J. MATER. CHEM., 1991, 1(4), 597-610 La,- ,Sr,CuO,-,: Structural, Magnetic and Transport Measurements on Antiferrornagnets, Insulators and Superconductors Matthew J. Rosseinsky,*."#t Kosmas Prassides*Tb and Peter Day" a Inorganic Chemistry Laboratory, Oxford University, Oxford OX1 3QR, UK School of Chemistry and Molecular Sciences, University of Sussex, Brighton BN 1 9QJ, UK lnstitut Laue Langevin, 38042 Grenoble, France The structural, magnetic and conducting properties of the La2-$rxCu0,-b system (01 ~50.13,0.01 16 10.04) are examined as functions of temperature, and combined with assignment of the formal Cu oxidation state. High-resolution powder neutron structural results confirm that the correct space group is Abma, ruling out charge-density wave behaviour as well as other Fermi-surface instability mechanisms, as being responsible for the tetragonal-to-orthorhombic phase transition.The reduced magnitude and eventual disappearance of the orthorhombic distortion as the formal Cu oxidation state increases is well described by the better matching of the (La,Sr)-0 and Cu-0 bond distances in the two layers, (Ln202) and (CuO,), resulting in the tolerance factor increasing into the stability range of the K,NiF, structure. The structural data reveal that there is a smooth variation of all structural parameters as the formal Cu oxidation state increases, except in the bond-length ratio (dax-deq)/(dax+deq),where d,, and deqare the axial and equatorial Cu-0 bond distances of the severely elongated CuO, octahedra. This ratio peaks at the formal Cu oxidation state nearest to +2 in our series (i.e.+2.01) to a value of 0.1207(3), decreasing at both higher and lower oxidation states. An electronic Jahn-Teller mechanism is found superior to a superexchange mechanism in explaining the orbital ordering, indicating that the holes formed on Sr2+ doping have c*character. Analysis of the magnetic Bragg scattering resulting from antiferromagnetic ordering of the copper spins leads to the evaluation of the staggered Cu moment which is reduced on doping and disappears at a formal Cu oxidation state of between +2.01 and +2.04. The data support localised models for the Cu spin system and provide no evidence for spin-density wave behaviour. Analysis of resistivity data at low temperatures shows the occurrence of variable-range hopping even after the long-range magnetic order has disappeared, demonstrating that the electronic states at the Fermi level are localised.Doping by oxygen vacancies and/or Sr2+ cations leads to the introduction of impurity states into the Mott-Hubbard gap. Each carrier extends over two or three copper sites, with the localisation length < increasing to beyond the mean interdopant separation on approaching the metal-insulator transition. As the temperature increases, there is a crossover to a transport mechanism based on excitation to the mobility edge in the overlapping upper-Hubbard impurity and valence bands with the metal-insulator transition being of the Anderson type. Keywords: Lanthanum-strontium-copper-oxygen la tor transition 1.Introduction Although numerous binary and ternary transition and B-subgroup metal oxides are metallic conductors, very few are' suaerconductors. Mixed valency' seems to be a prerequi- site for &perconductivity in these systems, e.g. in the spinel2 Lil +xTi2-x04 and the pero~skites~.~ BaBi, -,Pb,03 and Ba, -,K,Bi03; this may be because strong electron-phonon coupling is thereby asvured, despite t& relatively low density of states at the Fermi energy. However, traditional ideas about superconducting ceramics have changed dramatically with the discovery of superconducting oxides based on ternary cup rate^;^ these phases have proved to be immensely versatile, leading to a whole series of structurally distinct families of superconducting oxides with T, as high as 126 K6 However, despite the large progress made in raising the T, in this class of materials, no clear theoretical explanation of the phenom- enon of superconductivity in these and related systems has yet emerged.A common structural feature in the copper oxide ceramics has been the presence of layers of corner-sharing square Cu04 units. These CuO, layers are present in both hole- and electron-doped superconductors. For example, in the 1-Present address: AT&T Bell Laboratories, Murray Hill, NJ 07967, USA. system; Superconductivity; Antiferromagnetism; Metal-insu- La, -$~,CUO,-~ series (O/T phases), they form part of the strongly elongated octahedral CuO, units; in the Nd2-,Ce,CuO, -series (T' phase^),^ Cu has a square-planar co-ordination, while in the Nd, -,-,Ce,Sr,CuO, -series (T* phases),8 the CuO, layers are formed by corner-sharing square-pyramidal Cu05 units.The La, -,Sr,CuO, series of compounds have proved important prototypes to use as a test bed for evaluation of the mechanism of superconductivity in all the 'high-T,' materials. They are structurally simple; their stucture is based on that of K2NiF4 and there is only one Cu site per unit cell. One can also systematically vary the formal Cu oxidation state by simple chemical doping since the La: M" ratio controls the filling of the conduction band. Furthermore, simple variation of the dopant cation M does not have a monotonic influence on the magnitude of T, with changing ionic radius (for x =0.15, T, is as high as 42 K for Sr, 36 K for Ba, and 26 K for Ca).Finally, the existence of the parent compound in this series, L~,CUO~-~, with its own unusual magnetic behaviourg introduces the competition between magnetism and superconductivity in any model for the 'high- T,' compounds. The importance of the question of how lattice distortions and their temperature and composition evolution are related to the transition from insulating to metallic to supercon- ducting behaviour was immediately recognised. lo Initial 598 suggestions that charge-density wave onset in orthorhombic LazCu04-d is suppressed by IIA cation doping to give a tetragonal superconducting phase'', l2 were disproved by early powder neutron diffraction studies," and showed the import- ance of using high-resolution powder neutron diffraction to accurately determine the crystal structure.Similar arguments apply to the accurate knowledge of the magnetic structure since various model^'^-'^ emphasize the role of strong elec- tronic correlations, prompted by the high TN (ca. 250 K) of La,Cu04. For example, it was originally suggested" that the antiferromagnetic transition is a spin-density wave instability of the square two-dimensional Fermi surface at x =0, being rapidly suppressed on doping and giving a superconducting ground state. Furthermore, there has been some ambiguity in the literature16 about the true orthorhombic space group, adopted by the members of this series of oxides as a function of temperature and composition; besides Crn~a,'~*'~-'~ the space groups Pccn2' and Crnrnrn" have also been proposed on the basis of single-crystal X-ray diffraction and low-resolution powder neutron work.A possible monoclinic dis- tortion from orthorhombic symmetry has also been pro- Finally, for Ba2+ doping levels in the vicinity of x =0.12, a phase transition to a low temperature tetragonal phase (Cmca+P4,/ncrn) occurs.z4 The existence of the low- temperature tetragonal phase has a detrimental effect on the superconducting properties of these materials, strongly affect- ing the transport proper tie^.,^ In this paper, we report a systematic examination of the structural, magnetic and electron transport behaviour in the La, -,Sr,CuO, -model system for samples of well defined formal copper oxidation state in the vicinity of the metal- insulator transition. We have used four-probe conductivity measurements and high-resolution powder neutron diffraction together with careful analytical measurements to investigate such behaviour across the insulator-to-metal-to-superconduc-tor transition which occurs as a function of x and 6 in this system, with T, reaching a maximum of 42 K at x=O.15 and 6 =o.26 2.Experimental In order to prepare samples with highly homogeneous dopant distributions, the solution-based citrate sol-gel technique was empl~yed.'