Electronic anisotropy in single-crystal La2CuO

We have measured resistivity rho components both parallel and perpendicular to the Cu-O planes in single-crystalline La/sub 2/CuO/sub 4/. Substantial anisotropy, reaching values as large as 10/sup 3/, is observed in the resistivity. The temperature dependence of rho, together with Hall effect and thermoelectric power measurements, suggests hopping conduction between localized states at low temperatures, with diffusive transport at higher temperatures. These results are in contradistinction to previous reports.

S-W. Cheong, Z. Fisk, R. S. Kwok, J. P. Remeika, e J. D. Thompson, and G. Grunert Los A/amos Nations LoboI utory, Los A/amos, N~Mexico 87545 (Received 30 November 198?) %'e have measured resistivity p components both paraBel and perpendicular to the Cu-0 planes in single-crystalline LaqCuG~Substantial anisotropy, reaching values as large as 10, is observed in the resistivity. The temperature dependence of p, together with Hall efFect and thermoelectric power measurements, suggests hopping conduction bebveen locahzed states at low temperatures, with difFusive transport at higher temperatures. These results are in contradistinction to previous reports.
The crystal structure of the compound LasCuOs, which consists of layers of Cu& and La-O planes, suggests that crystallographic anisotropy could play an important role in determining the physical properties of this material' and related superconducting compounds in which divalent atoms are substituted for La. Indeed" the magnetic susceptibihty of LaqCuO j has been found t to vary by a factor of 3 depending upon the magnetic field direction with respect to the planar structure. However, recent measurementsl of the electrical resistivity surprisingly showed little evidence for amsotropic transport. The temperature dependence of the resistivity found in that study follows a lnp~T '/4 variation between roughly 300-10 K. Such behavior is characteristic of conduction by variable-range hopping.
In this Rapid Communication, we report electrical resistivity components of single crystalline La2CuO& both parallel and perpendicular to the Cu-0 planes. Contrary to earlier reports, we find that the resistivity is highly anisotropic and that the temperature dependence is not that of simple, unmrrelated variable-range hopping and also not that expecteds of a resonating-valence-bond state which has been suggesteds as a mechanism for superconductivity in La2Cu04-based materials.   Table I for one specimen. Several crystals from two diFerent batches were measured and values of pt and p& agreed with those given in Table I within a factor of 2. To check for possible artifacts introduced by the analysis procedure, the resistivity parallel to the Cu-0 planes was measured directly using the lead configuration shown in Fig. 1(b). For highly anisotropic conduction, current and voltage contacts ideally  (Rg) and perpendicular (R~) to the Cu-0 planes with the contact configuration shown in Fig. 1(a).
should extend around the perimeter of the sample; however, because of the small sample dimensions, this configuration could not be achieved. In spite of this experimental difliculty, resistivity values obtained using the configuration in Fig. 1(b) are in reassuringly good agreement with those determined by the Montgomery method (see Table I for a comparison). %'e point out the importance of a proper analysis of the measurements and the distinction between resistance and resistivity in a highly anisotropic sample. For example, Rt(300)/Rt (77)~31 but pt(300)/pt(77)~1 . 6; further, there is a peak in R & at low temperatures but no peak in p&. The Hall efl'ect was measured using the contact configuration shown in Fig. 1 where e is the conductivity and vp is the Fermi velocity, we estimate the room-temperature mean free path I to be 6.3 A, a value comparable to the lattice constant ao. Perpendicular to the Cu-0 planes the mean free path is ap-have not been obtained because of large magnetoresistance and heating problems. However, at liquid-helium temperatures, we could estimate an upper limit for the Hall coefllcient RH & 10 0 cm/G.
In Fig. 4 we show the thermoelectric power S of Efros has argued that Coulomb correlations modify the exponent to c T for 3D and 2D variable range hopping.
The temperature dependence of the thermoelectric power (Fig. 4, inset) further supports this interpretation. In the case of variable range hoppin " the thermoelectric power is predicted' to vary as S«T, as observed below 40 K.
Therefore, the temperature variation of ps can be understood as arising from strongly correlated variable range hopping at low temperatures with a gradual transition to nearest-neighbor hopping and eventually to diffusive transport as the temperature is raised. One expects a progressive dimensional crossover as the average hopping distance (R) decreases with increasing temperatures. At low temperatures, where (R) is significantly larger than the lattice constants both in the Cu-0 plane and perpendicular to the plane, the anisotropy is expected to be small; while at higher temperatures, where (R) approaches the nearest-neighbor distance, the anisotropic crystal struc-proximately two orders of magnitude smaller than ao at room temperature if we assume the same number of carriers in this direction. The short mean free path, small carrier concentration, and large room-temperature thermoelectric power together suggest that the parallel resistivity show'n in Fig. 3 is not due to band (i.e. , metaBic) conduction at high temperatures with a gradual crossover to semiconducting behavior at lower temperatures but more likely represents diffusive conduction at high temperatures and hopping between localized states at lower temperatures. The Einstein relation FIG. 6. The ratio of perpendicular to parallel resistivity in La2Cuog as a function of temperature. Note that near 60 K pĩ s over 1000 times larger than pl[, but as T~0 the anisotropy approaches a small value. ture plays a significant role and the hopping probability in the plane and perpendicular to the plane are different.
This behavior is evident from the temperature dependence of the anisotropy ps/p~d isplayed in Fig. 6. The anisotropy is small in the variable range hopping (lowtemperature) regime, approaches a maximum at T =60 K, and then decreases slowly with increasing temperature. The broad minimum in pt represents a smooth crossover from nearest-neighbor hopping to diffusive transport at temperatures kqT comparable to the average energy difference between the nearest-neighbor energy levels.
Finally we discuss the results of Birgeneau et al~who find lnp«(1/T) '/ and a small anisotropy in a La2Cu04 crystal prepared from a L4B20q fiux. Such an observation could arise from a relatively large Li impurity concentration or from a significantly different oxygen content in their crystals. Although the authors of Ref. 2 do not state explicitly the geometry of their lead configuration, we emphasize that careful attention to this matter and to a proper analysis of the measurement is essential. For example, the resistunee parallel to the Cu-0 planes (Fig. 2) at low temperatures behaves as lnRN«(I/T) '/ .
In conclusion, we find that electrical conduction in La2CuOq is strongly anisotropic, with the resistivity in the Cu-0 planes orders-of-magnitude smaller than that perpendicular to the Cu-0 planes. Hall effect and thermoelectric power measurements suggest a small concentration of holelike carriers in the Cu-0 plane. We interpret the temperature dependence of pt as a gradual crossover from variable range to nearest-neighbor hopping to diffusive transport as the temperature increases. Thermoelectric power data on the same specimens corroborate this interpretation.
Work at Los Alamos was performed under the auspices of the U.S. Department of Energy. Research at the University of California at Los Anglees was supported in part by National Science Foundation Grant No. DMR-86-02034.