- Email: [email protected]
Spontaneous magnetostriction of R2Fe13.6Si3.4 (R = U, Lu)
Journal of Alloys and Compounds 470 (2009) 24–26
Contents lists available at ScienceDirect
Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jallcom
Spontaneous magnetostriction of R2 Fe13.6 Si3.4 (R = U, Lu) A.V. Andreev a,∗ , S. Daniˇs b a
Institute of Physics, Academy of Sciences, Na Slovance 2, Prague 18221 Czech Republic Department of Condensed Matter Physics, Faculty of Mathematics and Physics, Charles University, Ke Karlovu 5, Prague 12116 Czech Republic b
a r t i c l e
i n f o
Article history: Received 11 February 2008 Received in revised form 19 February 2008 Accepted 20 February 2008 Available online 2 April 2008
a b s t r a c t The thermal expansion of U2 Fe13.6 Si3.4 and Lu2 Fe13.6 Si3.4 has been measured by X-ray powder diffraction. Both compounds exhibit a large spontaneous magnetostriction. In the ground state, the volume effect 11.2 × 10−3 in U2 Fe13.6 Si3.4 consists of almost equal contributions from the Fe–Fe and U–Fe exchange interactions (6 × 10−3 and 5 × 10−3 , respectively). In Lu2 Fe13.6 Si3.4 , the volume effect is 8.9 × 10−3 . © 2008 Elsevier B.V. All rights reserved.
Keywords: R2 T17 Uranium intermetallics Ferromagnetism Magnetostriction Magnetovolume effects
1. Introduction R2 Fe17 intermetallic compounds (R is a rare-earth metal) undergo a large spontaneous magnetostriction in the magnetically ordered state. This originates mainly from the Fe sublattice [1–3]. In combination with (for such a high Fe content) relatively low Curie temperatures TC , this leads to Invar behavior in a wide temperature range. U does not form “2–17” binary compounds with 3d metals but the hexagonal Th2 Ni17 -type crystal structure (space group P63 /mmc) can be stabilized by a small amount of a third element, e.g. Si [4]. In Refs. [5–7], the magnetization of U2 Fe13.6 Si3.4 was studied on single crystalline samples together with Lu2 Fe13.6 Si3.4 where Lu is non-magnetic analogue of U. The U contribution to the total magnetic moment estimated from the difference between the molecular magnetic moments of U2 Fe13.6 Si3.4 and Lu2 Fe13.6 Si3.4 is found to be almost negligible. Nevertheless, U influences strongly the magnetic properties. Based on comparison of magnetic anisotropy in of U2 Fe13.6 Si3.4 and Lu2 Fe13.6 Si3.4 ¨ [5–7], as well as on 57 Fe Mossbauer spectroscopy results [8], the magnetic state of uranium was deduced with the uranium magnetic moment up to MU = 2.6 B ferromagnetically coupled with Fe sublattice. In the present work, we studied the thermal-expansion anomalies accompanying the magnetic ordering in U2 Fe13.6 Si3.4 and
∗ Corresponding author. Tel.: +420 221911352. E-mail address: [email protected] (A.V. Andreev). 0925-8388/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2008.02.058
Lu2 Fe13.6 Si3.4 in order to determine influence of the U sublattice on the spontaneous magnetostriction. 2. Experimental Single crystals of U2 Fe13.6 Si3.4 and Lu2 Fe13.6 Si3.4 were grown by Czochralski method. The single-crystal preparation is described in Ref. [5]. A piece from each crystal was ground for X-ray powder diffraction measurements, which were carried out on a Siemens D-500 diffractometer equipped with a helium-flow cryostat (Oxford Instruments CF1108T) in the Bragg–Brentano geometry using filtered cobalt radiation (Co K␣). The diffraction patterns were taken by means of a positionsensitive detector in the 2 range 10–150◦ with a step of 0.05◦ . The sample temperature was stabilized with an accuracy of 0.1 K by an ITC-503 controller (Oxford Instruments) in the temperature range 5–500 K. Extension of the measurements to 600 K was performed in a home-made high-temperature chamber. The data reduction was performed using the Rietveld analysis [9] (the computer program Fullprof [10] was employed for the refinement). Magnetization as function of magnetic field and temperature was measured along the principal axes of single crystals at 2–600 K in fields up to 9 T using a PPMS-9 magnetometer (Quantum Design).
