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Anomalous electronic susceptibility in Bi2Sr2CuO6+d and comparison with other overdoped cuprates

We report magnetic susceptibility performed on overdoped Bi2Sr2CuO6+d powders as a function of oxygen doping d and temperature T. The decrease of the spin susceptibility with increasing T is confirmed. At sufficient high temperature, the spin susceptibility Chi_s presents an unusual linear temperature dependence Chi_s ~ Chi_s0 -Chi_1 T. Moreover, a linear correlation between Chi_1 and Chi_s0 for increasing hole concentration is displayed. A temperature Tchi, independent of hole doping characterizes this scaling. Comparison with other cuprates of the literature(LSCO, Tl-2201 and Bi-2212), over the same overdoped range, shows similarities with above results. These non conventional metal features will be discussed in terms of a singular narrow-band structure.

results with those presented in the literature for other cuprates reveals an universal trends of the susceptibility in the overdoped cuprates.
The compound Bi-2201 is a convenient system for studying the normal state in the overdoped regime. Indeed, in its as grown form (i.e. non substitued), this compound lies naturally in the overdoped range. It has a low critical temperature (T cmax ~ 20K), allowing the study of normal state properties over an extended temperature range. Polycrystalline samples were prepared by the classical solid-state reaction method 14 .
The absolute content of oxygen nonstoichiometry δ of the compound Bi 2 Sr 2 CuO 6+δ have been investigated by thermogravimetric techniques from 300°C to 700°C with oxygen partial pressure P O2 ranging from 10 -4 atm to 1 atm under thermodynamic equilibrium conditions.
We have explored the T-δ phase diagram for oxygen concentration varying from δ=0.09 to 0.18. Since the Bi-2201 compound does not contain CuO chains, we can directly study the influence of the hole doping on the properties of the CuO 2 planes.
Samples were characterized by powder X-ray diffraction revealing that all the peaks can be attributed to a Bi-2201 single phase 15 . The critical temperature is determined by the onset in the Zero Field Cooled (ZFC) susceptibility measurements. The hole concentration in the CuO 2 planes has been estimated by thermoelectric power measurements performed on sintered samples made from the same powder and submitted to the same oxygen treatment 10 . We found that p changes from 0.20 to 0.29 causing a decrease from T c ~16K to T c <1.5K.
Susceptibility measurements in the metallic state were performed using a commercial Squid magnetometer (Cryogenics). Figure 1 shows the temperature dependence between 50 K and 300 K of the normal-state susceptibility under 5T for the various hole concentrations.
As Lee, Klemm and Johnston 16 have shown that the normal state magnetic susceptibility of the superconducting oxides is altered for temperatures below ~ 2T c by the diamagnetism due to superconducting fluctuations, results below 50 K are omitted. A sizable Curie-Weiss contribution (~ 0.5%) which presumably arises from paramagnetic impurities or disorder effects 2 has been substracted from the susceptibility data shown in figure 1. χ(T) in the close-to-optimal doping sample (p ~ 0.20) has moderate temperature dependence with a positive slope in the range of temperature 50 K-200 K which may be a reminiscence of the pseudogap effect. On increasing hole concentration, χ(T) increases with decreasing temperature. The negative slope dχ/dT observed at room temperature (RT) is a universal trend observed in all overdoped cuprates. The susceptibility, corrected from the Curie-Weiss contribution, can be written, in a first approximation : where χ core , χ vv and χ spin are respectively the core diamagnetism, the Van Vleck paramagnetism and the spin terms. Since the Van Vleck paramagnetism and the core diamagnetism are essentially temperature independent (the values of these contributions are listed in the table 1 of Ref.2) the temperature dependence of the susceptibility arises from the spin contribution and can be linearly fitted : The linear temperature dependence χ 1 T is unusual and was first found by Allgeier et al 2 . It does not correspond to the first temperature correction of the susceptibility in T 2 , as observed in a conventional metal.
Parameters χ s0 (Fig. 2a), χ 1 (Fig. 2b) and T c max (insert in Fig. 2b) are reported as a function of p for Bi-2201 (our data) and for LSCO compounds (data from Ref. 11) treated in the same way. In the case of LSCO, Torrance 5 as well as Loram 11 have reported the hole doping dependence of the electronic susceptibility for the entire generic critical temperature carrier density phase diagram and have shown that there is no significant change at T cmax . The present work is focused on the " overdoped regime" ie p>0. 16, and the hole doping dependence of the two contributions to the spin susceptibility are shown separately.
