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Neutron scattering and μSR studies on the skutterudite Pr0.73Fe4Sb12
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 310 (2007) 286–288 www.elsevier.com/locate/jmmm
Neutron scattering and mSR studies on the skutterudite Pr0:73Fe4Sb12 E. Bauera,, A. Grytsivb, P. Roglb, W. Kockelmannc, A.D. Hillierc, E.A. Goremychkinc, D.T. Adrojac, J.-G. Parkd a
Institute of Solid State Physics, Vienna University of Technology, A-1040 Wien, Austria b Institut fu¨r Physikalische Chemie, Universita¨t Wien, A-1090 Wien, Austria c ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0 QX, UK d Department of Physics and Institute of Basic Science, Sungkyunkwan University, Suwon 440-746, Korea Available online 27 October 2006
Abstract Elastic and inelastic neutron scattering as well as mSR experiments were carried out at ISIS well above and below the ordering temperature of Pr0:73 Fe4 Sb12 . Our mSR study does not reveal a clear sign of long range magnetic ordering. Inelastic neutron scattering ð2Þ reveals the magnetic triplet Gð2Þ 4 to be the ground state of the system, followed by the singlet G1 , about 25 K above G4 . The non-vanishing intensity of G1 can only be explained if a more realistic and correct model of the crystal electric field (CEF) Hamiltonian for filled skutterudites is used, instead of that for simple cubic symmetries. r 2006 Published by Elsevier B.V. PACS: 71.20.Eh; 76.75.þi; 83.85.Hf Keywords: Skutterudite; Pr0:73 Fe4 Sb12 ; mSR; Elastic and inelastic neutron scattering
Filled skutterudites have been under intensive investigations for their elevated values of the Seebeck coefficient and their reduced thermal conductivity, defining these materials as potential candidates for thermoelectric applications. Besides their promising thermoelectric performance, Prbased skutterudites exhibit particularly rich physics, most likely inferred from CEF effects in the context of a nonKramers ion. Physical properties in these systems are governed by the Pr-4f electrons, resulting in several ground states: magnetic order, heavy fermion behaviour and superconductivity. Recently, we have shown that Pr0:73 Fe4 Sb12 [1] orders at 4.6 K and shows a very large value of the Sommerfeld constant g 1 J=molK2 , placing this material, like other Pr-based compounds, into the class of heavy fermions. The transition temperature, however, and the nature of ordered state, is presently a subject of intense discussions [2].
Corresponding author. Tel.: +43 1 58 801 131 60.
E-mail address: [email protected] (E. Bauer). 0304-8853/$ - see front matter r 2006 Published by Elsevier B.V. doi:10.1016/j.jmmm.2006.10.046
In order to figure out the ground state of Pr0:73 Fe4 Sb12 we have performed elastic and inelastic neutron studies, as well as mSR measurements over a wide temperature range above and below the phase transition, 4.6 K. In the present work we focus on mSR spectroscopy to characterize the ordered state and on inelastic neutron scattering to resolve the crystal field (CEF) level scheme. Preparation and characterization of Pr0:73 Fe4 Sb12 are reported in Ref. [1]. Fig. 1 shows the mSR spectra, plotted as muon asymmetry versus time, for several temperatures between 0.03 and 15 K. For temperatures above 4.6 K muon relaxation has two contributions, nuclear and electronic. The electronic contribution shows a strong increase below 4.6 K, which may indicate an approach to magnetic ordering. However, below 4.6 K no clear frequency oscillations have been observed. In order to decouple the nuclear contribution, measurements with 50 G applied field were carried out, which show the presence of oscillations, n ¼ 0:65ð3Þ MHz. However, the frequency of oscillations is temperature independent up to 4.76 K, hence this
ARTICLE IN PRESS E. Bauer et al. / Journal of Magnetism and Magnetic Materials 310 (2007) 286–288
0.30
15K 6K 5K 4.6K 3.6K 2K 0.03K
15 K
asymmetry
0.25
0.20
287
(a)
140
Pr0.73Fe4Sb12 Ei=11 meV
120
T = 10 K
100
θ = 4.9 deg 80
sum elastic quasielastic inelastic
60 0.15
0.10
0.03K zero field
0.05 0
1
2 time [μs]
3
4
Fig. 1. Time dependent muon asymmetry of Pr0:73 Fe4 Sb12 for various temperatures above and below the ordering temperature.
