Complex magnetic properties of the rare-earth copper oxides, R2CuO4, observed via measurements of the dc and ac magnetization, EPR, microwave magnetoabsorption, and specific heat.

We report the results of an extensive investigation of the magnetic properties of a large series of undoped {ital R}{sub 2}CuO{sub 4} single crystals with {ital R}==Pr, Nd, Sm, Eu, and Gd (which are the host compounds for the newly discovered series of electron cuprate superconductors) and mixture versions of the form {ital A}{sub 2{minus}{ital x}}B{sub x}CuO{sub 4}, with {ital A}==Pr, Nd, Sm, Eu, or Gd, and {ital B}==Gd, Tb, or Dy. We have measured dc and ac magnetization, microwave magnetoabsorption, EPR, and specific heat. These measurements reveal two characteristic transition temperatures associated with a novel complex magnetic behavior, including weak ferromagnetism, two sharp peaks in the low-field dc magnetization, an unusual anisotropy in the EPR resonance field for {ital R}=Gd, and two additional anisotropic microwave absorption modes. The higher characteristic transition temeperature at {similar to}270 K is associated with antiferromagnetic ordering of the Cu moments which are strongly coupled within the CuO{sub 2} layers. The lower, at {le}20 K, cannot be attributed to antiferromagnetic ordering of the {ital R} moments and is tentatively attributed to a spontaneous canted spin reorientation. An understanding of this magnetic behavior is important in order to ascertain its relationship to possible mechanisms of high-temperaturemore » superconductivity.« less


I. INTRODUCTION
The magnetic properties of the copper oxide hightransition-temperature (high-T, ) superconductors have been studied in great detail, ' and there have been many theoretical suggestions that the magnetic properties of these materials play an important role in the underlying superconducting mechanism.
Most of this focus has been on the original LazCu04, YaazCu30, , and related substitutional compounds, where antiferromagnetic order of the copper ions in the nonsuperconducting versions has been reported. Fluctuating two-dimensional antiferromagnetic spin correlations in the Cu02 planes has been reported to exist up to very high temperatures in these compounds, which persist even in samples that are doped to become superconductors, and the Neel temperature is reduced to zero.
Until recently, all the different versions of cuprates studied were hole doped. Holes were added to the Cu02 planes by replacing some La + by a divalent alkaline earth, or adding superstoichiometric amounts of oxygen. ' Recently a new series of cuprate superconductors has been discovered of the form R2 Ce Cu04 (R=Pr, Nd, Sm, or Eu) and also with the Ce replaced by Th. ' These materials are particularly interesting because electrons, rather than holes, in the Cu02 planes are suggested to be the charge carriers involved in the high-T, superconductivity. " The R 2 Cu04 with R = Pr through Gd form in a tetragonal crystal structure, with Cu02 planes on which oxygen atoms are square-planar coordinated about copper, with no apical (out-of-plane) oxygen, rather than the quasioctahedrally arrangement observed for the KzNiF4-type structure. ' The rare earths are coordinated by eight oxygens compared with nine oxygens in the case of La in La2Cu04. The space group of the R2Cu04 is an I/4mmm. ' We report the results of an extensive investigation of a large series of undoped R2CuO~single crystals (with R =Pr, Nd, Sm, Eu, and Gd), and also mixture versions of A2 "B Cu04, with A=Fr, Nd, Sm, Eu, or Gd and B=Gd, Tb, or Dy. We have investigated the magnetic properties via five instrumental signals: dc magnetization, ac magnetization, EPR, microwave magnetoabsorption, and specific heat. Preliminary data on these systems have been reported previously. ' %e have identified eight specific features, henceforth called signatures, S-1, . . . , S-8, and two characteristic temperatures, T& and TL (defined in Sec. III A), which are indicated by rapid 41 1934 1990 The American Physical Society changes or peaks in the instrumental signals corresponding to the specific property under investigation. An important conclusion of this work is a correlation between signatures measured by different techniques. Not all the signatures are found in every compound, although each of them is found in enough different compounds to be regarded as potentially present in the entire class.
The bulk of the experimental work reported here is a study of these signatures as a function of temperature, magnetic field amplitude and angle, rare-earth concentration, microwave frequency, etc. , and therefore the totality constitutes a large body of data. The data are summarized in Sec. III, where we present the features observed in (III A) dc magnetization (signatures S-l, S-2, and S-3), (III B) ac susceptibility (features similar to dc magnetization), (IIIC) microwave magnetoabsorption (signatures S-4, S-5, and S-6), (III D) EPR of Gd + (signature S-7), and (III E) specific heat (signature S-8). %e regard the clarification of the unusual magnetic properties of these compounds to be important for furthering our understanding of copper-oxide superconductivity from two perspectives. The first is obvious; there may be a magnetic origin to the underlying superconducting mechanism. The second is that, even if there is no specific magnetic superconducting mechanism, once the complex magnetic properties of these compounds are understood, it will be possible to utilize these experimental signals and their associated signatures as powerful probes into the internal states of the system. An explanation of the absence, presence, or changes that may occur in these signatures as the systems are doped into becoming superconductors may provide discriminating tests of the alternate models that are proposed.

