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The analysis of the specific heat of RFe2Si2 compounds
Physica B 328 (2003) 139–141
The analysis of the specific heat of RFe2Si2 compounds $ P. Svobodaa,*, J. Vejpravova! a, F. Hondaa, E. Santav a! b, O. Schneeweissc, d T. Komatsubara a
Department of Electronic Structures, Charles University, Ke Karlovu 5, 121 16 Prague 2, Czech Republic b Institute of Physics, Czech Academy of Sciences, Na Slovance 2, 182 21 Prague 8, Czech Republic c $ zkova 22, 616 62 Brno, Czech Republic Institute of Physics of Materials, Czech Academy of Sciences, Zi$ d Institute of Material Research, Tohoku University, Sendai, Japan
Abstract The series of isostructural intermetallics RFe2 Si2 ðR ¼ La; Pr; NdÞ crystallizes in the tetragonal ThCr2 Si2 -type structure with the space group I4=mmm: The specific heat of high-quality single crystals PrFe2 Si2 and NdFe2 Si2 was studied in comparison with nonmagnetic polycrystalline LaFe2 Si2 in the 1.5–300 K temperature region. The detailed analysis of the specific heat yielded the magnetic entropy and the crystal field level scheme of both crystals. r 2002 Elsevier Science B.V. All rights reserved. Keywords: RFe2 Si2 intermetallic compounds; Specific heat; Crystal field levels
PrFe2 Si2 makes a good candidate for the detailed study of its magnetic properties under high pressure on single crystals [1–3]. It belongs to the tetragonal series of RFe2 Si2 compounds ðR ¼ rare earthÞ crystallizing in the ThCr2 Si2 -type structure with the space group I4=mmm and exhibits strong uniaxial magnetocrystalline anisotropy [1,2]. Successful growth of the high-quality single crystal of PrFe2 Si2 has encouraged us to grow the following isostructural compound of the light rare-earth series, NdFe2 Si2 : The details of the crystal growth will be published elsewhere [4]. Simultaneously, a polycrystalline sample of LaFe2 Si2 was prepared as non-magnetic analogue of the Pr and Nd compounds. The microprobe analysis did not reveal any foreign phase and confirmed the 1-2-2 stoichio*Corresponding author. Tel.: +42-2-21-91-1227; fax: +42-221-91-1351. E-mail address: [email protected] (P. Svoboda).
metry of all samples. Powder X-ray diffraction yields the lattice parameters a¼ ( c¼ 3:9762ð1Þ; 4:0037ð9Þ and 3:9899ð1Þ A; ( with the 10:0023ð3Þ; 10:0542ð3Þ and 10:0382ð5Þ A symmetry free parameter zSi ¼ 0:370; 0.378 and 0.372 for R ¼ La; Pr and Nd, respectively. To ascertain the usage of LaFe2 Si2 as the non. magnetic analogue, the Mossbauer spectroscopy experiment was performed on this sample at T ¼ 15 K: No magnetic moment was found on Fe and we may say that iron fills its 3d-band in this series. This result is in good agreement with the previously reported results [1,2]. The aim of this paper is to show the results of the specific heat analysis of RFe2 Si2 : The specific heat data were measured in zero external magnetic field in the temperature range 1.5–300 K: Apart of the pronounced anomalies connected with the magnetic ordering—see arrows in Fig. 1—substantial Schottky contributions are observed on the specific heat of the magnetic species PrFe2 Si2 and
0921-4526/03/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. doi:10.1016/S0921-4526(02)01829-X
P. Svoboda et al. / Physica B 328 (2003) 139–141
140
LaFe2Si2 PrFe2Si2 NdFe2Si2
1.0
600 ∆i (K)
C/T (J/molK2)
1.5
Pr
Nd
400 200 0
0.5
0.0 10
100 T (K)
Fig. 1. Temperature dependencies of the specific heat of PrFe2 Si2 and NdFe2 Si2 in comparison with the non-magnetic analogue LaFe2 Si2 : The arrows point to the magnetic ordering temperatures and the full lines represent the fits as described in the text. The inset shows the crystal field level schemes yielded by the fit.
NdFe2 Si2 : These data were analyzed in the paramagnetic range to extract the crystal-field contribution to the magnetic entropy. First of all, the detailed analysis of the isobaric phonon specific heat data has been performed for the LaFe2 Si2 : The formula: "
Cph
12 X 1 1 CD þ CEi ¼R 1 aD T 1 aEi T i¼1
#
describes the involvement of both the Debye CD and Einstein CE models for acoustic and optical phonon branches, respectively, together with their, respective, anharmonic correction coefficients aD and aEi : (For details please see [5].) The fit yields the characteristic Debye temperature of the three acoustic branches as yD ¼ 20475 K with the anharmonic coefficient aD ¼ 0:3 104 K1 : The remaining 12 optical phonon branches are described by the Einstein model. To reduce the number of the adjustable parameters, the levels were grouped into three 4-times degenerated branches. The fit yields the corresponding Einstein temperatures yE ¼ 20275; 35377 and 50579 K and anharmonic coefficients aE ¼ 2:3; 3.2 and 8:7 104 K1 ; respectively.