SM (Q,ω ) (mb meV -1 sr-1 f.u.-1)
40 20 0 -2 50
0
2
4
6
8
(b) PrFe4Sb12 Ei= 40 meV,
40
T = 10K
behaviour cannot be attributed to a conventional long range magnetic ordering. The magnetic parts of the inelastic neutron spectra S M collected for Pr0:73 Fe4 Sb12 at T ¼ 10 K, E i ¼ 11 meV and E i ¼ 40 meV are shown in Figs. 2a,b. S M is derived by comparison with the respective data of LaFe4 Sb12 [3]. The low energy excitations are decomposed into a quasielastic line and an inelastic line centred at E 1 ¼ 2:2 meV. The spectrum at higher incident energy reveals additional inelastic lines at E 2 ¼ 10:7 meV and E 3 ¼ 16:8 meV. Very recently, Takegahara et al. [4] have shown that the standard CEF Hamiltonian for simple cubic materials cannot be used since systems with point groups T and T h do not contain two types of symmetry of Oh . Adding these symmetry properties reveals new six-order terms:
30 sum inelastic 20
10
0 0
5
10 15 Energy transfer [meV]
20
25
Fig. 2. Energy dependent magnetic scattering intensity SM of Pr0:73 Fe4 Sb12 . (a): T ¼ 10 K, E i ¼ 11 meV; (b): T ¼ 10 K, E i ¼ 40 meV. The solid, dashed, dashed-dot and dashed-dot-dot lines describe the sum, elastic, quasielastic, and inelastic contributions, respectively.
H cub ¼ B04 ðO04 þ 5O44 Þ þ B06 ðO06 21O46 Þ þ B26 ðO26 O66 Þ, (1) Om n
where Bm are the Stevens n are the CEF parameters and operators. While, in general, the Hamiltonian Eq. (1) leaves the degeneracy of the CEF states unchanged (in comparison to the standard CEF Hamiltonian for cubic symmetry), the wave functions, and thus matrix elements and magnetic moments are modified, depending on the magnitude of the additional six-order terms. Pr0:73 Fe4 Sb12 crystallizes in a body-centred cubic lattice; the local point symmetry of Pr is T h . Thus, an accurate description of CEF derived properties requires the use of Eq. (1). Considering the experimentally observed values of inelastic CEF excitations in the context of Eq. (1) allows to obtain a set of CEF parameters: B04 ¼ 0:03712 K, B06 ¼ 0:00125 K and B26 ¼ 0:001 K, matching the previously estimated parameters B04 ¼ 0:04 K and B06 ¼ 0:00133 K [1]. These values determine the wave functions of the
to be the various eigenstates and cause the triplet Gð2Þ 4 ground state of the system. Gð2Þ 4 , which in the simple version of the Hamiltonian corresponds to the triplet G5 , possesses a magnetic moment and thus can give rise to an ordered ground state. In fact, various bulk properties of Pr0:73 Fe4 Sb12 indicate ordering below about 4.6 K [1,5]. The singlet G1 is situated 25.8 K above the ground state. We also tried to fit neutron data observed at 10 and 32 K simultaneously using the full CF-model (Eq. (1)) together with a profile refinement and found that a singlet ground state can also account the observed inelastic response very well. Both the position and intensity of the three peaks around 2, 10 and 17 meV are reliably reproduced. However, in order to confirm the real ground state of Pr0:73 Fe4 Sb12 , i.e., triplet versus singlet, low energy inelastic neutron scattering measurements are under progress. The strong quasielastic peak (compare Fig. 2) would favour a
ARTICLE IN PRESS 288
E. Bauer et al. / Journal of Magnetism and Magnetic Materials 310 (2007) 286–288
triplet state, while an absence of this contribution would be in line with a singlet ground state. In conclusion, the present mSR and neutron study reveals a rather unconventional type of ordering in the context of CEF splitting of the Pr3þ ion in the specific environment of the skutterudite structure. Work supported by the Austrian FWF, P16370 and P19165.
References [1] E. Bauer, et al., Phys. Rev. B 66 (2002) 214421. [2] K. Tanaka, et al., Physica B 378–380 (2006) 213, and references cited therein. [3] D.T. Adroja, et al., Phys. Rev. B 68 (2003) 094425. [4] K. Takegahara, et al., J. Phys. Soc. Japan 70 (2001) 1190. [5] N.P. Butch, et al., Phys. Rev. B 71 (2005) 214417.
