Heat capacity (150–300 K) and anisotropic magnetic susceptibility (5–300 K) of single-crystal La2CuO4+x

Abstract Heat capacity measurements from 150 to 300 K were carried out on a single crystal of La 2 CuO 4+ x synthesized by subjecting an La 2 CuO 4 crystal to 3 kbar oxygen pressure at 575 °C. The data reveal three small (about 1%) anomalies at temperatures ( T ) of 206, 222 and 259 K. The first two are tentatively attributed to CuO inclusions in the crystal. The third is observed on warming, but not on cooling, and is attributed to the previously documented first-order transition from the orthorhombically distorted K 2 NiF 4 structure to a low T mixture of nearly stoichiometric La 2 CuO 4 and oxygen-rich superconducting La 2 CuO 4+ y ( y > x ). The size of the anomaly at 259 K is about one-seventh of that observed previously for a single crystal of La 2 CuO 4 at the second-order tetragonal-to-orthorhombic phase transition temperature of about 530 K. Magnetization measurements from 5 to 300 K and from 50 G to 50 kG are also reported for the La 2 CuO 4+ x crystal. The normal state magnetic susceptibility χ ( T ) is quite anisotropic, with χ ( T ) for H perpendicular to the CuO 2 layers ( χ c ) in good agreement with previous data on a different, but similarly prepared, crystal. The anisotropy in χ is nearly independent of T from 40 to 300 K and the magnitude of χ c - χ ab per CuO 2 layer is very similar to that at high T in YBa 2 Cu 3 O 6.1 , La 2 CuO 4 , Sr 2 CuO 2 Cl 2 and La 2− x M x CuO 4 (MSr, Ba).


Introduction
The system La2CuO4 +z exhibits a range of novel properties depending on the oxygen content 4+x.The lowest oxygen content samples (x=0) exhibit a second-order structural transition at a temperature To = 530 K [1][2][3][4], become antiferromagnetically ordered below a N6el temperature TN = 300 K [4,5] and are insulators as T goes to zero [6].The transition from the high T tetragonal K2NiF4 structure at an orthorhombically distorted structure at To results from tilting of the CuO6 octahedra about the tetragonal (110) axis [3,7].The heat capacity jump at To is ACp(T0)=20 mJ g-1 K-I or about 5% of the lattice heat capacity at To [8].For a single crystal the Cp anomaly had a shape indicative of fluctuations in the orthorhombic order parameter near To [8 l-The transition at To is evident in the powder magnetic susceptibility x(T) via a distinct decrease in dx/dT at To upon cooling [9].No anomalies were observed in Cp(T) at TN=304 K for the above single crystal [8].Only small effects are expected, because strong two-dimensional (2D) dynamic short-range antiferromagnetic (AF) order within the Cu02 planes [10-14l causes the magnetic entropy at TN to be only about 0.5% of the limiting high temperature value Rln2 [8].A pronounced peak in x(T) occurs at TN [6,[15][16][17][18][19][20], originating as follows [18,[20][21][22].Above TN, weak ferromagnetic (FM) correlations build up within the CuO2 layers with decreasing T below To, perpendicular to the instantaneous local axis of dynamic AF ordering.These FM correlations arise as a consequence of the orthorhombic distortion which introduces a Dzyaloshinsky-Moriya interaction D-(Si × Sj) into the intraplanar spin Hamiltonian below To [22].As the AF correlation length increases with decreasing T, the FM component within a correlated area increases in magnitude, tending towards a divergence near TN.Below TN the ferromagnetically canted components align perpendicular to the CuO2 layers, with AF alignment in adjacent layers, resulting in the peak in x(T) at TN.This peak does not occur in the absence of the orthorhombic distortion, as verified for the tetragonal insulators Sr2CuOeC12 [23] and Cao.ssSro.,~CuOa[24] at their respective N6el temperatures of about 300 and 540 K. (For a recent review of the normal state magnetic susceptibilities of the La2CuO4based compounds and the YBa2CuaO6+x system see the article by Johnston [25].)Subjecting La2CuO4 crystals to high (3 kbar) oxygen pressure at 500-600 °C induces bulk superconductivity below Tc--40 K [26,27].Excess oxygen apparently enters the lattice as O2 and an electron is transferred from Cu 2 ÷ to form a complicated oxygen complex and Cu a+ [28][29][30].The superconductivity results from a first-order phase separation [27,28,[31][32][33][34] of the La2CuO4 +x below Ts = 260-280 K into an oxygen-rich superconducting composition, estimated to be La2CuO4.oa,and nearly stoichiometric La2CuOt with TN----250 K = Ts.The relative fractions of the two phases at 0 K are typically about 2:1 respectively [27,28,32].This phase separation involves the bulk diffusion of atomic oxygen, showing that this diffusion is rapid even below room temperature.The To value of the homogeneous sample above T~ is markedly suppressed from the value for La2CuO4 (530 K) to about 400 K > Ts [27].
Herein we report C,(T) measurements from 150 to 300 K on a single crystal of La~Cu04 +x which were carried out to search for a thermal anomaly at T~ for comparison with the results at To for La2Cu04 [8] cited above.x(T) measurements (40-300 K) with H parallel to c were carried out for comparison with previous measurements [34] on a different crystal.Additional x(T) measurements above 40 K with H perpendicular to c were done to determine the x(T) anisotropy in the normal state.Finally, x(T) data from 5 to 40 K for H both parallel and perpendicular to c were obtained to characterize the superconducting state below T¢=37 K.

