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Magnetic structures of the rare earth heusler alloys Pd2DySn and Pd2HoSn
Journal of the Less-Common Metals, 127 (198’7) 93-98
MAGNETIC STRUCTURES Pd,DySn and Pd,HoSn*
93
OF THE RARE EARTH HEUSLER ALLOYS
R. L. DONABERGER
and C. V. STAGER
Department of Physics,
McMaster
Uniuersity,
Hamilton,
Ontario
L8S4Ml
(Canada)
(Received March 5,1986)
Summary The structures of the Heusler alloys Pd,DySn and Pd,HoSn have been investigated by powder neutron diffraction techniques at temperatures between 300K and 1.2K. Susceptibility measurements show that the paramagnetic moments for Pd,DySn and Pd,HoSn are both 10.8 & 0.3 pB, which is close to their free-ion values. Pd,DySn, at 4.2 K and 1.2 K, and Pd,HoSn, at 1.2 K, were shown to have a MnO-type antiferromagnetic order with a moment direction perpendicuIar to the [ill J axis and a magnetic unit cell lattice constant double the nuclear unit cell lattice constant. At 1.2K the magnetic moments in the and 4.4 f 0.1 p, for antiferromagnetic state are 6.7 + 0.5/~s for Pd,DySn Pd,HoSn. Decreases from the free-ion moments are attributed to crystal-field effects.
1. Introduction Recently, Heusler alloys of the type Pd,RESn, where RE is a rare earth element, have become of interest. Ishikawa et al. [l]first studied Pd,RESn alloys by a-c. susceptibility, specific heat and electrical resistivity measurements. They found that alloys containing gadolinium, terbium, dysprosium, holmium and erbium ordered antiferromagnetically at temperatures below 5K. Alloys with RE = Tm, Lu, Y were found to be superconducting whereas for Pd,YbSn a co-existence of superconductivity and antiferromagnetism was observed. More recently Malik et al. [Z] performed susceptibility and Mdssbauer measurements on Pd,RESn alloys. The results were similar although the values for the antiferromagnetic ordering temperatures were somewhat different. The paramagnetic moments deduced from susceptibility measurements on these alloys are close to the free-ion moments of the triply positive rare earth ions. Although
*Paper presented at the 17th Rare Earth Hamilton. Ontario, Canada, June g-12,1986.
Research
Conference,
McMaster
0022-5088/87/$X50
1’: Elsevier Sequoia/Printed
University.
in The Netherlands
magnetic properties have been investigated, no work has yet been reported on the magnetic structures of these alloys. The magnetic structures of Pd,DySn and Pd,HoSn have been determined using neutron diffraction techniques, the results of which are presented in this paper along with susceptibility measurements performed on the same samples.
2. Experimental
procedure
For each alloy a mixture of pure elements was arc melted in an argon atmosphere. As the rare earths are volatile, 5% excess was added to each stoichiometric mixture. The samples were annealed in a high vacuum furnace. Pd,DySn was annealed at 900 “C for 60 h, whereas Pd,HoSn was annealed at 900°C for 5 days then slow-cooled by 50 “C per 48 h to 600 “C where it was annealed for a further 5 days. All samples were furnace cooled. X-ray diffraction measurements on each sample showed the Heusler L2, structure, although the h + k + I= 2n + 1 reflections were weaker than expected. Neutron diffraction experiments were performed at the McMaster nuclear reactor. Measurements were taken on polycrystalline samples of the Heusler alloys at a neutron wavelength of 1.4 A with the aid of a position sensitive detector [3].