3. Results and discussion Both compounds crystallize in the hexagonal crystal structure of the Th2 Ni17 type. The Si atoms replace the Fe ones at the 6g and 12k positions, the other Fe sites are Si-free. Magnetic properties of U2 Fe13.6 Si3.4 and Lu2 Fe13.6 Si3.4 are illustrated in Fig. 1. Both compounds are ferromagnets with the easy-plane type of magnetic anisotropy. Temperature dependencies of the lattice parameters a, c and the unit-cell volume V are presented in Figs. 2–4, respectively. The structural, magnetic and magnetoelastic properties of U2 Fe13.6 Si3.4 and Lu2 Fe13.6 Si3.4 are listed in Table 1.
A.V. Andreev, S. Daniˇs / Journal of Alloys and Compounds 470 (2009) 24–26
Fig. 1. Magnetization curves along the principal axes of U2 Fe13.6 Si3.4 and Lu2 Fe13.6 Si3.4 single crystals at 2 K. The inset shows temperature dependence of spontaneous magnetic moment.
The experimental temperature dependencies of the lattice parameters in the paramagnetic range were extrapolated to the magnetically ordered range using a value for the Debye temperature of 450 K, as determined from acoustic measurements on R2 Fe17 [3]. (For details of the extrapolation procedure, see Ref. [3]). The relative differences between the experimental and the extrapolated values of the lattice parameters are the spontaneous linear magnetostrictive strains a and c (Figs. 2 and 3, respectively). The temperature dependencies of the spontaneous volume magnetostriction ωs = 2a + c are shown in Fig. 4.
Fig. 2. Temperature dependence of the lattice parameters a and the spontaneous linear magnetostriction a for U2 Fe13.6 Si3.4 and Lu2 Fe13.6 Si3.4 . The dashed lines represent the extrapolation of a(T) from the paramagnetic to the ferromagnetic range using a Debye temperature D of 450 K.
25
Fig. 3. The same as Fig. 2, but representing the lattice parameter c and the corresponding linear magnetostriction c .
The thermal expansion of U2 Fe13.6 Si3.4 and Lu2 Fe13.6 Si3.4 is qualitatively similar. In both compounds, it is isotropic, the c/a ratio is nearly constant at low and room temperatures (Table 1). The spontaneous magnetostriction is also rather isotropic, c exceeds a only by 15% (Lu) or 30% (U), in difference with binary R2 Fe17 where the uniaxial component c is very large, exceeds a by factor of 4 and leads to a pronounced Invar effect along the c-axis [1–3]. In
Fig. 4. Temperature dependence of the unit-cell volume V and spontaneous volume magnetostriction ωs . The dashed lines represent the extrapolation of V(T) dependence from the paramagnetic to the ferromagnetic range. The solid line corresponds to the fit ωs (T) = ωs (0)[Ms (T)/Ms (0)]2 .
26
A.V. Andreev, S. Daniˇs / Journal of Alloys and Compounds 470 (2009) 24–26
Table 1 Structural, magnetic and magnetoelastic properties of U2 Fe13.6 Si3.4 and Lu2 Fe13.6 Si3.4
a(300 K), pm a(5 K), pm c(300 K), pm c(5 K), pm c/a(300 K) c/a(5 K) V(300 K), nm3 V(5 K), nm3 ˛a (300 K), 10−5 K−1 ˛c (300 K), 10−5 K−1 ˛V (300 K), 10−5 K−1 TC , K Ms (5 K), B /f.u. a (5 K), 10−3 c (5 K), 10−3 ωs (5 K), 10−3
U
Lu
833.4 831.9 825.0 824.6 0.9900 0.9912 0.4962 0.4942 1.0 0.4 2.4 530 23.3 3.4 4.4 11.2
836.5 835.1 824.0 823.0 0.9850 0.9854 0.4994 0.4971 0.6 0.75 2.0 485 23.0 2.85 3.2 8.9
a and c are the lattice parameters; V is the unit-cell volume; ˛a , ˛c and ˛V are the thermal-expansion coefficients along a and c axes, and the volume coefficient, respectively; TC is the Curie temperature; Ms is the spontaneous magnetic moment per formula unit; a , c are the spontaneous linear magnetostrictions along the a and the c axis, respectively; ωs is the spontaneous volume magnetostriction.