~,~~Samples (20 g) of Laz -,Sr,Cu04 -(x =0,O.O 1, 0.03 and 0.06) were prepared in this way; firing temperatures of 650 (2 h) and 950 "C (48 h, one intermediate regrind) were used. The La1.87Sro.13Cu04-d sample used in this work was prepared by the carbonate co-precipitation technique." Powder X-ray diffraction confirmed that the samples were monophasic.Elemental analysis of Sr and Cu was performed by atomic absorption spectrometry. Sample homogeneity at the microscopic level was confirmed by energy-dispersive X-ray analysis on 15 crystallites of each sample in a JEOL 2000 FX electron microscope. Data to determine the La :Cu ratio were collected with the beam incident on the edges of the thinnest ~rystallites.,~ Oxygen concentration was evalu- ated by thermogravimetric reduction of 100 mg of the sample at 950°C in flowing 95%Ar-5%H2 on a Stanton Redcroft STA 785 thermobalance.The sample temperature was raised to 950 "Cat 10 "C min-' in flowing dry Ar (with no observable weight loss, except for a small amount of moisture at 100 "C), maintained at 950 "C for 30 min, followed by introduction of the Ar-H, mixture. Reduction proceeded to completion within 20 min (the flow of reductant was maintained until no further weight loss was observed for 30 min). Oxygen concen- J. MATER. CHEM., 1991, VOL. 1 tration was evaluated according to the reaction scheme: La, -xSr,Cu04-s(s)+ (1 -x/2)La,03(s) +xSrO(s)+Cu(s)+(1 -6)H20(g) The identity of the reaction products was confirmed by powder X-ray diffraction on samples cooled in the Ar flow.Measurements were repeated twice with consistent results. The copper oxidation state in was also deter- mined independently by iodometric titration using the double- titration method of Nazzal et aL3' Electrical conductivity measurements were performed between 300 and 4.2 K using the four-probe technique in an Oxford Instruments CF200 cryostat. Silver paint was used to make contact onto samples of dimensions 2mm x2mmx4mm cut from the sintered pellets with a diamond saw. Contact resistances were between 7 and 15 Q. The ratio of nested :unnested resistances was greater than 100:1. A.c. mutual inductance measurements show that the x =0.13 sample is superconducting with an onset temperature of 36 K and a transition width (10-90Y0) of 4 K.Powder neutron diffraction profiles of samples with x =0, 0.01, 0.03 and 0.06 were measured at 4.2 K on the D2b high- resolution powder diffractometer at the Institut Laue Lange- vin, Grenoble. The instrument was operated in its high- resolution mode at a mean neutron wavelength of 1.5942A. A profile of L~,CUO,-~ was also recorded at 300 K. The samples were mounted in vanadium cans placed in an ILL 'orange' cryostat. Diffraction data were collected in steps (28) of 0.025'. Diffraction profiles of the La1.87Sro.13Cu04-6 sample were recorded on the high-resolution powder diffractometer (HRPD) at the ISIS pulsed neutron source, Rutherford Appleton Laboratory, with the sample at the 1 m position over a range of temperatures.3. Results 3.1 Chemical Stoichiometry The analysis for Sr and Cu by atomic absorption spectrometry indicates that all the samples prepared by the citrate route have Sr concentrations close to those of the precursor prep- arations. In contrast, the sample prepared by the pH-adjusted carbonate route" had a slight Sr deficiency compared to the starting composition, i.e. La1.87Sr0,13C~04-dinstead of Lal~8sSro.15Cu04-s.The results of the oxygen concentration determination by thermogravimetric analysis (TG) reduction in flowing 95%Ar-5%Hz are shown in Table 1. We also note that the iodometric titration of L~,CUO,_~ gives a value of +1.90 for the formal oxidation state of Cu, in good agreement with the TG results. Furthermore, the electron-microscopy results show that homogeneous samples are prepared with no detectable vari- ation of La :Cu ratios, and hence, no consequent segregation.In all but the x=O.O6 sample, the Srz+ concentration was below the detectability limit. The samples were shown explicitly to correspond to the desired composition to within one standard deviation. Using calibration constants Table 1 Thermogravimetric analysis results and deduced stoichio- metries in the La, -,Sr,Cu04-b samples studied 6 deduced composition Cu oxidation state 0.04(1) La2CuO3.9, +1.92 0.04(1) .99sr0.01cu03.96 +1.93 0.01(1) La1 .97sr0.03cu0j.99 +2.01 0.01(1) La1 .9&0.06CU03 .99 +2.04 O.Ol(1) La, .87sr0.13cu03.99 +2.11 J. MATER. CHEM., 1991, VOL. 1 599 K(La-La/Cu-Ka)=0.94 and K(Sr-Kcr/Cu-Ka)= 1.61,,' rl;metal-insulator)which decreases with increasing x. The activa- the energy-dispersive X-ray analysis results led to compo- tion energy E, also decreases smoothly.The validity of more sitions .99(3)cu04 -6, La1.~9(4)~r0.01~u~4-complex alternatives to the simple Arrhenius model was also S, Lal.98(3)sr0.03cu04 -8 and .95(6)Sr0.05(2)CU04-S for the investigated. The anti-adiabatic small-polaron model3, samples with intended Sr2+ dopant levels of x=O, 0.01, 0.03 proved the most satisfactory, except for the x=O.O3 material and 0.06, respectively. The small error limits reflect the where a totally satisfactory fit could not be obtained. Inclusion precision of the measurements rather than the accuracy of of the temperature-dependent polaron mobility did remove the energy-dispersive X-ray analysis which is ca.10%. We the change of sign in the temperature dependence.7 The note that the largest spread in composition is shown by the parameters extracted from both the Arrhenius and anti- x=O.O6 sample. It will be shown later that this sample is in adiabatic small polaron models of the resistivity are collected the region of the phase diagram close to the metal-insulator in Table 2. transition. It is a feature of materials close to such transitions Below ca. 70 K, the Arrhenius plots developed marked that they are susceptible to phase separation as the material curvature. In view of the three-dimensional variable-range becomes unstable close to the transition.The reduced micro- hopping observed in La, -.LiXCuO4-pellets and single scopic homogeneity of this sample then may reflect this crystals,34 a temperature dependence of the resistivity of the tendency. Finally, we find no evidence for La non-stoichi- form ometry, although it should be noted that La-deficient phases exist owing to the possibility of forming intergrowths of P =Po(T/To)"2 exp C(TO/T)"I (2) LaCuO, perovskite layers3, was assumed35 at low temperatures. Owing to the limited temperature range over which variable range hopping is 3.2 Conductivity found, it is difficult to evaluate the exponent v unambiguously. Two independent fitting techniques were employed: (i) the The temperature dependence of the resistivity of gradient of a plot of log [In (pT-'12)]versus T was evaluated La,-xSrxCuO,-S samples with x=O, 0.01, 0.03 and 0.06 is by least-squares fitting; (ii) the exponent v was increased from shown in Fig.1. There is an upturn in the resistivity that 0.16 to 0.60 in increments of 0.01 and a least-squares fit to a moves to lower temperatures with increasing dopant level x. plot of In p versus T-' was carried out for every value of v; The magnitude of the resistivity also decreases. Assuming an the quality of the fit was evaluated by the magnitude of the Arrhenius behaviour appropriate for broad-band semi-conductors, a plot of the logarithm of resistivity against t Supplementary material available (SUP 56834, 2 pages); details T-' shows that the slope changes sign at a temperature from Editorial Office.'