3. Results Susceptibility measurements were performed at temperatures down to 4.2 K using a vibrating-sample magnetometer. The Pd,DySn measurement showed antiferromagnetic ordering below 7.0 f 0.5 K. No ordering temperature was observed for Pd,HoSn above 4.2 K. The paramagnetic moments for Pd,DySn and Pd,HoSn are both 10.8 f 0.3 ps, which is close to their respective free-ion moments. For neutron diffraction, the intensities of the nuclear reflections from a polycrystalline sample are given as I N
= KmJ%,e-2WA sin 8 sin 20
(1)
hkl
where K is a constant, m is the multiplicity, Fhkl the nuclear structure factor, 29 the scattering angle, exp( - 2W) the Debye-Waller temperature factor and A,,, an absorption factor. The expression for the magnetic intensities, for one type of magnetic atom per unit cell, is similar: IM =
Km,.,.,. C(pf12q2F,Z.,.,,eptWA sin
e sin 28
h’k’l’
(2)
In eqn. (2) the primed indices refer to magnetic reflections, /* is the effective moment, f is the form factor, q is the magnetic interaction vector and = 7.253 x 10-26cm2p,’
95
3.1. PdlDySn The neutron diffraction pattern for the polycrystalline Pd,DySn sample, which reflects the L2, structure, is shown in Fig. 1. To investigate the magnetic structure, the powdered sample was cooled to 4.2 K, well below the measured ordering temperature of 7.0 f 0.5K. Figure 2 shows the diffraction pattern at 4.2 K over a 30” angular scattering range. The additional reflections indicate a lowering of the symmetry. These peaks index as the (tt*); ($t$; (32)); and ($33) + ($$$) reflections, indicating a magnetic unit cell constant of double the nuclear unit cell constant. As this antiferromagnetic structure is not cubic, the moment direction may be determined relative to a unique crystallographic axis. The model which best fits the experimental data is an antiferromagnetic structure in sheets perpendicular to the [111] axis with a moment direction in the (111) plane. The direction within the (111) plane cannot be determined from a polycrystalline sample at zero field. A least-squares fit to the data results in an effective magnetic moment of 6.8 f 0.5~s, well below the free-ion moment of 10 pLs. It is interesting to note that the widths of the magnetic reflections (FWHM) are almost twice as wide as the FWHM of the nuclear reflections. The same effect is noticeable at 1.2K where the effective magnetic moment was determined to be 6.7 + 0.5~~. The experimental form factors at 1.2K decrease
. (2 2 0)
(422)
..
..
.
16
24
32
40
46
. (420)
56
SCATTERlNC ANGLE Fig. 1 Neutron diffraction pattern for Pd,DySn at room temperature.
*
(511)
64
72
96
4000
f220) . .
3000
1000
0
6
14
22
Fig. 2. Neutron difFraction pattern for Pd,DySn reflections from the magnetic unit cell.
38
30
SCATTERING
ANSLE
at 4.2K.
Half-integral
indices
correspond
to
more rapidly than those given by Stassis et al. [4]. This indicates that the 4f wavefunctions, at 1.2 K, aremore extended than those used by Stassis et al. [4]. It has been observed that the susceptibility data on Pd,DySn shows a kink at 50 K [Z, 51. X-ray diffraction measurements on such a sample show that a structural transformation from the high symmetry cubic phase to a lower symmetry tetragonal phase occurs at this temperature [5]. Preliminary measurements on a Pd,DySn sample, prepared by a somewhat different procedure, showed susceptibility data similar to that obtained by Malik et al. [Z]. The resolution of the position sensitive detector was not sufficient to determine whether such a structural transition had indeed occurred. The neutron data on this sample did not show a broadening of the magnetic reflection widths; however, the magnetic structure appears to be identical to that discussed above. 3.2. Pd, HoSn The neutron diffraction pattern for Pd,HoSn at 1.2K showed coherent reflections indexing as (if+), (+44), (jjf), (333) + ($if) and ($$3), indicating an ordering temperature between 4.2K and 1.2K. The magnetic structure for Pd,HoSn was determined to be identical with that discussed above for Pd,DySn. The effective magnetic moment was found to be 4.4 & 0.1 gs at 1.2 K, again much
97
smaller than the free ion moment of 10~~. As for Pd,DySn, the FWHM of the magnetic reflections were greater than those for nuclear reflections, however, this effect was not as pronounced as for the Pd,DySn alloy.
4. Discussion The reductions in the magnetic moments may be due to crystal-field effects. The inclusion of crystal-field effects has been shown to be important for these alloys [2,6,7]. Malik et al. [6] have estimated crystal field parameters and ground states for Pd,DySn and Pd,HoSn. For Pd,DySn a ratio of fourth- to sixth-order crystal field terms of -0.4 led to a I, ground state with a I6 first excited state. Lea et al. [S] have given cubic crystal-field wavefunctions. At the region of interest the r6, I-, and IA states are very close, within a 26 K energy separation. If the exchange energy is large, mixing between these states is possible, however, the largest moment in this region is 4.4~~ in the IA state. Mixing will not account for the observed moment of 6.7 f 0.2~~. The ground state for Pd,HoSn, predicted by Malik et al. [S] is the r: state. The crystal-field parameters lead to a fourth- to sixth-order crystal-field term ratio of 0.25. The crystal field wavefunctions given by Lea et al. [S] indicate a moment of approximately 5.5~~. In the region between a 0.6 and a 0.4 ratio, the moment ranges from 2.5 to 5.4 pB; the experimental moment of 4.4 + 0.1 ps lying well within this range. However, it must be noted that the ordering temperature for PdzHoSn was not determined. Therefore, the effective moment may not be saturated and must be considered as a lower limit. There is evidence that the Pd,RESn alloys are structurally unstable at low temperatures [5]. It is speculated that the larger magnetic reflection widths, compared with the nuclear reflection widths, and the extended 4f wavefunctions revealed by the form factors for Pd,DySn at 1.2 K are evidence of a local disorder related to a low temperature phase transition.