U2 Fe13.6 Si3.4 and Lu2 Fe13.6 Si3.4 , c is not high enough to overcome the phonon thermal-expansion contribution and to provide Invarlike behavior. This is also result of relatively high Curie temperature TC (larger by ∼150–200 K than in binary R2 Fe17 ). Since both compounds have the easy-plane magnetic anisotropy, they should undergo an orthorhombic magnetostrictive distortion at the magnetic ordering. However, no distortion was observed which means that the anisotropic magnetostriction responsible for the distortion is below the experimental sensitivity 2 × 10−4 , i.e., at least by one order of magnitude smaller than the exchange magnetostriction seen in the volume effect ∼1%. The observed similarity of spontaneous magnetostriction in U2 Fe13.6 Si3.4 and Lu2 Fe13.6 Si3.4 points to a dominant role of the Fe sublattice in formation of this property. Nevertheless, a certain quantitative difference allows us to distinguish the contributions originated from the Fe–Fe and U–Fe exchange interactions. One can see in Fig. 4 that the volume effect in the ground state of U2 Fe13.6 Si3.4 is larger than in the Lu analogue, however, it becomes the same at elevated temperatures. In Lu2 Fe13.6 Si3.4 , it follows satisfactorily the square of the magnetic moment (solid line in Fig. 4) in a
wide temperature range whereas in U2 Fe13.6 Si3.4 it decreases evidently faster at low temperatures. Both features can be attributed to the contribution to the total volume effect ωs from the U–Fe exchange interaction ωU–Fe which is expected to decrease faster with increasing temperature than the main contribution from the Fe–Fe exchange interaction ωFe–Fe . Direct subtraction of ωFe–Fe from ωs gives the lowest limit of ωU–Fe = 2 × 10−3 . However, this procedure assumes that the Fe sublattice is the same in both compounds. This also means that ωU–Fe vanishes and, respectively, U becomes non-magnetic state above 200 K whereas it is known from the measurements of magnetic ¨ spectroscopy [8] anisotropy [5,6] and from the 57 Fe Mossbauer that U is still magnetic at 300 K. U has larger effective valence in compounds with 3d metals than the trivalent rare-earths and contributes the additional electrons to the 3d band of Fe decreasing the average Fe magnetic moment MFe . MFe in the ground state of Lu2 Fe13.6 Si3.4 and U2 Fe13.6 Si3.4 is estimated to be 1.69 B and 1.33 B , respectively [8]. Assuming ωFe–Fe to be proportional to the square of the Fe magnetic moment, we can estimate ωFe-Fe in U2 Fe13.6 Si3.4 as 6 × 10−3 . Therefore, ωU–Fe = ωs − ωFe–Fe = 5 × 10−3 is surprisingly high, almost the same as ωFe–Fe . Acknowledgements The work is part of the research project AVOZ10100520 and has been supported by the grant GACR 202/06/0185. References [1] D. Givord, R. Lemaire, IEEE Trans. Magn. MAG-10 (1974) 109. [2] A.V. Andreev, A.V. Deryagin, S.M. Zadvorkin, N.V. Kudrevatykh, R.Z. Levitin, V.N. Moskalev, Y.F. Popov, R.Y. Yumaguzhin, in: D.D. Mishin (Ed.), Fizika Magnitnykh Materialov (Physics of Magnetic Materials), Kalinin University, Kalinin, USSR, 1985, p. 21 (in Russian). [3] A.V. Andreev, in: K.H.J. Buschow (Ed.), Handbook of Magnetic Materials, vol. 8, North-Holland, Amsterdam, 1995, pp. 59–187, references therein. [4] T. Berlureau, P. Gravereau, B. Chevalier, J. Etourneau, J. Solid State Chem. 104 (1993) 328. [5] A.V. Andreev, Y. Homma, Y. Shiokawa, Phys. B 319 (2002) 208. [6] A.V. Andreev, Y. Homma, Y. Shiokawa, J. Alloy Compd. 383 (2004) 195. [7] A.V. Andreev, A.V. Kolomiets, T. Goto, J. Alloy Compd. 387 (2005) 60. ˇ ´ Y. Homma, H. Onodera, Y. Shiokawa, I. Satoh, Phys. [8] A.V. Andreev, D. Niˇznansk y, B 369 (2005) 100. [9] H.M. Rietveld, J. Appl. Cryst. 2 (1969) 65. [10] J. Rodriguez-Carvajal, Phys. B 192 (1993) 55.
