0) on IN12. The dashed line represents the background.
4. Discussion Previous TOF experiments on polycrystalline CeNiSn showed an intense quasielastic line centered on u"0 meV and a weak broad peak at 4 meV [6]. The present measurements, also on a CeNiSn polycrystalline sample, permitted the observation of the well known gap-like magnetic excitation peaked at around 2 meV. Compared to the previous data [6], we have simply resolved a mode which was hidden in the intense quasielastic line observed with a coarser resolution. We also find that the gap is partially filled with some residual magnetic signal. In agreement with previous studies [7], the low energy quasielastic signal is also observed in the TAS measurements on a single crystal and shows no Q-dependence. The striking difference between the results in Fig. 1a and Fig. 3 is that the relative magnitudes of the signals within the gap and within the hump are inverted between the two. This can be understood from the fact that the quasielastic signal within the gap is Q-independent whereas the ‘peak’ is strongly Q-dependent, especially along the b-axis, and has a short extension in Q-space (there is a factor 4 difference in the Q-width of the 2 meV excitation along the b and c axis, respectively). It thus follows that integration over
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the Brillouin zone as in a TOF measurements yields a stronger quasielastic signal compared with the hump, whereas the constant-Q measurements at Q"(0 1 0), where the intensity of the 2 meV excitation is maximum, will exhibit a smaller quasielastic contribution and a high intensity of the hump. In fact, in view of this strong anisotropy of CeNiSn, the observation of the gap-like response in a polycrystalline sample is quite remarkable. Our measurements stress the fact that the quasielastic signal observed is different and quite unlike that inferred from the semimetallic behavior of the compound. Transport measurements along the aaxis leads to the expectation of some nodes within the gap. It would thus appear that the bulk measurements are in agreement with the recent model of Ikeda and Miyake [15], based on a hybridization gap picture, where a node appears in the hybridization potential assuming that the crystal field level "5/2,$3/22 hybridizes with the conduction electrons (with the quantization axis along the a-axis). This leads to a metallic behavior along the a-axis and a semiconducting behavior along the b and c axes. The pseudogap observed in thermodynamic measurements such as the specific heat [2] follows immediately. The present observations by INS of a quasielastic signal everywhere in the Brillouin zone and no enhancement at the symmetry point of the crystal favors a separation between the spin and charge gap. This conclusion was also drawn on the basis of the break-junction tunneling measurements [16,17] which exhibit very pronounced magnetic field effects. Another model [18] for CeNiSn considers the interplay between HF and crystal field excitations, also takes the spincharge separation as a starting point. In the framework of this model, quasielastic scattering is not excluded a priori but it is not considered in the simplest published version of the model. As a final remark we mention that, as for the 2 and 4 meV excitations, the low-energy part of the signal does not appear to be sample dependent, since early experiments [19] performed in almost the same conditions on another powder sample with the TOF technique gave almost the same results except for the slightly different intensity ratio between the signal within the gap and the hump around 1.5 meV.
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5. Conclusions Both the high resolution TOF and TAS data on poly and single crystals, respectively, give a common picture of the low-energy spin dynamics of CeNiSn, which is consistent with the occurrence of the well-known gap-like excitation at 2 meV having a strong Q-dependence along the b-axis. The presence of a quasielastic signal within the gap with the energy scale C"0.2 meV and without any Q-dependence is also well established by these measurements. Acknowledgements We thank E. Ressouche and B. Ouladiaff for helping us with the neutron powder diffraction experiments performed in order to check the sample quality. One of us (P.A.) thanks the Russian State Program ‘Neutron Investigations of Condensed Matter’ for financial support. References [1] G. Aeppli, Z. Fisk, Comm. Condens. Matter Phys. 16 (1992) 155. [2] T. Takabatake, H. Fujii, Jpn. J. Appl. Phys. 8 (1993) 254. [3] G. Nakamoto, T. Takabatake, H. Fujii, A. Minami, K. Maezawa, I. Oguro, A. Menovsky, J. Phys. Soc. Jpn. 64 (1995) 4834. [4] M. Kyagoku, Y. Kitaoka, K. Asayama, T. Takabatake, H. Fujii, J. Phys. Soc. Japan 61 (1992) 43. [5] P.A. Alekseev, E.S. Clementyev, V.N. Lazukov, I.P. Sadikov, E.A. Goremychkin, I.L. Sashin, Physica B 186—188 (1993) 416.