Acknowledgments The authors would like to thank Mr. Gordon Hewitson for performing the susceptibility measurements and Dr. J. E. Greedan for helpful discussions. One of us (R.L.D.) is grateful to the National Science and Engineering Research Council of Canada for the award of a Postgraduate Scholarship. The work was supported by the National Science and Engineering Research Council.
References 1
M. Ishikawa, J-L. Jorda and A. Junod, in W. Buckel and W. Weber (eds.), Superconductivity in d and f-band metals, Proc. 4th Conf. Karlsruhe, 1982, Kernforschungszentrum, Karlsruhe, 1982, p. 141.
98
2 3 4 5 6 7 8
S. K. Malik, A. M. Umarji and G. K. Shenoy, Phys. Rev. B 31(1985) 6971. C. W. Tompson, D. F. R. Mildner, M. Mehregany, J. Sudol, R. Berliner and W. B. Yelon, J. Appl. Crystallogr. 17(1984) 385. C. Stassis, H. W. Deckman, B. N. Harmon, J. P. Desclaux and A. J. Freeman, Phys. Rev. B 15 (1977) 369. A. M. Umarji, S. K. Malik and G. K. Shenoy, Solid State Commun. 53 (1985) 1029. S. K. Malik, A. M. Umarji and G. K. Shenoy, Phys. Rev. B 32(1985) 4426. H. A. Kierstead, B. D. Dunlap, S. K. Malik, A. M. Umarji and G. K. Shenoy, Phys. Reu. B 32, (1985) 135. K. R. Lea, M. J. M. Leask and W. P. Wolf, J. Phys. Chem. SoZids, 23 (1962) 1381.
MAGNETIC STRUCTURES Pd,DySn and Pd,HoSn*
93
OF THE RARE EARTH HEUSLER ALLOYS
R. L. DONABERGER
and C. V. STAGER
Department of Physics,
McMaster
Uniuersity,
Hamilton,
Ontario
L8S4Ml
(Canada)
(Received March 5,1986)
Summary The structures of the Heusler alloys Pd,DySn and Pd,HoSn have been investigated by powder neutron diffraction techniques at temperatures between 300K and 1.2K. Susceptibility measurements show that the paramagnetic moments for Pd,DySn and Pd,HoSn are both 10.8 & 0.3 pB, which is close to their free-ion values. Pd,DySn, at 4.2 K and 1.2 K, and Pd,HoSn, at 1.2 K, were shown to have a MnO-type antiferromagnetic order with a moment direction perpendicuIar to the [ill J axis and a magnetic unit cell lattice constant double the nuclear unit cell lattice constant. At 1.2K the magnetic moments in the and 4.4 f 0.1 p, for antiferromagnetic state are 6.7 + 0.5/~s for Pd,DySn Pd,HoSn. Decreases from the free-ion moments are attributed to crystal-field effects.
1. Introduction Recently, Heusler alloys of the type Pd,RESn, where RE is a rare earth element, have become of interest. Ishikawa et al. [l]first studied Pd,RESn alloys by a-c. susceptibility, specific heat and electrical resistivity measurements. They found that alloys containing gadolinium, terbium, dysprosium, holmium and erbium ordered antiferromagnetically at temperatures below 5K. Alloys with RE = Tm, Lu, Y were found to be superconducting whereas for Pd,YbSn a co-existence of superconductivity and antiferromagnetism was observed. More recently Malik et al. [Z] performed susceptibility and Mdssbauer measurements on Pd,RESn alloys. The results were similar although the values for the antiferromagnetic ordering temperatures were somewhat different. The paramagnetic moments deduced from susceptibility measurements on these alloys are close to the free-ion moments of the triply positive rare earth ions. Although
*Paper presented at the 17th Rare Earth Hamilton. Ontario, Canada, June g-12,1986.
