Dynamics of the magnetization in the heavy fermion system CeCu6

We have studied CeCu6 by inelastic neutron scattering. We found both quasielastic and also inelastic transitions, which we interpret as residual crystal field transitions. The quasielastic linewidth is a strongly nonlinear function of temperature, with approximately ΓQE=5.0 meV at 300 K, with a crossover ΓQE=kT at about 13 K and with a residual value of ΓQE=(0)=0.50 meV forT=0 K. Below 5 K the quasielastic intensityIQE decreases linearly with temperature. χstαIQE/T is in good agreement with direct measurements of the static susceptibility. The data are fully consistent with a nonordering groundstate of CeCu6.


Introduction
CeCu 6 is a new member [1][2][3] of the rapidly growing class of the so called heavy fermion systems.This class of intermetallic compounds is characterized by a large effective mass of the conduction electrons near the fermi level, as detected by specific heat measurements at helium temperatures [1,4].The modern heavy fermion classification may be regarded as a generalization of the older classification by the term Kondo compounds or Kondo lattice systems, which has been applied to some of these systems for a long time.Some of these heavy fermion systems become superconducting (CeCu2Si2, UBe13 ) or order magnetically (UCdll , CeA12, CePb 3 [5], YbPd [6], YbCuA1 [7]) or show both types of phase transitions (URu2Si 2 [8]).Others remain paramagnetic (CeA13).CeCu 6 seems to belong to the latter subclass, according to the static suceptibility and especially the specific heat, which shows a * Present address: Materials Science and Technology Division, Argonne National Laboratory, Argonne, IL 60439, USA temperature independent coefficient 7 = C/T =1.53 J/mol.K 2 [9] (=320 states per eV and unit cell) below 0.5 K; no gap of any type seems to be developing in this compound at the fermi level above 40 mK [9].Apart from the high electronic specific heat at low temperatures, heavy fermion systems, at least those with Rare Earth components, show a very abnormal temperature dependence of the quasielastic (QE) magnetic line width FQE(T), as detected by inelastic neutron scattering: while at low temperatures this width is very close to the inverse linear specific heat coefficient FQE(0)_~7-1(0) *, the width FQE(T ) grows by one order of magnitude or more when the temperature grows to a few 100K.The Rare Earth heavy fermion systems CeCu2Si2, CeA1B [11], YbPd [12] and YbCuA1 [13] show invariably also inelastic excitations in the magnetic neutron spectra at energies * This relationship follows immediately if one refers the linear specific heat coefficient not to the mole but to the unit cell of the compound, i.e. if one expresses ~ in states/energy interval.atom.We feel that this is the most transparent description of the essential physics of about 10meV, which are usually interpreted as CF-excitations.
In this paper we report a study of the magnetic excitation spectrum of CeCu 6 between 1.5 K-120K by inelastic neutron scattering.The measurements were done with cold neutrons (E 0 = 3.07 meV) at the TOF-spectrometer IN6 at the high flux reactor at the ILL/Grenoble.The choice of cold neutrons was motivated by the following facts: -the subtraction of phonon scattering is particulary easy at low momentum (Q) transfer, which can be best achieved by low incoming energy; -the incoming energy of Eo=3.07meV is on the other hand large enough to ensure a nearly complete view of the QE-spectrum at low temperatures in energy loss, where it is essential to have Eo>>FQE(O ), when k r ~ FQE(0); -the spectrometer IN6 has a resolution, which is at least one order of magnitude higher compared to all the other high flux TOF-spectrometers used in the past to study the magnetic spectra of heavy fermions.