[6] M. Koghi, K. Ohoyama, T. Osakabe, M. Kasaya, T. Takabatake, H. Fujii, Physica B 186—188 (1993) 409. [7] T.E. Mason, G. Aeppli, A.P. Ramirez, K.N. Clausen, C. Broholm, N. Stu¨cheli, E. Bucher, T.T.M. Palstra, Phys. Rev. Lett. 69 (1992) 490. [8] H. Kadowaki, T. Sato, H. Yoshizawa, T. Ekino, T. Takabatake, H. Fujii, L.P. Regnault, Y. Ishikawa, J. Phys. Soc. Japan 63 (1994) 2074. [9] A. Schro¨der, G. Aeppli, T.E. Mason, E. Bucher, Physica B 234—236 (1997) 861. [10] S. Raymond, L.P. Regnault, T. Sato, H. Kadowaki, N. Pyka, G. Nakamoto, T. Takabatake, H. Fujii, Y. Ishikawa, G. Lapertot, J. Flouquet, J. Phys.: Condens. Matter 9 (1997) 1599. [11] H. Kadowaki, T.J. Sato, G. Nakamoto, T. Takabatake, H. Fujii, Y. Ishikawa, Physica B 230—232 (1997) 664. [12] S. Kambe, S. Raymond, H. Suderow, J.Mc. Donough, B. Fa k, L.P. Regnault, R. Calemczuk, J. Flouquet, Physica B 223&224 (1996) 135. [13] H. Hiess, I. Zobkalo, M. Bonnet, J. Schweizer, E. Lelie`vre Berna, F. Tasset, Y. Isikawa, G.H. Lander, J. Phys.: Condens Matter 9 (1997) 9321. [14] A.P. Murani, K. Knorr, K.H.J. Buschow, A. Benoit, J. Flouquet, Solid State Commun. 36 (1980) 523. [15] H. Ikeda, K. Miyake, J. Phys. Soc. Japan 65 (1996) 1769. [16] S. Kambe, S. Raymond, H. Suderow, G. Lapertot, H. Bioud, P. Haen, L.P. Regnault, J. Flouquet, Proc. 21st Int. Conf. on Low Temperature Physics, Czec. J. Phys. 46 (1996) 1999. [17] D.N. Davydov, S. Kambe, A.G.M. Jansen, P. Wyder, N. Wilson, G. Lapertot, J. Flouquet, Phys. Rev. B 55 (1997) 7299. [18] Y. Kagan, K.A. Kikoin, A.S. Mishenko, Phys. Rev. B 55 (1997) 12348. [19] A.P. Murani, Unpublished results, ILL, 1989. [20] T. Sato, H. Kadowaki, H. Yoshizawa, T. Ekino, T. Takabatake, H. Fujii, L.P. Regnault, Y. Ishikawa, J. Phys.: Condens. Matter 7 (1995) 8009. [21] M. Loewenhaupt, K.H. Fisher, in: Handbook on the Physics and Chemistry of Rare Earths, Vol. 16, Elsevier, Amsterdam, 1993.
Low energy excitations in CeNiSn S. Raymond *, A.P. Murani, B. Fa k , L.P. Regnault , G. Lapertot , P.A. Alekseev, J. Flouquet CEA-Grenoble, De& partement de Recherche Fondamentale sur la Matie% re Condense& e/SPSMS/MDN, 38 054 Grenoble Cedex 9, France Institut Laue Langevin, BP 156, 38 042 Grenoble Cedex 9, France ISSS, Kurchatov Institute, 12 3182 Moscow, Russia Received 14 April 1998; received in revised form 15 June 1998
Abstract We have studied the magnetic excitation spectrum of CeNiSn at low energies both on a polycrystalline sample using time-of-flight technique and on a single crystal with a triple axis spectrometer. The energy gap in the excitation spectrum is clearly observed in the polycrystalline sample reconciling the earlier discrepancies between the two kinds of measurements. The experimental results are consistent with the occurrence of a quasielastic signal within the gap without any significant wave vector dependence and characterized by an energy scale C+0.2 meV. 1998 Elsevier Science B.V. All rights reserved. PACS: 75.20.H; 75.30.M; 78.70.N Keywords: CeNiSn; Kondo insulator; Neutron scattering
1. Introduction CeNiSn has attracted considerable attention in recent years as a novel system among Ce-based intermetallic compounds because of its non-conventional ground state. While most Ce-based intermetallic compounds are good metals (for example, a Fermi liquid state is realized in the so-called heavy fermion (HF) compounds), CeNiSn is classified as a ‘Kondo insulator’ [1,2]. It is now well
* Corresponding author. Tel.: #33-4-76-883738; fax: #334-76-885109; e-mail: [email protected].
