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Antiferromagnons in Fe-Mn-Ni alloys
272 A N T I F E R R O M A G N O N S IN F e - M n - N i ALLOYS J. S C H R E I B E R and W. MATZ Joint Institute for Nuclear Research, Head Office, P.O. Box 79, 101000 Mosco~
U.S.S.R.
Inelastic neutron scattering was performed on disordered antiferromagnetic F e - M n - N i alloys. Certain peaks in the spectra can be attributed to magnon scattering. For theoretical interpretation the modified Zener model was treated within R P A which yields acoustical and optical antiferromagnons. A satisfactory explanation of the angle dependence of magnetic peaks was found.
1. Experimental results The experiments were performed at the pulsed reactor IBR-30 of the JINR using the time-offlight method. The elastic and inelastic spectra were obtained at 300 K with a soiler collimator or nitrogen cooled beryllium filter in front of the detector (inverted geometry), respectively [ 1]. In both cases the flight path moderator sample and the flight path sample detector were 30.6 m and 1.1 m, respectively. Polycrystalline samples were prepared in the Zentralinstitut for Festk6rperphysik und Werkstofforschung Dresden, GDR. The samples contain 60at.% Fe, 30.5 at.% Mn, and 9.5 at.% Ni and are h o m o g e n ized at 1060°C for 1 hour and quenched in water. The diffraction spectrum (see also [2]) is typical for the antiferromagnetic structure of the 3,-phase, having 4 spins in the unit cell aligned in the four different [111] directions. There appear pure magnetic [e.g. (110), (210), (211)] and pure nuclear Bragg reflections [e.g. (111), (200), (220)]. The intensities of the nuclear Bragg peaks s h o w that the considered F e - M n - N i samples are disordered alloys. A small amount of inhomogenities of the c o m p o s i t i o n and short range order are indicated by a remaining amount of magnetic reflections (~5% left) above T~. Inelastic spectra are measured at different scattering angles. In fig. 1 the spectra measured at a scattering angle of 90 ° and room temperature are shown. The broad peak at N = 230 (e = 21-+2 meV) is due to phonons of the 3'phase. In order to get more information about the peak Ml in the 90 ° spectra further measurements at scattering angles q~ = 60 °, 75 °, 90 °, 105 °, and 120 ° were made (fig. 2). With increasing scattering angle the peak intensities b e c o m e smaller. Additional experiments on a sample temperatt, re T = 500 K > TN ( T N = 380 K) at q~ = 90 ° and 60 ° Physica 86-88B (1977)272-274 © North-Holland
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Fig. 1. Time-of-flight spectra of inelastic scattered neutrons on F e - M n - N i alloys at 90 ° scattering angle. Numbers at the spectra: 1,2 Be-free samples, 3-6 samples containing 4.8 at.% Be instead of Fe. I - c o u n t s per 20 hours and channel, N - c h a n n e l number (channel width 64 t~s), e - e n e r g y loss of neutrons in meV, S-satellites of fast neutrons, caused by the reactor's operating regime.
