- Email: [email protected]
NQR investigation on multipolar ordering systems
ARTICLE IN PRESS
Physica B 403 (2008) 1633–1635 www.elsevier.com/locate/physb
NQR investigation on multipolar ordering systems T. Mitoa,, S. Tomisawaa, S. Masakia, M. Takemuraa, S. Wadaa, H. Harimaa, Y. Katob, M. Kosakab, D. Kikuchic, H. Satoc, H. Sugawarad, N. Takedae, G.-q. Zhengf a
Department of Physics, Faculty of Science, Kobe University, Nada, Kobe 657-8501, Japan b Department of Physics, Saitama University, Saitama 338-8570, Japan c Department of Physics, Tokyo Metropolitan University, Hachioji, Tokyo 192-0397, Japan d Department of Mathematical and Natural Sciences, Faculty of the Integrated Arts and Sciences, The University of Tokushima, Tokushima 770-8502, Japan e Department of Materials Science and Technology, Faculty of Engineering, Niigata University, Niigata 950-2181, Japan f Department of Physics, Okayama University, Okayama 700-8530, Japan
Abstract We have carried out nuclear quadrupolar resonance (NQR) measurements on SmRu4 P12 and YbAl3 C3 , both of which have attracted much interest in terms of multipolar ordering. Although no structural anomalies have been detected by diffraction experiments so far, the NQR resonance frequencies nQ ’s of both compounds show marked anomalies just below each phase transition temperature, which probably probes the order parameters. The results provide important information to shed light on the ordered structures in the low temperature phases of these compounds. r 2007 Elsevier B.V. All rights reserved. PACS: 71.20.Eh; 71.30.+h; 76.60.k; 76.60.Gv Keywords: Nuclear quadrupole resonance; Multipolar order; Filled-skutterudite compound; Yb-based compound
The role of multipolar degrees of freedom is an important issue in the field of strongly correlated electron systems, because this freedom may bring about phase transitions as a ‘‘hidden’’ order parameter. Indeed, the phase transitions of several materials are well understood in terms of the multipolar order, such as CeB6 (quadrupole) [1], NpO2 (octupole) [2], and so on. However, it is generally not easy to identify contributions from multipolar ordering because of experimental difficulties in observing it directly. Resonant X-ray scattering has been known as almost only a probe to observe the orbital order directly. Nuclear magnetic resonance (NMR) is also a useful microscopic technique to detect the orbital order, although this is an indirect observation, namely nuclear spins couple with field-induced magnetic dipole and/or octupole moments. In this paper, we report our new results of nuclear quadrupole resonance (NQR) measurements on SmRu4 P12 Corresponding author. Tel./fax: +81 78 803 5664.
E-mail address: [email protected] (T. Mito). 0921-4526/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2007.10.206
and YbAl3 C3 . Here the temperature dependence of the NQR spectrum probes the order parameters associated with the phase transitions, most probably quadrupolar ordering. If a nucleus has a finite nuclear quadrupole moment Q, Q interacts with local charge distributions surrounding the nucleus through the electric-field gradient (EFG) at the nuclear position. The nuclear quadrupole interaction is given by HQ ¼ ðhnQ =6Þ½3I 2z I 2 þ ZðI 2x I 2y Þ,
(1)
