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Neutron diffraction study of incommensurate magnetic order in TbOs2Si2 and HoOs2Si2
L
Journal of Alloys and Compounds 305 (2000) 153–156
www.elsevier.com / locate / jallcom
Neutron diffraction study of incommensurate magnetic order in TbOs 2 Si 2 and HoOs 2 Si 2 a b c a a, M. Kolenda , M. Hofmann , J. Leciejewicz , B. Penc , A. Szytul«a * b
a ´ , Poland Institute of Physics, Jagiellonian University, 30 -059 Krakow Berlin Neutron Scattering Center, Hahn-Meitner Institute, Berlin-Wannsee, Germany c Institute of Chemistry and Nuclear Technology, Warszawa, Poland
Received 16 December 1999; accepted 5 January 2000
Abstract Neutron diffraction data collected at low temperatures for TbOs 2 Si 2 and HoOs 2 Si 2 indicate that in the former compound magnetic moments localized on Tb 31 ions form an incommensurate, sine wave modulated structure with the wave vector k5(0.3138(5), 0, 0) and ´ point at 45 K. In HoOs 2 Si 2 , an moments aligned along the tetragonal axis. This structure is stable between 1.5 K and the Neel incommensurate magnetic order described by two wave vectors k 1 5(0.3, 0, 0) and k 2 5(0.22, 0, 0) is observed between 1.5 and 8.6 K – ´ the transition temperature to a new also sine wave modulated magnetic phase with the wave vector k5(0.3, 0, 0), stable up to the Neel point at 15.8 K. 2000 Elsevier Science S.A. All rights reserved. Keywords: Rare earth osmium silicides; Magnetic structure; Neutron diffraction
1. Introduction ROs 2 Si 2 compounds (R5lanthanide element) are the members of a large class of ternary compounds exhibiting the well-known tetragonal structure of the ThCr 2 Si 2 -type (also referred to as CaAl 2 Ge 2 -type) [1–5]. This type of crystal structure is described by the space group I4 /mmm and shows c /a ratio values of ca. 2.5. Therefore, the magnetic properties of these compounds are often influenced by frustration of magnetic interactions associated with the large magnetocrystalline anisotropy, which in many compounds results in the appearance of complex magnetic ordering [6]. Magnetometric data collected at low temperatures for (Pr,Nd,Ho,Er,Tm)Os 2 Si 2 have shown that all compounds exhibit ferromagnetic order, whereas (Sm,Gd,Tb,Dy)Os 2 Si 2 are antiferromagnetic [1]. Later, HoOs 2 Si 2 and ErOs 2 Si 2 were reported, to be also antiferromagnetic [7]. A neutron diffraction study carried out for polycrystalline samples of TbOs 2 Si 2 , HoOs 2 Si 2 and ErOs 2 Si 2 has shown that all these compounds order antiferromagnetically at 4.2 K in a sine wave modulated *Corresponding author. E-mail address: [email protected] (A. Szytul«a)
structure with the wave vector k5(0, k y , 0) where k y equals 0.312 for R5Tb, 0.298 for R5Ho and 0.291 for R5Er [7]. A neutron diffraction study repeated for ErOs 2 Si 2 at 1.6 K with larger resolution revealed squaring up of the modulation of the sine wave modulated structure with wave vector k5(5 / 17, 0, 0) stable above 4.7 K [8]. Since our neutron diffraction study reported in [7] was carried out at 4.2 K using an instrument with rather low resolution, we have collected new data for the same samples of TbOs 2 Si 2 and HoOs 2 Si 2 as in [7] but on the E6 diffractometer at the BERII reactor in the Berlin Neutron Scattering Center. This instrument, apart from a better incident neutron intensity, offers excellent resolution. Neutron data were collected at a number of temperatures above 1.5 K. The results of this study are reported below. Table 1 Crystal structure data for TbOs 2 Si 2 and HoOs 2 Si 2 Compound T (K)