II. EXPERIMENTAL DETAILS
Thin, platelike crystals of RzCu04 have been grown from PbO and CuO fluxes with the crystallographic c axis parallel to the thin dimension. ' In the case of GdzCu04, refinement of the x-ray spectra gives lattice constants a =6=3. 892 A and c= 11.878 A with a site occupancy of 0.99(2) for Gd and 1.01(5) for oxygen, indicating that the crystals grow at, or very close to, the stoichiometric composition. ' Samples grown with PbO flux, when examined by electron-microprobe analysis, show that the Pb content, if any, is less than 1 at. % of Cu. In contrast to La2Cu04, the electronic and magnetic properties of the R2Cu04 are insensitive to anneal in various gas atmospheres, suggesting that the oxygen content is highly stable. ' The microwave magnetoabsorption and EPR experiments were performed on 9 and 35 6Hz spectrometers, operated in the conventional derivative absorption mode at temperatures between 1.7 and 600 K. The dc magnetization, M~"was measured with a SQUID magnetometer for temperatures between 1.8 and 400 K and fields up to 50 kOe, or with a vibrating sample magnetometer for temperatures between 77 and 700 K. Specific heat, C~, was measured from 1.6 to -30 K in a small-mass calorimeter described in detail elsewhere. ' The ac susceptibility was measured between 4 and 300 K and from 1 to 1000 Hz in a system described elsewhere. '

A. dc Magnetization
In Fig. 1  the CuOz planes) as a function of temperature between 2 and 700 K, for both Pr2Cu04 and Nd2Cu04. We note that the curvature below -70 K is understood as being due to the crystal-field splitting of the low-lying states.
Above -300 K the magnetization for all the systems studied (see Table I) is linear in applied magnetic field, with a magnetic moment per formula unit corresponding to that expected for the trivalent rare-earth ion. However, below -300 K we find that, in contrast to the behavior shown in Fig. 1, other R compositions of these materials exhibit a nonlinearity' that becomes evident as the field is reduced, and evolves into a sharp peak when the field is in the vicinity of 1 -10 Oe. Another peak may be found at temperatures 20 K. We identify these peaks as signatures S-1 and S-2 as follows.  Fig. 2 we present the dc magnetization, Md"measured in a field of -1 Oe (applied parallel to the Cu02 planes), as a function of temperature for a EuTbCu04 sample. Two sharp peaks are observed. The highertemperature peak, which we call signature S-1, always has an onset at 275+10 K. Values of the onset are presented in Table I for compounds exhibiting the signature S-1. We define its characteristic temperature, T&, as the temperature at which Md, peaks when measured in a field of l Oe. The lower-temperature peak we call signature S-2 and its characteristic temperature, TI, is defined similarly to Tz. Other systems which also exhibit the two signature peaks S-1 and S-2 are indicated in Table I FIG. 2. The dc magnetization vs temperature for EuTbCu04 measured in a field of about 1 Oe applied parallel to the a-b plane. The two peaks at 270 and 10 K are associated with the high and low characteristic temperatures, T& and TL, respectively. These peaks depend on the field angle to the a-b plane as discussed in the text. The solid line is a guide to the eye. TABLE I~Presence of signatures for R2Cu04 samples studied. S-1 to S-8 are measured signatures discussed in the text. An entry of Y (or N) in the table means that the signature was (or was not) observed for the sample indicated. An asterisk (+) means that the EPR of the R moment was not observed. A blank means the sample was not tested for that signature. System Signature S-1 (onset) S-2 (TL) S-3 S-4 $-5 S-6 (peak) S-7 S-8 (peak) 'Possible nuclear Schottky anomaly.
Down to 1 K. 'Observed onset is -210 K compared to -280 K for all other "Y" S-4 entries. the dc magnetization, we found that both maxima get weaker, broader, and shift to lower temperatures when the applied magnetic field is increased. In Fig. 9 we present data for g"as a function of temperature in the vicinity of TI, for GdTbCu04 measured at three different values of the magnetic field (applied parallel to the a-b plane).