where I is the nuclear spin, the NQR frequency nQ ¼ eQV zz =6Ið2I þ 1Þ, V aa is the EFG along the a direction, and the asymmetry parameter Z ¼ ðV xx V yy Þ=V zz following V zz XV xx XV yy . Therefore nQ is in principle a good probe of changes in local charge distributions associated with quadrupolar ordering. SmRu4 P12 and YbAl3 C3 are of considerable interest: the transition at T MI ¼ 16:5 K in SmRu4 P12 , which is accompanied with a metal–insulator (M–I) transition, is one of promising candidates for octupole ordering [3–5]. And the
ARTICLE IN PRESS T. Mito et al. / Physica B 403 (2008) 1633–1635
phase transition at T n ¼ 80 K in YbAl3 C3 is presumably associated with ‘‘high-temperature quadrupolar ordering’’ [6]. For both compounds, specific heat data are commonly indicative of second-order transitions at each transition temperature, and no structural anomalies have been detected by diffraction measurements [6–8]. There was to date no information on symmetry lowering in their ordered states. Our 101 Ru and 27 Al-NQR measurements on SmRu4 P12 and YbAl3 C3 , respectively, give important information to shed light on the ordered structures of these compounds. Observed total 101 Ru-NQR signals of SmRu4 P12 for T4T MI are well understood with nQ 13:6 MHz and Z ¼ 0. As seen in Fig. 1(a), a single NQR spectrum splits into two resonance lines in the ordered state. According to the report of zero-field mSR studies, the transition at T MI is accompanied with spontaneous magnetic internal field [4,9]. However, the splitting and shift in the resonance lines without any broadening are not explained by assuming internal field at the Ru-sites. Instead, these experimental facts are satisfactorily understood with another scheme, where there are two Ru-sites with different nQ ’s and Z0 for both sites. Because the Ru atoms are located at the middle between two Sm-sites, internal field is canceled out at Ru-sites due to the form factor of hyperfine interactions. It is likely that the ordered structure is characterized by a wave vector of q ¼ ð1; 0; 0Þ [10]. The temperature dependence of the shift in nQ below T MI , jnQ ðTÞ nQ ðT MI Þj, is shown in Fig. 1(b). The continuous change in nQ is typical of a second-order transition. From the observed signal intensity ratio between the two split signals, approximately 3:1, it was found that eight equivalent Ru-sites in the bcc structure separate into two groups of six and two below T MI . These experimental results lead to a reasonable conclusion that
the symmetry is lowered from a cubic Im 3¯ space group to a trigonal R3¯ in the ordered state. We fit the shift of nQ to jnQ ðTÞ nQ ðT MI Þj / ðT MI TÞb in the T-region just below T MI , as seen in Fig. 1(b). The critical exponent b is found close to 1 rather than 0.5. bp0:5 is known to be what is expected for a primary order parameter within the Landau theory for the second-order phase transition [11]. We here recall that the present NQR spectra are not influenced from the spontaneous internal field at all, as mentioned above. It is therefore speculated that the shift in nQ reflects a ‘‘secondary’’ order, possibly ferro-quadrupolar ordering. As for YbAl3 C3 , no magnetic reflections were observed at T n ¼ 80 K by neutron powder diffraction experiments 300 β=0.5
β=0.3
250
|νQ(T) - νQ(T *)| [kHz]
1634
YbAl3C3 27Al-NQR
200
150
100
50
0 40
60
80 Temperature [K]
100
120
Fig. 2. Temperature dependence of the shift in nQ , jnQ ðTÞ nQ ðT n Þj, below T n 80 K.
50 SmRu4P12 101Ru-NQR
0.9 8.9 K
15.3K 15.8 K 16.3 K
TMI
|νQ(T) - νQ(TMI)| [kHz)]
Intensity [arb. units]
40
13.7K
SmRu4P12 101Ru-NQR
β=0.8
30
20
0.5
10
17.5 K 0 13.55 13.60 13.65 13.70 13.75 Frequency [MHz] Fig. 1. (a) Temperature variation of the jnQ ðTÞ nQ ðT MI Þj, below T MI 16:5 K.
