Hall effect in YbXCu4 and the role of carrier density in the YbInCu4 valence transition

Abstract An unrealistically large value of the Gruneisen parameter is required to explain the valence transition which occurs at 42 K in YbInCu4 as due to a Kondo Volume Collapse. A hint as to the origin of the transition lies in the large change in carrier density which occurs at the transition, from trivalent semimetallic behavior at high temperature to mixed valent metallic behavior at low temperature. In this paper we report measurements of the Hall coefficient RH for temperatures in the range 15–300 K for a series of RXCu4 compounds (R = Yb, Lu and X = Au, Zn, Cd, Mg, Tl) that form in the cubic C15b structure. For all X the Hall coefficients are small (∼ 10−10 m3/C) so that the transport appears to be metallic. The observation that low carrier density is unique to RInCu4 leads us to hypothesize that the valence transition (which is also unique to YbInCu4) is connected with the existence of a quasigap, which is a common feature of the band structure of RXCu4. The quasigap allows for two competing hybridization states of the 4f electrons: a small TK semimetallic state and a large TK metallic state.


INTRODUCTION
In the prevailing Kondo Volume Collapse (KVC) YbInCu4 has a phase transition at T, = 42 K [l-3] at which the Yb, which is nearly trivalent at high temperature, becomes strongly mixed valent (z = 2.8) at low temperature [ 1, 41. The Kondo energy, which is small (Tk.+ = 25 K) at high temperature, becomes large (TK-= 500 K) [4][5][6] in the low tem~rature state. Furthermore there is no change in the C15b crystal symmetry at the transition [7, 81. Such an "isomorphic" valence transition is fundamentally similar to the cr-y transition in cerium [9, lo], which raises the question whether both transitions have a common origin.
volume change but also on the sensitivity of the Kondo temperature to changes in the cell volume; quantitatively should be it requires a value of order 50 for the Gruneisen parameter I' = -a In T&I In V. Such  . This reasons given above (and as is seen experimentally [ 121) observation allows us to hypothesize that the valence T, = TK+ so that F can also be estimated from the slope transition (which is also unique to YbInCtQ is connected of the a-y phase boundary (lIT,)aTJdP = 2Slkbar; with the existence of a quasigap, which is a common given the bulk modulus B = 200 kbar [ 131 this implies feature in the band structure [19, 203 of Cl5b RInCu., r = 50.
compounds. The valence transition in YbInCu4 also can be viewed as a competition between a low temperature state with a large Kondo condensation energy and a high temperature state with a large spin entropy (J = 7/2 for Yb). However, the change in cell volume at the valence transition in YbInCu4 is so small (AVlV, = 0.005) [3,5,81 that to drive a change in TK from 25 K to 500 K would require an unphysically large value (-4000) of the Gruneisen parameter. Since it has been determined experimentally [4] for YbInCu4 that T, = TK+, we estimate F = -(BIT,)aTJaP = 56 where we have used dT,/aP = -2 K kbar-' [14] and B = 1120 kbar [ 151. Hence, while it is reasonable to speak of the YbInCu4 valence transition as a "Kondo Collapse", it is not a "Volume Collapse" driven by a large change in cell volume as for Ce.

EXPERIMENTAL DETAILS
In addition to the issue of the relation between the phase transitions in Ce and YbInCu4, a further question is why the valence transition is unique to YbInCu4 in the larger set of YbXCu4 compounds (X = Ag, Au, Pd etc. [ 161) that grow in the same Cl56 crystal structure. A clue to the origin of the transition comes from the observation that the compounds RInCu4, where R is a heavy rare earth, are semimetals with low carrier density and large Hall coefficients [17]. In a recent study [4] of YbInl_,Ag,Cu4 alloys, we have shown that the Hall coefficients Ru in LuAgCu4, YbAgCu4 and in the low temperature state of YbInCu4 have values (-lo-" m3/ C) typical of ordinary metals, but Ru is anomalously large ( -[4-6] X 10e9 m3/C) in LuInCud and in the high temperature state of YbInCu4 (-[4-81 X lop9 m3/C). Hence the carrier density changes at the phase transition; this changes the density of states at the Fermi level N(Q) and consequently changes the Kondo temperature TK -exp[ -]I$ -c~]/(2J + l)A] which depends sensitively on N(Q) through the 4f-conduction hybridization strength A = VAN as well as on Ae = (I$ -EF), the distance from the Yb 4f level to the Fermi level and the degeneracy (U + 1 = 8 for Yb). Our hypothesis is that specific features of the RInCud band structure allow for two nearly degenerate states: a metallic state with strong hybridization and a semimetallic state with weak hybridization.

