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Magnetic excitations in the antiferromagnetic Kondo compound CePd2Si2
Journal of Magnetism and Magnetic Materials !(18(1992) 177-178 North-Holland
Magnetic excitations in the antiferromagnetic Kondo compound CePdzSi 2 F. Hippert a, B. Hennion t,, J.-M. Mignot b and P. Lejay c a Laboratoire de Physique des Sdides, Unit,ersit6 de Paris-Sud, 91405 Orsay Ceder, France t, Laboratoire L~on Brillou#~ (CEA-CNRS), CEN-Saclay, 91191 Gif sur Yrette, France ' CRTBT *, CNRS, BP 166X, 38042 Grenoble Cedex, France
The magnetic excitations of the Kondo compound CePd2Si 2 below its N&I temperature (T N = 10 K) have been studied Their linewidth
by inelastic neutron scattering. At T = 1.6 K the data are best represented by two dispersive inelastic modes. ( ~ 0.5 m e V ) indicates substantial broadening, which is ascribed to Kondo-type local fluctuations.
Whereas several detailed studies have been devoted to magnetic correlations in hea~-fermion materials, little is known on the nature of magnetic excitations below the ordering temperature in magnetically ordered Kondo lattices. One reason is certainly the difficulty of growing the large single crystals required by such experiments. The question of how the spin fluctuations, responsible for the reduction of the ordered moment, affect the magnetic excitations, remains open. Previous work on CeSil. 7 and CeGel. 7 ferromagnetic Kondo compounds [1] revealed that the observed magnons are substantially damped even at T<< T c. Their linewidth seems to be correlated with the Kondo temperature. A good candidate for further studies of these effects is CePd2Si 2. It belongs to the CeM2Si = family ( I 4 / m m m tetragonal structure) with M = Au, Pd, Rh, Ru, Cu, etc., which exhibits a large variety of magnetic behaviours [2,3]. CePd2Si 2 turns out to bc close to the borderline between magnetic and nonmagnetic compounds. It shows Kondo-type fluctuations, revealed by susceptibility, resistivity and specific heat measurements [4], and mders antiferromagnetically at T_,N = 10 K [2,4]. The antiferromagnetic wave vector is k = (0.5, 0.5, 0) and the moments lie parallel to-k. The estimated Ce moment at 4.2 K is = 0.65/z a, smaller than that calculated in a mean-field approximation when taking into account crystal field effects only (see below). This moment reduction has been considered an additionnal piece of evidence in favour of Kondo fluctuations. An order of magnitude of the Kondo temperature, TK--10 K, has been deduced from specific heat data [5] and from the linewidth of the quasielastic neutron scattering observed just above T N [3,6]. Inelastic neutron scattering mcasurcments have been performed on a cylinder-shaped, Czochralskigrown, single crystal with a volume ---0.3 cm 3. Structural checks revealed a good homogeneity, with a mosaicity of = 0.8 degrees. The experiments were carried
* Associ6 ~ l'Universitd Joseph Fourier.
out on the triple-axis spectrometers 4F1 and 4F2 (cold source) at the O r p h & reactor in Saclay. Constant-Q scans ((~ = ~'+ q) at fixed filial neutron energy (Ef = 8.04 meV)were performed at T = 1.6 K. Two directions, ~ = (q, q, 0) and ~ = (0, - q , 0), for 0 _
0312-8853/92/$05.00 © 1992 - Elsevier Science Publishers B.V. All rights reserved
178
F. Hippert et al. / Magnetic ercitations in the antiferromagnetic Kondo compound CePd aSi 2 300
,
•
•
i
•
"1
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T = 1.65 K O = (0.5, 0.4, 0)
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100 L
-1,6
-0,8
0
0.8
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2.4
3.2
4
Energy (meV)
Fig. 1, Inelastic scattering at constant (~ = (0.5, 0.4, 0) at !.6 K with final neutron energy Er = 8.04 meV. The solid and dashed lines show the best fits to the data (including incoherent scattering) using hypothesis (A) and (B), respectively. The horizontal bar indicates experimental resolution.