\,0 , I '?., 3 La2Cu03.96 -1 Q CJ) ............-..--2 ......................"1 160 200 TIK Fig. 1 Temperature dependence of the resistivity for samples L~,-,S~,CUO,-~ with x=O, 0.01, 0.03 and 0.06 Table 2 Parameters extracted from the Arrhenius and small polaron fits to the conductivity data of the La2-,Sr,Cu04-d samples studied composition E,"/meV a0"/Q-' cm-' Eab/meV tpdbleV La2cu03.96 10 40 25 0.01 La 1.9gSr0 .01 3.96 5 35 18 0.01 La1.97Sr0.03Cu03.99 1 28 13 0.03 La1.94Sr0.06Cu03.99 0.6 300 I1 0.03 ~~~~~ ~~~~~~~~~~~~~~~~ ~ ~~~~~ ~ a Arrhenius model: Q =o0exp (-E,/kBT); Anti-adiabatic small polaron model:33 Q =(n~1'2e2u2t~,)/(2hk~~2E~~2T3/2)exp (-E,/kBT). discrepancy index p, given by The dimensionality of the hopping process was then evaluated from the dependence of variable-range hopping (VRH) in d dimension^^^^^^ on the dimension d, using the expression: pccexp (-1/P+') (4) Thus it was found that LazCuO3.,, shows the presence of a Coulomb gap in the density of states,37 whereas the doped materials showed two- or three-dimensional VRH behaviour.Table 3 summarizes the preferred exponents v on the basis of the above tests and the corresponding variable-range hopping mechanism. 3.3 Powder Neutron Diffraction 3.3.1 La2-xSr,Cu04-a; x=O-0.06 The aims of this part of the study were to evaluate, in detail, the structural evolution in the La2-,Sr,Cu04-, series as the formal Cu oxidation increases and to address the question of itinerant uersus localised electron behaviour by investigating the effect of cation doping on the periodicity of the antiferro- magnetic order.Long scan times of up to 18 h were used in an effort to measure the extremely weak magnetic scattering from the S =4Cu2+ ions above the background. As a conse- quence, the much more intense nuclear scattering was recorded with excellent counting statistics. The raw data were merged and, after background subtrac- ti~n,~*profile refinements were performed by using the Rietveld profile method,39 and incorporating a pseudo-Table3 Variable-range hopping fits to the conductivity data of the La, -.Sr,CuO, -samples studied composition .96 La1.99Sr0.01 3.96 .Wsr0.03cu03.99 La 1.94Sr0 .06cu03 .99 2D =two-dimensional; 3D V mechanism" 1/2 Shklov~kii-Efros~~ 113, 1/4 1/4 1/4 2D, 3D 3D 3D =three-dimensional. J.MATER. CHEM., 1991, VOL. 1 Voigt function peak shape des~ription.~' The starting model for all the refinements was the 22K structure" of La1.87Sr0.13C~03.99in space group Abma. The refinements were completed with anisotropic temperature factors on the (La/Sr) and the oxygen sites. Oxygen deficiency was handled by constraining the total oxygen content to be that given by the chemical analysis and allowing refinement to determine the best oxygen distribution over axial and equatorial sites. The observed, calculated and difference profiles for La1~99Sro~olCu03,96at 4.2 K are shown in Fig. 2.The pos- itional parameters from the refinements are given in Table4 with the bond lengths and angles for the copper and La/Sr sites in Tables 5 and 6, respectively. Initial inspection of the bond lengths resulting from the x =0.03 refinement revealed a Cu-Oo,, bond length of 2.422(1)A which was unexpectedly long in comparison with the other compounds. To ensure that the refinement had not converged to a false minimum, the z coordinate of the axial oxygen was initially started from several different positions. The refinements always converged to the same point. Refinement of the profiles was also carried out in the Cmmm and Pccn orthorhombic subgroups of the tetragonal Z4/mmrn space group which describes the K2NiF4 structure.These were also proposed to account for the structures of this series of compounds20,21 and describe different possible structural distortions of the square-planar layer of corner-sharing CuO, octahedra in the parent K2NiF4structure. The Cmmm space group describes a charge-density wave with a periodic expan- sion-contraction distortion of the CuO, units with a modu- lation wavevector 4CDw=(OOc*). In Pccn there is a rigid tilt of the Cu06 octahedra about the [loo] direction of the 14/mmm cell, i.e. the Oe,-Cu-Oe, bond direction. The Cu atoms are also located at a centre of symmetry and are surrounded by three crystallographically independent 0 atoms. This would result in the existence of two unequal Cu-Oe, bonds on the basal plane with corresponding unequal transfer integrals.Refinement of the profiles using the Cmmm space group and initial parameters from ref. 21 gave clearly inferior results to the other space groups which have only one Cu site; for example, full refinement of the low-temperature profile of La2Cu03.,, led to a weighted-profile R factor R,, =0.226. As a result, the Cmmm space group was discounted. It was 6000 5000 4000 (/) 3000 c C s 2000 1000 0 I -1000 -2000 11 IIIIIIIIIIIIIIIIII~IIIIII IIIIII~III~IIH~II I I 1111 ni IIIIIII IIIIIII ~IIIII~III~IIIIIIIIII~I~IIIIIII IIIIIIIII I 11 h, 4 I I I I 77 1 I I I 1 T-Fig. 2 Observed (points), calculated (full curve), and difference profiles for La,~9,Sro~06Cu03~9, at 4.2 K J. MATER.CHEM., 1991, VOL. 1 601 Table 4 Final parameters derived from the Rietveld refinements of La2 -,ST,CUO~-~ (space group Abma)" X 0.0 0.0 0.01 0.03 0.06 T/K 300 4.2 4.2 4.2 4.2LaiSr X 0.0069(2) 0.0088(2) 0.0086(2) 0.0077(2) 0.0076( 2) z 0.36 145(6) 0.36 166(6) 0.36 I 68(5) 0.361 27(6) 0.36103(6)0.79( 3) 0.39(2) 0.44(2) 0.42(2) 0.45(2)0.72(3) 0.25(2) 0.24(2) 0.26(2) 0.31(2)0.58(2) 0.23(2) 0.1 8( 2) 0.22(2) 0.25(2)0.14(4) 0.03(3) 0.03(3) -0.03(3) -0.06(3)0.63(2) 0.30(2) 0.33(2) 0.31(2) 0.33(2)-0.330(3 -0.040l(2) -0.0393(2) -0.0379(2) -0.0346(2)0.1837( 1 0.18367(9) 0.18341(9) 0.18365(9) 0.1 8 300( 9 1.42(6) 0.72(5) 0.68(4) 0.63(4) 0.89(4)1.89(5) 0.99(4) 0.90(4) 0.92(4) 0.83(3)0.51(4) 0.32(4) 0.23(3) 0.22(4) 0.22(3) -0.22(6) -0.33(4) -0.28(4) -0.23(4) -0.18(5)7.94(2) 7.98(2) 7.97(2) 8.O 1 (2) 7.98(2)0.0076( 0.0083( 1) 0.0082( 1) 0.0076(1) 0.0068(1)0.62(4) 0.50(3) 0.44(2) OSO(4) 0.63( 3) 0.52(3) 0.37(3) 0.36(3) 0.46(3) 0.51(3)1.17(6) 0.60(5) 0.50(2) 0.43(5) 0.4 1 (4) 0.23(3) O.OO(2) 0.05(3) O.Ol(2) -0.02( 3) 7.90(2) 7.86(2) 7.87(2) 7.95(2) 7.98(2)5.40359( 6) 5.4 1622(5) 5.41232(6) 5.40381(6) 5.38992(5) 5.35783(5) 5.33438(4) 5.333 12(5) 5.331Iq5) 5.32823(5) 13.1599(2) 13.1 148(1) 13.1209(1) 13.1325(1) 13.15 12(2) 9.4 9.2 9.5 10.0 9.0 2.9 1.9 1.9 1.9 2.1 3.6 3.1 3.0 3.1 3.0 1.3 0.9 0.9 0.9 1.o " The atoms were refined in the following positions in the unit cell.La/Sr, O(1) in 8f (m):(x, 1/2, z); Cu in 2b (2/m): (0,0,O); O(2) in 8e (2): (1/4, 1/4, 4.The R factors are defined as follows:3994oR,, =[cwiI x(obs)-~(~alc)l~/~w~Y~(obs)]'/~;R:, =[(N -P + C)/cwiY,2(obs)]lj2; Rmod(l)= cII,(obs)-Zi(calc)l/cZi(obs);Re=(N -P + C)/CZ,(obs) with N =number of observables, P =number of parameters and C =number of cons train ts. Table 5 Selected copper-oxygen bond distances and angles in La, -,Sr,CuO, at 4.2 K -Oeq/OX cu -oe,/A Cu-Oax/A cu-o,,-CU/O oeq-cu (dax -deq)/(dax+deq) 0.0 1.9037( 1) 2.4 17( 1) 173.40(9) 88.9( 1) 0.1 188(3) 0.0 1 1.9026( 1) 2.416(1) 173.5(1) 89.0(1) 0.1 I89(3) 0.03 1.9004( 1) 2.422(1) 173.9( 1) 89.1(1) 0.1207(3) 0.06 1.8968(1) 2.413(1) 174.q 1) 89.2(I) 0.1 198(3) 0.13" 1.8859(3) 2.395( 1) 176.6(6) 89.7(I) 0.1 189(3) " Ref. 10 at 22 K. Table 6 Selected La/Sr-0 bond distances in La,-,Sr,CuO,-, at 4.2 K 0.0 2.349(1) 3.032(1) 2.5 15( 1) 2.7379( 3) 2.579(1) 2.680(2) 2.654(1) 0.01 2.353(1) 3.024( 1) 2.5 18( 1) 2.7 364(3) 2.579(1) 2.679(1) 2.653( 1) 0.03 2.346(2) 3.007(I) 2.525(1) 2.7349( 1) 2.585( 1) 2.680(2) 2.653( 1) 0.06 2.353(1) 2.979( 2) 2.534(2) 2.7302( 3) 2.593(I) 2.675( 