- Email: [email protected]
Crystal field effects using polarised neutron spectroscopy
Nuclear Instruments and Methods in Physics Research A 380 (1996) 572-575
ELSEWIER
NUCLEAN INSTNUMENTS & METNODS IN PHVSICS RESEARCH SectIonA
Crystal field effects using polarised neutron spectroscopy D.J. Goossensa,
S.J. Kennedyb,
T.J. Hicks”‘”
‘Department of Physics, Monash University, Clayton 3168, Australia hNeutron Scattering Group, Australian Nuclear Science and Technology Organisation, Lucas Heights Laboratories, Menai 2234. Australia
Received 22 January 1996; revised form received 22 April 1996
Abstract Crystal field transitions and quasielastic magnetic scattering were observed in PrAl, using a polarised neutron diffractometer/spectrometer. These were positively identified using neutron polarisation analysis. Transitions were observed at 3.5 and 4.5 meV, and both magnetic and nuclear elastic scattering were successfully separated.
Many crystal field transitions in rare-earth intermetallics have been accessed using neutron spectroscopy. The interaction of the magnetic dipole moment of a neutron with the magnetic induction in the material can give rise to magnetic scattering. This is in addition to nuclear scattering from the strong force interaction with nuclei. Conventional neutron spectroscopy uses an unpolarised neutron beam which produces a spectrum consisting of nuclear scattering from excitations in the lattice as well as magnetic excitations like crystal field transitions. However, if the incident neutron beam is polarised, and if the polarisation vector is parallel to the scattering vector, then magnetic scattering occurs with neutron spin flip [ 11. The inelastic differential cross-section from a magnetic system of volume V can be expressed as
where the neutron goes from wavevector k to wavevector k’ through the scattering vector K with an energy change hw. x” is the absorptive part of the generalised susceptibility which has a maximum at a frequency w corresponding to a magnetic excitation. In the case of crystal field excitation there is no scattering vector dependence. The final polarisation is given by
P’
( >= d’a dO dE
k.l’
V k’
ey
2
= k (-1fit
X:,(4
XC (I C”
W)
-Cfinw)
* Corresponding author. Tel. +61 [email protected].
[P - P”ii1 .
3 9905 3681, e-mail
where P is the initial neutron polarisation. The sum in both expressions is over the two Cartesian directions, (Y, perpendicular to the scattering vector and P,, is the component of initial polarisation along (Y. When the polarisation is placed along the scattering vector direction the polarisation is completely reversed on scattering. This means that a polarisation analysis spectrometer can discriminate magnetic scattering from nuclear scattering for which there is no change in polarisation on scattering. In the past, magnetic features have been identified by comparing the obtained spectrum with that from a nonmagnetic but otherwise identical compound [2,3] or by the variation of the features with temperature or scattering vector magnitude. The LONGPOL long wavelength polarisation analysis neutron spectrometer at the HIFAR reactor in Australia is a time of flight (TOF) spectrometer fitted with polarisation analysis. As crystal field transition energies have previously been measured [2-51 using TOF methods, although without polarisation analysis, it was therefore thought that the spectrometer could be applied to the study of such transitions with a view to demonstrating the effectiveness of the method and its possible use to discriminate against other inelastic scattering. The material chosen for study was the rare earth trialuminide PrAI,. This was selected because of the strength of the transitions and because the transition energies were known [2]. This would allow a determination of LONGPOL’s ability to make the measurements. PrAI, has a hexagonal Ni,Sn-type structure in which the Pr atoms are at sites of hexagonal symmetry D,,. The outer electrons are lost to the conduction band, and the nine-fold ground state of the ion is split into three doublets and three singlets by the crystal field of the surrounding ions [3]. The lowest energy level is a singlet. The ground
0168-9002/96/$15.00 Copyright 0 1996 Elsevier Science B.V. All rights reserved PII SO168-9002(96)00574-8
D.J.
Goossens
et (11. I Nucl.
Instr.
and Meth.
in Phys.