We performed a spin wave calculation following the method of ref. [7] (to be detailed elsewhere). The mean-field ground state was obtained assuming Heisenberg couplings up to the third-nearest neighbours, for a suitable set of crystal field parameters, B~ = 0.36 meV, B~) = 0.02 n;,:V, B44 = 0.355 meV, determined from fits of the susceptibility curves of a single crystal [4] and from the inelastic neutron scattcring data of i cfs. [3,8]. This choice actually diffcrs from
2.5 CePd2Si ~ f ~ . ~ . - . ~ - . ~ ? -
> ~1.5
!
v
I
? /
T = 1.6K Q= (0.5, 0.5-q, 0)
I E UJ
0.5 0
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0
I ....
0.1
I ....
I,
0.2 0.3 q ('.I.u.)
,I,
T
, I ....
0.4
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~5
Fig. 2. Energy of the two observed inelastic modes at 1.6 K, using hypothesis (B), at reduced wavevectors ~" = (0, -q, 0) in the ÷'= (0.5, 0.5, 0) magnetic Brillouin zone. Solid lines are guides for the eye.
those of rcfs. [8,9], which do not reproduce thc anisotropy of the susceptibility curves and give an ordered moment parallel to the c-axis. In out case, the ordered moment in the ground state lies along [110] and has a magnitude of l / x a / C e at 4.2 K. We obtain one dispersive mode which can reasonably account for the higher-energy mode found using hypotheses (B) or (C). The nature (quasielastic or inelastic) and the origin of the lower-energy mode remain presently unclear. In all cases, tne excitations are found to have an appreciable, slightly ~-dependent, linewidth F ( H W H M ) ~ 0.5 meV. It is interesting to note that his linewidth is comparable to that of the quasielastic scattering observed just above TN: the published values are 0.75 meV [3] and 0.9 meV [6]. Preliminary measurements on our single crystal lead to a slightly smaller value --0.6 meV. In concl' 'ion, the observation in CePd,,Si,, of damped excitations at temperatures, T - ~ T N , where magnon-magnon interactions are believed to be negligible, corroborates previous studies on CeSil. 7 and CeGei. 7 [1] and provides additional evidence of the effect of quantum fluctuations on magnetic excitations in the magnetically ordered phase of Kondo lattices, whether ferromagnetic or antiferromagnetic. We thank Ph. Boutrouille for his help during the neutron experiments.
References [I] F. Hippert. B. Hennion, F.L. Chui, M. Kohgi and T. Satoh, J. Magn. Magn. Mater. 76 & 77 (1988) 417. [2] B.H. Grier, J.M. Lawrence, V. Murgai and R.D. Parks, Plays. Rex,. B 29 (1984) 2664. [3] B.H. Grier, J.M. Lawrence, S. Horn and J.D. Thompson, J. Phys. C 21 (1988) 1099. [4] R.A. Steeman, E. Frikkee, R.B. Helmholdt, A.A. Menovsky, J. van den Berg, G.J. Nieuwenhuys and J.A. Mydosh, Solid State Commun. 66 (1988) 103. [5] M.J. Besnus, A. Braghta, J.P. Kappler and A. Meyer, in: Theoretical and Experimental Aspects of Valence Fluctuations and Heavy Fermions, eds. L.C. Gupta and S.K. Malik (Plenum, New York, 1987); A Braghta, Thesis (University of Strasbourg, 1988). [6] A. Severing, E.H. Holland-Moritz and B. Frick, Phys. Rev. B 39 (1989) 4164• t'.l .............. ~.JlSlI~..)uX atl~,l IJ. ltlt~lllilOll, rhy~. r ~ c v . B 39 (1982) 337. W.J.L. Buyers, T.M. Holden and A. Perreault, Phys. Rev. B 11 (1975) 266. [8] A. Severing, E. Holland-Moritz, B.D. Raintord, S.R. Cuiverhouse and B. Frick, Phys. Rev. B 39 (1989) 2557. [9] R.A. Steeman, T.E. Mason, H. Lin, W.J.L. Buyers, A.A. Menovsky, M.F. Collins, E. Frikkee, G.J. Nieuwenhuys and J.A. Mydosh, J. Appl. Phys. 67 (1990) 5203•
Magnetic excitations in the antiferromagnetic Kondo compound CePdzSi 2 F. Hippert a, B. Hennion t,, J.-M. Mignot b and P. Lejay c a Laboratoire de Physique des Sdides, Unit,ersit6 de Paris-Sud, 91405 Orsay Ceder, France t, Laboratoire L~on Brillou#~ (CEA-CNRS), CEN-Saclay, 91191 Gif sur Yrette, France ' CRTBT *, CNRS, BP 166X, 38042 Grenoble Cedex, France
The magnetic excitations of the Kondo compound CePd2Si 2 below its N&I temperature (T N = 10 K) have been studied Their linewidth
by inelastic neutron scattering. At T = 1.6 K the data are best represented by two dispersive inelastic modes. ( ~ 0.5 m e V ) indicates substantial broadening, which is ascribed to Kondo-type local fluctuations.