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Fig. 2. Time-of-flight spectra of inelastically scattered neutrons at 60°, 75°, 90°, and 105°. The spectra are corrected for background and intensity of incident neutron spectrum. /-intensity per channel in arbitrary units, N--channel number (width 32/xs), e-energy loss of neutrons in meV. show an increasing of the intensity of the phonon hump while the higher energy peaks vanish. F r o m the dependence of the intensity on temperature and scattering angle the peaks in the energy range f r o m 40 to 80 meV can be attributed to magnon scattering. This can be understood as a coherent inelastic process with a m o m e n t u m transfer q to the magnons 2rrrhkt - qmax~ Q = 2~"rhkl + q <~ 2"rr'rhk~ + qmax (1)
with [qrnaxl = "rr/a = 0.87 A J the wave vector of the magnons at the zone boundary and 'rhkt the reciprocal lattice vector. 2. D i s c u s s i o n
According to [2] the properties of Fe60Mn30Nil0 can be explained by a model which contains the so-called "induced m o m e n t s " (caused by the band antiferromagnetic properties of F e - M n subsystem) and " p e r m a n e n t m o m e n t s " (localized spins at Ni-sites). Just these features can be
described by the modified Zener model (MZM) [3-5] which has recently been used to explain the properties of ferromagnetic Fe65(Mn x Nil_x)35 [5]• In [3] it was shown that antiferromagnetism (AF) occurs in the MZM if the concentration of itinerant Zener electrons (or holes) is high enough• In agreement with the available experimental results [2] one can suppose that in the given concentration range of Ni (CNi ~ 9.5 at.%) Fe and Mn have no localized m o m e n t s or only a very small coupling between Zener holes and localized spins due to H u n d ' s rule coupling. Since the Ni atoms can yet be regarded as a perturbation of the F e - M n subsystem, the appearance of AF may be understood within the MZM. The influence of localized m o m e n t s increases as a consequence of increasing Ni-concentration, a change of the ground state from AF to ferromagnetism occurs [2]. To the authors' knowledge so far spin wave calculations for antiferromagnetic MZM were not made, although an extension of the RPA theory f r o m the ferromagnetic system [4] to the antiferromagnetic one is possible without general difficulties. We have done such a calculation under the following simplifying assumptions and approximations: (i) The antiferromagnetic state is produced by a H a r t r e e - F o c k gap mechanism, where the Fermi level is in the gap. (ii) The averaged crystal approximation for the Hamiltonian of the MZM is (cf. [4])
u= E
÷ uE
- 2IY. ,,',S,
(2)
The potential parameters are all configurationai averaged values where according to the a b o v e discussion I ~ C s i ' / N i . (iii) The calculation is restricted to a twosublattice AF. H e r e we give only final results for the spin-wave spectrum. One of the interesting features of the MZM is the appearance of acoustical and optical magnons, because of the existence of two subsystems, the itinerant electron and the localized m o m e n t system. The dispersion relation for small q-values b e c o m e 2 __ 2 2 2 J r ¢.Oq, (Oop -- Cop q
2 (Oac=
2 roan
2 2 Jr Cac q ,
(3)
roan is a gap produced by anisotropy fields; tOq is the optical gap where the calculations show that tOq ~ C N i l N i . The analytical expressions for Cop,
274 Cac, and wq are very extensive and here not of interest. In the ferromagnetic system the optical branch was not observed until now, since ~Oq is too high for neutron experiments or is lying in the Stoner continuum [4]. However, in the antiferromagnetic system under consideration the effect of the localized moments is much smaller because of the small amount of Ni-atoms. Hence the optical gap should be small enough, so that optical magnons could be observed in the Fe60Mn30Ni,0 system. In order to interpret our experimental results in the framework of this model, we must take into account two more facts. At first we can only work with (3) in the case of small ]q{, since otherwise Stoner excitations in our metallic system can destroy magnons. On the other hand we assume isotropic dispersion relations. Assuming, that the dispersion curves begin at the magnetic Bragg-reflections (210), (211), (300), (310), (320), and (321), we have finally found a satisfactory explanation of our results in sense of (3) with the
parameter set: Co0=0.94×104 ms ',
tOq=73meV,
104 ms 1
OJan= 5 meV.
cac = 1.75
x
The indication of optical antiferromagnons is important in verifying if the MZM is appropriate for the description of magnetic properties in transition metals and alloys. Further investigations in this direction are therefore desirable. The authors would like to express their thanks to Dr. M. MOiler from Z F W Dresden for preparing the samples and to Drs. L. Wei6 and K. Henning for helpful discussions.
References [1] K. Parlinski et al. in: Research Applications of Nuclear Pulsed Systems (IAEA Vienna, 1%7) p. 179. [2] M. Shiga, J. Phys. Soc. Japan 22 (1967) 539. [3] T. Arai et al. Phys. Rev. Lett. 27 (1971) 1226. [4] L.C. Bartel, Phys. Rev. B7 (1973) 3153. [5] L.R. Edwards et al., Phys. Rev. BI0 (1974) 2044.
U.S.S.R.
Inelastic neutron scattering was performed on disordered antiferromagnetic F e - M n - N i alloys. Certain peaks in the spectra can be attributed to magnon scattering. For theoretical interpretation the modified Zener model was treated within R P A which yields acoustical and optical antiferromagnons. A satisfactory explanation of the angle dependence of magnetic peaks was found.