TbOs 2 Si 2 55
HoOs 2 Si 2 25
˚ a (A) ˚ c (A) c /a ˚ 3) V (A z
4.1220(6) 9.6753(25) 0.4258 164.23(9) 0.3783(5)
4.1251(6) 9.6566(27) 0.4272 164.32(10) 0.3806(5)
0925-8388 / 00 / $ – see front matter 2000 Elsevier Science S.A. All rights reserved. PII: S0925-8388( 00 )00703-9
154
M. Kolenda et al. / Journal of Alloys and Compounds 305 (2000) 153 – 156
2. Experiment and results ˚ recorded Neutron diffraction patterns ( l 52.4485 A) ´ points show that both comabove the respective Neel pounds crystallize in the ThCr 2 Si 2 -type crystal structure (space group I4 /mmm), with an ordered distribution of Tb(Ho) atoms at 2(a); 0, 0, 0; Os at 4(d): 0, 1 / 2, 1 / 4; 1 / 2, 0, 1 / 4; 0, 1 / 2, 3 / 4; 1 / 2, 0, 3 / 4 and Si at 4(e): 0, 0, z;
¯ 1 / 2, 1 / 2, 1 / 21z; 1 / 2, 1 / 2, 1 / 22z. The deter0, 0, z; mined lattice parameters and z value are given in Table 1. Data analysis was done using the FULLPROF program [9]. Neutron intensities are available from the corresponding author on request. The neutron diffraction patterns of TbOs 2 Si 2 obtained at 1.5 K and at 55 K are shown in Fig. 1. The magnetic reflections observed in the pattern recorded at 1.5 K were
Fig. 1. Neutron diffractograms of TbOs 2 Si 2 recorded at 1.5 K and 55 K. The lower graph in each case shows the difference between the observed and calculated intensities. The rows of vertical bars going from the top to the bottom indicate the positions of the Bragg peaks for the nuclear and incommensurate magnetic structures.
M. Kolenda et al. / Journal of Alloys and Compounds 305 (2000) 153 – 156
identified as satellites of the nuclear peaks indicating the presence of a sine wave modulated structure with the wave vector k5(0.3138(5), 0, 0). The magnetic moment distribution is described by the formula m (r)5 m0 ?cos(2p k? r), where m0 is the amplitude of the magnetic moment localized on the Tb 31 ion amounting to 11.3(1) mB , r is the real-space distance. The magnetic moments are aligned ´ point is at 45 K. The along the tetragonal axis. The Neel above data are similar to the results of the study reported in [7]. Neutron diffraction patterns of HoOs 2 Si 2 taken at a number of temperatures in the range from 2.7 to 18.2 K are displayed in Fig. 2. Two groups of magnetic peaks can be identified at 1.5 K as belonging to two magnetic structures: the first is described by the wave vector k 1 5(3 / 10, 0, 0), the second by k 2 5(0.22, 0, 0). The analysis of the intensities of observed magnetic reflections indicates that both structures are sine wave modulated. However, in the first one the magnetic moment localized on Ho 31 ions is parallel to the tetragonal axis (Fig. 3) and its amplitude amounts to m0 510.55(15) mB . In the second structure the moment is parallel to the b-axis and m0 54.59(16) mB . This structure is schematically illustrated in Fig. 4. The magnitudes of the magnetic moments determined at different temperatures are collected in Fig. 5. The value of the magnetic moment connected with the structure de-
155
Fig. 3. The magnetic structure observed in TbOs 2 Si 2 between 1.5 K and 45 K and in HoOs 2 Si 2 between 1.5 K and 15.8 K. Only the positions of the lanthanide ions at (0, 0, 0) and (1 / 2, 1 / 2, 1 / 2) are shown.
scribed by the wave vector k 1 falls to zero at 15.8 K, the ´ point of HoOs 2 Si 2 . The value of the magnetic Neel moment due to the k 2 structure becomes zero at 8.6 K, the transition temperature. Below this temperature the magnetic ordering in HoOs 2 Si 2 is represented by the two wave vectors k 1 and k 2 .
