Magnetic field dependence of the cyclotron effective mass in the Kondo lattice CeB6

We report the first observation of a field‐dependent mass in a hybridizing f‐electron system. CeB6 is an ordered moment heavy fermion system with an electronic specific heat coefficient γ of order 225–300 mJ/mole K2. Using the de Haas–van Alphen effect at temperatures as low as 60 mK in steady magnetic fields as large as 22 T, we observe a cyclotron orbit of frequency 8680 T for fields along the [100] direction. The mass of this orbit was measured at eight fixed fields and found to decrease from 18me to 8me as the field increases from 12 to 22 T. The observed Fermi surface is very similar to that of LaB6, indicating that the f‐electrons are largely local rather than itinerant in CeB6, a picture confirmed by bandstructure calculations. The observed field dependence of the cyclotron mass is consistent with the low‐energy scale of the system as measured, for example, by the Kondo temperature. Our results are compared with Fermi surface observations in other heavy fermion systems.

the system as measured, fcr exampie, by the Kondo temperature. Our results are compared with Fermi surface observations in other heavy fermion systems.
The heavy fermion materials form a major challenge to our understanding ofthe physics ofmetals. 1 They are unusual in almest every physicaI property but the most characteristic cne is the high value of the low-temperature specific heat (LTSH). Many  ( 1) At low temperatures the conduction electrons form coherent states and the mean free path is severa1 hundreds of nanometers long.
( 3) The electron mass is very high and one or two orders ofmagnitude larger than found by conventional bandstructure calculations. Estimates show that the masses found in dHvA experiments explain the large values of the LTSH (with thc possible exception ofCeCu 6 ).
Here we discuss the resuits for CeB 6 and we show in addition that the electron mass is strongly suppressed in high magnetic fields ( see also Ref. 5). This is the first observation of a field-dependent electron mass in this type of compound.
It shows that the many body interactions which make the electrons heavy (or in other words slow) are strongly reduced in high fields and the electrons become light again (speed up). At the same time it is observed that the size of the Fermi surface, as measure<l by the dHvA frequency, is field independent. Thus the numberof particles is conserved.
CeB 6 is one cf the most typical Kondo lattice systems and has therefore received a lot of attention, see, e.g" Kasuya et al. 6 The Kondo temperature is verylow, only l-2 K . 7 lt is interesting to compare the experimental Fermi surface information to that ofLaB 6 and to bandstructure caiculations by Norman and Min. 8 The results indicate that the/ electron of CeB 0 is locaiized and can be treated as part of the ion core. This is in sharp contrast to the Situation for UPt 3 and CeSn 3 • We conclude that CeB 6 belon.gs to a different class of heavy fermion compounds: the hybridization is apparently not strong enough to bring the f electrons to the Fermi ievel. Y et an electron mass enhancement of roughly a factor 100 is observed.
Tue dHvA etfect measures the oscillatory magnetization in high magnetic fields which arises due to the quantiza- tion ofthe electron motion on Landau orbits. 9 Tue frequency observed w hen changing the appiied field is directly proportional to the cross-sectional area of the Fermi surface. The field and temperature dependen.ce of the oscillation amplitude allow a determination of the mean free path with respect to the effective mass for this orbit. Tue dHvA etfect is usually only observed in high magnetic fields and at low temperatures. These restrictions are the more severe as the mean free path is shorter and the effective mass is !arger. In order to obtain these conditions our experirnents were carried out in a special dilution refrigerato.r designed to operate in the 25T polyhelix magnet of the Grenoble high magnetic field facility (SNCI/MPI). A low-frequency large-amplitude modulation technique and phase sensitive detection at the second harmonic of the modulation frequency were used to measure the signals.
The angular dependence of the dHvA frequencies 10 closeiy resembles that for the isostructural compound LaB 6 • 11 The latter is an ordinary metal with a L TSH coeffi-cient12 r = 2.6 mJ/mole K 2 • Its Fermi surfäce consists of spheres centered at the X points of the Brillouin zone which are connected by small necks and contain one electron per cell per spin. 11 In addition, CeB 6 has one f electron. However, the Fermi surface does not seern to be affected very strongly by this extra electron and we conclude that the f e!ectron is localized and sits below the Fermi energy. Strong evidence for this interpretation is also found from the bandstructure calculations by Norman and Min. 8 They performed ca!culations using several apprcximations first treating the f electron on equal footing with the other valence electrons and next treating it as part of the ion core allowing no hybridization with the conduction electrons. Only for the second approach a satisfactory agreement with tbe experimental Fermi surfäce information is found, althougb an important discrepancy of 10% in size remains to be explained. This conclusion is opposite to the results for UPt 3 (Ref. splitting of the Fermi surface. In the strong fields used here the induced magnetic moment is close to 1µ 8 /Ce. As a consequence the exchange interaction between the conduction electrons and the local magnetic mornents of the f electrons must be very small.