Experimental Results and Discussion
We In Fig. 1 we have plotted S(Q, h co) and in Fig.In the spectra of LaCu~ (Fig. 1) there are clear in-2O The spectra of CeCH 6 contain contributions from phonons and from magnetic scattering.As usual the phonon contribution can be identified by comparison with the pure phonon spectra of LaCu 6, assuming that the phonon spectra are nearly identical in both compounds.Since the phonons at 3.2 meV and 6.0 meV are less intense and correspond to less momentum transfer than the phonons at higher energies, they quickly diminish in intensity on the way to the forward scattering angles used in taking the CeCu~ spectra.Thus, in the case of CeCu6, only the high energy phonons give rise to visible small phonon contributions for AE<-9meV at all temperatures on top of the magnetic spectrum, which dominates for IAEI meV (Fig. 2).
The spectrum of CeCu 6 at T--50 K shown in Fig. 2 is typical of a high temperature spectrum.From this spectrum two features can be extracted clearly: a distinct QE-line with Lorentzian shape and with a width of FQE(50 K)=2.3 meV, and a broad inelastic excitation at about AE=5.5 meV.The existence of any other QE-line with a width of less than 10 meV and with an intensity of more than 10 ~o of the first QE-line can be excluded.
To interpret the broad inelastic magnetic excitation one may start as usual by assuming that the excitation at AE=5.5meV is a crystal field (CF) transition.Support for this interpretation is given by the observation that the excitation energy remains constant at all temperatures.Moreover, specific heat measurements [1,4] of CeCu 6 at 1K<T<80K show a Schottky type anomaly due to a doublet at 5.6meV above a doublet ground state (the degeneracy follows from the entropy in the specific heat measurements).In order to interpret the magnetic neutron spectra in terms of a CF-scheme, one must realize that in principle three IN-lines are expected, because of the monoclinic point symmetry of Ce in CeCu 6.The absence of the other two inelastic excitations in the spectrum may be either due to the fact that the uppermost CF-doublet is at energies of about 11 meV (about twice the first excitation energy) or very far above that value.The recent measurement of the CF-splitting in PrCu 6 [14], which reveals a total CF-splitting of 8.95 meV, suggests that CeCu 6 should show a corresponding total CF-splitting of roughly 10meV, due to the slightly more extended 4f-shell of trivalent Cerium.Since this is in good agreement with the first assumption, we suggest the following CF-scheme for CeCu6: 0-5.5 meV-11.0meV.In Fig. 3 we show the neutron spectra of CeCu 6 below t0 K.In this temperature range the inelastic transitions can be ignored for two reasons: On the energy gain side (left hand side from AE=0) the excited levels are no longer thermally occupied and on the energy loss side (right hand side) the incoming energy is less than the first CF-excitation.This We point out, that there is no indication of any QEline with Gaussian shape in our spectra.On the other hand, such additional Gaussian QE-line were found in the magnetically ordering intermediate valent systems YbBe13 [15] and YbPd and Yb3Pd 4 [12].In these compounds an additional Gaussian QE-line precedes the onset of magnetic order.In all of them the Gaussian line could clearly be distinguished up to temperatures which were roughly 10 times larger than the ordering temperature.From this experience we conclude that CeCu 6 will not order magnetically above approximately T=0.1 K.This is in fact consistent with the specific heat, which was measured down to 40 mK 1-9] and showed no temperature dependence of the linear specific heat coefficient.We observe a drastic decrease of the QE-line width with decreasing temperature.At T= 13.2 K the QElinewidth is equal to kT (FQE=I.1 meV).There is a substantial further decrease of the QE-line width below this temperature, but finally one observes a clear saturation at FQE=0.50meV below 3K (insert of Fig. 4).tn Fig. 5 we have plotted the QE-line width versus temperature in a double logarithmic plot.We find FQE(T)ocT t/2 above 5 K, which is the same as in CeA13 at comparable temperatures [11].
We define the QE-intensity IQE (Fig. 4, lower part) by where Z~[ are the diagonal parts of the Q-dependent susceptibility [16].IQE is constant above 150 K.This corresponds to a Curie like behavior of Zc at these temperatures.Below 150 K IQE first decreases slowly with temperature, perhaps due to a decrease of the effective magnetic moment.At helium temperatures the decrease is linear with temperature.The constant QE-line width below 3 K as well as the linearly decreasing QE-intensity can be observed clearly in Fig. 4 (By definition of ( 1), the QE-intensity is just the integrated area below the lorentzian (QE) lines in Fig. 3).The linear behavior of IQE indicates that Zc has become constant below 3 K.
In order to show the correspondence of the measured magnetic scattering intensity to the measured static susceptibility Zst, we have calculated Zc and Zst from the QE-intensity tQE alone and the total magnetic scattering, respectively (Fig. 6).The full dots give Z~.This corresponds to the pure Curie terms.The open circles give the susceptibility calculated from the QE-and from the inelastic intensity together; this corresponds to Curie and Van Vleck terms together.Also shown is the susceptibility as measured by Stewart et al. [1].It is obvious from Fig. 6, that the susceptibility calculated from the measured neutron data does not give the full static susceptibility.
For instance a slope of )~ 1 vs. T, taken from the open symbols gives an effective moment of kt~ff =2.21~B, which is 11 ~ below the effective moment of the measured susceptibility.The deficiency may be due either to a broad magnetic inelastic scattering, or to a very broad QE-line (FQE > 6 meV), which both could be hidden by an overestimation of the phonon contribution.However, it may also be simply due to the uncertainty in the normalization of the spectra by independent vanadium measurements.Unfortunately we cannot decide between these possibilities on the basis of the experimental data taken with cold neutrons.Besides the QE-intensity IQE there is also the zero temperature QE-line width FQE(0 ), which should be related directly to the static susceptibility at lowest temperatures.A more general equation for this dependence is given by the Korringa relation [17,18], which reads in our case