established that this behavior was partly due to impurity effects [3] and it is believed that the compound is a semimetal with a partially closed gap. A metallic behavior is indeed observed when the measurements are performed along the a-axis. The spin dynamics probed by NMR also reveals the pseudogap behavior which was interpreted with a V-shaped density of states [4]. The first inelastic neutron scattering (INS) experiments performed on time-of-flight (TOF) spectrometers using powder samples exhibited a quasielastic linewidth of the order of 3—4 meV at 10 K [5]. At the lowest temperature of 3 K, a broad inelastic contribution was observed at about 4 meV superposed to a quasielastic contribution [6]. Measurements performed
0304-8853/98/$ — see front matter 1998 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 9 8 ) 0 0 2 9 9 - 6
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S. Raymond et al. / Journal of Magnetism and Magnetic Materials 190 (1998) 245—250
on triple-axis spectrometers (TAS) using single crystal samples reveal the existence of two excitations below 10 K. The first one is peaked at the Brillouin zone center and is inelastic with a characteristic energy gap of 2 meV [7]. The second excitation is centered at the zone boundary along the b-axis and is also inelastic with a characteristic energy of 4 meV [8,20]. Macroscopic measurements show that the heavy fermion-like behavior is restored by applying a magnetic field or on alloying [2]. From the point of view of the spin dynamics this effect is linked to the appearance of a quasielastic signal which is clearly observed on alloying with Cu [9]. On the other hand the effect is less pronounced when a magnetic field (limited to 12 T for neutron scattering experiments) is applied, although some additional scattering appears at lower energy due to the broadening of the excitation [9,10]. The effect of an applied external pressure is quite puzzling, since bulk measurements indicate a decrease of the gap [2] whereas INS measurements are consistent with an increase in the gap energy [11]. The aim of the present work is to search and characterize the quasielastic signal in the pure CeNiSn compound at low temperatures, expected because of the semimetallic behavior of the compound. A quasielastic signal due to local Kondo-like fluctuations is in fact frequently observed in metallic heavy fermion compounds. In addition, the apparent discrepancy between TOF and TAS measurements which exhibit either a strong quasielastic line (down to 3 K) or a sharp gapped signal centered at u"2 meV and u" 4 meV has motivated us to reinvestigate the spin dynamics in this compound in the low-energy range with improved instrumental resolution.
2. Experimental conditions Experiments using a TAS were performed on IN12 spectrometer, installed at the high flux reactor of ILL, Grenoble. The single crystal sample of mass +6 g, obtained by the Czochralsky method, is the same crystal as previously used in the investigation reported in Ref. [12]. Although two orthorhombic space groups are reported for CeNiSn, a description with the centrosymmetric Pnma
space group seems as good a description as that obtained with the non-centrosymmetric space group Pn2 a [13] and yields the lattice parameters a"7.542 As , b"4.601 As and c"7.617 As at room temperature. For the TAS measurements the single crystal sample was mounted in a variable temperature cryostat with the (a, b)-plane forming the scattering plane and the c-axis vertical. Measurements were performed with a constant final wave vector of k "1.55 As \ (j"4 As ). Use of open col limations 60 —60 resulted in an energy resolution at u"0 of 0.16 meV, as measured on a vanadium sample. Prior to the TOF inelastic scattering measurements, neutron and X-ray powder diffraction spectra were taken in order to check the structure and single phase character of the polycrystalline samples. Due to the strong texture, the neutron diffraction measurements performed on the bulk sample allowed us to check the position of the Bragg peaks only. Concerning inelastic neutron scattering, this texture is not penalyzing for the low wave vector measurements, the advantage being of working on a larger amount of matter. However, X-ray diffraction measurements performed on several small pieces were successfully analyzed and confirmed the CeNiSn structure, except for three small unaccountable Bragg peaks which were observed over a wide range of scattering angles but which did not correspond to the well known impurity phases found in CeNiSn samples (e.g. Ce O , CeNi Sn , CeNi Sn [3]). The measure ments were performed on the IN6 spectrometer at ILL on a powdered sample of 48 g of CeNiSn. A non-magnetic reference sample consisting of 47 g of LaNiSn was also measured under identical conditions in order to determine and subtract out the phonon contribution. The powdered samples were mounted in a flat rectangular aluminium foil which was placed inside a variable temperature cryostat. The wavelength used was j"5.1 As (k "1.23 As \) which gave an elastic energy resolution of 0.11 meV. The measurements were corrected for background including sample holder and cryostat scattering taking due account of the sample transmission. The data were corrected for detector efficiency and normalized with respect to scattering from a vanadium plate.