The effective mass study was carried out for the field along [ 100]. In this field direction and with the present technique one strong frequency is observed of F = 8680 T. This frequency is constant with field and temperature to a precision of0.5% showing that the number of particles is field and temperature independent. The electron mass was determined at different field values by fitting the temperature de· pendence to the usual Liftshitz-Kosevich theory for the dHvA effect. 9 The resulting masses are plotted as a function of field in Fig. l . Tue mass measured in fieids above 30 T by van Deursen et al. 10 is also included in the figure. A substantial suppression of the electron mass with fieid is observed. Also, even in high fields, the masses are very high compared to m* = 0.61m" for the equivalent orbitin LaB 6 • In order to allow a comparison to the spedfic heat the data in Fig. 1 are presented on a semi logarithmic scale. The L TSH of CeB 6 has been measured to very low temperatures and in fie!ds up to 8 T by Marcenat and by Bredl. 13 There appears tobe some sample dependence of the absolute values: the linear term r in zero field ranges between 225 and 300 mJ/mole K 2 • However, the generai behavior is the same and it. was found that r initial!y increases with fieid toward ihe transition from the low~field antiferromagnetic phase to the high-field phase II.
Then a strong decrease of r with field is observed. The curve in Fig. 1 represents this field dependence of r schematically.
The cyclotron mass is an integral of the inverse Fermi velocity l/u F over the cyclotron orbit. The LTSH coefficient y, if conventionai theory applies, is proportional to the density of electronic states at the Fermi level which in turn is an integral of l!v...over the entire Fermi surface. The zero field specific heat for CeB 6 Yce = 260 mJ/mole K 2 is enhanced over the value of LaB 6 ru.. = 2.6 mJ/mole K 2 • This enhancement corresponds to an enhancement of the electron mass and a reduction ofthe Fermi velocity. Ifwe assume that the enhancement is near1y isotropic tben we can relate the measured r value for CeB 6 to the cyclotron mass for the present orbit via m~ = {YcclY1..a}m~a· The mass for the corresponding orbit in LaB 6 is mt. = 0. 61m~. 11 The relation above is used to adjust the scales in Fig. 1. It shows that the zero field effective mass for this orbit should be roughly 60me. W e find from Fig. 1 that there is a fairly good agree- ment, though not yet quantitative, between r and m* and that these are both enhanced by the same amount.
The mean free path of the electrons on this orbit was determined by analysing the field dependence of the amplitude ofthe dHvA osciUations. First the temperature dependent factor in the amplitude was eliminated by linear extrapolation to T = 0. Tue field dependence of the resulting zero temperature ampfüudes is given in Fig. 2. The straight line gives 14 m* TD = 2.4 K where 1/J is tbe so-cal!ed Dingle temperature which is inverseiy proportional to the scattering time r. Now, since m* is field dependent, so are T 0 and r. A possibly more fundamental property is the mean free path l whicb is inversely proportional to the product m* T 0 . We find no evidence that this product is field dependent although this might be hard to distinguish in a Iimited field interval. (Fora discussion of the 12.7 T point in Fig. 2 see below.) From the quoted value form* T 0 we calculate a mean free path l = 0.30 µm. The circumference of the real space orbit at 10 T is 21Tr = 2.13 µm. Thus, we find that the electrons form coherent states which extend over a very !arge number of unit cells.
Finally, a remarkable etfect was observed on thermal cyding of the samples. In three different samples from two different batches the signal after the first cool down was roughly ofthe same amplitude. Thermal cycling reduced the signal amplitude drastically. After 2 or 3 cycles the signa! in all three samples was below noise level. To our knowledge there is no crystalline phase transition below room temperature which wou1d explain this phencmenon. The samples were carefully mounted in cotton wool and no glue or grease was used, in order to avoid stress due to differential thermal contraction on cooling. All data in Figs. l and 2 were taken without heating above 1 K, except for the lowest field point.
This was taken after one room temperature cycle and m * T 0 for this point appears significantly higher. The field dependence of the cyclotron mass was reproduced in one other sample and found tobe consistent with the results presented here.
The most salient feature of the results presented here is the direct observation of a strong suppression of the heavy mass in CeB 6 • In order to describe this etfect one could start from an impurity Kondo model or, alternatively, from a spin ftuctuation model. However, the situation here is complicated by the fact that Kondo effect and magnetic order play an important role and the characteristic temperatures are all · small: TK = l-2K, TN = 2.4K. Itisduetothesmallnessof these energy scales that the etfect is so clearly observed. In UPt 3 the characteristic temperatures are an order of magnitude higher and up to l S T no fieid effects are observed. 3 For CeCu 6 the problem is even more interesting: the electronic 3895 J. Appl. Phys., Vo!. 63, No. 8, 15 April 1988 specific heat is suppressed by a factor 2 or 3 in high fields but in dHv A experiments a search for a field dependence in the electron mass did not show any corresponding etfect.
Further, it is observed that the/electron is loca! and has only minor effects on the Fermi surface. These smaH etfects, however, deserve our full attention and should be studied in more detail. More experiments are under way.
We would like to thank J. Flouquet and P. Wyder for their stimulating support and P. Stamp for helpful discussions. The assistance of M. Caussignac in development and maintenance of the dilution refrigerator is gratefully acknowledged. The werk was partially supported by the US-DOE-BES-Materials Sciences under Contract No.W-31-109-ENG-38. 'G. R. Stewart, Rev. Mod. Phys. 56, 755 ( 1984); P. A. Lee, T. M. Rice, J. W. Sereue, L. J . Sham, and J. W. Will<lns, Comments Cond. Mat. Phys. !2, 99 (1986).