1) 2.65 I( I) 0.13" 2.3 7 6( 7) 2.87( 1) 2.59(1) 2.72 l(2) 2.60 l(9) 2.65 l(9) 2.642(9) considerably more difficult to distinguish between the Pccn perature factors) of the two independent in-plane oxygen and Abma space groups on the basis of our data.Initial atoms. The quality of the Pccn refinement was also inferior parameters were taken from ref. 20. Pccn gave marginally in terms of the larger estimated standard deviations (up to lower R factors than Abma and the values of the calculated five times larger) found for the positional parameters. Inspec- structure factors were very similar.However, any improve- tion of the observed and calculated Fourier maps (cf. section ment on moving from the Abma to the Pccn space group was 3.3.2) also leads to the conclusion that Abma is the correct rejected as statistically insignificant at the 99.5% confidence space group for the structure of the compounds level on the basis of the Hamilton significance applied La2 -,Sr,CuO, -x =0-0.06 at 4.2 K. This conclusion was to the integrated intensity R factors. Pccn was also rejected also reached in a single-crystal neutron diffraction study on as the correct space group on the basis of very large corre- La2C~O~95Li0.0504,which showed that Abma was correct and lations (> 95%) observed in the variance-covariance matrix explained Pccn on the basis of a twinning law, although between the refinement parameters (z-coordinates and tem- extinction prevented refinement of temperature factors.I6 J.MATER. CHEM., 1991, VOL. 1 The search for magnetic scattering led us to a careful investigation of the low-angle part of the 4.2 K diffraction profiles for extra intensity near the background level. Weak peaks were clearly visible above the background level, while they were absent from the 300 K diffraction profile of La2Cu03.96. Data evaluation was complicated by the occur- rence of weak 1/2 scattering from the (1 10) nuclear peak which overlapped with the magnetic (010) peak (indexed on the Abma unit cell).All other magnetic peaks predicted by the collinear model of Vaknin et aL9 were masked by A/2 scattering or background, and hence no refinement of magnetic structure was possible. Two overlapping Gaussians were fitted to the region of the (OlO), peak in order to determine the variation of peak position and integrated intensity with dopant level x. The (010) peak remained centred at the commensurate (010) position within a 0.1" precision of our data, and its intensity decreased markedly until it was not observed for x=O.O6. In order to evaluate the Cu moment, using I, =CF~molo/sin8 sin 28 (5) we normalised with respect to the structure factor of the weak (040) nuclear reflection and used the antiferromagnetic form factor Aq)=0.835 at q= 1.164A-', measured by Freltoft et ~1.~'mOIOis the multiplicity of the (010) reflection.The moment direction is taken parallel to u with modulation of its direction along b. The magnetic structure factor is given by where p is given by y0SJq) with yo the gyromagnetic ratio of the neutron, Aq) the form factor, S the spin, and (4) the magnetic interaction term given by q =sin a= 1 (ais the angle between the moment direction and the scattering vector). The variation of the Cu moment calculated in this way as a function of Cu formal oxidation state is presented in Fig. 3. 3*3*2La1.87Sr0.13CU03.99 The structural characterisation of this sample has been described before." There is a second-order tetragonal-to- orthorhombic phase transition at 180 K, characterised by co- operative rotation of the Cu06 octahedra about the [llO] direction of the tetragonal Z4/mmm space group.Here we report a re-examination of these data, considering the alterna- tive space group Pccn." As in the previous section, the x2 values were very similar for both the Abma and Pccn structure refinements. The site symmetry of the La/Sr cations is reduced from m to 1 in going from Abma to Pccn, i.e. the cations are moved off the mirror plane. These cations occupy general rn0.0 I I I U 1.90 1.95 2.00 2.05 Cu oxidation state Fig. 3 Average calculated moment per Cu atom as a function of formal Cu oxidation state in La, -xSrxCu04-6 positions in Pccn and their position in the nine-co-ordinate site is not fixed along any crystallographic axis.During Rietveld refinement of the Pccn structural model, the y coordinate of the La/Sr cation oscillated about zero. Reduction of the applied shift by a factor of 0.01 combined with the introduction of a slack constraint on the La,Sr-Cu distance, allowed the refinements to converge but, as in section 3.3.1, the Pccn refinement was judged inferior to that obtained in Abma. In particular, the z coordinates of the two indepen- dent in-plane oxygen atoms differed by an order of magnitude less than their estimated standard deviations, and the e.s.d.s obtained in Pccn were again considerably larger. As the two structures differ in the axis about which the octahedral tilt occurs, inspection of difference Fourier sections at x=O.25 in the (100) plane was undertaken in order to investigate whether there was any evidence for two different oxygen positions. This showed unambiguously the superiority of the Abma refinement, with large differences between Fobs and Fcalc apparent for Pccn (Fig.4).It was therefore concluded that there was insufficient evidence for two distinct oxygen pos- itions to prefer Pccn to its supergroup Abma. 4. Discussion 4.1 Crystal and Electronic Structures The orthorhombic structure of the x<O.O6 and x=O.13 (T<180 K) phases results from alternate rigid tilting of the Cu06 octahedra about the [I lo] direction of the tetragonal unit cell, which becomes the b axis of the enlarged orthorhom- bic unit cell.The two cells are related by a 45" rotation: a0 =(21'2aT + 2E)cos CI (7) bo =(21'2aT-2E) where E is the elastic deformation of the basal plane and CI is the tilt angle about the [l lo] axis. The octahedral tilt can be taken as the primary order parameter of the tetragonal+or- thorhombic transiti01-1,~~ while the elastic shear does not lead to a change in the unit-cell dimensions and behaves like a secondary order parameter. In Fig. 5, we plot the orthorhom- bic distortion (a-b)/(a+b) as a function of formal Cu oxi- dation state at 4.2 K. The occurrence of the tilting transition in La2Cu04 and its suppression at room temperature in superconducting La1.85Sr0.15C~04led to suggestions that the transition" was of a Peierls nature leading to a gap at E~.This was discarded when high-resolution powder neutron diffraction" showed that doping only served to reduce the transition temperature for the tilting transition.In fact, although the vector Q= (1/2)(u*+b*), where u* and b* are reciprocal primitive unit vectors, nests the square two-dimensional Fermi surface, the tilting nature of the distortion cannot open a gap as it does not create two crystallographically inequivalent copper sites. Weak coupling theories were then built on the assumptionu that the van Hove singularity in the two-dimensional density of states of the tight binding square lattice splits upon the T+O transition. If the transition was driven by an instability of the two-dimensional Fermi surface, it was suggested that the orthorhombic distortion would change the Brillouin zone from a square to a rectangle, the two saddle points becoming inequivalent and the van Hove singularity in the density of states would split into two parts, symmetric with respect to half filling.However, this would require two different Cu-0 distances in the CuOz sheets with two different Cu-0 hopping integrals. The distinction between Pccn and Abma is of vital importance in this respect as there are two different Cu-0 distances in the plane in Pccn. We have shown that Pccn is not the correct space group, discounting the possibility J. MATER. CHEM., 1991, VOL. 1 0 ........... ......