Experimental details
A single crystal of La2CuO4 of mass 72.8 mg was grown in a CuO flux as described previously [34].The irregularly shaped crystal was annealed in an oxygen atmosphere at 3 kbar pressure and 575 °C for 12 h, followed by cooling to room temperature at a rate of about 100 °C min-1.From previous work on similarly annealed crystals [28] the oxygen excess in the resulting La2CuO4+x crystal is estimated to be x=0.03-0.04.
Heat capacity (Cp) data were obtained from 150 to 300 K using a Perkin-Elmer DSC-7 differential scanning calorimeter (DSC).The DSC was calibrated using pure indium metal.The calibration was checked by measuring Cp(T) of pure colorless sapphire and comparing with high accuracy literature data [35].This comparison showed that the accuracy of the DSC measurements of Cp is better than 8% for the 150-400 K temperature range.The precision of the measurements is better than 1% in this T range.Further calibration details can be found in ref. 8. Cp(T) data for the La2CuO4+x crystal were obtained on both warming and cooling, using various temperature ramp rates from 2.5 to 80 K min -1.The upper temperature limit of both the Cp measurements and the x(T) measurements was 300 K, to avoid evolving the excess oxygen from the crystal which occurs at somewhat higher temperatures [ 30 ].The DSC was cooled by liquid nitrogen and measurements were conducted after the DSC had reached a steady state using this coolant.The crystal was placed in a clean aluminum pan and the sample chamber was continuously purged with helium gas at a rate of 30 mL rain-1.The DSC was enclosed in a nitrogen-purged dry-box to avoid water condensation.
Magnetization (M) measurements of the LaeCuOa+z crystal were carried out using a SQUID magnetometer (Quantum Design, Inc.).The crystal was mounted on a rigid sample holder, with H either parallel or perpendicular to the CuO2 layers, using a small amount of GE 7031 varnish (which yielded a small diamagnetic contribution to the magnetization).Data were obtained from 5 to 300 K in applied magnetic fields (H) from 50 G to 50 kG in a low pressure helium atmosphere.Isothermal M(H) data were taken from H= 1 to 50 kG at various temperatures.Before each M(H) scan with T< 100 K, H was set to zero and the sample temperature allowed to equilibrate at 100 K before lowering T to the desired value and measuring the M(H) data.Analysis of the M(/-/) data revealed no evidence for the presence of either ferromagnetic or paramagnetic (i.e. with Curie-type x(T)) impurities.between the sample and thermometer, the apparent temperatures of the peaks are higher than obtained at 10 K min-1.Many data sets as in Figs.