Contents lists available at ScienceDirect
Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jallcom
Spontaneous magnetostriction of R2 Fe13.6 Si3.4 (R = U, Lu) A.V. Andreev a,∗ , S. Daniˇs b a
Institute of Physics, Academy of Sciences, Na Slovance 2, Prague 18221 Czech Republic Department of Condensed Matter Physics, Faculty of Mathematics and Physics, Charles University, Ke Karlovu 5, Prague 12116 Czech Republic b
a r t i c l e
i n f o
Article history: Received 11 February 2008 Received in revised form 19 February 2008 Accepted 20 February 2008 Available online 2 April 2008
a b s t r a c t The thermal expansion of U2 Fe13.6 Si3.4 and Lu2 Fe13.6 Si3.4 has been measured by X-ray powder diffraction. Both compounds exhibit a large spontaneous magnetostriction. In the ground state, the volume effect 11.2 × 10−3 in U2 Fe13.6 Si3.4 consists of almost equal contributions from the Fe–Fe and U–Fe exchange interactions (6 × 10−3 and 5 × 10−3 , respectively). In Lu2 Fe13.6 Si3.4 , the volume effect is 8.9 × 10−3 . © 2008 Elsevier B.V. All rights reserved.
Keywords: R2 T17 Uranium intermetallics Ferromagnetism Magnetostriction Magnetovolume effects
1. Introduction R2 Fe17 intermetallic compounds (R is a rare-earth metal) undergo a large spontaneous magnetostriction in the magnetically ordered state. This originates mainly from the Fe sublattice [1–3]. In combination with (for such a high Fe content) relatively low Curie temperatures TC , this leads to Invar behavior in a wide temperature range. U does not form “2–17” binary compounds with 3d metals but the hexagonal Th2 Ni17 -type crystal structure (space group P63 /mmc) can be stabilized by a small amount of a third element, e.g. Si [4]. In Refs. [5–7], the magnetization of U2 Fe13.6 Si3.4 was studied on single crystalline samples together with Lu2 Fe13.6 Si3.4 where Lu is non-magnetic analogue of U. The U contribution to the total magnetic moment estimated from the difference between the molecular magnetic moments of U2 Fe13.6 Si3.4 and Lu2 Fe13.6 Si3.4 is found to be almost negligible. Nevertheless, U influences strongly the magnetic properties. Based on comparison of magnetic anisotropy in of U2 Fe13.6 Si3.4 and Lu2 Fe13.6 Si3.4 ¨ [5–7], as well as on 57 Fe Mossbauer spectroscopy results [8], the magnetic state of uranium was deduced with the uranium magnetic moment up to MU = 2.6 B ferromagnetically coupled with Fe sublattice. In the present work, we studied the thermal-expansion anomalies accompanying the magnetic ordering in U2 Fe13.6 Si3.4 and
∗ Corresponding author. Tel.: +420 221911352. E-mail address: [email protected] (A.V. Andreev). 0925-8388/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2008.02.058
Lu2 Fe13.6 Si3.4 in order to determine influence of the U sublattice on the spontaneous magnetostriction. 2. Experimental Single crystals of U2 Fe13.6 Si3.4 and Lu2 Fe13.6 Si3.4 were grown by Czochralski method. The single-crystal preparation is described in Ref. [5]. A piece from each crystal was ground for X-ray powder diffraction measurements, which were carried out on a Siemens D-500 diffractometer equipped with a helium-flow cryostat (Oxford Instruments CF1108T) in the Bragg–Brentano geometry using filtered cobalt radiation (Co K␣). The diffraction patterns were taken by means of a positionsensitive detector in the 2 range 10–150◦ with a step of 0.05◦ . The sample temperature was stabilized with an accuracy of 0.1 K by an ITC-503 controller (Oxford Instruments) in the temperature range 5–500 K. Extension of the measurements to 600 K was performed in a home-made high-temperature chamber. The data reduction was performed using the Rietveld analysis [9] (the computer program Fullprof [10] was employed for the refinement). Magnetization as function of magnetic field and temperature was measured along the principal axes of single crystals at 2–600 K in fields up to 9 T using a PPMS-9 magnetometer (Quantum Design).