~ ~(0)
This expression for )~st is valid for an N-fold degenerate multiplet at temperatures very small compared to FQE(0 ) assuming a Lorentzian distribution of the amplitude of each of the N states over energy.FQE(0 ) is the HWHM of the Lorentzian at T= 0.
As an aside we mention that another phenomenological formula is often used to describe the suscepti- We shall now show that the neutron data given above enable an unequivocal determination of #err from (2) for T<3 K.Note first of all, that FQE(0 ) can be taken directly from the spectra.Secondly, our above discussion shows, that we are dealing with a CF-doublet groundstate; therefore N=2.Thirdly, since the measured integrated intensity IQ~ gives )G (Eq.( 1)), which agrees with Z~t below 3K (Zst =0.035 emu/mol), we can determine #af with confidence.We find #eff=l.60For CeCu 6 we find 1.95 for the r.h.s, of Eq. ( 3) with ?= 1.53 J/mol/K 2 and )G(0)=0.035emu/mol and #af = 1.60#B.With the assumption that Kondo theory of dilute alloys holds also for Kondo compounds, a more elaborate theory of the Kondo effect [19] implies that the r.h.s, of Eq. ( 3) has to be lowered by a factor of N-1/N leading to 0.98 for the Wilson ratio in CeCu 6.

Conclusion
Above T=3 K CeCu 6 exhibits the same square root like behavior of the QE-linewidth as other heavy fermion systems (CeCu2Si2, CeAl3) or Kondo lattice systems (CeB6, CeA12).Below 3 K neutron spectra exhibit only a single QE-lorentzian of constant line width (FQE(0)=0.50meV).No additional gaussian QE-line could be observed, which indicates that no magnetic ordering can occur above T=0.1 K.This prediction is in agreement also with the measured QE-intensity, which vanishes linearly with temperature below 3 K.This corresponds to a finite value of the measured static susceptibility.The neutron scattering cross section is evaluated to extract the effective moment and the QE-line width near T=0.We find #eff = 1.60 #R from our measurements.Using this effective moment and the measured linear specific heat coefficient, we find a Wilson ratio of 1.95.At high temperatures the neutron spectra show only one inelastic transition at 5.5 meV, from which we indirectly derive the CF-scheme: 0-5.5 meV-11.0meV.We are grateful to U. Steigenberger for her attentive assistance in course of the measurements at the ILL in Grenoble and to E. Miiller-Hartmann and E. Holiand-Moritz for many fruitful discussions.This work was supported by the Deutsche Forschungsgemeinschaft through SFB 125.

Fig. l .Fig. 2 .
Fig. l.Phonon spectrum of the reference sample LaCu 6 at high momentum transfer (high scattering angles).The full line is a fit to the spectrum

Fig. 3 .Fig. 4 .
Fig. 3. Quasielastic magnetic spectrum of CeCu 0 below T= 10 K.The fit to the spectrum (full line) considers the incoherent nuclear scattering (shaded area) and one QE-line with Lorentzian shape

Fig. 5 .
Fig. 5.The square root like temperature behavior of the QE-line width FQE above T = 5 K, shown in a double logarithmic plot

Fig. 6 .
Fig.6.The temperature dependence of the static susceptibility of CeCu 6 as measured (broken line[1]), compared to the values calculated from the neutron spectra (full lines).The full circles denote the susceptibility calculated from the pure QE-scattering and the open circles that from the total magnetic scattering