Fig. 2. Neutron diffractograms of HoOs 2 Si 2 taken at different temperatures between 2.7 and 18.2 K.
M. Kolenda et al. / Journal of Alloys and Compounds 305 (2000) 153 – 156
156
Fig. 4. The magnetic structure of HoOs 2 Si 2 at 1.5 K.
instrument made it possible to observe magnetic reflections corresponding to an antiferromagnetic order described by the wave vector k 2 5(0.22, 0, 0) which vanishes at a transition temperature of 8.6 K. A magnetic order described by two wave vectors has been also found in the isostructural DyAg 2 Si 2 for temperatures below 4.3 K. Above this temperature a magnetic structure characterized by only one wave vector is observed [10]. Long range magnetic ordering observed in both title compounds is the result of the action of exchange interactions via conduction electrons (RKKY model) and the crystalline electric field (CEF) [11]. The RKKY exchange interactions give the observed magnetic structures their oscillatory character. The single ion anisotropy of the Tb 31 and Ho 31 ions results in an easy magnetization direction along the tetragonal axis, as observed in TbOs 2 Si 2 in the temperature range from 1.5 K to 45 K, and in HoOs 2 Si 2 from 8.6 K to 15.8 K. The magnetic structure of HoOs 2 Si 2 below 8.6 K may be the result of the influence of higher B mn parameters in the CEF hamiltonian.
Acknowledgements The kind hospitality and financial support by the HahnMeitner Institute to perform neutron experiments is gratefully acknowledged by three of the authors (JL, BP and AS). This work has been supported in part by the State Committee for Scientific Research in Poland.
References
Fig. 5. The temperature variation of magnetic moment values and the x-component of the wave vector in HoOs 2 Si 2 for the k 1 and k 2 structures and the total holmium magnetic moment (d).
3. Conclusions High resolution neutron diffraction data obtained in the course of the present study show that in TbOs 2 Si 2 a sine wave modulated antiferromagnetic order is maintained in ´ point at 45 the temperature range from 1.5 K to the Neel K, in fair accordance with results reported in Ref. [7]. The new data obtained for HoOs 2 Si 2 confirm also the results of Ref. [7] that a sine wave modulated antiferromagnetic order is stable in the range from 1.5 K and 15.8 ´ point. However, the high resolution of the E6 K, the Neel
[1] K. Hiebl, C. Horvath, P. Rogl, M.J. Sienko, Solid State Commun. 48 (1983) 211. [2] Z. Ban, M. Sikirica, Acta Crystallogr. 18 (1965) 594. [3] Z. Ban, M. Sikirica, Croat. Chim. Acta 36 (1964) 151. [4] O.S. Zarechnyuk, P.I. Kripyakevich, E.I. Gladyshevskij, Sov. Phys. Crystallogr. 8 (1964) 477. [5] O.S. Zarechnyuk, P.I. Kripyakevich, E.I. Gladyshevskij, Sov. Phys. Crystallogr. 9 (1965) 706. [6] A. Szytul«a, J. Leciejewicz, in: K.A. Gschneidner Jr., L. Eyring (Eds.), Handbook on the Physics and Chemistry of the Rare Earth, Vol. 12, North-Holland, Amsterdam, 1989, p. 133. [7] M. Kolenda, A. Szytul«a, J. Leciejewicz, A. Zygmunt, J. Magn. Magn. Mater. 49 (1985) 250. ´ B. Malaman, E. Ressouche, J.P. Sanchez, K. [8] A. Blaise, R. Kmiec, Tomala, G. Venturini, J. Magn. Magn. Mater. 135 (1994) 171. [9] J. Rodriguez-Carvajal, Physica B 192 (1993) 55. [10] M. Ohashi, K. Koizuka, H. Onodera, H. Yamauchi, Y. Yamaguchi, T. Kaneko, S. Funahashi, Physica B 213–214 (1995) 312. [11] D. Gignoux, D. Schmitt, in: K.H.J. Buschow (Ed.), Handbook of Magnetic Materials, Vol. 10, Elsevier Science, Amsterdam, 1997, p. 239.