-* .. ... ...... .........: ................................. .... .... . . .. I. '....,..: ... ..' ...... .. ... .......... 0 :..__. . . ._..... ..': .-.. *.. -0.32 ClOO] -3 0.32 .... 0.32....*.,.V; f...........................: .I ... ... ...........; ;' ........ ..,......... . . ........ . .. -. .....a: ._.. .. ..... .. .... ;... ...................... *.. . .. ..,:. ; .. ........... .__....... rn c .. 0 0 Y ....... ... . .. .....L.. ........:. . ..... .*. ._. . ,..*; : ! ............ ........... ... ...... ..... : ; ........ ...... .. .. ....,. ..1. r -. ..... .. .. ,. ,.,. .. ..... ..;. ....t : ..:. ._ .......... ..-0.32 .. ...:.. ..-18 lii Fig. 4 Observed (a),(c),and calculated (b),(d),Fourier maps at x =0.25 in the (1 10) plane of (a) and (b)the Abma and (c) and (d) Pccn structural models for La,,,,Sr,,,,CuO,,,, of such a Fermi surface instability mechanism. In Aha, the four Cu-0 near-neighbour distances remain equal and very similar in magnitude to the tetragonal phase, and (a,,co), (b,,co) are maintained as mirror planes. The Brillouin zone becomes a truncated rhombus and the Fermi surface for half 0 filling is a rectangle;43although this surface is distorted from square, its four corners are equivalent under the symmetry0 operations of the lattice and the orthorhombic phase, like the tetragonal, has a single van Hove singularity.Electronic energy stabilisation due to the band Jahn-Teller effect observed in the A-15 compounds, moving the Fermi energy away from the van Hove singularity and reducing the density of states at E~,is also not responsible for the T-tO phase transition. Alternatively, the tilting distortion and its variation with 1.90 1.95 2.00 2.05 2.10 2.15 copper oxidation state may be explained by a non-electronicCu oxidation state mechanism, noting that the stability of the layer perovskites Fig. 5 Dependence of the orthorhombic distortion (a-b)/(a+b) on is determined by the matching of the intralayer distances. formal Cu oxidation state Then a tolerance factor4' for an A,B04 system may be 604 defined as t =dAo/21/2d~o (8) where dAOand dBO are the bond lengths in nine- and six-fold co-ordination, respectively.Use of the Shannon-Prewitt ionic radii for La2Cu04 gives t =0.86, indicating that the K2NiF4 structure will be subject to distortion and that pressure will be exerted on the Cu-0 bonds in the basal plane to shorten them below their ionic values.46 Using the method of the tolerance factor is given by t =$A/21/2fiB, where PB and are invariant values associated with nine- and six-co-ordinated A-0 and B-0 bond distances, respectively. The distances are related via fiB+21'2+A= O.996V1l3,where V is the volume of the unit cell. This method gives t =0.83. Thus, purely ionic considerations show that the La-0 distance in the La202 bilayers is too short relative to the in-plane Cu-0 distance for the undistorted structure to be stable. The effect of oxidation by Sr2+ doping is to increase the tolerance factor as the Cu-0,, bond lengths decrease and the (La,Sr) effective ionic radius increases.Thus, we may qualitatively understand the reduced magnitude of the tilting on doping and its eventual disappearance at x =0.248in terms of the tolerance factor increasing into the stability range of the Z4/mmm structure. The orthorhombic distortion due to the tilting produces better matching of the bond lengths in the two layers as buckling of the Cu02 layers leads to Cu-Cu distances below the sum of the two Cu-0 distances (Table 5). This leads to a reduction of the Cu-Cu antibonding interaction by dimin- ishing the overlap integral with the bridging oxygen atom.The (La,Sr) co-ordination polyhedron is in the shape of a square antiprism with one capped face and the (La,Sr) ions displaced off the centre of the antiprism. In the T phase, each ion occupies a site of symmetry C4", with four equidistant, oxygen neighbours in the rock-salt layer, four in the adjacent Cu02 layer and one axial oxygen of another layer. The effect of tilting is to increase the average (La,Sr)-0 distance (Table 6). Very importantly, the (La,Sr)-Oax bond length increases monotonically as the tilt angle increases. In the tetragonal phase, distances in the (La,Sr),O, planes are longer than the (La,Sr) distances to the oxygen atoms of the Cu02 planes; on tilting, however, one of the (La,Sr)-0 bonds in the lanthanide bilayer contracts significantly and its value is taken below the La,Sr distances to 0 atoms belonging to the CuO, planes.This is accompanied by the weakening of one of the (La,Sr)-0 bonds in the (La,Sr),O, layers. The net effect is that the pressure exerted on the basal plane decreases as the tilting angle increases and the bonding within the Cu02 layers is strongly affected by the relative disposition of the lanthanide ions within their co-ordination polyhedron. If we consider the combined effect of Sr2+ doping and tilting on the lanthanide co-ordination, we note that the La-Oax distance should increase smoothly (note the discrepancy at x =0.03)as the formal Cu oxidation state increases, but should decrease as the tilt angle is reduced upon doping.The first effect combined with the larger size of Sr2+ predominates. In general, upon doping the difference between long and short (La,Sr)-0 bonds decreases, tending towards the average value of the tetragonal phase, whereas the average (La,Sr)- 0 bond length decreases smoothly on doping. We now discuss the variation of the shape of the distorted CuO, octahedron with change in valence electron count given in terms of formal oxidation state, deduced from the observed chemical stoichiometry. Table 5 shows that the Cu-0 in-plane bond length contracts smoothly as a function of formal Cu oxidation state, indicating that, upon oxidation, electrons are removed from Cu-0 antibonding orbitals.A similar monotonic increase towards 180" is observed in the Cu- J. MATER. CHEM., 1991, VOL. 1 O,,-Cu angle, decreasing the tilting and producing improved overlap between the x2-y2 orbitals of the Cu atoms via the bridging oxygens. In contrast, variation of the Cu-0 axial bond length with x seems anomalous, with La, .97Sro.03Cu03,99 displaying an unexpectedly long bond. The site symmetry of the metal site for the I4/mmm space group is D4h.The resulting tetragonal crystal-field component is expected to produce some bond-length anisotropy. This is indeed observed, for example, in La2Ni0, (Ni" has a d* configuration and is not a Jahn-Teller ion), where (dax-deq)/ (dax+deq)=0.054 and the (c/a)=3.282.,'~,~As an empirical rule, it is observed that c/a ratios of the order of 3.3 are always found in the absence of Jahn-Teller distortion^.^' The formal Cu oxidation state in the series of compounds La2-xSr,Cu04-d is directly related to the number of anti- bonding electrons per Cu atom. Upon oxidation the contrac- tion of the Cu-0 in-plane bonds is larger than the contraction in the Cu-0 axial bonds, leading to a reduced (dax-deq)/(dax+deq) ratio.Then the anomaly in the Cu-0 axial bond lengths as a function of x can be rationalised by consideration of the Cu oxidation state and the Jahn-Teller effect. A co-operative Jahn-Teller effect in L~,CUO,.