The electronic part of the specific heat can be described using the linear coefficient g ¼ 22:770:2 mJ=molK2 : This value is in a very good agreement with the g coefficients reported on several other tetragonal RT2 X2 compounds, ranging from 20 to 25 mJ=molK2 [6]. Both the phonon and electronic terms were then used without any change for the following analysis of the Scottky contribution of Pr and Nd samples. In the case of PrFe2 Si2 the crystal field splits the ground-state 3 H4 multiplet of the Pr3þ ion into 9 singlets. The best fit corresponds to the energy distances from the ground-state level as D ¼ 28:570:3; 13672; 23075; 37077; 48078; 505710; 540715 and 600715 K; respectively. On the other hand, the 5 Kramers doublets of the Nd3þ ground-state multiplet 4 I9=2 in NdFe2 Si2 yields the best fit for D ¼ 9375; 13575; 215710 and 280710 K; respectively. In the case of PrFe2 Si2 the energy gaps of the lowest levels correspond well to the inelastic neutron scattering data [2] and our fit significantly improves the position of the higher levels. Due to the energy gaps exceeding 500 K; the magnetic entropy does not saturate at room temperature but the strong tendency to saturation at Rln 9 is visible. In NdFe2 Si2 ; the magnetic entropy reaches about 20 J=molK which is in a good agreement with the theoretical value Rln 10: Present work is restricted to the analysis of the specific heat of selected RFe2 Si2 compounds, mainly in the paramagnetic range. Further detailed analysis including the microscopic study is in progress.
Acknowledgements This work is a part of the ME CR research program MSM113200002. Part of it was also supported by the GACR 106/02/0940, GAUK 165/01 and VAKUUM-Praha 2002 grants.
References [1] A. Szytula, J. Leciejewicz, in: K.A. Gschneider Jr, L. Eyring (Eds.), Handbook on the Physics and Chemistry of Rare
P. Svoboda et al. / Physica B 328 (2003) 139–141 Earths, North-Holland, Amsterdam, 1989, p. 133 and references therein. [2] A. Blaise, et al., J. Phys.: Condens. Matter 7 (1995) 8317. [3] F. Honda, et al., to be published.
[4] J. Vejpravov!a, et al., Physica B, in press. [5] P. Svoboda, et al., Phys. Rev. B 6321 (2001) 2408. % ! 2002. [6] Y. Onuki, lecture at SCES’02, Krakow
141
The analysis of the specific heat of RFe2Si2 compounds $ P. Svobodaa,*, J. Vejpravova! a, F. Hondaa, E. Santav a! b, O. Schneeweissc, d T. Komatsubara a
Department of Electronic Structures, Charles University, Ke Karlovu 5, 121 16 Prague 2, Czech Republic b Institute of Physics, Czech Academy of Sciences, Na Slovance 2, 182 21 Prague 8, Czech Republic c $ zkova 22, 616 62 Brno, Czech Republic Institute of Physics of Materials, Czech Academy of Sciences, Zi$ d Institute of Material Research, Tohoku University, Sendai, Japan
Abstract The series of isostructural intermetallics RFe2 Si2 ðR ¼ La; Pr; NdÞ crystallizes in the tetragonal ThCr2 Si2 -type structure with the space group I4=mmm: The specific heat of high-quality single crystals PrFe2 Si2 and NdFe2 Si2 was studied in comparison with nonmagnetic polycrystalline LaFe2 Si2 in the 1.5–300 K temperature region. The detailed analysis of the specific heat yielded the magnetic entropy and the crystal field level scheme of both crystals. r 2002 Elsevier Science B.V. All rights reserved. Keywords: RFe2 Si2 intermetallic compounds; Specific heat; Crystal field levels
PrFe2 Si2 makes a good candidate for the detailed study of its magnetic properties under high pressure on single crystals [1–3]. It belongs to the tetragonal series of RFe2 Si2 compounds ðR ¼ rare earthÞ crystallizing in the ThCr2 Si2 -type structure with the space group I4=mmm and exhibits strong uniaxial magnetocrystalline anisotropy [1,2]. Successful growth of the high-quality single crystal of PrFe2 Si2 has encouraged us to grow the following isostructural compound of the light rare-earth series, NdFe2 Si2 : The details of the crystal growth will be published elsewhere [4]. Simultaneously, a polycrystalline sample of LaFe2 Si2 was prepared as non-magnetic analogue of the Pr and Nd compounds. The microprobe analysis did not reveal any foreign phase and confirmed the 1-2-2 stoichio*Corresponding author. Tel.: +42-2-21-91-1227; fax: +42-221-91-1351. E-mail address: [email protected] (P. Svoboda).