Polycrystalline
samples of RXCu4 (R = Yb, Lu and X = Au, Zn, Tl, Mg) were prepared by sealing the starting materials in evacuated tantalum tubes which were then sealed in evacuated quartz tubes and heated to 115O"C for 12 h, cooled to 800°C and held at that temperature for 7 days. Single crystal samples of RCdCu4 (R = Yb, Lu) and of YbXCu4 (X = Zn, Tl and Mg) were also grown in fluxes by the method outlined in [3]. Using conventional X-ray diffraction we established that all these samples crystallize in the C15b structure. The Hall coefficients were measured using a He-flow cryostat for temperatures in the range 15-325 K. The samples were shaped into thin plates of typical dimension 0.5 X 2 X 3 mm. The Hall voltage was measured in fields of 2 1T at various fixed temperatures using an LR400 resistance bridge and an operating frequency of 16 Hz. Small misalignment voltages were compensated electronically and the magnetoresistance was cancelled by reversing the polarity of the field. The Hall voltage was linear in applied field for Hs IT.

RESULTS AND ANALYSIS
In this paper we report measurements of the Hall coefficient Ru for a set of Cl56 YbXCu4 and LuXCu4 The Hall coefficients Ru of YbXCu4 and LuXCu4 compounds are shown in Fig. 1. The Hall coefficients of LuXCu4 for X = Au, Zn, Cd, Mg are weakly temperature dependent, small ( -[0.3-1.71 X lo-" m3/C) and negative. (For LuTlCu4, Rn is even smaller in magnitude, but positive below 25 K; the latter may be extrinsic behavior.) For RXCu4 there are four formula units in a cell of side 7.1 A, so that in sample one-band model a Hall coefficient of -1 X lo-lo m3/C corresponds to 5.6 electrons per formula unit. This suggests that these LuXCu4 compounds are good metals. The Hall coefficients of the YbXCu4 compounds are also relatively small, being in the range -[l-lo] X lo-lo m3/C (with the exception of YbZnCu4 where Ru reaches the value -20 X lo-lo m3/C at the lowest temperatures).
As for other Yb compounds [21], the temperature dependence of Ru observed in YbXCu4 is not due to changes in the carrier density, but is associated with skew scattering YbXCu4 where x is the susceptibility, p is the resistivity and /3 is a constant.  Fig. 1 then implies that p is negative for YbMgCu4 but positive for YbTlCu+ The background (non-48 contributions Ro(X) can be estimated from the high temperature asymptotic values (where x is small); these lie close to the values for the corresponding LuXCu4 compounds. Our basic result is, then, that the RXCu4 compounds for R = Yb, Lu and X = Au, Zn, Cd, Mg and Tl have Hall coefficients that are more than an order of magnitude smaller than the values seen in semimetallic LuInCu4 and the high temperature state of YbInCu4, which suggests that the RXCu4 compounds are all good metals.