S. Raymond et al. / Journal of Magnetism and Magnetic Materials 190 (1998) 245—250
3. Experimental results The magnetic excitation spectrum obtained at low temperatures on IN6 reproduced in Fig. 1a for ¹"1.6 K shows clearly an inelastic excitation even for a polycrystalline sample, exhibiting a plateau in the range 0.75—1.25 meV followed by a hump at 1.5 meV. In order to increase the statistical accuracy the observed scattering was summed over the angular range 37.2°(2h(57.4° corresponding to the Q-range 0.71 As \(Q(1.18 As \ (at zero energy transfer), which covers slightly more
Fig. 1. (a) Inelastic magnetic scattering from CeNiSn measured on IN6 at ¹"1.6 K using neutrons of incident energy 3.24 meV. The data are integrated over the scattering angular range 37.2°(2h(57.4°. (b) Spectrum at ¹"20 K. The solid line is a fit as described in the text performed in the energy range outside the vertical dashed lines.
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than the first Brillouin zone. The measurements presented in Fig. 1 are phonon corrected with reference to the LaNiSn data normalized to their total scattering cross sections. In this approximation, we neglect the spectral dependence of the partial density of states. Since the spectral region around u"0 meV is overshadowed by the elastic incoherent scattering, broadened by the instrumental energy resolution, as well as a high angle Bragg peak from the sample backscattered from the cryostat walls which appeared in the region around 0.3—0.4 meV, the data inside the interval !0.5( u(0.5 meV were considered unreliable and hence ignored. The appearance below 10 K of the shallow valley followed by the hump at &1.5 meV does not strictly imply the formation of a gap, but suggests that only a single quasielastic line cannot describe the data at all temperatures. The main feature of these measurements is the relatively high intensity remaining inside the gap region compared to the background determined from the scattering at negative energy transfers at the lowest temperature. In the range of energies studied, the maximum intensity inside the gap represents of the magnetic signal and the hump at 1.5 meV represents of the signal. The solid line is a fit to the data using a quasielastic Lorentzian lineshape and a damped harmonic oscillator to represent the hump. This description is not unique and may not even be physically justified. Its only purpose is to take one step beyond a qualitative analysis of the data. Within the limitations of this analysis the quasielastic line is found to have a half-width at half-maximum C+0.2 meV and the harmonic oscillator is characterized by a centroid at u +1.7 meV and a damping constant of K+0.5 meV. The data obtained at 20 K are shown in Fig. 1b. The signal in the region 0.75—2 meV is almost flat and the hump as well as the dip, which are the signature of the gap, have disappeared. More likely the two contributions to the scattering have merged in a single quasielastic line characterized with C+2.7 meV. An almost symmetric spectral shape, as expected due to the detailed balance condition, is re-established at 100 K, with a C of less than 10 meV. The temperature dependence of the magnetic excitation spectrum of CeNiSn is shown in Fig. 2 over the extended energy range available on the energy gain
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Fig. 2. Inelastic scattering from CeNiSn for different temperatures measured on IN6. The lines are best fits to a Lorentzian lineshape. The peak appearing at 12 meV at 150 K is due to inadequate phonon subtraction as explained in the text. The inset shows the temperature dependence of the half-width at half-maximum C of the Lorentzian. The solid line is a fit to a square root law; the dashed line indicates a linear temperature dependence C"k¹.
side, since we are limited to energies less than 2 meV on the energy loss side. The lines are best fits using a Lorentzian lineshape with a single energy scale represented by its half width C. Once again the phonon contribution is subtracted out with reference to the LaNiSn spectra measured at the same temperatures, except for the 150 K spectrum where the subtraction is performed using the 100 K LaNiSn data. This inadequacy is reflected by the observed hump related to phonon scattering [5] around 12 meV. The temperature dependence of C is shown in the inset of Fig. 2. It follows roughly a square root behavior as observed in CeAl and several other HF compounds [14,21]. A line representing the linear temperature dependence C"k ¹, expected from a purely thermally driven relaxation phenomenon, is shown in the figure as well as the best fit to the form C"a(¹, which yields a"0.7 meV K\ . In order to better understand these data, we have studied the Q-dependence of the signal within the
Fig. 3. Constant-Q scan performed at Q"(0 1 0) at T"1.5 K on IN12 using k "1.55 As \. The line is the best fit to the signal using a Gaussian for the incoherent signal, a Lorentzian for the quasielastic signal and an oscillator for the inelastic signal.