Journal of Alloys and Compounds 305 (2000) 153–156
www.elsevier.com / locate / jallcom
Neutron diffraction study of incommensurate magnetic order in TbOs 2 Si 2 and HoOs 2 Si 2 a b c a a, M. Kolenda , M. Hofmann , J. Leciejewicz , B. Penc , A. Szytul«a * b
a ´ , Poland Institute of Physics, Jagiellonian University, 30 -059 Krakow Berlin Neutron Scattering Center, Hahn-Meitner Institute, Berlin-Wannsee, Germany c Institute of Chemistry and Nuclear Technology, Warszawa, Poland
Received 16 December 1999; accepted 5 January 2000
Abstract Neutron diffraction data collected at low temperatures for TbOs 2 Si 2 and HoOs 2 Si 2 indicate that in the former compound magnetic moments localized on Tb 31 ions form an incommensurate, sine wave modulated structure with the wave vector k5(0.3138(5), 0, 0) and ´ point at 45 K. In HoOs 2 Si 2 , an moments aligned along the tetragonal axis. This structure is stable between 1.5 K and the Neel incommensurate magnetic order described by two wave vectors k 1 5(0.3, 0, 0) and k 2 5(0.22, 0, 0) is observed between 1.5 and 8.6 K – ´ the transition temperature to a new also sine wave modulated magnetic phase with the wave vector k5(0.3, 0, 0), stable up to the Neel point at 15.8 K. 2000 Elsevier Science S.A. All rights reserved. Keywords: Rare earth osmium silicides; Magnetic structure; Neutron diffraction
1. Introduction ROs 2 Si 2 compounds (R5lanthanide element) are the members of a large class of ternary compounds exhibiting the well-known tetragonal structure of the ThCr 2 Si 2 -type (also referred to as CaAl 2 Ge 2 -type) [1–5]. This type of crystal structure is described by the space group I4 /mmm and shows c /a ratio values of ca. 2.5. Therefore, the magnetic properties of these compounds are often influenced by frustration of magnetic interactions associated with the large magnetocrystalline anisotropy, which in many compounds results in the appearance of complex magnetic ordering [6]. Magnetometric data collected at low temperatures for (Pr,Nd,Ho,Er,Tm)Os 2 Si 2 have shown that all compounds exhibit ferromagnetic order, whereas (Sm,Gd,Tb,Dy)Os 2 Si 2 are antiferromagnetic [1]. Later, HoOs 2 Si 2 and ErOs 2 Si 2 were reported, to be also antiferromagnetic [7]. A neutron diffraction study carried out for polycrystalline samples of TbOs 2 Si 2 , HoOs 2 Si 2 and ErOs 2 Si 2 has shown that all these compounds order antiferromagnetically at 4.2 K in a sine wave modulated *Corresponding author. E-mail address: [email protected] (A. Szytul«a)
structure with the wave vector k5(0, k y , 0) where k y equals 0.312 for R5Tb, 0.298 for R5Ho and 0.291 for R5Er [7]. A neutron diffraction study repeated for ErOs 2 Si 2 at 1.6 K with larger resolution revealed squaring up of the modulation of the sine wave modulated structure with wave vector k5(5 / 17, 0, 0) stable above 4.7 K [8]. Since our neutron diffraction study reported in [7] was carried out at 4.2 K using an instrument with rather low resolution, we have collected new data for the same samples of TbOs 2 Si 2 and HoOs 2 Si 2 as in [7] but on the E6 diffractometer at the BERII reactor in the Berlin Neutron Scattering Center. This instrument, apart from a better incident neutron intensity, offers excellent resolution. Neutron data were collected at a number of temperatures above 1.5 K. The results of this study are reported below. Table 1 Crystal structure data for TbOs 2 Si 2 and HoOs 2 Si 2 Compound T (K)
TbOs 2 Si 2 55
HoOs 2 Si 2 25
˚ a (A) ˚ c (A) c /a ˚ 3) V (A z
4.1220(6) 9.6753(25) 0.4258 164.23(9) 0.3783(5)