A typical Cp(T) data set for our
1 and 2 were obtained using heating rates of 10-80 K min-'.Shown in Fig. 3 are the values of T1, T2 and T3 obtained vs. the heating rate.By leastsquares fitting the T~ data to straight lines and extrapolating to zero heating rate, the values in the absence of thermal lag between sample and thermometer were obtained: TI=205.6±1.1,T2=221.6±2.2 and T3=259.1±1.6 K.
In an attempt to ascertain whether the three peaks in Cp depend on the thermal history of the sample, two additional types of experiments were carried out.In the first the crystal was first cooled to just above T2, then heated to 300 K.It was found that the peak at T3 was still always present in Cp(T) obtained on warming but not on cooling.In the second the sample was first brought to thermal equilibrium at 250 K, then Cp(T) data were obtained on cooling to 170 K and subsequent warming back to 250 K (i.e.without traversing the peak at T3); the peaks at T1 and T2 were the same as observed above.
By examining the Cp(T) data obtained on cooling and warming at the various temperature ramp rates, we could not identify any thermal hysteresis intrinsic to the transitions at T1 and T2.Of course, the transition at T3 is hysteretic because no peak was observed in Cp(T) on cooling, indicating that this transition is first order.The order of the other transitions at T1 and T2 could not be determined from analysis of the peak shapes in the present data owing to the small size of the respective Cp anomalies.
La~Cu04+= crystals synthesized using an oxygen pressure annealing schedule similar to that for our crystal undergo phase separation below room temperature, as noted in Section 1.We identify the peak in Cp(T) at T~ = 259 K observed on warming with this phase transition, which was deduced in ref. 34 to be first order from the thermal hysteresis found in resistance and x(T) measurements, consistent with the thermal hysteresis we observe in Cp(T).The reason why this transition is observed in our Cp(T) data on warming but not on cooling is not clear.The peak is apparently broadened beyond our resolution during cooling.The x(T) data below (taken on warming) are consistent with the phase transition occurring at Ts= T3.An expanded plot of the 10 K min -t ramp rate data of Fig. 1 in the vicinity of 2"3 is shown in Fig. 4. The size of the anomaly may be characterized by the heat capacity jump at Ta shown in the figure, ACp(Ta)=3 mJ g-t K-t, which is about one-seventh of that seen [8] in La2CuO4 at T0=530 K.
The peaks in Cp(T) at T1 and T2 are most likely not associated with the bulk phase transition in La2CuO4+~ at T3, since the former peaks occur independently of whether the peak at 2"3 is observed on warming and cooling.We tentatively attribute the peaks at T, and 2"2 to phase transitions within CuO inclusions in the La2CuO4+= crystal, from the following considerations.For a sintered and annealed polycrystalline CuO sample, Cp(T) measurements made with our DSC under the same operating conditions showed two transitions between 200 and 230 K [8].A second-order transition was observed at TN = 225.0(2)K associated with long-range incommensurate AF order.A firstorder transition occurred at T~ = 209.5(2)K arising from a commensurateto-incommensurate AF transition on warming.We therefore identify T~ with T~ and T2 with TN.Comparing the size of the anomalies at TI and 2"2 with those at T~ and TN in the pure CuO sample, we estimate that our La2CuO4+x crystal contains about 4 wt.% of CuO inclusions.These inclusions presumably originate from the CuO flux during crystal growth.

Magnetization measuremv~s
The zero-field-cooled (ZFC) and field-cooled (FC) susceptibility data O((T)--M(T)/H) below 50 K for H=50 G are shown in Figs.5(a  for perfect diamagnetism.Demagnetization effects are not taken into account in Fig. 5 because of the irregular shape of the crystal.The ZFC data in Fig. 5(a) indicate that a large fraction (at least half) of the crystal exhibits bulk superconductivity at 5 K.In contrast, the FC Meissner effect x(T) data in Fig. 5(b) are smaller in magnitude by factors of about 60--100.This discrepancy suggests either that flux pinning is strong below Tc or that only a small fraction (on the order of 196) of the crystal volume exhibits bulk superconductivity.Quantitative analyses of neutron diffraction [27], muon spin rotation (~SR) [32] and 189La nuclear quadrupole resonance (NQR) [33] experiments on similar samples indicate that the first interpretation is the correct one.Strong flux pinning might be expected because of the finegrained macroscopic phase segregation occurring below Ts=260 K (see below).
Multiple inflections in the FC xc(T) data at 9 and 25 K and in the ZFC data at 26 and 35 K for Xc(T) and at 31 and 35 K for Xab(T) suggest multiple superconducting transitions.However, the lower inflection temperatures for the respective measurements are not the same and therefore most likely are manifestations of temperature-dependent flux-pinning effects.The temperatures corresponding to selected points on the transition curves in Fig. 5 are listed in Table 1, where corresponding temperatures for data at H= 10 kG (not shown) are included.Also listed are the superconducting onset temperatures obtained by the intersection of straight line extrapolations of the data above 40 K and the first linear region below the first detectable onset of diamagnetism.
The susceptibilities from 40 to 300 K with H= 10 kG parallel (Xab) and perpendicular (Xc) to the CuO2 planes are shown in Fig. 6(a); the data were taken on warming after zero-field cooling to 5 K and applying the field at that T. From the figure the high temperature onset of the phase separation transition is at 260--270 K.The maximum negative slope in both x¢(T) and Xab(T) occurs at 7", = 255-260 K.The temperature of the peak in the above Cp(T) measurements at 7'3= 259_ 1.6 K is equal (within the errors) to Ts, consistent with assigning this peak in Cp(T) to the phase separation transition.However, the presence of 4 wt.%CuO inclusions in our La2CuO4+x crystal, as deduced from anomalies at 7"i = 206 and T2 = 222 K in the Cp(T) measurements, is not evident in the x(T) data in Fig. 6(a) (or Fig. 6