range 0.75—1.25 meV inside the gap using the TAS technique on a single crystal sample. Both constant-Q scans and constant energy scans were performed. A typical constant-Q scan is shown in Fig. 3 at Q"(0 1 0) (center of the ‘second’ Brillouin zone) at ¹"1.5 K. The corresponding value of the momentum transfer is Q"1.37 As \ at u"0 meV. The magnetic excitation spectrum exhibits the 2 meV excitation [7,8,20] (in fact, the centroid is situated at 2.3 meV with a half width at half height of the order of 0.5 meV) and a quasielastic signal with a half-width at half-maximum of the order of 0.2 meV. Various constant-u scans were performed in different directions with u"0.6 meV i.e. within the gap. One such scan is shown in Fig. 4 at ¹"1.5 K. It shows no Q-dependence of the signal. Guided by some new theoretical insight [15], we studied carefully the magnetic excitation spectrum at each high symmetry point of the Brillouin zone. The same weak quasielastic signal is observed at 1.5 K for Q"(0 0.5 0), Q"(0.5 0.5 0), Q" (1 0.5 0), Q"(0.5 1 0), and Q"(1 0 0). It appears that the quasielastic signal as measured on a TAS has no Q-dependence and is relatively weak all over the Brillouin zone.
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Fig. 4. Constant energy scan performed at E"0.6 meV and ¹"1.5 K along Q"(q 1 0) on IN12. The dashed line represents the background.
4. Discussion Previous TOF experiments on polycrystalline CeNiSn showed an intense quasielastic line centered on u"0 meV and a weak broad peak at 4 meV [6]. The present measurements, also on a CeNiSn polycrystalline sample, permitted the observation of the well known gap-like magnetic excitation peaked at around 2 meV. Compared to the previous data [6], we have simply resolved a mode which was hidden in the intense quasielastic line observed with a coarser resolution. We also find that the gap is partially filled with some residual magnetic signal. In agreement with previous studies [7], the low energy quasielastic signal is also observed in the TAS measurements on a single crystal and shows no Q-dependence. The striking difference between the results in Fig. 1a and Fig. 3 is that the relative magnitudes of the signals within the gap and within the hump are inverted between the two. This can be understood from the fact that the quasielastic signal within the gap is Q-independent whereas the ‘peak’ is strongly Q-dependent, especially along the b-axis, and has a short extension in Q-space (there is a factor 4 difference in the Q-width of the 2 meV excitation along the b and c axis, respectively). It thus follows that integration over
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the Brillouin zone as in a TOF measurements yields a stronger quasielastic signal compared with the hump, whereas the constant-Q measurements at Q"(0 1 0), where the intensity of the 2 meV excitation is maximum, will exhibit a smaller quasielastic contribution and a high intensity of the hump. In fact, in view of this strong anisotropy of CeNiSn, the observation of the gap-like response in a polycrystalline sample is quite remarkable. Our measurements stress the fact that the quasielastic signal observed is different and quite unlike that inferred from the semimetallic behavior of the compound. Transport measurements along the aaxis leads to the expectation of some nodes within the gap. It would thus appear that the bulk measurements are in agreement with the recent model of Ikeda and Miyake [15], based on a hybridization gap picture, where a node appears in the hybridization potential assuming that the crystal field level "5/2,$3/22 hybridizes with the conduction electrons (with the quantization axis along the a-axis). This leads to a metallic behavior along the a-axis and a semiconducting behavior along the b and c axes. The pseudogap observed in thermodynamic measurements such as the specific heat [2] follows immediately. The present observations by INS of a quasielastic signal everywhere in the Brillouin zone and no enhancement at the symmetry point of the crystal favors a separation between the spin and charge gap. This conclusion was also drawn on the basis of the break-junction tunneling measurements [16,17] which exhibit very pronounced magnetic field effects. Another model [18] for CeNiSn considers the interplay between HF and crystal field excitations, also takes the spincharge separation as a starting point. In the framework of this model, quasielastic scattering is not excluded a priori but it is not considered in the simplest published version of the model. As a final remark we mention that, as for the 2 and 4 meV excitations, the low-energy part of the signal does not appear to be sample dependent, since early experiments [19] performed in almost the same conditions on another powder sample with the TOF technique gave almost the same results except for the slightly different intensity ratio between the signal within the gap and the hump around 1.5 meV.