Res. A 380
(1996)
t REACTOR
graphite
monochromaton. / M2
573
scattered, and pass through the analyser, which again preferentially transmits spin up neutrons. They then pass into one of eight detectors (71. Path length uncertainties total approximately 2 cm. Neutron velocity is I 100 m s ’ , resulting in a time uncertainty of 20 ps. As data are collected at 4 ps intervals, this allows a five point running average to be applied to the data. The data are analysed by cross correlating the received intensity with the pulse train applied to the flipper. The cross correlated spectrum will contain a peak if non-spin flip (NSF) scattering is taking place, and a dip for spin flip (SF) scattering. It can thus immediately distinguish a magnetic scattering event, which will be SF, from a nuclear event, which will be NSF. The spin flipper pulse train is a shift register sequence resulting in a triangular peak and a flat background in the self correlation [7]. The triangular peak is convoluted with the observed peak width. The polarisation direction was constrained to be parallel
state transition is of approximately 4.5 meV, with other possibly observable transitions at approximately 3 and 5 meV A sample of the material was prepared by melting stoichiometric quantities of Pr and Al together under an ultra pure argon atmosphere. The resulting ingot was annealed for approximately 120 h, and its composition analysed. Neutron diffraction followed by Rietveld fitting showed the sample composition to be approximately 72% PrAI,. 14% Pr,AI,, and 6% PrAI,, with 8% unidentified. This was considered acceptable, as only the PrAI, was likely to give rise to strong spin flip (SF) scattering. LONGPOL is shown in Fig. I [6]. It uses a pyrolytic graphite monochromator to produce a beam of 6.3 meV neutrons, with a Gaussian wavelength distribution of 8% FWHM [7]. The neutron beam is polarised by preferential transmission of spin up neutrons by a magnetically saturated iron filter. A pair of 90” spin turning coils can then be used to invert the neutron spins. The neutrons are then
Pyrolytic
572-57.~
/
FACE
DOUBLE CRYSTAL UONOCHROUATOR.
p
I
Fig. 1. The layout of the LONGPOL
spectrometer/diffractometer.
574
D.J. Govssens et al.
I Nucl. Instr.
and Met/z. in Phys. Res. A 380 (1996)
to the scattering vector by applying a magnetic field to the sample in that direction as required by the expression above and in Ref. [I]. Since eight detectors were in use, and because of sample holder geometry, the polarisation vector could not be parallel to the scattering vector for neutrons scattering into all detectors. The direction of the scattering vector also depends on energy change for the same scattering angle. The spin flip scattering intensity has a cosine-squared dependence on angle from the scattering vector direction, however, and this meant that even for 20” misset, 90% of the magnetic scattering was still occurring with spin flip. The magnetic field was applied by situating permanent magnets at each end of the sample mounting, and aligning the sample itself with the scattering vector. In this experiment, two experimental runs were conducted, one at 295 K and a second at 25 K. Because the intensity but not the energy measured depends on the angle, the spectra could be summed across detectors to improve the statistics. This could be coupled with a five point running average to dramatically increase the effective length of the experimental run. Fig. 2 shows the spectrum summed across detectors for the initial room temperature experiment. The horizontal scale shows the energy gained by the scattered neutrons. Visible is a nuclear (NSF) elastic event, and a large SF feature at approximately 4.0 meV. This large feature can be resolved into two peaks, one at 4.5 meV and a second at 3.5 meV. This implies a machine resolution of. at worst, 1 meV An energy of 4.5 meV agrees closely with that from other experiments [2,3,5], and the lower energy peak has also been seen before [3.5]. The peaks could immediately be identified as a crystal field transition because they are inelastic and the polarisation analysis shows them to be magnetic in origin. It is noteworthy that this experiment has unambiguously determined the crystal held transitions in a single measurement. By contrast the two methods which have been
PrA13
295
K