3. Results and discussion Both compounds crystallize in the hexagonal crystal structure of the Th2 Ni17 type. The Si atoms replace the Fe ones at the 6g and 12k positions, the other Fe sites are Si-free. Magnetic properties of U2 Fe13.6 Si3.4 and Lu2 Fe13.6 Si3.4 are illustrated in Fig. 1. Both compounds are ferromagnets with the easy-plane type of magnetic anisotropy. Temperature dependencies of the lattice parameters a, c and the unit-cell volume V are presented in Figs. 2–4, respectively. The structural, magnetic and magnetoelastic properties of U2 Fe13.6 Si3.4 and Lu2 Fe13.6 Si3.4 are listed in Table 1.
A.V. Andreev, S. Daniˇs / Journal of Alloys and Compounds 470 (2009) 24–26
Fig. 1. Magnetization curves along the principal axes of U2 Fe13.6 Si3.4 and Lu2 Fe13.6 Si3.4 single crystals at 2 K. The inset shows temperature dependence of spontaneous magnetic moment.
The experimental temperature dependencies of the lattice parameters in the paramagnetic range were extrapolated to the magnetically ordered range using a value for the Debye temperature of 450 K, as determined from acoustic measurements on R2 Fe17 [3]. (For details of the extrapolation procedure, see Ref. [3]). The relative differences between the experimental and the extrapolated values of the lattice parameters are the spontaneous linear magnetostrictive strains a and c (Figs. 2 and 3, respectively). The temperature dependencies of the spontaneous volume magnetostriction ωs = 2a + c are shown in Fig. 4.
Fig. 2. Temperature dependence of the lattice parameters a and the spontaneous linear magnetostriction a for U2 Fe13.6 Si3.4 and Lu2 Fe13.6 Si3.4 . The dashed lines represent the extrapolation of a(T) from the paramagnetic to the ferromagnetic range using a Debye temperature D of 450 K.
25
Fig. 3. The same as Fig. 2, but representing the lattice parameter c and the corresponding linear magnetostriction c .
The thermal expansion of U2 Fe13.6 Si3.4 and Lu2 Fe13.6 Si3.4 is qualitatively similar. In both compounds, it is isotropic, the c/a ratio is nearly constant at low and room temperatures (Table 1). The spontaneous magnetostriction is also rather isotropic, c exceeds a only by 15% (Lu) or 30% (U), in difference with binary R2 Fe17 where the uniaxial component c is very large, exceeds a by factor of 4 and leads to a pronounced Invar effect along the c-axis [1–3]. In
Fig. 4. Temperature dependence of the unit-cell volume V and spontaneous volume magnetostriction ωs . The dashed lines represent the extrapolation of V(T) dependence from the paramagnetic to the ferromagnetic range. The solid line corresponds to the fit ωs (T) = ωs (0)[Ms (T)/Ms (0)]2 .
26
A.V. Andreev, S. Daniˇs / Journal of Alloys and Compounds 470 (2009) 24–26
Table 1 Structural, magnetic and magnetoelastic properties of U2 Fe13.6 Si3.4 and Lu2 Fe13.6 Si3.4
a(300 K), pm a(5 K), pm c(300 K), pm c(5 K), pm c/a(300 K) c/a(5 K) V(300 K), nm3 V(5 K), nm3 ˛a (300 K), 10−5 K−1 ˛c (300 K), 10−5 K−1 ˛V (300 K), 10−5 K−1 TC , K Ms (5 K), B /f.u. a (5 K), 10−3 c (5 K), 10−3 ωs (5 K), 10−3
U
Lu
833.4 831.9 825.0 824.6 0.9900 0.9912 0.4962 0.4942 1.0 0.4 2.4 530 23.3 3.4 4.4 11.2
836.5 835.1 824.0 823.0 0.9850 0.9854 0.4994 0.4971 0.6 0.75 2.0 485 23.0 2.85 3.2 8.9
a and c are the lattice parameters; V is the unit-cell volume; ˛a , ˛c and ˛V are the thermal-expansion coefficients along a and c axes, and the volume coefficient, respectively; TC is the Curie temperature; Ms is the spontaneous magnetic moment per formula unit; a , c are the spontaneous linear magnetostrictions along the a and the c axis, respectively; ωs is the spontaneous volume magnetostriction.