~, (and related compounds like LaSrMnO,) results in a large c/a ratio (3.451) compared to the Nil* analogues owing to the ferrodistortive coupling of the Jahn-Teller distortions at the Cu" centres.If we consider the dimensionless quantity (dax-deq)/(dax +deq) to represent the magnitude of the Jahn- Teller distortion (Fig. 6), this is clearly a maximum for a Cu oxidation state of +2.01 and decreases when the oxidation state changes from +2. We may apply the linear Jahn-Teller E-e problem" to the CuO, units in La2-,SrXCuO4-~; this results in the familiar 'Mexican hat'-type adiabatic potential for a two-fold degenerate electronic E term (dZ2, dX2-,,2) inter-acting with the two-fold degenerate vibrations (Qt, QJ. From the observed axial and equatorial bond lengths, we can estimate the radius po of the circle at the bottom of the trough.The depth from the degeneracy point of the two surfaces at p=O [p is the polar coordinate defined by (Q:+Q:)1/2] to the bottom of the trough at po is the measure of the Jahn-Teller stabilisation energy, EIT.As we see from Table 7, the maximum stabilisation energy [E,, = 19.12(5)hvY where v z500 cm-is the frequency of the Jahn-Teller active mode] occurs at x=O.O3, which corresponds to a formal Cu oxidation state of +2.01, with the number of Jahn-Teller active Cu" centres being at a maximum and co-operative ordering of the distortions of the CuO, octahedra occurring through the shared 0 atomss1 in an analogous fashion to three-dimensional perovskites. A mean-field treatment shows na"0.120+mo*121* 0.118! .. ' l . 1.90 1.95 2.00 2.05 2.10 2.15 Cu oxidation state Fig. 6 Dependence of the Jahn-Teller distortion on formal Cu oxi-dation state J. MATER. CHEM., 1991, VOL. I 605 Table 7 Jahn-Teller parameters in La, -xSrxCu04-6 0.0 0.395 l(5) 18.5 1 (5)0.01 0.3952(5) 18.52(4)0.03 0.4015(5) 19.12(5)0.06 0.3974(5) 18.73(5)0.13 0.39 19(5) 18.22(5) “~~=(4/3’”)[(d,,-d,,)/3];E,, =(1/2)pirnv2; rn is the mass of an oxygen atom and hv z 500 cm-* for the Jahn-Teller active mode. the order parameter in co-operative Jahn-Teller transitions is maximised when the number of contributing centres is largest,52i.e. at the oxidation state closest to 11. This implies that oxidation via Sr2+ doping is removing a* rather than n* antibonding electrons, as the a* electrons are responsible for the Jahn-Teller distortion.The possible complication with the above interpretation of the data is that superexchange as well as the conventional Jahn-Teller electron-phonon coupling mechanism can lift the degeneracy of the x2-y2 and z2 orbitals. Khomskii and K~gel~~have shown that antiferromagnetic superexchange favours ferrodistortive orbital ordering; this possibility must therefore be considered in view of the very large anti- ferromagnetic copper-copper superexchange interaction (Jc--cu z1000 K54,55)found in these systems. This mechanism would then allow n*,rather than a*, holes to frustrate the antiferromagnetic superexchange via the strong ferromagnetic potential exchange between the Cu x2-y2 orbitals and 0pn: holes in orthogonal orbitals [Fig.7(a)]. However, the distor- X 2-y PX x 2-y * cu 0 cu (b) tX 2-y x *-y 2PCI tion persists to higher doping levels where no magnetic long- range order is observed, and the maximum in the staggered moment at x=O.O does not correspond to that in the Jahn- Teller distortion. 4.2 Magnetic Ordering Despite the difficulties experienced in the analysis of the magnetic reflections because of their weakness, certain con- clusions may be tentatively arrived at. The ordered staggered moment is reduced on doping and disappears between a Cu oxidation state of +2.01 and +2.04. The absolute value of the moment estimated from our data is in reasonable agree- ment with the 0.48(15)pB found earlier in La2C~03,98,9 Fur-thermore, neutron measurements on single crystals have shown that local moments with correlation lengths inversely proportional to the hole-hole separation persist in the metallic and superconducting La2 -,Sr,Cu04 -The rapid reduction of the moment on doping may be rationalised as follows. Photoelectron spectroscopy and NMR measurements on oxidised samples in both the YB~,CU~O~-~ and the L~,-,S~,CUO~-~ systems imply that the states at cF may have up to 70% oxygen ~haracter.’~ The structural data of the previous section would then suggest that 2pa holes on the oxygen sublattice couple antiferromagnetically to a* holes on both neighbouring Cu2 ions, giving a net ferromagnetic + Cu-Cu interaction that will frustrate the Nee1 state [Fig.7(b)].The Cu-0 superexchange dominates the antifer- romagnetic Cu-Cu superexchange, as it is to second-order in the copper-oxygen transfer integral, and its energy has +-t If ++-Vdd It Fig. 7 Models for the reduction of Cu moment on doping. (a) n* hole producing ferromagnetic S= 3/2 unit and frustrating Cu-Cu antiferromagnetic superexchange; (b)frustration of the Nkel state by 0 r~* holes; (c)destruction of the Niel state by hole hopping within its localisation length; (d)antiferromagnetic next-nearest-neighbour coupling due to available Cu’”level been estimated as ca. 4000 K.'* This contrasts with the much more benign effects of non-magnetic diluents, such as Mg2+, below the percolation threshold (x, =0.59 on a two-dimen- sional square lattice59) on antiferromagnetic order in the prototype two-dimensional antiferromagnetic insulators Rb2MnF4 and Rb2CoF4.60 This model, incorporating the spectroscopic evidence of oxygen 2p character at E~ in the oxidised samples, can qualitatively account for the experimental observations, but in view of the large hole radii (more than twice the Cu-Cu distance, as deduced from the conductivity measurements), there are two other possibilities arising from dominant Cu character at E~,depending on whether hole motion is real or virtual.(i) Hopping of the hole within its localisation length will destroy the time-averaged moments within this radius as the spins are flipped at each passage of the hole through the site with a frequency thopmuch greater than Jt:-cu [Fig.7(c)]. Since ca.4% of holes lead to a 100% reduction in moment, the holes must spread to 25 Cu sites. The localisation length at the metal-insulator transition is ca. 15 A, corresponding to a radius of ca. 4 Cu-Cu bond lengths and containing ca. 40Cu sites. So the large hole radius makes such a model possible irrespective of the relative copper and oxygen contri- butions to the wavefunctions at E~.(ii) The availability of an empty x2-y2 level at low-spin d8 Cu"' states produces an antiferromagnetic next-nearest-neighbour interaction due to virtual hopping of two Cu" spins to the intervening Cu"' site which would frustrate the next-nearest-neighbour ferromag- netic coupling of the Nee1 state in La2Cu03.96 [Fig. 7(d)].This interaction is weaker than both Jcu--cuand Jcu--o but it disrupts a larger number of bonds. It may be estimated as 4t4/~~dUdd=4J~u-cu(t/Vdd)2,with Udd and Gd the intra- and inter-site repulsion parameters, respectively, and t the transfer integral; such long-range interactions could well be important in a system with very strong Cu-Cu coupling. We commented earlier that the (OIO)M magnetic peak does not shift with band filling within the resolution of our data. This observation may be used to test the predictions of itinerant models for the Cu" spin system. In such cases, the spontaneous magnetism in La2Cu04 would result from a spin-density wave produced by perfect nesting; doping would change the band filling and lead to an incommensurate spin- density wave.The incommensurate peak positions may then be generated by using a simple model, based on the nesting properties of a square two-dimensional Fermi surface.I2 Assuming that nesting is retained for small dopant concen- trations, the change in the nesting vector may be calculated from the requirement that the volume enclosed by the Fermi surface is equal to the number of electrons. This leads to the following expression for the dependence of the nesting vector Qon doping level x: Q={[I- x/21(4a), C1-x/21(4a)> (9) Hence if there is incommensurate spin-density wave behaviour, we expect a 0.3"shift from the commensurate position when x=O.O3. The fits indicate that this does not occur, favouring non-itinerant