(b) below).
The value of T~ is in agreement with values determined from x(T) [34], resistivity [34] and 139La NQR [33] measurements of similarly prepared crystals.The xc(T) data are nearly identical to those taken previously on warming for a different La~CuOa+x crystal synthesized under the same conditions as our crystal [34].Measurements of the hysteretic behavior of x(T), observed in xc(T) in ref. 34 upon warming and cooling, were not made in the present work.TABLE 1 Superconducting transition values for single-crystal La2CuO4+~.The 'T--H process' refers to whether the crystal was cooled to 5 K in zero applied field prior to measurement (ZFC) or whether the indicated field was applied above Tc (FC); all data were obtained upon increasing the temperature from 5 K.The transition temperatures indicated are the onset temperature (see text) and the temperatures at which the magnetization attained 10% and 50% of its maximum diamagnetic value at 5 K. Xv is the dimensionless c.g.s, volume susceptibility (X defined as M/H); the last column is normalized to the value expected for perfect diamagnetism

Data set Applied
T-H  The ~SR measurements on a powder sample of La2CuO4 += revealed AF ordering below TN = 250 K (with roughly equal amounts of the oxygen-rich superconducting phase and the antiferromagnetically ordered La~CuO4 phase at low T) [32].The phase separation temperature in our La2CuO4+x crystal is T~= 260 K. Thus Ts and T~ axe expected to be identical or close to each other.The LaeCu04 phase is expected to exhibit a pronounced peak in x(T) at TN as discussed in Section 1, whereas the data in Fig. 6(a) show only a shallow peak at about 240 K.We speculate that this discrepancy arises from smearing of the peak resulting from a fine-grained morphology of the phase mixture below T~ and/or to associated lattice strain below T~ [44].Additionally, the proximity of Ts and TN makes extraction of the individual influences of phase separation and AF ordering from x(T) difficult.
Both xc(T) and Xab(T) in Fig- 6(a) increase slowly with T above T~ = 260 K.This is similar to the x(T) behavior above Tc or TN for other superconducting cuprates and insulating parent compounds not containing magnetic ions other than Cu e+ and is believed to reflect the occurrence of dynamic 2D shortrange AF ordering of the (nearly) localized Cu e+ spin-½ magnetic moments resulting from strong (J= 1500 K) AF exchange coupling between these ions [25].In support of this interpretation the high temperature anisotropy (Ax) in Fig. 6(b) is about the same per CuOe layer as in YBaeCu306.1 [45] and in other KeNiF4-type compounds such as LaeCu04 [8], SreCuOeCle [23] and Lae_~(Sr,Ba)~Cu04 [18]; this suggests that the local electronic states and state occupations in the vicinity of the Cu e+ ions are similar in these compounds.Indeed, the anisotropy in both the insulating and superconducting cuprates is believed to arise primarily from the anisotropic Van Vleck paramagnetic orbital susceptibility of the (nearly) localized Cu e+ ions, with a small additional anisotropic spin susceptibility contribution coming from an anlsotropic spectroscopic splitting factor (g) of these ions [40,41,[45][46][47][48].