Research
Conference,
McMaster
0022-5088/87/$X50
1’: Elsevier Sequoia/Printed
University.
in The Netherlands
magnetic properties have been investigated, no work has yet been reported on the magnetic structures of these alloys. The magnetic structures of Pd,DySn and Pd,HoSn have been determined using neutron diffraction techniques, the results of which are presented in this paper along with susceptibility measurements performed on the same samples.
2. Experimental
procedure
For each alloy a mixture of pure elements was arc melted in an argon atmosphere. As the rare earths are volatile, 5% excess was added to each stoichiometric mixture. The samples were annealed in a high vacuum furnace. Pd,DySn was annealed at 900 “C for 60 h, whereas Pd,HoSn was annealed at 900°C for 5 days then slow-cooled by 50 “C per 48 h to 600 “C where it was annealed for a further 5 days. All samples were furnace cooled. X-ray diffraction measurements on each sample showed the Heusler L2, structure, although the h + k + I= 2n + 1 reflections were weaker than expected. Neutron diffraction experiments were performed at the McMaster nuclear reactor. Measurements were taken on polycrystalline samples of the Heusler alloys at a neutron wavelength of 1.4 A with the aid of a position sensitive detector [3].
3. Results Susceptibility measurements were performed at temperatures down to 4.2 K using a vibrating-sample magnetometer. The Pd,DySn measurement showed antiferromagnetic ordering below 7.0 f 0.5 K. No ordering temperature was observed for Pd,HoSn above 4.2 K. The paramagnetic moments for Pd,DySn and Pd,HoSn are both 10.8 f 0.3 ps, which is close to their respective free-ion moments. For neutron diffraction, the intensities of the nuclear reflections from a polycrystalline sample are given as I N
= KmJ%,e-2WA sin 8 sin 20
(1)
hkl
where K is a constant, m is the multiplicity, Fhkl the nuclear structure factor, 29 the scattering angle, exp( - 2W) the Debye-Waller temperature factor and A,,, an absorption factor. The expression for the magnetic intensities, for one type of magnetic atom per unit cell, is similar: IM =
Km,.,.,. C(pf12q2F,Z.,.,,eptWA sin
e sin 28
h’k’l’
(2)
In eqn. (2) the primed indices refer to magnetic reflections, /* is the effective moment, f is the form factor, q is the magnetic interaction vector and = 7.253 x 10-26cm2p,’
95
3.1. PdlDySn The neutron diffraction pattern for the polycrystalline Pd,DySn sample, which reflects the L2, structure, is shown in Fig. 1. To investigate the magnetic structure, the powdered sample was cooled to 4.2 K, well below the measured ordering temperature of 7.0 f 0.5K. Figure 2 shows the diffraction pattern at 4.2 K over a 30” angular scattering range. The additional reflections indicate a lowering of the symmetry. These peaks index as the (tt*); ($t$; (32)); and ($33) + ($$$) reflections, indicating a magnetic unit cell constant of double the nuclear unit cell constant. As this antiferromagnetic structure is not cubic, the moment direction may be determined relative to a unique crystallographic axis. The model which best fits the experimental data is an antiferromagnetic structure in sheets perpendicular to the [111] axis with a moment direction in the (111) plane. The direction within the (111) plane cannot be determined from a polycrystalline sample at zero field. A least-squares fit to the data results in an effective magnetic moment of 6.8 f 0.5~s, well below the free-ion moment of 10 pLs. It is interesting to note that the widths of the magnetic reflections (FWHM) are almost twice as wide as the FWHM of the nuclear reflections. The same effect is noticeable at 1.2K where the effective magnetic moment was determined to be 6.7 + 0.5~~. The experimental form factors at 1.2K decrease
. (2 2 0)
(422)
..
..
.
16
24
32
40
46
. (420)
56
SCATTERlNC ANGLE Fig. 1 Neutron diffraction pattern for Pd,DySn at room temperature.
*
(511)
64
72
96
4000
f220) . .
3000
1000
0
6
14
22
Fig. 2. Neutron difFraction pattern for Pd,DySn reflections from the magnetic unit cell.
38
30
SCATTERING
ANSLE
at 4.2K.