magnetic models.4.3 Conductivity The conductivity data show variable-range hopping (VRH) at low temperatures, indicating that for Cu oxidation states < +2.04, the states at E~ are localised rather than extended. The intrinsic gap for the creation of charged excitations in La2Cu04 is 2.0 f0.1 eV, as determined by photoconductivity experiments;61 carriers introduced by the dopants are lifted into the correlation gap between the CulI/I1' and the Cu*/" couples, to form impurity states. In the reduced samples, these J. MATER. CHEM., 1991, VOL. 1 are associated with oxygen vacancies and are pulled below the conduction band by the reduced ligand-field destabilis- ation of the e, electrons.The activation energy observed in La2Cu03,96 (Table 2) corresponds to the energy required for thermal ionisation of the bound electron into the upper Hubbard band. The x=O.Ol sample is compensated as the Sr2+ dopants empty the upper Hubbard impurity band, resulting in a reduced activation energy. The oxidised samples with formal Cu oxidation state greater than I1 have hole carriers associated with Sr2 dopant sites which are raised + above the lower Hubbard sub-band; compensation in this case occurs through the simultaneous presence of Sr2+ dopants and 0 vacancies. Owing to the limited temperature range over which VRH behaviour is observed, the determination of the exponent v is not totally unambiguous.Nonetheless, La2Cu03.96 can tenta- tively be said to have v = 1/2 due to the existence of a Coulomb gap in the density of states arising from the absence of compensation in the impurity band. The value of the To parameter [eq. (2)] derived from the VRH data allows evalu- ation of the localisation lengths through the expre~sion:~~ To=e2/4n~,~05,where E, is the average relative permittivity of the material, and taken to be z20, yielding 5=4 A. Thus 5 is of the order of the distance (R) between impurity states, given approximately by (Ni,;l3) z17 &where Nimpis the num- ber density of impurity ions), and impurity conduction (trans- port not involving wavefunctions associated with the +unperturbed Cu2 background) must be considered.The localisation length 5 may be further used to estimate the effective mass of the carriers through the expression62 (m*/ rne)=~/Erao,with a. the Bohr radius, yielding (rn*/rne)%2,in good agreement with that determined by measurements of the frequency-dependent relative permitti~ity.~~ This leads to an estimate of the dopant ionisation energy through the relationship Ei=(13.6/e2)(rn*/m,) of 0.06 eV. We have assumed that the carriers are bound to the impurity atoms in hydrogen- like orbits. La, .99Sro.01Cu03.96 shows either two- or three-dimensional VRH behaviour, while La1~97Sro~03Cu03~99and La, .94Sro.06C~03 display three-dimensional VRH behav- .99 iour. To now allows evaluation of the product t3N(&F),where N(E~)is the density of states at the Fermi energy through the relation35 kB TO =4qc/5 N(EF ) (10) with qc a dimensionless constant characteristic of the perco- lation network36 in three dimensions. Similarly, in two dimen- sions we have kBTO= 3/52N(EF) (1 1) However, to make further progress we need to evaluate This is done in two ways: (i) by assuming that the density of states is so large that is pinned and N(+) is constant across the series and equal to the value obtained by band-structure calculations (3 x lo2' states eV-' ~m-~);'~ and (ii) by calculat- ing N(E)within the space of singly occupied impurity states, assuming a two-dimensional tight-binding model for the Hub- bard sub-band in question: N(E)=[4N/z2(8t-E)]K[E/(~~-E)] (12) with K an elliptic integral of the first kind.64 The density of states in mid-band (~~4t) is then given approximately by N(E)=(Nim,/2n2t)In [16t/(~-4t)l (13) The Fermi energy is then evaluated from the condition N(E)dE =N(1-y)/2 J.MATER. CHEM., 1991, VOL. 1 where y is the fractional deviation from half filling the Hubbard sub-band, determined by the level of compensation. Evaluation of eqn. (14) at cF=4t in the limit (1 -u)% ulnu, where u= 1 -(+/4t) gives EF M4t(1-y) allowing estimation of cF and hence N(+) from eqn. (13), as a function of Cu oxidation state. The transfer integral is approximated to that arising from the overlap of two hydro- genic wavefunctions of the form exp (-(R)/l). The variation of localisation lengths, derived in the two approximations, with oxidation state is shown in Fig.8. We may have confidence in the values of the localisation lengths thus derived as the two models yield similar values. It is notable that as becomes greater than the interlayer distance 42, three-dimensional variable-range hopping occurs. The percolation pathway can now be completed within three dimensions rather than two, as the localisation length allows interlayer hops. The oxidation state of +2.04 corresponds to the disappear- ance of ordered magnetic moments in the o* orbitals and is in the vicinity of the transition to the metallic and supercon- ducting phase. It also corresponds to the radius of the impurity wavefunction becoming greater than the average interparticle separation.In this case, 5=2(R) (Table 8) and the uncorre- lated single-particle hopping model will break down; if the carriers are polaronic, they will exclude a carrier from hopping into a region within the localisation length of another. oo derived from the Arrhenius equation (Table2) is also much higher at this oxidation state. The localisation lengths may be used to calculate other parameters of interest associated with the carriers in the insulating region of the phase diagram such as the transfer 30 1J 25 -0 5. 20-0 C0,-05 15-0.-c u).-2 10-0. -e5-0 I'I'I'I0 ' Table 8 Parameters derived from the localisation lengths for the impurity bands in La, -.Sr,CuO, - ~~~~ ~ ~ ~ ~ Sr2+ concentration x 0.00 0.01 0.03 0.06 localisation length r/8, interdopant separation (R)/A effective mass (m*/m,) ionisation energy E,,cU/eV transfer integral t/eV" Hubbard U/eVb t/ u disorder broadening V/eV 4 17 2 0.06 0.07 0.12 0.6 0.07 6 17 1.8 0.05 0.11 0.06 1.8 0.07 14 15 0.9 0.03 0.07 0.03 2.3 0.06 20 12 0.6 0.02 0.05 0.02 2.5 0.08 " t =(3/2Me2/4n~o~,t)Cl +(1/6X(R)/5)fl exp (--(R)/5); !=+((W/O(5/8)(e2/4nq,&,<);V =e2/4n~O~,( where E, is the average relative R)permittivity of the material. integral t, the Hubbard repulsion parameter U and the disorder energy V.65 These are collected in Table 8.We now discuss these in view of the possible impurity transport mechanisms. Polaron formation is generally of importance in narrow band materials and in this case where the carriers are localised, a local lattice distortion is expected.However, in all cases except La2Cu03.96, the localisation lengths are larger than the Cu-Cu distances and the small polaron model is not strictly valid; the polarisation clouds will overlap to reduce the hopping energy significantly (intermediate polaron) or produce large effective mass band transport (large polaron). Two important parameters are the polaronic transfer integral tpoland the Holstein coupling constant g. For small polarons, the transfer integral is given by tpo,=t exp (-E,/hcuo), where E, is the polaron binding energy and oois an optical phonon frequency; using E, =0.2 eV5' and oo=0.075 eV,66 we obtain t,,,=0.01 eV, of the same order as oo with the Holstein coupling constant estimated as 3, much lower than the lower limit for adiabatic behaviour to be valid.67 Hence the anti- adiabatic model is expected to be more appropriate, as found experimentally.Thus although the inclusion of a temperature- dependent mobility term makes the Arrhenius plots mono- tonic and allows an approximate one-function description down to the temperature range at which VRH is important, its interpretation as small polaron hopping is inconsistent with the carrier radii and the activation energies. Thus while we expect localised narrow band carriers to have some polaronic character, there is no quantitative evidence for a hopping energy. In narrow bands with kBTxW, the mobility is expected to have a complex temperature dependen~e.