employed in previous experiments to distinguish crystal field transitions have required complementary measurements to determine the origin of the peaks. One method was to study the temperature dependence of the inelastic peaks and the other was the subtraction of the spectrum of LaAl,, which is structurally similar but lacks the 4f electrons which are responsible for the crystal fields effects 131. Fig. 3 shows the equivalent spectrum from the 25 K experiment. It can be seen that the SF dip is narrower - the FWHM has dropped from 3.3 to 2.8 meV As this width contains machine factors which are constant, and two SF peaks, the actual narrowing of the intrinsic width of the transitions will be more pronounced than this. The broadening mechanism is lifetime broadening. Two mechanisms for carrying away energy and reducing lifetime are phonon interactions and outer electron interactions. As both the electron mechanism [8] and the phonon interaction will be more pronounced at high temperatures, these limited data cannot determine which is dominant. At the lower temperature. the 3.5 meV peak is less pronounced, due to lesser upper state populations. It can be seen as a small shoulder on the left of the large SF peak. Of interest is the elastic scattering. As in Fig. 2, there is a notable elastic NSF peak. However. due to a substantial narrowing of the SF inelastic peak, it can be seen to be situated within a wider quasielastic SF peak. This peak is due to scattering from the excited states of the Pr atoms. This scattering is quasielastic because of energy uncertainty in the levels. but is not associated with a transition. so energy transfer is centred on zero. Since the interaction between the neutron dipole moment and the atom magnetic moment is via the sample induction. the width of this peak gives an indication of the strength of the interaction of the Pr atoms with their environment. The feature was fitted by the difference between Gaussians. Since the central NSF peak has no intrinsic width, being nuclear elastic, this
s !z
Energy
transfer
(md)
Fig. 2. The energy spectrum obtained from PrAl, at room temperature. As explained in the text the crystal field (magnetic) scattering appears as dips or negative going peaks and lattice scattering appears as positive peaks. The line through the points is obtained by fitting the group of crystal field transitions with a Gaussian in the raw time of flight spectrum.
572-575
s . .*
Pi-Al3
25
K
.
Energy
transfer
(meV)
Fig 3. The energy spectrum obtained from PrAI, at 25 K. As explained in the text the crystal field (magnetic) scattering appears as dips or negative going peaks and lattice scattering appears as positive peaks. The line through the points is obtained by fitting the group of crystal field transitions wnh a Gaussian in the raw time of flight spectrum.
D.J. Goossens et al.
I Nucl. Instr.
and Meth.
could be used to factor out the width due to machine factors to reveal the interaction strength. This was found to be in the vicinity of 0.4 meV. Further, the machine width was found to be around 0.5 meV, indicating a probable best value for resolution. It can be noted that the peak-withinpeak nature of the elastic scattering was made more explicit by the peaks being subtracted rather than added. It can be said that LONGPOL successfully observed crystal field transitions of 4.5 and 3.5 meV. as well as nuclear and quasielastic scattering. Polarisation analysis allowed the scattering mechanism to be immediately identified, and aided in extracting detail concerning the elastic scattering.
Acknowledgements We are grateful to Roman Liebach of Monash Physics and to David Stathers of Ansto for assistance in preparing the specimen. Financial support was supplied by the Australian Institute of Nuclear Science and Engineering.
irr Phys. Rrs. A .I80 (19961 57%57.r
s7s
References [I] T.J. Hicks, Magnetism in Disorder (Oxford University Press. 1995) Chap. 1. 121 P.A. Alekseev. I.P. Sadikov, Yu.L. Shitikov. LA. Markova, O.D. Christyakov, E.M. Savitskii and J. Kjems, Phys. Status Solidi 114 (1982) 161. ]3] A. Andreef, L.P. Kaun. B. Lippold, W. Matz. NJ. Moreva and K. Walther. Phys. Status Solidi 87 ( 1978) 535. [4] PA. Alekseev. I.P. Sadikov. I.A. Markova. E.M. Savitskii,V.F. Terekhova and O.D. Christyakov. Sov. Phys. Solid State 18 (19761 389. [S] P.A. Alekseev. E.A. Goremychkin. B. Lippold. E. Mtihle and I.P. Sadikov. Phys. Status Solid1 II9 ( 1983) 651. [6] Tao Fang. Ph.D. Thesis, Monash University, 1992. [7] T.J. Hicks. Mater. Sci. Forum 27/28 (1988) 167. [8] V.N. Peregudov. A.M. Afanas’ev and V.D. Gorobchenko, Phys. JETP 56 ( 1982) 1059.