The first thing to note is that χ s0 as well as χ 1 of both compounds have a similar behavior as a function of p. At p~0.16, T c is maximum and χ 1 is nearly 0 (as shown above in Fig.1, χ is nearly temperature independent at optimal doping).
For the Bi-2201 compound, χ s0 and χ 1 increase drastically for all hole concentration whereas in the case of LSCO, χ s0 and χ 1 reach a plateau at p~0.22 which is extended until p~0.32; the middle of the plateau corresponds to the characteristic hole doping p~0.27. At p~0.32, χ s0 and χ 1 begin to decrease; χ 1 falls to 0 at p~0.45 which means that the electronic susceptibility recovers a classical Fermi-liquid behavior, independent of the temperature only well above the vanishing of the superconductivity. . Figure 4 shows an apparent correlation between T χ and T c max . T χ increases with increasing maximal critical temperature. On the other hand, the value of T χ seems not to depend of the number of CuO 2 planes in a unit cell. Indeed, the value of T χ obtained for Tl-2201 is more than twice as high that the values obtained for Bi-2201 and LSCO compounds containing, as well as Tl-2201, one CuO 2 plane in a unit cell.
χ s reflects the density of states averaged over an energy range ~ (E F ± 2k B T). Thus the behavior of χ s as a function of hole doping (Fig.2) should reflect the presence of a peak in the energy dependence of the DOS. Such a deduction is in good agreement with ARPES measurements on HTSC that have allowed to identify the presence of saddle points centered at k= (π, 0) and (0, π) in the band structure which give rise to van  On the other hand, in LSCO, it has been unambiguously observed that a band of flat dispersion at ( π, 0) moves from below E F for p<0.2 to above E F for p>0.2, so that the topological center of the FS is turned over from (π,π) to (0,0) and the hole-like FS becomes electron-like 23,24 . This change of character of the FS gives rise to a decrease of the susceptibility (as well as to a decrease of the electronic specific heat 11,13 ), however, not as expected, at the characteristic hole doping p~0.2 corresponding at the point where the VHS and the Fermi level coincides, but for p>0.3. Indeed, at p~0.2, χ s reachs a plateau extended from 0.2<p<0.3. This plateau might results from the three-dimensionnal character of LSCO over the whole temperature range in the overdoped regime as displayed by anisotropic transport measurements 25 . Moreover, it should be noticed that this change of topology of FS at p~0.2 is accompanied of an orthorombic to tetragonal structural phase transition (SPT) 26 which may lead to other complicated effects.
It therefore seems on one hand, that the behavior of χ s as a function of hole doping, is strongly related to the topology of the Fermi Surface. On the other hand, we have shown that the change of the topology of FS appears well above p(T cmax ) in the case of LSCO and certainly at more higher doping for Bi-2201. This result is surprising as it is in contradiction with several theoritical predictions which indicate that the maximum of T c corresponds to a maximum in the DOS 27,28 .
In a metal with a constant density of states near the Fermi level, the electronic susceptibility χ s is temperature independent in contradiction with observations; we have shown above a linear decreasing of χ s with increasing temperature in the overdoped cuprates.
This unusual linear temperature dependence has also been provided by a NMR study 7  plane. In this context, they found that in the overdoped regime p<0.2, and at sufficient high temperature, χ s increases with decreasing temperature (Fig.1 of the ref. 29), in good agreement with our experimental observations. However, in this range of temperature, for which χ s increases with decreasing T, the curves have been calculated with a law in ln(1/T) (resulting from the VHS logarithmic DOS) which can not be used to fit our experimental susceptibility curves. This suggests that the singularity in the DOS might be of an another type. The difference could be ascribed to many-body effects, such as quasiparticle decay which, morover, are modified in the vicinity of a VHS. But, our formula (3) reveals an intriguing scaling in which doping and temperature dependences are well separated, and that whatever explanation should account for.
In conclusion, the present study features that in the overdoped regime, the spin susceptibility as a function of doping p and temperature T shows a departure from the conventional FL which can be interpreted by the presence of a growing peak near E F in the DOS, in good agreement with the ARPES observations. We have also shown that the maximum of this peak is not located at p(T cmax ) but seems to be related to the change of the topology of the Fermi surface.A VHS in a rigid band model does not allow to fit our experimental curves. More complicated effects such as the coulomb interaction or the lifetime of the quasi-particles should certainly be taken in account. It is important to note that we have defined in numerous overdoped systems a characteristic temperature independent of the hole concentration, that might be correlated to T cmax .