~~ In La2Cu04+ Preyer et aL6*find that the in-plane Hall mobility pHxl cm2 V-' s-' is temperature independent, whereas Che~ng~~et al.prefer a diffusive mobility term pz(eD/kBT) to explain the high-temperature behaviour of Pb-doped La,Cu04. The Arrhenius energies (Table 2), though their exact values depend on the existence or not of a temperature-dependent mobility, may be discussed within the framework of doped, compensated semiconductors. The carrier-dopant ionisation energies Ei in Table 8 are calculated using ~,=20 and hence are upper bounds as the relative permittivity is expected to increase with increasing carrier concentration. The Eivalues are too high to explain the observed activation energies and impurity-band transport competes with valence/conduction band transport.The Hubbard splitting of the impurity band is opposed both by the bandwidth W=2zt and by the spread in site energies, governed by the disorder which becomes more important for heavy carriers. Even though the vaues for t and U (Table 8) are only approximate, it can clearly be seen that t/U increases as the formal oxidation state increases. The disorder potential may then be sufficient to cause the reduced Hubbard gap to disappear. If transport via doubly occupied impurity sites in the upper Hubbard sub-band was operative c2 = U -W would decrease rapidly with concentration, with nobeing only weakly dependent on carrier density.Both these criteria are fulfilled for the low oxidation states (< +2.01) and such a mechanism appears a good candidate for transport in this regime. Hopping between localised states on opposite sides of cF may occur if the disorder potential causes the two sub-bands to overlap. The condition (R) % 5 allows use of the Miller-Abrahams formula for one-phonon nearest-neigh- bour hopping for x=O and 0.01,70 giving EMIA=0.07and 0.02 eV, respectively. Given that overlap occurs between the two Hubbard impurity bands, or the upper Hubbard band with the edge of the conduction or valence bands, Anderson localisation of the states in the band tails will occur, and excitation to the mobility edge at cC (Fig. 9) then competes with near-neighbour hopping: o=ooexp [-(E~-cF)/kBq, Udd cun/cu= cu'/cu* E Impurity band cuu/cu= -2 N (E) Fig.9 Impurity band-structure (a)at low carrier concentrations and (b)close to the metal-insulator transition in La, -xSrxCu04-d where a,(= 0.03e2/ha)is the minimum metallic conductivity, assuming the inelastic scattering length is equal to a, the interdopant spacing, at higher temperatures. Taking a = 15 A gives a. =50 R-' cm-' which is of the correct order of magnitude and would explain the similar values of a, for oxidation states -= +2.04. The mobility edge mechanism can crossover directly to VRH at low temperature without an intermediate lower activation energy regime due to hopping in localised states in the tail of the valence band if N(+) is high, as is the case here.35 Considering the magnitude and variation of the 0, prefactor, excitation to the mobility edge in the upper Hubbard band/valence band at high temperatures with a crossover to VRH between localised states at E~ at low temperatures seems preferable.The Sr2 lower Hubbard band + will be narrow as the Sr2+ dopants bind one charge but the separation of the upper Hubbard band from the valence band will be much reduced as the binding of an extra electron to Sr2+ will be greatly reduced [Fig. lO(a)]. It is therefore J. MATER. CHEM., 1991, VOL. 1 possible that the upper Hubbard band will overlap the edge of the valence band and will merge into it at higher dopant concentrations [Fig.1 O(b)].The metal-insulator transition in the Cu oxidation range +2.04 to +2.05 implies that the Hubbard splitting between the impurity bands disappears in this concentration range, with the transition being of the Anderson type, i.e. non-zero N(E~)with the wavefunctions of the carriers changing from localised to extended as crosses E,. The sharp increase of a. at +2.04 indicates the system is close to delocalisation. 5. Conclusions We have presented structural, magnetic and transport measurements on La, -xSrxCu04-samples of well defined formal Cu oxidation state. The structural evolution in the L~,-,S~,CUO~-~series as the formal Cu oxidation state increases has been investigated. The orthorhombic space group Aha, resulting from alternate rigid tilting of the Cu06 octahedra along the [llO] direction of the tetragonal unit cell, describes the orthorhombic phase throughout the compo- sition and temperature range investigated.No evidence of charge-density wave formation and Fermi surface instabilities is found and there is no splitting of the van Hove singularity in the density of states in the metallic samples. The mechanism of the tetragonal-to-orthorhombic phase transition was rationalised in terms of tolerance-factor arguments, based on the mismatch in size between the lanthanide bilayers and the CuO, sheets; doping by the larger and more basic Sr2 + results in the tolerance factor increasing towards the stability range of the tetragonal phase, through the relief of pressure exerted on the Cu02 basal plane.Closer examination of the distortion of individual CuO, units reveals that the Cu-0 bond lengths do not change monotonically with increasing oxidation state. The (dax-deq)/(dax+deq)ratio peaks at a formal Cu oxidation state of +2.01; this was interpreted in terms of the co-operative Jahn-Teller effect as implying that the holes pro- duced by oxidation occupy a* orbitals rather than n*. The magnetic neutron diffraction measurements show no incommensurate behaviour and weigh against the interpret- ation of the long-range magnetic order observed in the system as a spin-density wave instability of the square two-dimen- sional Fermi surface, suggesting a Mott-Hubbard model. The magnetic long-range order disappears at a Cu oxidation state of +2.04, i.e.before the metal-insulator transition and the onset of superconductivity. The rapid destruction of the N6el state on doping is attributed to frustration. Location of the holes in the pa oxygen orbitals will lead to ferromagnetic Cu-Cu nearest-neighbour interactions (one bond disrupted per hole) that will frustrate the antiferromagnetic order. Alternatively, the availability of empty x2-y2 orbitals in low- spin Cu"' could similarly lead to frustration through the introduction of antiferromagnetic Cu-Cu next-nearest-neighbour interactions (four bonds disrupted per hole). The magnetic behaviour on hole doping is in contrast to the benign effect of Cu' 'electron doping' on magnetic long-range order in Nd, -,CeXCuO4 Finally, the nature of the carriers associated both with oxygen vacancies and with Sr2+ dopants, as the metal- insulator transition is approached was clarified.Doping intro- duces impurity states into the large intrinsic Mott-Hubbard gap, in analogy with classical doped semiconductors. The conductivity measurements reveal variable-range hopping behaviour at low temperatures, showing that the states near E~ are localised in the samples even after the ordered moments have disappeared. The data allowed the evaluation of the localisation lengths 5 of the carriers as a function of formal Cu oxidation state. They increase monotonically upon oxi- J. MATER. CHEM., 1991, VOL. 1 609 dation, and at a composition close to the metal-insulator 24 J.D.Axe, A.H. Moudden, D. Hohlwein, D. E. Cox, K. 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