Sov.
ELSEWIER
NUCLEAN INSTNUMENTS & METNODS IN PHVSICS RESEARCH SectIonA
Crystal field effects using polarised neutron spectroscopy D.J. Goossensa,
S.J. Kennedyb,
T.J. Hicks”‘”
‘Department of Physics, Monash University, Clayton 3168, Australia hNeutron Scattering Group, Australian Nuclear Science and Technology Organisation, Lucas Heights Laboratories, Menai 2234. Australia
Received 22 January 1996; revised form received 22 April 1996
Abstract Crystal field transitions and quasielastic magnetic scattering were observed in PrAl, using a polarised neutron diffractometer/spectrometer. These were positively identified using neutron polarisation analysis. Transitions were observed at 3.5 and 4.5 meV, and both magnetic and nuclear elastic scattering were successfully separated.
Many crystal field transitions in rare-earth intermetallics have been accessed using neutron spectroscopy. The interaction of the magnetic dipole moment of a neutron with the magnetic induction in the material can give rise to magnetic scattering. This is in addition to nuclear scattering from the strong force interaction with nuclei. Conventional neutron spectroscopy uses an unpolarised neutron beam which produces a spectrum consisting of nuclear scattering from excitations in the lattice as well as magnetic excitations like crystal field transitions. However, if the incident neutron beam is polarised, and if the polarisation vector is parallel to the scattering vector, then magnetic scattering occurs with neutron spin flip [ 11. The inelastic differential cross-section from a magnetic system of volume V can be expressed as
where the neutron goes from wavevector k to wavevector k’ through the scattering vector K with an energy change hw. x” is the absorptive part of the generalised susceptibility which has a maximum at a frequency w corresponding to a magnetic excitation. In the case of crystal field excitation there is no scattering vector dependence. The final polarisation is given by
P’
( >= d’a dO dE
k.l’
V k’
ey
2
= k (-1fit
X:,(4
XC (I C”
W)
-Cfinw)
* Corresponding author. Tel. +61 [email protected].
[P - P”ii1 .
3 9905 3681, e-mail
where P is the initial neutron polarisation. The sum in both expressions is over the two Cartesian directions, (Y, perpendicular to the scattering vector and P,, is the component of initial polarisation along (Y. When the polarisation is placed along the scattering vector direction the polarisation is completely reversed on scattering. This means that a polarisation analysis spectrometer can discriminate magnetic scattering from nuclear scattering for which there is no change in polarisation on scattering. In the past, magnetic features have been identified by comparing the obtained spectrum with that from a nonmagnetic but otherwise identical compound [2,3] or by the variation of the features with temperature or scattering vector magnitude. The LONGPOL long wavelength polarisation analysis neutron spectrometer at the HIFAR reactor in Australia is a time of flight (TOF) spectrometer fitted with polarisation analysis. As crystal field transition energies have previously been measured [2-51 using TOF methods, although without polarisation analysis, it was therefore thought that the spectrometer could be applied to the study of such transitions with a view to demonstrating the effectiveness of the method and its possible use to discriminate against other inelastic scattering. The material chosen for study was the rare earth trialuminide PrAI,. This was selected because of the strength of the transitions and because the transition energies were known [2]. This would allow a determination of LONGPOL’s ability to make the measurements. PrAI, has a hexagonal Ni,Sn-type structure in which the Pr atoms are at sites of hexagonal symmetry D,,. The outer electrons are lost to the conduction band, and the nine-fold ground state of the ion is split into three doublets and three singlets by the crystal field of the surrounding ions [3]. The lowest energy level is a singlet. The ground
0168-9002/96/$15.00 Copyright 0 1996 Elsevier Science B.V. All rights reserved PII SO168-9002(96)00574-8
D.J.
Goossens
et (11. I Nucl.
Instr.
and Meth.
in Phys.