101
10
12 14 Temperature [K]
16
Ru-NQR resonance lines for the 122 32 transition. (b) Temperature dependence of the shift in nQ ,
ARTICLE IN PRESS T. Mito et al. / Physica B 403 (2008) 1633–1635
[6]. This compound has crystallographically two inequivalent Al-sites (2d and 4f sites) in the unit cell. We found that the NQR spectrum of the Al-2d site showed a clear shift without any splitting or broadening. Fig. 2 is the plot of jnQ ðTÞ nQ ðT n Þj versus temperature and the result is indicative that the transition is electric and of second order. We attempt to fit the data with the critical exponent b, in the same manner as in SmRu4 P12 . Seemingly bp0:5 reproduces the data well, in contrast with the case of SmRu4 P12 . This suggests that the temperature dependence of nQ below T n mainly probes a primary order parameter. Analysis of the ordered structure is now in progress. In summary, we have carried out 101 Ru and 27 Al-NQR measurements on SmRu4 P12 and YbAl3 C3 , respectively. The NQR spectra clearly show anomalies just below the ordering temperatures, which reflects ordered structures of these compounds. Our results show that the NQR spectrum measurement is a good probe of the quadrupolar order.
1635
This work was partially supported by Grant-in-Aid for Scientific Research Priority Area, Skutterudite (Nos. 15072204 and 15072202) and Scientific Research (No. 14740211) from the Ministry of Education, Culture, Sports, Science and Technology of Japan, and by JSPS under the Japan-Russia Research Cooperative Program. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
O. Sakai, et al., J. Phys. Soc. Japan 66 (1997) 13005. P. Santini, G. Amoretti, Phys. Rev. Lett. 85 (2000) 2188. M. Yoshizawa, et al., J. Phys. Soc. Japan 74 (2005) 2141. K. Hachitani, et al., Phys. Rev. B 73 (2006) 052408. S. Masaki, et al., J. Phys. Soc. Japan 75 (2006) 053708. M. Kosaka, et al., J. Phys. Soc. Japan 74 (2005) 2413. K. Matsuhira, et al., J. Phys. Soc. Jpn. 71 (Suppl.) (2002) 237. K. Iwasa, S. Tsutsui, K. Ishii, et al., private communication. T.U. Ito, et al., J. Phys. Soc. Jpn. 76 (2007) 053707. S. Masaki, et al., J. Phys. Soc. Jpn. 76 (2007) 043714. L.D. Landau, E.M. Lifshitz, Course of Theoretical Physics, vol. 5, Pergamon Press, Oxford, 1980, p. 446.
Physica B 403 (2008) 1633–1635 www.elsevier.com/locate/physb
NQR investigation on multipolar ordering systems T. Mitoa,, S. Tomisawaa, S. Masakia, M. Takemuraa, S. Wadaa, H. Harimaa, Y. Katob, M. Kosakab, D. Kikuchic, H. Satoc, H. Sugawarad, N. Takedae, G.-q. Zhengf a
Department of Physics, Faculty of Science, Kobe University, Nada, Kobe 657-8501, Japan b Department of Physics, Saitama University, Saitama 338-8570, Japan c Department of Physics, Tokyo Metropolitan University, Hachioji, Tokyo 192-0397, Japan d Department of Mathematical and Natural Sciences, Faculty of the Integrated Arts and Sciences, The University of Tokushima, Tokushima 770-8502, Japan e Department of Materials Science and Technology, Faculty of Engineering, Niigata University, Niigata 950-2181, Japan f Department of Physics, Okayama University, Okayama 700-8530, Japan
Abstract We have carried out nuclear quadrupolar resonance (NQR) measurements on SmRu4 P12 and YbAl3 C3 , both of which have attracted much interest in terms of multipolar ordering. Although no structural anomalies have been detected by diffraction experiments so far, the NQR resonance frequencies nQ ’s of both compounds show marked anomalies just below each phase transition temperature, which probably probes the order parameters. The results provide important information to shed light on the ordered structures in the low temperature phases of these compounds. r 2007 Elsevier B.V. All rights reserved. PACS: 71.20.Eh; 71.30.+h; 76.60.k; 76.60.Gv Keywords: Nuclear quadrupole resonance; Multipolar order; Filled-skutterudite compound; Yb-based compound
The role of multipolar degrees of freedom is an important issue in the field of strongly correlated electron systems, because this freedom may bring about phase transitions as a ‘‘hidden’’ order parameter. Indeed, the phase transitions of several materials are well understood in terms of the multipolar order, such as CeB6 (quadrupole) [1], NpO2 (octupole) [2], and so on. However, it is generally not easy to identify contributions from multipolar ordering because of experimental difficulties in observing it directly. Resonant X-ray scattering has been known as almost only a probe to observe the orbital order directly. Nuclear magnetic resonance (NMR) is also a useful microscopic technique to detect the orbital order, although this is an indirect observation, namely nuclear spins couple with field-induced magnetic dipole and/or octupole moments. In this paper, we report our new results of nuclear quadrupole resonance (NQR) measurements on SmRu4 P12 Corresponding author. Tel./fax: +81 78 803 5664.