Half-integral
indices
correspond
to
more rapidly than those given by Stassis et al. [4]. This indicates that the 4f wavefunctions, at 1.2 K, aremore extended than those used by Stassis et al. [4]. It has been observed that the susceptibility data on Pd,DySn shows a kink at 50 K [Z, 51. X-ray diffraction measurements on such a sample show that a structural transformation from the high symmetry cubic phase to a lower symmetry tetragonal phase occurs at this temperature [5]. Preliminary measurements on a Pd,DySn sample, prepared by a somewhat different procedure, showed susceptibility data similar to that obtained by Malik et al. [Z]. The resolution of the position sensitive detector was not sufficient to determine whether such a structural transition had indeed occurred. The neutron data on this sample did not show a broadening of the magnetic reflection widths; however, the magnetic structure appears to be identical to that discussed above. 3.2. Pd, HoSn The neutron diffraction pattern for Pd,HoSn at 1.2K showed coherent reflections indexing as (if+), (+44), (jjf), (333) + ($if) and ($$3), indicating an ordering temperature between 4.2K and 1.2K. The magnetic structure for Pd,HoSn was determined to be identical with that discussed above for Pd,DySn. The effective magnetic moment was found to be 4.4 & 0.1 gs at 1.2 K, again much
97
smaller than the free ion moment of 10~~. As for Pd,DySn, the FWHM of the magnetic reflections were greater than those for nuclear reflections, however, this effect was not as pronounced as for the Pd,DySn alloy.
4. Discussion The reductions in the magnetic moments may be due to crystal-field effects. The inclusion of crystal-field effects has been shown to be important for these alloys [2,6,7]. Malik et al. [6] have estimated crystal field parameters and ground states for Pd,DySn and Pd,HoSn. For Pd,DySn a ratio of fourth- to sixth-order crystal field terms of -0.4 led to a I, ground state with a I6 first excited state. Lea et al. [S] have given cubic crystal-field wavefunctions. At the region of interest the r6, I-, and IA states are very close, within a 26 K energy separation. If the exchange energy is large, mixing between these states is possible, however, the largest moment in this region is 4.4~~ in the IA state. Mixing will not account for the observed moment of 6.7 f 0.2~~. The ground state for Pd,HoSn, predicted by Malik et al. [S] is the r: state. The crystal-field parameters lead to a fourth- to sixth-order crystal-field term ratio of 0.25. The crystal field wavefunctions given by Lea et al. [S] indicate a moment of approximately 5.5~~. In the region between a 0.6 and a 0.4 ratio, the moment ranges from 2.5 to 5.4 pB; the experimental moment of 4.4 + 0.1 ps lying well within this range. However, it must be noted that the ordering temperature for PdzHoSn was not determined. Therefore, the effective moment may not be saturated and must be considered as a lower limit. There is evidence that the Pd,RESn alloys are structurally unstable at low temperatures [5]. It is speculated that the larger magnetic reflection widths, compared with the nuclear reflection widths, and the extended 4f wavefunctions revealed by the form factors for Pd,DySn at 1.2 K are evidence of a local disorder related to a low temperature phase transition.
Acknowledgments The authors would like to thank Mr. Gordon Hewitson for performing the susceptibility measurements and Dr. J. E. Greedan for helpful discussions. One of us (R.L.D.) is grateful to the National Science and Engineering Research Council of Canada for the award of a Postgraduate Scholarship. The work was supported by the National Science and Engineering Research Council.
References 1
M. Ishikawa, J-L. Jorda and A. Junod, in W. Buckel and W. Weber (eds.), Superconductivity in d and f-band metals, Proc. 4th Conf. Karlsruhe, 1982, Kernforschungszentrum, Karlsruhe, 1982, p. 141.
98
2 3 4 5 6 7 8
S. K. Malik, A. M. Umarji and G. K. Shenoy, Phys. Rev. B 31(1985) 6971. C. W. Tompson, D. F. R. Mildner, M. Mehregany, J. Sudol, R. Berliner and W. B. Yelon, J. Appl. Crystallogr. 17(1984) 385. C. Stassis, H. W. Deckman, B. N. Harmon, J. P. Desclaux and A. J. Freeman, Phys. Rev. B 15 (1977) 369. A. M. Umarji, S. K. Malik and G. K. Shenoy, Solid State Commun. 53 (1985) 1029. S. K. Malik, A. M. Umarji and G. K. Shenoy, Phys. Rev. B 32(1985) 4426. H. A. Kierstead, B. D. Dunlap, S. K. Malik, A. M. Umarji and G. K. Shenoy, Phys. Reu. B 32, (1985) 135. K. R. Lea, M. J. M. Leask and W. P. Wolf, J. Phys. Chem. SoZids, 23 (1962) 1381.