Res. A 380
(1996)
t REACTOR
graphite
monochromaton. / M2
573
scattered, and pass through the analyser, which again preferentially transmits spin up neutrons. They then pass into one of eight detectors (71. Path length uncertainties total approximately 2 cm. Neutron velocity is I 100 m s ’ , resulting in a time uncertainty of 20 ps. As data are collected at 4 ps intervals, this allows a five point running average to be applied to the data. The data are analysed by cross correlating the received intensity with the pulse train applied to the flipper. The cross correlated spectrum will contain a peak if non-spin flip (NSF) scattering is taking place, and a dip for spin flip (SF) scattering. It can thus immediately distinguish a magnetic scattering event, which will be SF, from a nuclear event, which will be NSF. The spin flipper pulse train is a shift register sequence resulting in a triangular peak and a flat background in the self correlation [7]. The triangular peak is convoluted with the observed peak width. The polarisation direction was constrained to be parallel
state transition is of approximately 4.5 meV, with other possibly observable transitions at approximately 3 and 5 meV A sample of the material was prepared by melting stoichiometric quantities of Pr and Al together under an ultra pure argon atmosphere. The resulting ingot was annealed for approximately 120 h, and its composition analysed. Neutron diffraction followed by Rietveld fitting showed the sample composition to be approximately 72% PrAI,. 14% Pr,AI,, and 6% PrAI,, with 8% unidentified. This was considered acceptable, as only the PrAI, was likely to give rise to strong spin flip (SF) scattering. LONGPOL is shown in Fig. I [6]. It uses a pyrolytic graphite monochromator to produce a beam of 6.3 meV neutrons, with a Gaussian wavelength distribution of 8% FWHM [7]. The neutron beam is polarised by preferential transmission of spin up neutrons by a magnetically saturated iron filter. A pair of 90” spin turning coils can then be used to invert the neutron spins. The neutrons are then
Pyrolytic
572-57.~
/
FACE
DOUBLE CRYSTAL UONOCHROUATOR.
p
I
Fig. 1. The layout of the LONGPOL
spectrometer/diffractometer.
574
D.J. Govssens et al.
I Nucl. Instr.
and Met/z. in Phys. Res. A 380 (1996)
to the scattering vector by applying a magnetic field to the sample in that direction as required by the expression above and in Ref. [I]. Since eight detectors were in use, and because of sample holder geometry, the polarisation vector could not be parallel to the scattering vector for neutrons scattering into all detectors. The direction of the scattering vector also depends on energy change for the same scattering angle. The spin flip scattering intensity has a cosine-squared dependence on angle from the scattering vector direction, however, and this meant that even for 20” misset, 90% of the magnetic scattering was still occurring with spin flip. The magnetic field was applied by situating permanent magnets at each end of the sample mounting, and aligning the sample itself with the scattering vector. In this experiment, two experimental runs were conducted, one at 295 K and a second at 25 K. Because the intensity but not the energy measured depends on the angle, the spectra could be summed across detectors to improve the statistics. This could be coupled with a five point running average to dramatically increase the effective length of the experimental run. Fig. 2 shows the spectrum summed across detectors for the initial room temperature experiment. The horizontal scale shows the energy gained by the scattered neutrons. Visible is a nuclear (NSF) elastic event, and a large SF feature at approximately 4.0 meV. This large feature can be resolved into two peaks, one at 4.5 meV and a second at 3.5 meV. This implies a machine resolution of. at worst, 1 meV An energy of 4.5 meV agrees closely with that from other experiments [2,3,5], and the lower energy peak has also been seen before [3.5]. The peaks could immediately be identified as a crystal field transition because they are inelastic and the polarisation analysis shows them to be magnetic in origin. It is noteworthy that this experiment has unambiguously determined the crystal held transitions in a single measurement. By contrast the two methods which have been
PrA13
295
K