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5. Conclusions Both the high resolution TOF and TAS data on poly and single crystals, respectively, give a common picture of the low-energy spin dynamics of CeNiSn, which is consistent with the occurrence of the well-known gap-like excitation at 2 meV having a strong Q-dependence along the b-axis. The presence of a quasielastic signal within the gap with the energy scale C"0.2 meV and without any Q-dependence is also well established by these measurements. Acknowledgements We thank E. Ressouche and B. Ouladiaff for helping us with the neutron powder diffraction experiments performed in order to check the sample quality. One of us (P.A.) thanks the Russian State Program ‘Neutron Investigations of Condensed Matter’ for financial support. References [1] G. Aeppli, Z. Fisk, Comm. Condens. Matter Phys. 16 (1992) 155. [2] T. Takabatake, H. Fujii, Jpn. J. Appl. Phys. 8 (1993) 254. [3] G. Nakamoto, T. Takabatake, H. Fujii, A. Minami, K. Maezawa, I. Oguro, A. Menovsky, J. Phys. Soc. Jpn. 64 (1995) 4834. [4] M. Kyagoku, Y. Kitaoka, K. Asayama, T. Takabatake, H. Fujii, J. Phys. Soc. Japan 61 (1992) 43. [5] P.A. Alekseev, E.S. Clementyev, V.N. Lazukov, I.P. Sadikov, E.A. Goremychkin, I.L. Sashin, Physica B 186—188 (1993) 416.
[6] M. Koghi, K. Ohoyama, T. Osakabe, M. Kasaya, T. Takabatake, H. Fujii, Physica B 186—188 (1993) 409. [7] T.E. Mason, G. Aeppli, A.P. Ramirez, K.N. Clausen, C. Broholm, N. Stu¨cheli, E. Bucher, T.T.M. Palstra, Phys. Rev. Lett. 69 (1992) 490. [8] H. Kadowaki, T. Sato, H. Yoshizawa, T. Ekino, T. Takabatake, H. Fujii, L.P. Regnault, Y. Ishikawa, J. Phys. Soc. Japan 63 (1994) 2074. [9] A. Schro¨der, G. Aeppli, T.E. Mason, E. Bucher, Physica B 234—236 (1997) 861. [10] S. Raymond, L.P. Regnault, T. Sato, H. Kadowaki, N. Pyka, G. Nakamoto, T. Takabatake, H. Fujii, Y. Ishikawa, G. Lapertot, J. Flouquet, J. Phys.: Condens. Matter 9 (1997) 1599. [11] H. Kadowaki, T.J. Sato, G. Nakamoto, T. Takabatake, H. Fujii, Y. Ishikawa, Physica B 230—232 (1997) 664. [12] S. Kambe, S. Raymond, H. Suderow, J.Mc. Donough, B. Fa k, L.P. Regnault, R. Calemczuk, J. Flouquet, Physica B 223&224 (1996) 135. [13] H. Hiess, I. Zobkalo, M. Bonnet, J. Schweizer, E. Lelie`vre Berna, F. Tasset, Y. Isikawa, G.H. Lander, J. Phys.: Condens Matter 9 (1997) 9321. [14] A.P. Murani, K. Knorr, K.H.J. Buschow, A. Benoit, J. Flouquet, Solid State Commun. 36 (1980) 523. [15] H. Ikeda, K. Miyake, J. Phys. Soc. Japan 65 (1996) 1769. [16] S. Kambe, S. Raymond, H. Suderow, G. Lapertot, H. Bioud, P. Haen, L.P. Regnault, J. Flouquet, Proc. 21st Int. Conf. on Low Temperature Physics, Czec. J. Phys. 46 (1996) 1999. [17] D.N. Davydov, S. Kambe, A.G.M. Jansen, P. Wyder, N. Wilson, G. Lapertot, J. Flouquet, Phys. Rev. B 55 (1997) 7299. [18] Y. Kagan, K.A. Kikoin, A.S. Mishenko, Phys. Rev. B 55 (1997) 12348. [19] A.P. Murani, Unpublished results, ILL, 1989. [20] T. Sato, H. Kadowaki, H. Yoshizawa, T. Ekino, T. Takabatake, H. Fujii, L.P. Regnault, Y. Ishikawa, J. Phys.: Condens. Matter 7 (1995) 8009. [21] M. Loewenhaupt, K.H. Fisher, in: Handbook on the Physics and Chemistry of Rare Earths, Vol. 16, Elsevier, Amsterdam, 1993.