DISCUSSION
We now consider whether the bandstructure of RXCu4 supports our hypothesis that the phase transition in YbInCu4 is connected intimately with the high temperature semimetallic behavior and in addition which features of the bandstructure yield our basic result that semimetallic behavior appears to be unique to RInCu, in the class of RXCu4 compounds in the Cl% structure. Bandstructures have been reported for RInCu4 (R = Yb, Lu) [19] and for RAgCud (R = Yb, Lu) YbAuCu4 and YbPdCud [20]. A sketch of the non-4f density of states common to all cases studied is given in Fig. 2. A large peak due to Cud and X-d states resides 2-6 eV below the Fermi level CF. For most cases the Fermi level lies in a smaller double-peak due to Cu-p, d and X-p, d states, which is of maximum magnitude -1-3 states/eV-atom and of width -1.5 eV. This is separated by a quasigap (of very low density of states) of width 0.5-l eV from a peak of width 3 eV and magnitude -5 states/eV-atom due primarily to R-5d states and secondarily to Cu-s, p states. For the Yb compounds, the calculations [19, 201 treat the Yb 4f electrons as band states (as opposed to frozen core states) which forces a partial occupancy (of  Table governing the relevant X. The Fermi level moves from the low energy side to the high energy side of the double-peak p, d structure as the X atom moves to the right in the Periodic Table. For X atoms in columns to the left of In the resulting behavior is metallic. For LuInCu4 and the high temperature state of YbInCu4, the Fermi level lies in the low density of states (quasigap) region and the behavior is semimetallic. order 13.6) for the 4f state; the Fermi level lies near the top of this 4fband. The Fermi level moves progressively from the bottom (low energy side) of the double-peak p, d structure for YbPdCu4, to the middle for YbAgCu4, LuAgCu4 and YbAuCuh and then to the top (high energy side) for YbInCu+ Given the similarity of the density of states in all cases and given this trend in the position of the Fermi level it is clear that rigid band concepts apply at least qualitatively. The Fermi level pushes up through the p, d double-peak as the X atom moves to the right in the Periodic Table. The Fermi level for LuInCu4 lies in the quasigap [ 193, which can also be understood as a consequence of rigid band motion: in the calculation for YbInCu, the Yb atoms are formally in the 4f14 -"(5d, 6~)~'" configuration with n -0.4 and contribute 13.6 4f electrons and therefore 2.4 5d and 6s electrons to the valence band, whereas for LuInCu4 the Lu atoms are in the 4f14(5d, 6~)~ configuration and hence contribute 0.6 more (5d, 6s) electrons to the valence band, pushing the Fermi level up into the quasigap. Closer examination [19] shows the LuInCu4 is a semimetal, with a closed hole sheet around the W point and a closed electron sheet around the X point, with the number of electrons equal to the number of holes (0.04 per formula unit). We note that the Hall coefficient of LuInCu4 (which is -60 X lo-lo m3/C at low temperature [4]) suggests in a one band model that there are 0.09 electrons per formula unit.
There is an important difference between the expected 4f states of YbInCu4 and those calculated in the band structure: the strong intraatomic correlations cause the 4f states to be highly localized and description of them as a simple band at the Fermi level is inappropriate. Nevertheless, the difference between the high temperature and low temperature electronic configurations of YbInCu4 is similar to the difference between the electron configurations of LuInCu4 and YbInCu4 in the band calculations in the following respect: the Yb changes from a mixed valent 4f".2(5d,6s)2.8 configuration at low temperature to a trivalent 4f1 3(5d, 6~)~ configuration at high temperature. The observed change in the carrier density at the phase transition suggests that the extra electrons contributed to the valence band at high temperatures push the Fermi level up into the quasigap, just as occurs for LuInCu4. This provides justification for our hypothesis that by a small increase in electron count (-0.1-0.2) the system can move the Fermi energy in such a manner as to decrease significantly the density of states N(E~) and hence decrease the 4f-conduction hybridization strength A = V'N(EF) in such a manner as to cause a large decrease in the Kondo temperature TK -exp [ -II!$ -e~]/(25 + l)A]. It is this feature of the bandstructure which allows for the phase transition in YbInCu4, as opposed to the sensitivity of the Kondo temperature to changes in cell volume as in Ce.
For X atoms which are in columns of the Periodic  Table to the left of In, the Fermi level of YbXCu4 and LuXCu4 should be located in the p, d double-peak with a healthy density of states and concomitant metallic behavior. As reported here for X = Au, Cd, Zn and Mg and as reported elsewhere [ 161 for X = Pd and Ag the YbXCu4 and LuXCQ compounds for these X appear to be good metals. The small Hall coefficients seen in LuT1Cu4 and YbT1Cu4 suggest that these are also good metals. This means that position of the Fermi level can't be determined simplistically from the column of the X element in the Periodic Table. The positive value of the skew scattering coefficient in YbInCul may, however, be an indication of significant differences between RTlCu4 and the other RXCu4.
Our hypothesis, which in a straightforward way links the experimental behavior to features of the bandstructure, is compelling and general. We are currently measuring the resistivity, susceptibility, specific heat and L3 X-ray absorption spectra of the YbXCu4 compounds [23]. This should allow us to determine whether the Kondo temperature and valence can be related to the position of the Fermi level relative the quasigap as required by our hypothesis. More detailed tests of the hypothesis will require such measurements as photoemission, de Haas van Alphen (dHvA) and optical absorption to establish the background band structures and the position of the renormalizedf bands.