Whereas several detailed studies have been devoted to magnetic correlations in hea~-fermion materials, little is known on the nature of magnetic excitations below the ordering temperature in magnetically ordered Kondo lattices. One reason is certainly the difficulty of growing the large single crystals required by such experiments. The question of how the spin fluctuations, responsible for the reduction of the ordered moment, affect the magnetic excitations, remains open. Previous work on CeSil. 7 and CeGel. 7 ferromagnetic Kondo compounds [1] revealed that the observed magnons are substantially damped even at T<< T c. Their linewidth seems to be correlated with the Kondo temperature. A good candidate for further studies of these effects is CePd2Si 2. It belongs to the CeM2Si = family ( I 4 / m m m tetragonal structure) with M = Au, Pd, Rh, Ru, Cu, etc., which exhibits a large variety of magnetic behaviours [2,3]. CePd2Si 2 turns out to bc close to the borderline between magnetic and nonmagnetic compounds. It shows Kondo-type fluctuations, revealed by susceptibility, resistivity and specific heat measurements [4], and mders antiferromagnetically at T_,N = 10 K [2,4]. The antiferromagnetic wave vector is k = (0.5, 0.5, 0) and the moments lie parallel to-k. The estimated Ce moment at 4.2 K is = 0.65/z a, smaller than that calculated in a mean-field approximation when taking into account crystal field effects only (see below). This moment reduction has been considered an additionnal piece of evidence in favour of Kondo fluctuations. An order of magnitude of the Kondo temperature, TK--10 K, has been deduced from specific heat data [5] and from the linewidth of the quasielastic neutron scattering observed just above T N [3,6]. Inelastic neutron scattering mcasurcments have been performed on a cylinder-shaped, Czochralskigrown, single crystal with a volume ---0.3 cm 3. Structural checks revealed a good homogeneity, with a mosaicity of = 0.8 degrees. The experiments were carried
* Associ6 ~ l'Universitd Joseph Fourier.
out on the triple-axis spectrometers 4F1 and 4F2 (cold source) at the O r p h & reactor in Saclay. Constant-Q scans ((~ = ~'+ q) at fixed filial neutron energy (Ef = 8.04 meV)were performed at T = 1.6 K. Two directions, ~ = (q, q, 0) and ~ = (0, - q , 0), for 0 _
0312-8853/92/$05.00 © 1992 - Elsevier Science Publishers B.V. All rights reserved
178
F. Hippert et al. / Magnetic ercitations in the antiferromagnetic Kondo compound CePd aSi 2 300
,
•
•
i
•
"1
"
I
•
•
i
'
•
•
I
•
•
T = 1.65 K O = (0.5, 0.4, 0)
.-., E
o 200
I
•
•
CePd
]
• -
•
•
I
2
Si
•
•
'
2
1 mode + quasielastic
I
I'
'
~/ ]/~"1~ I ~
2 modes
100 L
-1,6
-0,8
0
0.8
1,6
2.4
3.2
4
Energy (meV)
Fig. 1, Inelastic scattering at constant (~ = (0.5, 0.4, 0) at !.6 K with final neutron energy Er = 8.04 meV. The solid and dashed lines show the best fits to the data (including incoherent scattering) using hypothesis (A) and (B), respectively. The horizontal bar indicates experimental resolution.