employed in previous experiments to distinguish crystal field transitions have required complementary measurements to determine the origin of the peaks. One method was to study the temperature dependence of the inelastic peaks and the other was the subtraction of the spectrum of LaAl,, which is structurally similar but lacks the 4f electrons which are responsible for the crystal fields effects 131. Fig. 3 shows the equivalent spectrum from the 25 K experiment. It can be seen that the SF dip is narrower - the FWHM has dropped from 3.3 to 2.8 meV As this width contains machine factors which are constant, and two SF peaks, the actual narrowing of the intrinsic width of the transitions will be more pronounced than this. The broadening mechanism is lifetime broadening. Two mechanisms for carrying away energy and reducing lifetime are phonon interactions and outer electron interactions. As both the electron mechanism [8] and the phonon interaction will be more pronounced at high temperatures, these limited data cannot determine which is dominant. At the lower temperature. the 3.5 meV peak is less pronounced, due to lesser upper state populations. It can be seen as a small shoulder on the left of the large SF peak. Of interest is the elastic scattering. As in Fig. 2, there is a notable elastic NSF peak. However. due to a substantial narrowing of the SF inelastic peak, it can be seen to be situated within a wider quasielastic SF peak. This peak is due to scattering from the excited states of the Pr atoms. This scattering is quasielastic because of energy uncertainty in the levels. but is not associated with a transition. so energy transfer is centred on zero. Since the interaction between the neutron dipole moment and the atom magnetic moment is via the sample induction. the width of this peak gives an indication of the strength of the interaction of the Pr atoms with their environment. The feature was fitted by the difference between Gaussians. Since the central NSF peak has no intrinsic width, being nuclear elastic, this
s !z
Energy
transfer
(md)
Fig. 2. The energy spectrum obtained from PrAl, at room temperature. As explained in the text the crystal field (magnetic) scattering appears as dips or negative going peaks and lattice scattering appears as positive peaks. The line through the points is obtained by fitting the group of crystal field transitions with a Gaussian in the raw time of flight spectrum.
572-575
s . .*
Pi-Al3
25
K
.
Energy
transfer
(meV)
Fig 3. The energy spectrum obtained from PrAI, at 25 K. As explained in the text the crystal field (magnetic) scattering appears as dips or negative going peaks and lattice scattering appears as positive peaks. The line through the points is obtained by fitting the group of crystal field transitions wnh a Gaussian in the raw time of flight spectrum.
D.J. Goossens et al.
I Nucl. Instr.
and Meth.
could be used to factor out the width due to machine factors to reveal the interaction strength. This was found to be in the vicinity of 0.4 meV. Further, the machine width was found to be around 0.5 meV, indicating a probable best value for resolution. It can be noted that the peak-withinpeak nature of the elastic scattering was made more explicit by the peaks being subtracted rather than added. It can be said that LONGPOL successfully observed crystal field transitions of 4.5 and 3.5 meV. as well as nuclear and quasielastic scattering. Polarisation analysis allowed the scattering mechanism to be immediately identified, and aided in extracting detail concerning the elastic scattering.
Acknowledgements We are grateful to Roman Liebach of Monash Physics and to David Stathers of Ansto for assistance in preparing the specimen. Financial support was supplied by the Australian Institute of Nuclear Science and Engineering.
irr Phys. Rrs. A .I80 (19961 57%57.r
s7s
References [I] T.J. Hicks, Magnetism in Disorder (Oxford University Press. 1995) Chap. 1. 121 P.A. Alekseev. I.P. Sadikov, Yu.L. Shitikov. LA. Markova, O.D. Christyakov, E.M. Savitskii and J. Kjems, Phys. Status Solidi 114 (1982) 161. ]3] A. Andreef, L.P. Kaun. B. Lippold, W. Matz. NJ. Moreva and K. Walther. Phys. Status Solidi 87 ( 1978) 535. [4] PA. Alekseev. I.P. Sadikov. I.A. Markova. E.M. Savitskii,V.F. Terekhova and O.D. Christyakov. Sov. Phys. Solid State 18 (19761 389. [S] P.A. Alekseev. E.A. Goremychkin. B. Lippold. E. Mtihle and I.P. Sadikov. Phys. Status Solid1 II9 ( 1983) 651. [6] Tao Fang. Ph.D. Thesis, Monash University, 1992. [7] T.J. Hicks. Mater. Sci. Forum 27/28 (1988) 167. [8] V.N. Peregudov. A.M. Afanas’ev and V.D. Gorobchenko, Phys. JETP 56 ( 1982) 1059.
Sov.