U2 Fe13.6 Si3.4 and Lu2 Fe13.6 Si3.4 , c is not high enough to overcome the phonon thermal-expansion contribution and to provide Invarlike behavior. This is also result of relatively high Curie temperature TC (larger by ∼150–200 K than in binary R2 Fe17 ). Since both compounds have the easy-plane magnetic anisotropy, they should undergo an orthorhombic magnetostrictive distortion at the magnetic ordering. However, no distortion was observed which means that the anisotropic magnetostriction responsible for the distortion is below the experimental sensitivity 2 × 10−4 , i.e., at least by one order of magnitude smaller than the exchange magnetostriction seen in the volume effect ∼1%. The observed similarity of spontaneous magnetostriction in U2 Fe13.6 Si3.4 and Lu2 Fe13.6 Si3.4 points to a dominant role of the Fe sublattice in formation of this property. Nevertheless, a certain quantitative difference allows us to distinguish the contributions originated from the Fe–Fe and U–Fe exchange interactions. One can see in Fig. 4 that the volume effect in the ground state of U2 Fe13.6 Si3.4 is larger than in the Lu analogue, however, it becomes the same at elevated temperatures. In Lu2 Fe13.6 Si3.4 , it follows satisfactorily the square of the magnetic moment (solid line in Fig. 4) in a
wide temperature range whereas in U2 Fe13.6 Si3.4 it decreases evidently faster at low temperatures. Both features can be attributed to the contribution to the total volume effect ωs from the U–Fe exchange interaction ωU–Fe which is expected to decrease faster with increasing temperature than the main contribution from the Fe–Fe exchange interaction ωFe–Fe . Direct subtraction of ωFe–Fe from ωs gives the lowest limit of ωU–Fe = 2 × 10−3 . However, this procedure assumes that the Fe sublattice is the same in both compounds. This also means that ωU–Fe vanishes and, respectively, U becomes non-magnetic state above 200 K whereas it is known from the measurements of magnetic ¨ spectroscopy [8] anisotropy [5,6] and from the 57 Fe Mossbauer that U is still magnetic at 300 K. U has larger effective valence in compounds with 3d metals than the trivalent rare-earths and contributes the additional electrons to the 3d band of Fe decreasing the average Fe magnetic moment MFe . MFe in the ground state of Lu2 Fe13.6 Si3.4 and U2 Fe13.6 Si3.4 is estimated to be 1.69 B and 1.33 B , respectively [8]. Assuming ωFe–Fe to be proportional to the square of the Fe magnetic moment, we can estimate ωFe-Fe in U2 Fe13.6 Si3.4 as 6 × 10−3 . Therefore, ωU–Fe = ωs − ωFe–Fe = 5 × 10−3 is surprisingly high, almost the same as ωFe–Fe . Acknowledgements The work is part of the research project AVOZ10100520 and has been supported by the grant GACR 202/06/0185. References [1] D. Givord, R. Lemaire, IEEE Trans. Magn. MAG-10 (1974) 109. [2] A.V. Andreev, A.V. Deryagin, S.M. Zadvorkin, N.V. Kudrevatykh, R.Z. Levitin, V.N. Moskalev, Y.F. Popov, R.Y. Yumaguzhin, in: D.D. Mishin (Ed.), Fizika Magnitnykh Materialov (Physics of Magnetic Materials), Kalinin University, Kalinin, USSR, 1985, p. 21 (in Russian). [3] A.V. Andreev, in: K.H.J. Buschow (Ed.), Handbook of Magnetic Materials, vol. 8, North-Holland, Amsterdam, 1995, pp. 59–187, references therein. [4] T. Berlureau, P. Gravereau, B. Chevalier, J. Etourneau, J. Solid State Chem. 104 (1993) 328. [5] A.V. Andreev, Y. Homma, Y. Shiokawa, Phys. B 319 (2002) 208. [6] A.V. Andreev, Y. Homma, Y. Shiokawa, J. Alloy Compd. 383 (2004) 195. [7] A.V. Andreev, A.V. Kolomiets, T. Goto, J. Alloy Compd. 387 (2005) 60. ˇ ´ Y. Homma, H. Onodera, Y. Shiokawa, I. Satoh, Phys. [8] A.V. Andreev, D. Niˇznansk y, B 369 (2005) 100. [9] H.M. Rietveld, J. Appl. Cryst. 2 (1969) 65. [10] J. Rodriguez-Carvajal, Phys. B 192 (1993) 55.