Journal of Magnetism and Magnetic Materials 310 (2007) 286–288 www.elsevier.com/locate/jmmm
Neutron scattering and mSR studies on the skutterudite Pr0:73Fe4Sb12 E. Bauera,, A. Grytsivb, P. Roglb, W. Kockelmannc, A.D. Hillierc, E.A. Goremychkinc, D.T. Adrojac, J.-G. Parkd a
Institute of Solid State Physics, Vienna University of Technology, A-1040 Wien, Austria b Institut fu¨r Physikalische Chemie, Universita¨t Wien, A-1090 Wien, Austria c ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0 QX, UK d Department of Physics and Institute of Basic Science, Sungkyunkwan University, Suwon 440-746, Korea Available online 27 October 2006
Abstract Elastic and inelastic neutron scattering as well as mSR experiments were carried out at ISIS well above and below the ordering temperature of Pr0:73 Fe4 Sb12 . Our mSR study does not reveal a clear sign of long range magnetic ordering. Inelastic neutron scattering ð2Þ reveals the magnetic triplet Gð2Þ 4 to be the ground state of the system, followed by the singlet G1 , about 25 K above G4 . The non-vanishing intensity of G1 can only be explained if a more realistic and correct model of the crystal electric field (CEF) Hamiltonian for filled skutterudites is used, instead of that for simple cubic symmetries. r 2006 Published by Elsevier B.V. PACS: 71.20.Eh; 76.75.þi; 83.85.Hf Keywords: Skutterudite; Pr0:73 Fe4 Sb12 ; mSR; Elastic and inelastic neutron scattering
Filled skutterudites have been under intensive investigations for their elevated values of the Seebeck coefficient and their reduced thermal conductivity, defining these materials as potential candidates for thermoelectric applications. Besides their promising thermoelectric performance, Prbased skutterudites exhibit particularly rich physics, most likely inferred from CEF effects in the context of a nonKramers ion. Physical properties in these systems are governed by the Pr-4f electrons, resulting in several ground states: magnetic order, heavy fermion behaviour and superconductivity. Recently, we have shown that Pr0:73 Fe4 Sb12 [1] orders at 4.6 K and shows a very large value of the Sommerfeld constant g 1 J=molK2 , placing this material, like other Pr-based compounds, into the class of heavy fermions. The transition temperature, however, and the nature of ordered state, is presently a subject of intense discussions [2].
Corresponding author. Tel.: +43 1 58 801 131 60.
E-mail address: [email protected] (E. Bauer). 0304-8853/$ - see front matter r 2006 Published by Elsevier B.V. doi:10.1016/j.jmmm.2006.10.046
In order to figure out the ground state of Pr0:73 Fe4 Sb12 we have performed elastic and inelastic neutron studies, as well as mSR measurements over a wide temperature range above and below the phase transition, 4.6 K. In the present work we focus on mSR spectroscopy to characterize the ordered state and on inelastic neutron scattering to resolve the crystal field (CEF) level scheme. Preparation and characterization of Pr0:73 Fe4 Sb12 are reported in Ref. [1]. Fig. 1 shows the mSR spectra, plotted as muon asymmetry versus time, for several temperatures between 0.03 and 15 K. For temperatures above 4.6 K muon relaxation has two contributions, nuclear and electronic. The electronic contribution shows a strong increase below 4.6 K, which may indicate an approach to magnetic ordering. However, below 4.6 K no clear frequency oscillations have been observed. In order to decouple the nuclear contribution, measurements with 50 G applied field were carried out, which show the presence of oscillations, n ¼ 0:65ð3Þ MHz. However, the frequency of oscillations is temperature independent up to 4.76 K, hence this
ARTICLE IN PRESS E. Bauer et al. / Journal of Magnetism and Magnetic Materials 310 (2007) 286–288
0.30
15K 6K 5K 4.6K 3.6K 2K 0.03K
15 K
asymmetry
0.25
0.20
287
(a)
140
Pr0.73Fe4Sb12 Ei=11 meV
120
T = 10 K
100
θ = 4.9 deg 80
sum elastic quasielastic inelastic
60 0.15
0.10
0.03K zero field
0.05 0
1
2 time [μs]
3
4
Fig. 1. Time dependent muon asymmetry of Pr0:73 Fe4 Sb12 for various temperatures above and below the ordering temperature.