4.1251(6) 9.6566(27) 0.4272 164.32(10) 0.3806(5)
0925-8388 / 00 / $ – see front matter 2000 Elsevier Science S.A. All rights reserved. PII: S0925-8388( 00 )00703-9
154
M. Kolenda et al. / Journal of Alloys and Compounds 305 (2000) 153 – 156
2. Experiment and results ˚ recorded Neutron diffraction patterns ( l 52.4485 A) ´ points show that both comabove the respective Neel pounds crystallize in the ThCr 2 Si 2 -type crystal structure (space group I4 /mmm), with an ordered distribution of Tb(Ho) atoms at 2(a); 0, 0, 0; Os at 4(d): 0, 1 / 2, 1 / 4; 1 / 2, 0, 1 / 4; 0, 1 / 2, 3 / 4; 1 / 2, 0, 3 / 4 and Si at 4(e): 0, 0, z;
¯ 1 / 2, 1 / 2, 1 / 21z; 1 / 2, 1 / 2, 1 / 22z. The deter0, 0, z; mined lattice parameters and z value are given in Table 1. Data analysis was done using the FULLPROF program [9]. Neutron intensities are available from the corresponding author on request. The neutron diffraction patterns of TbOs 2 Si 2 obtained at 1.5 K and at 55 K are shown in Fig. 1. The magnetic reflections observed in the pattern recorded at 1.5 K were
Fig. 1. Neutron diffractograms of TbOs 2 Si 2 recorded at 1.5 K and 55 K. The lower graph in each case shows the difference between the observed and calculated intensities. The rows of vertical bars going from the top to the bottom indicate the positions of the Bragg peaks for the nuclear and incommensurate magnetic structures.
M. Kolenda et al. / Journal of Alloys and Compounds 305 (2000) 153 – 156
identified as satellites of the nuclear peaks indicating the presence of a sine wave modulated structure with the wave vector k5(0.3138(5), 0, 0). The magnetic moment distribution is described by the formula m (r)5 m0 ?cos(2p k? r), where m0 is the amplitude of the magnetic moment localized on the Tb 31 ion amounting to 11.3(1) mB , r is the real-space distance. The magnetic moments are aligned ´ point is at 45 K. The along the tetragonal axis. The Neel above data are similar to the results of the study reported in [7]. Neutron diffraction patterns of HoOs 2 Si 2 taken at a number of temperatures in the range from 2.7 to 18.2 K are displayed in Fig. 2. Two groups of magnetic peaks can be identified at 1.5 K as belonging to two magnetic structures: the first is described by the wave vector k 1 5(3 / 10, 0, 0), the second by k 2 5(0.22, 0, 0). The analysis of the intensities of observed magnetic reflections indicates that both structures are sine wave modulated. However, in the first one the magnetic moment localized on Ho 31 ions is parallel to the tetragonal axis (Fig. 3) and its amplitude amounts to m0 510.55(15) mB . In the second structure the moment is parallel to the b-axis and m0 54.59(16) mB . This structure is schematically illustrated in Fig. 4. The magnitudes of the magnetic moments determined at different temperatures are collected in Fig. 5. The value of the magnetic moment connected with the structure de-
155
Fig. 3. The magnetic structure observed in TbOs 2 Si 2 between 1.5 K and 45 K and in HoOs 2 Si 2 between 1.5 K and 15.8 K. Only the positions of the lanthanide ions at (0, 0, 0) and (1 / 2, 1 / 2, 1 / 2) are shown.
scribed by the wave vector k 1 falls to zero at 15.8 K, the ´ point of HoOs 2 Si 2 . The value of the magnetic Neel moment due to the k 2 structure becomes zero at 8.6 K, the transition temperature. Below this temperature the magnetic ordering in HoOs 2 Si 2 is represented by the two wave vectors k 1 and k 2 .
Fig. 2. Neutron diffractograms of HoOs 2 Si 2 taken at different temperatures between 2.7 and 18.2 K.