1. Experimental results The experiments were performed at the pulsed reactor IBR-30 of the JINR using the time-offlight method. The elastic and inelastic spectra were obtained at 300 K with a soiler collimator or nitrogen cooled beryllium filter in front of the detector (inverted geometry), respectively [ 1]. In both cases the flight path moderator sample and the flight path sample detector were 30.6 m and 1.1 m, respectively. Polycrystalline samples were prepared in the Zentralinstitut for Festk6rperphysik und Werkstofforschung Dresden, GDR. The samples contain 60at.% Fe, 30.5 at.% Mn, and 9.5 at.% Ni and are h o m o g e n ized at 1060°C for 1 hour and quenched in water. The diffraction spectrum (see also [2]) is typical for the antiferromagnetic structure of the 3,-phase, having 4 spins in the unit cell aligned in the four different [111] directions. There appear pure magnetic [e.g. (110), (210), (211)] and pure nuclear Bragg reflections [e.g. (111), (200), (220)]. The intensities of the nuclear Bragg peaks s h o w that the considered F e - M n - N i samples are disordered alloys. A small amount of inhomogenities of the c o m p o s i t i o n and short range order are indicated by a remaining amount of magnetic reflections (~5% left) above T~. Inelastic spectra are measured at different scattering angles. In fig. 1 the spectra measured at a scattering angle of 90 ° and room temperature are shown. The broad peak at N = 230 (e = 21-+2 meV) is due to phonons of the 3'phase. In order to get more information about the peak Ml in the 90 ° spectra further measurements at scattering angles q~ = 60 °, 75 °, 90 °, 105 °, and 120 ° were made (fig. 2). With increasing scattering angle the peak intensities b e c o m e smaller. Additional experiments on a sample temperatt, re T = 500 K > TN ( T N = 380 K) at q~ = 90 ° and 60 ° Physica 86-88B (1977)272-274 © North-Holland
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4
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4.
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-.,.
- "¢,.
5
N~
3.:
"':~,
~0
an W
~
"~mm
,~
300
~
~
400
500 N ~
S
0 ~
t
Fig. 1. Time-of-flight spectra of inelastic scattered neutrons on F e - M n - N i alloys at 90 ° scattering angle. Numbers at the spectra: 1,2 Be-free samples, 3-6 samples containing 4.8 at.% Be instead of Fe. I - c o u n t s per 20 hours and channel, N - c h a n n e l number (channel width 64 t~s), e - e n e r g y loss of neutrons in meV, S-satellites of fast neutrons, caused by the reactor's operating regime.
273 5
I
-
%
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la - 7 5 "
.;
1 4
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.~. •
,% ..: •~•.~-• o.O
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%-
;,,'..",k"
3
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.... 2
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o~°
t
I
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p-I05"
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.)
.~'"
b
•
..%.o..%,.. o.
3 s.~.- • /.
2
...>~ :.,l•
-.'