E-mail address: [email protected] (T. Mito). 0921-4526/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2007.10.206
and YbAl3 C3 . Here the temperature dependence of the NQR spectrum probes the order parameters associated with the phase transitions, most probably quadrupolar ordering. If a nucleus has a finite nuclear quadrupole moment Q, Q interacts with local charge distributions surrounding the nucleus through the electric-field gradient (EFG) at the nuclear position. The nuclear quadrupole interaction is given by HQ ¼ ðhnQ =6Þ½3I 2z I 2 þ ZðI 2x I 2y Þ,
(1)
where I is the nuclear spin, the NQR frequency nQ ¼ eQV zz =6Ið2I þ 1Þ, V aa is the EFG along the a direction, and the asymmetry parameter Z ¼ ðV xx V yy Þ=V zz following V zz XV xx XV yy . Therefore nQ is in principle a good probe of changes in local charge distributions associated with quadrupolar ordering. SmRu4 P12 and YbAl3 C3 are of considerable interest: the transition at T MI ¼ 16:5 K in SmRu4 P12 , which is accompanied with a metal–insulator (M–I) transition, is one of promising candidates for octupole ordering [3–5]. And the
ARTICLE IN PRESS T. Mito et al. / Physica B 403 (2008) 1633–1635
phase transition at T n ¼ 80 K in YbAl3 C3 is presumably associated with ‘‘high-temperature quadrupolar ordering’’ [6]. For both compounds, specific heat data are commonly indicative of second-order transitions at each transition temperature, and no structural anomalies have been detected by diffraction measurements [6–8]. There was to date no information on symmetry lowering in their ordered states. Our 101 Ru and 27 Al-NQR measurements on SmRu4 P12 and YbAl3 C3 , respectively, give important information to shed light on the ordered structures of these compounds. Observed total 101 Ru-NQR signals of SmRu4 P12 for T4T MI are well understood with nQ 13:6 MHz and Z ¼ 0. As seen in Fig. 1(a), a single NQR spectrum splits into two resonance lines in the ordered state. According to the report of zero-field mSR studies, the transition at T MI is accompanied with spontaneous magnetic internal field [4,9]. However, the splitting and shift in the resonance lines without any broadening are not explained by assuming internal field at the Ru-sites. Instead, these experimental facts are satisfactorily understood with another scheme, where there are two Ru-sites with different nQ ’s and Z0 for both sites. Because the Ru atoms are located at the middle between two Sm-sites, internal field is canceled out at Ru-sites due to the form factor of hyperfine interactions. It is likely that the ordered structure is characterized by a wave vector of q ¼ ð1; 0; 0Þ [10]. The temperature dependence of the shift in nQ below T MI , jnQ ðTÞ nQ ðT MI Þj, is shown in Fig. 1(b). The continuous change in nQ is typical of a second-order transition. From the observed signal intensity ratio between the two split signals, approximately 3:1, it was found that eight equivalent Ru-sites in the bcc structure separate into two groups of six and two below T MI . These experimental results lead to a reasonable conclusion that
the symmetry is lowered from a cubic Im 3¯ space group to a trigonal R3¯ in the ordered state. We fit the shift of nQ to jnQ ðTÞ nQ ðT MI Þj / ðT MI TÞb in the T-region just below T MI , as seen in Fig. 1(b). The critical exponent b is found close to 1 rather than 0.5. bp0:5 is known to be what is expected for a primary order parameter within the Landau theory for the second-order phase transition [11]. We here recall that the present NQR spectra are not influenced from the spontaneous internal field at all, as mentioned above. It is therefore speculated that the shift in nQ reflects a ‘‘secondary’’ order, possibly ferro-quadrupolar ordering. As for YbAl3 C3 , no magnetic reflections were observed at T n ¼ 80 K by neutron powder diffraction experiments 300 β=0.5
β=0.3
250
|νQ(T) - νQ(T *)| [kHz]
1634
YbAl3C3 27Al-NQR
200
150
100
50
0 40
60
80 Temperature [K]
100
120
Fig. 2. Temperature dependence of the shift in nQ , jnQ ðTÞ nQ ðT n Þj, below T n 80 K.