M. Kolenda et al. / Journal of Alloys and Compounds 305 (2000) 153 – 156
156
Fig. 4. The magnetic structure of HoOs 2 Si 2 at 1.5 K.
instrument made it possible to observe magnetic reflections corresponding to an antiferromagnetic order described by the wave vector k 2 5(0.22, 0, 0) which vanishes at a transition temperature of 8.6 K. A magnetic order described by two wave vectors has been also found in the isostructural DyAg 2 Si 2 for temperatures below 4.3 K. Above this temperature a magnetic structure characterized by only one wave vector is observed [10]. Long range magnetic ordering observed in both title compounds is the result of the action of exchange interactions via conduction electrons (RKKY model) and the crystalline electric field (CEF) [11]. The RKKY exchange interactions give the observed magnetic structures their oscillatory character. The single ion anisotropy of the Tb 31 and Ho 31 ions results in an easy magnetization direction along the tetragonal axis, as observed in TbOs 2 Si 2 in the temperature range from 1.5 K to 45 K, and in HoOs 2 Si 2 from 8.6 K to 15.8 K. The magnetic structure of HoOs 2 Si 2 below 8.6 K may be the result of the influence of higher B mn parameters in the CEF hamiltonian.
Acknowledgements The kind hospitality and financial support by the HahnMeitner Institute to perform neutron experiments is gratefully acknowledged by three of the authors (JL, BP and AS). This work has been supported in part by the State Committee for Scientific Research in Poland.
References
Fig. 5. The temperature variation of magnetic moment values and the x-component of the wave vector in HoOs 2 Si 2 for the k 1 and k 2 structures and the total holmium magnetic moment (d).
3. Conclusions High resolution neutron diffraction data obtained in the course of the present study show that in TbOs 2 Si 2 a sine wave modulated antiferromagnetic order is maintained in ´ point at 45 the temperature range from 1.5 K to the Neel K, in fair accordance with results reported in Ref. [7]. The new data obtained for HoOs 2 Si 2 confirm also the results of Ref. [7] that a sine wave modulated antiferromagnetic order is stable in the range from 1.5 K and 15.8 ´ point. However, the high resolution of the E6 K, the Neel
[1] K. Hiebl, C. Horvath, P. Rogl, M.J. Sienko, Solid State Commun. 48 (1983) 211. [2] Z. Ban, M. Sikirica, Acta Crystallogr. 18 (1965) 594. [3] Z. Ban, M. Sikirica, Croat. Chim. Acta 36 (1964) 151. [4] O.S. Zarechnyuk, P.I. Kripyakevich, E.I. Gladyshevskij, Sov. Phys. Crystallogr. 8 (1964) 477. [5] O.S. Zarechnyuk, P.I. Kripyakevich, E.I. Gladyshevskij, Sov. Phys. Crystallogr. 9 (1965) 706. [6] A. Szytul«a, J. Leciejewicz, in: K.A. Gschneidner Jr., L. Eyring (Eds.), Handbook on the Physics and Chemistry of the Rare Earth, Vol. 12, North-Holland, Amsterdam, 1989, p. 133. [7] M. Kolenda, A. Szytul«a, J. Leciejewicz, A. Zygmunt, J. Magn. Magn. Mater. 49 (1985) 250. ´ B. Malaman, E. Ressouche, J.P. Sanchez, K. [8] A. Blaise, R. Kmiec, Tomala, G. Venturini, J. Magn. Magn. Mater. 135 (1994) 171. [9] J. Rodriguez-Carvajal, Physica B 192 (1993) 55. [10] M. Ohashi, K. Koizuka, H. Onodera, H. Yamauchi, Y. Yamaguchi, T. Kaneko, S. Funahashi, Physica B 213–214 (1995) 312. [11] D. Gignoux, D. Schmitt, in: K.H.J. Buschow (Ed.), Handbook of Magnetic Materials, Vol. 10, Elsevier Science, Amsterdam, 1997, p. 239.