: 's."'J: t ...•
,
.2';" 1
* 250
i
300
16o"io' ;o
3;0
N~
2o
3 0
!50
i i
i
ooBo
i
350
i
t
6o
5o
N ~ |
Fig. 2. Time-of-flight spectra of inelastically scattered neutrons at 60°, 75°, 90°, and 105°. The spectra are corrected for background and intensity of incident neutron spectrum. /-intensity per channel in arbitrary units, N--channel number (width 32/xs), e-energy loss of neutrons in meV. show an increasing of the intensity of the phonon hump while the higher energy peaks vanish. F r o m the dependence of the intensity on temperature and scattering angle the peaks in the energy range f r o m 40 to 80 meV can be attributed to magnon scattering. This can be understood as a coherent inelastic process with a m o m e n t u m transfer q to the magnons 2rrrhkt - qmax~ Q = 2~"rhkl + q <~ 2"rr'rhk~ + qmax (1)
with [qrnaxl = "rr/a = 0.87 A J the wave vector of the magnons at the zone boundary and 'rhkt the reciprocal lattice vector. 2. D i s c u s s i o n
According to [2] the properties of Fe60Mn30Nil0 can be explained by a model which contains the so-called "induced m o m e n t s " (caused by the band antiferromagnetic properties of F e - M n subsystem) and " p e r m a n e n t m o m e n t s " (localized spins at Ni-sites). Just these features can be
described by the modified Zener model (MZM) [3-5] which has recently been used to explain the properties of ferromagnetic Fe65(Mn x Nil_x)35 [5]• In [3] it was shown that antiferromagnetism (AF) occurs in the MZM if the concentration of itinerant Zener electrons (or holes) is high enough• In agreement with the available experimental results [2] one can suppose that in the given concentration range of Ni (CNi ~ 9.5 at.%) Fe and Mn have no localized m o m e n t s or only a very small coupling between Zener holes and localized spins due to H u n d ' s rule coupling. Since the Ni atoms can yet be regarded as a perturbation of the F e - M n subsystem, the appearance of AF may be understood within the MZM. The influence of localized m o m e n t s increases as a consequence of increasing Ni-concentration, a change of the ground state from AF to ferromagnetism occurs [2]. To the authors' knowledge so far spin wave calculations for antiferromagnetic MZM were not made, although an extension of the RPA theory f r o m the ferromagnetic system [4] to the antiferromagnetic one is possible without general difficulties. We have done such a calculation under the following simplifying assumptions and approximations: (i) The antiferromagnetic state is produced by a H a r t r e e - F o c k gap mechanism, where the Fermi level is in the gap. (ii) The averaged crystal approximation for the Hamiltonian of the MZM is (cf. [4])
u= E
÷ uE
- 2IY. ,,',S,
(2)
The potential parameters are all configurationai averaged values where according to the a b o v e discussion I ~ C s i ' / N i . (iii) The calculation is restricted to a twosublattice AF. H e r e we give only final results for the spin-wave spectrum. One of the interesting features of the MZM is the appearance of acoustical and optical magnons, because of the existence of two subsystems, the itinerant electron and the localized m o m e n t system. The dispersion relation for small q-values b e c o m e 2 __ 2 2 2 J r ¢.Oq, (Oop -- Cop q
2 (Oac=
2 roan
2 2 Jr Cac q ,
(3)
roan is a gap produced by anisotropy fields; tOq is the optical gap where the calculations show that tOq ~ C N i l N i . The analytical expressions for Cop,
274 Cac, and wq are very extensive and here not of interest. In the ferromagnetic system the optical branch was not observed until now, since ~Oq is too high for neutron experiments or is lying in the Stoner continuum [4]. However, in the antiferromagnetic system under consideration the effect of the localized moments is much smaller because of the small amount of Ni-atoms. Hence the optical gap should be small enough, so that optical magnons could be observed in the Fe60Mn30Ni,0 system. In order to interpret our experimental results in the framework of this model, we must take into account two more facts. At first we can only work with (3) in the case of small ]q{, since otherwise Stoner excitations in our metallic system can destroy magnons. On the other hand we assume isotropic dispersion relations. Assuming, that the dispersion curves begin at the magnetic Bragg-reflections (210), (211), (300), (310), (320), and (321), we have finally found a satisfactory explanation of our results in sense of (3) with the
parameter set: Co0=0.94×104 ms ',
tOq=73meV,
104 ms 1
OJan= 5 meV.
cac = 1.75
x
The indication of optical antiferromagnons is important in verifying if the MZM is appropriate for the description of magnetic properties in transition metals and alloys. Further investigations in this direction are therefore desirable. The authors would like to express their thanks to Dr. M. MOiler from Z F W Dresden for preparing the samples and to Drs. L. Wei6 and K. Henning for helpful discussions.
References [1] K. Parlinski et al. in: Research Applications of Nuclear Pulsed Systems (IAEA Vienna, 1%7) p. 179. [2] M. Shiga, J. Phys. Soc. Japan 22 (1967) 539. [3] T. Arai et al. Phys. Rev. Lett. 27 (1971) 1226. [4] L.C. Bartel, Phys. Rev. B7 (1973) 3153. [5] L.R. Edwards et al., Phys. Rev. BI0 (1974) 2044.