50 SmRu4P12 101Ru-NQR
0.9 8.9 K
15.3K 15.8 K 16.3 K
TMI
|νQ(T) - νQ(TMI)| [kHz)]
Intensity [arb. units]
40
13.7K
SmRu4P12 101Ru-NQR
β=0.8
30
20
0.5
10
17.5 K 0 13.55 13.60 13.65 13.70 13.75 Frequency [MHz] Fig. 1. (a) Temperature variation of the jnQ ðTÞ nQ ðT MI Þj, below T MI 16:5 K.
101
10
12 14 Temperature [K]
16
Ru-NQR resonance lines for the 122 32 transition. (b) Temperature dependence of the shift in nQ ,
ARTICLE IN PRESS T. Mito et al. / Physica B 403 (2008) 1633–1635
[6]. This compound has crystallographically two inequivalent Al-sites (2d and 4f sites) in the unit cell. We found that the NQR spectrum of the Al-2d site showed a clear shift without any splitting or broadening. Fig. 2 is the plot of jnQ ðTÞ nQ ðT n Þj versus temperature and the result is indicative that the transition is electric and of second order. We attempt to fit the data with the critical exponent b, in the same manner as in SmRu4 P12 . Seemingly bp0:5 reproduces the data well, in contrast with the case of SmRu4 P12 . This suggests that the temperature dependence of nQ below T n mainly probes a primary order parameter. Analysis of the ordered structure is now in progress. In summary, we have carried out 101 Ru and 27 Al-NQR measurements on SmRu4 P12 and YbAl3 C3 , respectively. The NQR spectra clearly show anomalies just below the ordering temperatures, which reflects ordered structures of these compounds. Our results show that the NQR spectrum measurement is a good probe of the quadrupolar order.
1635
This work was partially supported by Grant-in-Aid for Scientific Research Priority Area, Skutterudite (Nos. 15072204 and 15072202) and Scientific Research (No. 14740211) from the Ministry of Education, Culture, Sports, Science and Technology of Japan, and by JSPS under the Japan-Russia Research Cooperative Program. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
O. Sakai, et al., J. Phys. Soc. Japan 66 (1997) 13005. P. Santini, G. Amoretti, Phys. Rev. Lett. 85 (2000) 2188. M. Yoshizawa, et al., J. Phys. Soc. Japan 74 (2005) 2141. K. Hachitani, et al., Phys. Rev. B 73 (2006) 052408. S. Masaki, et al., J. Phys. Soc. Japan 75 (2006) 053708. M. Kosaka, et al., J. Phys. Soc. Japan 74 (2005) 2413. K. Matsuhira, et al., J. Phys. Soc. Jpn. 71 (Suppl.) (2002) 237. K. Iwasa, S. Tsutsui, K. Ishii, et al., private communication. T.U. Ito, et al., J. Phys. Soc. Jpn. 76 (2007) 053707. S. Masaki, et al., J. Phys. Soc. Jpn. 76 (2007) 043714. L.D. Landau, E.M. Lifshitz, Course of Theoretical Physics, vol. 5, Pergamon Press, Oxford, 1980, p. 446.