SM (Q,ω ) (mb meV -1 sr-1 f.u.-1)
40 20 0 -2 50
0
2
4
6
8
(b) PrFe4Sb12 Ei= 40 meV,
40
T = 10K
behaviour cannot be attributed to a conventional long range magnetic ordering. The magnetic parts of the inelastic neutron spectra S M collected for Pr0:73 Fe4 Sb12 at T ¼ 10 K, E i ¼ 11 meV and E i ¼ 40 meV are shown in Figs. 2a,b. S M is derived by comparison with the respective data of LaFe4 Sb12 [3]. The low energy excitations are decomposed into a quasielastic line and an inelastic line centred at E 1 ¼ 2:2 meV. The spectrum at higher incident energy reveals additional inelastic lines at E 2 ¼ 10:7 meV and E 3 ¼ 16:8 meV. Very recently, Takegahara et al. [4] have shown that the standard CEF Hamiltonian for simple cubic materials cannot be used since systems with point groups T and T h do not contain two types of symmetry of Oh . Adding these symmetry properties reveals new six-order terms:
30 sum inelastic 20
10
0 0
5
10 15 Energy transfer [meV]
20
25
Fig. 2. Energy dependent magnetic scattering intensity SM of Pr0:73 Fe4 Sb12 . (a): T ¼ 10 K, E i ¼ 11 meV; (b): T ¼ 10 K, E i ¼ 40 meV. The solid, dashed, dashed-dot and dashed-dot-dot lines describe the sum, elastic, quasielastic, and inelastic contributions, respectively.
H cub ¼ B04 ðO04 þ 5O44 Þ þ B06 ðO06 21O46 Þ þ B26 ðO26 O66 Þ, (1) Om n
where Bm are the Stevens n are the CEF parameters and operators. While, in general, the Hamiltonian Eq. (1) leaves the degeneracy of the CEF states unchanged (in comparison to the standard CEF Hamiltonian for cubic symmetry), the wave functions, and thus matrix elements and magnetic moments are modified, depending on the magnitude of the additional six-order terms. Pr0:73 Fe4 Sb12 crystallizes in a body-centred cubic lattice; the local point symmetry of Pr is T h . Thus, an accurate description of CEF derived properties requires the use of Eq. (1). Considering the experimentally observed values of inelastic CEF excitations in the context of Eq. (1) allows to obtain a set of CEF parameters: B04 ¼ 0:03712 K, B06 ¼ 0:00125 K and B26 ¼ 0:001 K, matching the previously estimated parameters B04 ¼ 0:04 K and B06 ¼ 0:00133 K [1]. These values determine the wave functions of the
to be the various eigenstates and cause the triplet Gð2Þ 4 ground state of the system. Gð2Þ 4 , which in the simple version of the Hamiltonian corresponds to the triplet G5 , possesses a magnetic moment and thus can give rise to an ordered ground state. In fact, various bulk properties of Pr0:73 Fe4 Sb12 indicate ordering below about 4.6 K [1,5]. The singlet G1 is situated 25.8 K above the ground state. We also tried to fit neutron data observed at 10 and 32 K simultaneously using the full CF-model (Eq. (1)) together with a profile refinement and found that a singlet ground state can also account the observed inelastic response very well. Both the position and intensity of the three peaks around 2, 10 and 17 meV are reliably reproduced. However, in order to confirm the real ground state of Pr0:73 Fe4 Sb12 , i.e., triplet versus singlet, low energy inelastic neutron scattering measurements are under progress. The strong quasielastic peak (compare Fig. 2) would favour a
ARTICLE IN PRESS 288
E. Bauer et al. / Journal of Magnetism and Magnetic Materials 310 (2007) 286–288
triplet state, while an absence of this contribution would be in line with a singlet ground state. In conclusion, the present mSR and neutron study reveals a rather unconventional type of ordering in the context of CEF splitting of the Pr3þ ion in the specific environment of the skutterudite structure. Work supported by the Austrian FWF, P16370 and P19165.
References [1] E. Bauer, et al., Phys. Rev. B 66 (2002) 214421. [2] K. Tanaka, et al., Physica B 378–380 (2006) 213, and references cited therein. [3] D.T. Adroja, et al., Phys. Rev. B 68 (2003) 094425. [4] K. Takegahara, et al., J. Phys. Soc. Japan 70 (2001) 1190. [5] N.P. Butch, et al., Phys. Rev. B 71 (2005) 214417.