Summary and concluding remarks
Heat capacity (Cp) measurements between 150 and 300 K of singlecrystal LaeCuO4+x revealed small (about 1%) thermal anomalies at T1 = 206, T2 = 222 and T3=259 K.The first two transitions are tentatively ascribed to about 4 wt.%CuO inclusions in the crystal.The anomaly at Ta is attributed to the previously documented [27,28,[31][32][33][34] first-order transition from the homogeneous orthorhombically distorted LaeCu04+~ phase above Ts = Ts to the low T phase-separated mixture of nearly stoichiometric LaeCu04 with TN= 250 K [32] and oxygen-rich LaeCuO4+y; x and y were found in previous work to be about 0.03-0.04 and 0.08 respectively [23].The size of the C, anomaly at Ts, ACp=3 mJ g-1 K-l, is about one-seventh of that found previously [8 ] at the second-order tetragonal-to-orthorhombic phase transition temperature To =530 K in an LaeCuO4 crystal with TN = 304 K.The firstorder character of the transition at Ts is manifested in Cp(T) by the appearance of an anomaly on heating but not on cooling, although no explicit evidence for a latent heat at Ts was observed.
The similarity of our La2CuO4+x crystal and a different one on which extensive magnetic susceptibility (x(T)) and transport measurements were carried out previously [34] was verified here via magnetization measurements.The X data obtained on heating from 40 to 300 K with the applied field H perpendicular to the CuO2 planes (xc(T)) are essentially identical to those reported previously [34], including the data in the important T region near Ts.The X data with H parallel to the CuO2 planes (X~b(T)) were also measured with increasing T. The anisotropy AX, defined as Xc-Xab, was found to be nearly independent of T from 40 to 300 K, although a small (10°/0) increase in A X was observed below Ts.Superconducting fluctuation diamagnetism between T¢ and about 60 K was apparent in the x(T) data.
The interpretation of the Xab(T) and x~(T) anomalies in our crystal below Ts is ambiguous at present.~SR experiments on a powder sample of LaeCuO4 +x (annealed similarly under oxygen pressure) showed that the TN--250 K.However, the anisotropy and size of the anomalies we see in X~(T) and Xo~(T) near 250 K are different than In single-crystal LaeCuO4 with TN = 250 K [32].The apparent near coincidence of T~ and TN makes extraction of the individual magnetic ordering and chemical-crystallographic contributions to the X(T) anomalies problematic; further complications arise from possible size effects and strain in the phase-separated mixture below Ts.We hope to address these issues in part through future magnetic and crystallographic neutron diffraction measurements on the present La2CuO4+x crystal.
Finally, from the above discussion and that in Section 1, one would infer that (i) the most oxygen-rich composition of the antiferromagnetically ordered La2CuO4 phase has a minimum TN of about 250 K.This is to be contrasted with (ii) the observations that TN values as low as 50 K are seen by magnetic neutron diffraction for some single crystals [ 18 ] and that annealing at 500 °C in only modest (100 bar) oxygen pressures is sufficient to drive TN from 290 K to near 0 K in certain powder samples without inducing any trace of superconductivity above 4 K [6,9]; the increase in oxygen content in the latter case is about 0.03 [9].We speculate that the reason for the contradictory results (i) and (ii) is that some La2CuOz samples contain cation vacancies, up to about 1%, on the lanthanum and/or copper sites.For example, for 1% La vacancies the oxygen composition giving all Cu e+ ions and presumably the highest TN would be La1.gsCu08.97.By increasing the oxygen content to 4.00, TN might be driven to zero without, however, inducing phase separation and superconductivity.These ideas are currently under investigation.

Fig. 3 .
Fig.3.Dependences of apparent temperatures of heat capacity peaks at T1, T2 and T3, obtained using a DSC, vs. healing rate.Linear extrapolations to zero heating rate are shown.

Fig. 4 .
Fig.4.Expanded plot near transition at Ta of heat capacity Cp vs. temperature for singlecrystal La2CuO4+ x.The data were obtained using a DSC at a heating rate of 10 K min -1.The construction for characterizing the size of the anomaly at the apparent 2"3 is shown.

Fig. 5 .
Fig. 5. Volume magnetic susceptibility Xv vs. temperature for single-crystal La2CuO4+= below 50 K.The applied H= 50 G was either parallel to the CuO2 planes (Xab) or perpendicular to them 0(c).The data were obtained upon warming from 5 K either (a) after cooling to 5 K in zero applied field (ZFC) or (b) after cooling to 5 K in the field of 50 G (FC).

Fig. 6 . 6 ( 1 .
Fig. 6.(a) Magnetic susceptibility X vs. temperature for single-crystal La2Cu04+=.The applied field of 10 kG was either parallel 0(~) or perpendicular (Xc) to the CuO2 planes.The data were obtained on warming after cooling to 5 K in zero applied field.Co) Magnetic susceptibility anisotropy AX, defined as Xc--X~, vs. temperature above about 40 K, computed from (a).