metry of all samples. Powder X-ray diffraction yields the lattice parameters a¼ ( c¼ 3:9762ð1Þ; 4:0037ð9Þ and 3:9899ð1Þ A; ( with the 10:0023ð3Þ; 10:0542ð3Þ and 10:0382ð5Þ A symmetry free parameter zSi ¼ 0:370; 0.378 and 0.372 for R ¼ La; Pr and Nd, respectively. To ascertain the usage of LaFe2 Si2 as the non. magnetic analogue, the Mossbauer spectroscopy experiment was performed on this sample at T ¼ 15 K: No magnetic moment was found on Fe and we may say that iron fills its 3d-band in this series. This result is in good agreement with the previously reported results [1,2]. The aim of this paper is to show the results of the specific heat analysis of RFe2 Si2 : The specific heat data were measured in zero external magnetic field in the temperature range 1.5–300 K: Apart of the pronounced anomalies connected with the magnetic ordering—see arrows in Fig. 1—substantial Schottky contributions are observed on the specific heat of the magnetic species PrFe2 Si2 and
0921-4526/03/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. doi:10.1016/S0921-4526(02)01829-X
P. Svoboda et al. / Physica B 328 (2003) 139–141
140
LaFe2Si2 PrFe2Si2 NdFe2Si2
1.0
600 ∆i (K)
C/T (J/molK2)
1.5
Pr
Nd
400 200 0
0.5
0.0 10
100 T (K)
Fig. 1. Temperature dependencies of the specific heat of PrFe2 Si2 and NdFe2 Si2 in comparison with the non-magnetic analogue LaFe2 Si2 : The arrows point to the magnetic ordering temperatures and the full lines represent the fits as described in the text. The inset shows the crystal field level schemes yielded by the fit.
NdFe2 Si2 : These data were analyzed in the paramagnetic range to extract the crystal-field contribution to the magnetic entropy. First of all, the detailed analysis of the isobaric phonon specific heat data has been performed for the LaFe2 Si2 : The formula: "
Cph
12 X 1 1 CD þ CEi ¼R 1 aD T 1 aEi T i¼1
#
describes the involvement of both the Debye CD and Einstein CE models for acoustic and optical phonon branches, respectively, together with their, respective, anharmonic correction coefficients aD and aEi : (For details please see [5].) The fit yields the characteristic Debye temperature of the three acoustic branches as yD ¼ 20475 K with the anharmonic coefficient aD ¼ 0:3 104 K1 : The remaining 12 optical phonon branches are described by the Einstein model. To reduce the number of the adjustable parameters, the levels were grouped into three 4-times degenerated branches. The fit yields the corresponding Einstein temperatures yE ¼ 20275; 35377 and 50579 K and anharmonic coefficients aE ¼ 2:3; 3.2 and 8:7 104 K1 ; respectively.
The electronic part of the specific heat can be described using the linear coefficient g ¼ 22:770:2 mJ=molK2 : This value is in a very good agreement with the g coefficients reported on several other tetragonal RT2 X2 compounds, ranging from 20 to 25 mJ=molK2 [6]. Both the phonon and electronic terms were then used without any change for the following analysis of the Scottky contribution of Pr and Nd samples. In the case of PrFe2 Si2 the crystal field splits the ground-state 3 H4 multiplet of the Pr3þ ion into 9 singlets. The best fit corresponds to the energy distances from the ground-state level as D ¼ 28:570:3; 13672; 23075; 37077; 48078; 505710; 540715 and 600715 K; respectively. On the other hand, the 5 Kramers doublets of the Nd3þ ground-state multiplet 4 I9=2 in NdFe2 Si2 yields the best fit for D ¼ 9375; 13575; 215710 and 280710 K; respectively. In the case of PrFe2 Si2 the energy gaps of the lowest levels correspond well to the inelastic neutron scattering data [2] and our fit significantly improves the position of the higher levels. Due to the energy gaps exceeding 500 K; the magnetic entropy does not saturate at room temperature but the strong tendency to saturation at Rln 9 is visible. In NdFe2 Si2 ; the magnetic entropy reaches about 20 J=molK which is in a good agreement with the theoretical value Rln 10: Present work is restricted to the analysis of the specific heat of selected RFe2 Si2 compounds, mainly in the paramagnetic range. Further detailed analysis including the microscopic study is in progress.
Acknowledgements This work is a part of the ME CR research program MSM113200002. Part of it was also supported by the GACR 106/02/0940, GAUK 165/01 and VAKUUM-Praha 2002 grants.
References [1] A. Szytula, J. Leciejewicz, in: K.A. Gschneider Jr, L. Eyring (Eds.), Handbook on the Physics and Chemistry of Rare
P. Svoboda et al. / Physica B 328 (2003) 139–141 Earths, North-Holland, Amsterdam, 1989, p. 133 and references therein. [2] A. Blaise, et al., J. Phys.: Condens. Matter 7 (1995) 8317. [3] F. Honda, et al., to be published.
[4] J. Vejpravov!a, et al., Physica B, in press. [5] P. Svoboda, et al., Phys. Rev. B 6321 (2001) 2408. % ! 2002. [6] Y. Onuki, lecture at SCES’02, Krakow
141