We performed a spin wave calculation following the method of ref. [7] (to be detailed elsewhere). The mean-field ground state was obtained assuming Heisenberg couplings up to the third-nearest neighbours, for a suitable set of crystal field parameters, B~ = 0.36 meV, B~) = 0.02 n;,:V, B44 = 0.355 meV, determined from fits of the susceptibility curves of a single crystal [4] and from the inelastic neutron scattcring data of i cfs. [3,8]. This choice actually diffcrs from
2.5 CePd2Si ~ f ~ . ~ . - . ~ - . ~ ? -
> ~1.5
!
v
I
? /
T = 1.6K Q= (0.5, 0.5-q, 0)
I E UJ
0.5 0
tx.a,,
0
I ....
0.1
I ....
I,
0.2 0.3 q ('.I.u.)
,I,
T
, I ....
0.4
I
~5
Fig. 2. Energy of the two observed inelastic modes at 1.6 K, using hypothesis (B), at reduced wavevectors ~" = (0, -q, 0) in the ÷'= (0.5, 0.5, 0) magnetic Brillouin zone. Solid lines are guides for the eye.
those of rcfs. [8,9], which do not reproduce thc anisotropy of the susceptibility curves and give an ordered moment parallel to the c-axis. In out case, the ordered moment in the ground state lies along [110] and has a magnitude of l / x a / C e at 4.2 K. We obtain one dispersive mode which can reasonably account for the higher-energy mode found using hypotheses (B) or (C). The nature (quasielastic or inelastic) and the origin of the lower-energy mode remain presently unclear. In all cases, tne excitations are found to have an appreciable, slightly ~-dependent, linewidth F ( H W H M ) ~ 0.5 meV. It is interesting to note that his linewidth is comparable to that of the quasielastic scattering observed just above TN: the published values are 0.75 meV [3] and 0.9 meV [6]. Preliminary measurements on our single crystal lead to a slightly smaller value --0.6 meV. In concl' 'ion, the observation in CePd,,Si,, of damped excitations at temperatures, T - ~ T N , where magnon-magnon interactions are believed to be negligible, corroborates previous studies on CeSil. 7 and CeGei. 7 [1] and provides additional evidence of the effect of quantum fluctuations on magnetic excitations in the magnetically ordered phase of Kondo lattices, whether ferromagnetic or antiferromagnetic. We thank Ph. Boutrouille for his help during the neutron experiments.
References [I] F. Hippert. B. Hennion, F.L. Chui, M. Kohgi and T. Satoh, J. Magn. Magn. Mater. 76 & 77 (1988) 417. [2] B.H. Grier, J.M. Lawrence, V. Murgai and R.D. Parks, Plays. Rex,. B 29 (1984) 2664. [3] B.H. Grier, J.M. Lawrence, S. Horn and J.D. Thompson, J. Phys. C 21 (1988) 1099. [4] R.A. Steeman, E. Frikkee, R.B. Helmholdt, A.A. Menovsky, J. van den Berg, G.J. Nieuwenhuys and J.A. Mydosh, Solid State Commun. 66 (1988) 103. [5] M.J. Besnus, A. Braghta, J.P. Kappler and A. Meyer, in: Theoretical and Experimental Aspects of Valence Fluctuations and Heavy Fermions, eds. L.C. Gupta and S.K. Malik (Plenum, New York, 1987); A Braghta, Thesis (University of Strasbourg, 1988). [6] A. Severing, E.H. Holland-Moritz and B. Frick, Phys. Rev. B 39 (1989) 4164• t'.l .............. ~.JlSlI~..)uX atl~,l IJ. ltlt~lllilOll, rhy~. r ~ c v . B 39 (1982) 337. W.J.L. Buyers, T.M. Holden and A. Perreault, Phys. Rev. B 11 (1975) 266. [8] A. Severing, E. Holland-Moritz, B.D. Raintord, S.R. Cuiverhouse and B. Frick, Phys. Rev. B 39 (1989) 2557. [9] R.A. Steeman, T.E. Mason, H. Lin, W.J.L. Buyers, A.A. Menovsky, M.F. Collins, E. Frikkee, G.J. Nieuwenhuys and J.A. Mydosh, J. Appl. Phys. 67 (1990) 5203•