C. Micro~ave magnetoabsorption signals
FIG. 10. Spectra for a 0.5 mg single crystal of EuTbCu04 measured at 245 K and 9.2 GHz with the field applied parallel to the Cu02 planes. There are two signals that we call the lowfield and midfield absorptions as discussed in the text.
For samples which exhibit the S-1 to S-3 signatures but do not contain any Gd, a typical EPR spectrometer field sweep at 9 GHz for TL & T & T& is shown in Fig. 10. In general, there are two signals. If the applied magnetic field is parallel to the CuOz planes, as in Fig. 10, one signal occurs at very low magnetic fields, and the other at UO4 intermediate values, when compared to H, -3 kOe for normal g=2 EPR signals. The signal occurring at intermediate magnetic field values we call the midfield absorption, signature S-4, and the signal ocurring at low magnetic fields we call the low-field absorption, signature S-5.
The S-4 and S-5 signals first appear at -270 K, and their amplitude is largest at temperatures near T (as h defined in Sec. IIIA). As the temperature is lowered below TI" the amplitude steadily decreases, and the sig- FIG. 11. . Microwave magnetoabsorption at 9 GHz as a function of magnetic field applied parallel to the Cu02 planes for Gd2Cu04 at different temperatures below TL. The broad weak absorption is the EPR of Gd + and the sharper, stronger absorption is the signature S-6 as discussed in the text. nals eventually disappear at temperatures near TL. At TL a new magnetoabsorption signal appears, which we call signature S-6. Its signal is shown in Fig. 11 for GdzCu04 at three temperatures below Tt (the broad, weak signal present is the EPR of Gd +). We now present the behavior of the microwave magnetoabsorption signals S-4, S-5, and S-6.  Fig. 12 we present the temperature dependence of the magnetic field at which the maximum value of the midfield absorption signal occurs, H (as identified in the inset of Fig. 13) for 8 values of 0 and 85', and for a frequency of 35 GHz. The line shape of the midfield absorption makes it difficult to define a center value, which is why we use H as defined in Fig. 13 for most of the data analysis. At all temperatures between TL and Tz, the variation of H with 8 is as shown in Fig. 13. The solid lines are a fit to the data of the form H~= K/cos8, where K depends on both the microwave frequency and the rare earths used. Fig. 14 illustrates the frequency dependence of S-4, where we find that K is typically a factor of 2 -3 larger at 35 6Hz than at 9 GHz.
The intensity of the midfield absorption signal as a function of temperature for EuTbCu04 is shown in Fig.  15. A maximum is observed at a temperature near Tz. The midfield absorption signal amplitude was found to be strongly dependent on (1) the frequency of the field modulation applied parallel to the dc magnetic field, (2) the angle of the dc magnetic field in the a bplane (t-he rf magnetic field was also kept parallel to the a bplane, b-ut always perpendicular to the dc field), and (3) the angle of the rf magnetic field out of the plane. The midfield absorption amplitude does not go to zero as the dc and rf fields become parallel, as would be the case for a standard EPR signal. The intensity of the midfield absorption signal is very large by EPR standards. The integrated signal corresponds to a paramagnetic moment with an e6'ective number between 3 and 100 Bohr magnetons per formula unit, depending on the angle, temperature, and system.
In the inset of Fig. 15 we present the angular dependence of the peak-to-peak linewidth for EuTbCu04 at 245 K, which is found to exhibit a 1/cos8 dependence.
Note that in this case the midfield absorption peak-topeak linewidth and center position, H", are easily interpreted (see Fig. 10). H"(not shown) is also found to vary as 1/cos8. For the (Eu, "Gd )zCu04 system there is a correlation of the intensity with increasing Gd concentration. GHz EPR spectrometer output (dg" /dH ) as a function of magnetic field for EuTbCu04 at 100 K. The low-field absorption appears to be related to the signature S-1. It also behaves in a similar manner to the midfield absorption, in that they both exhibit a 1/cosO anisotropic behavior and both signals die out as T decreases to TL. However, their relative intensity depends on the particular RzCu04 system. The low-field absorption signal first appears 5 -10 K below the appearance of the midfield absorption.  Fig. 11 we presented the S-6 signal for Gd2Cu04 at three different temperatures. Note that as the temperature is lowered, the signal peak is suppressed and moves to higher fields. If instead of sweeping field at a fixed temperature, one sweeps temperature at fixed magnetic field, the spectrometer output for signature S-6 is as shown in Fig. 16. A signal peak is observed that is suppressed and shifts to lower temperature as the field is increased. (This behavior is similar to that observed for signature S-2. ) From a study of peak temperature as a function of dc field magnitude and angle, it is found that the temperature shift is only dependent on the component of field in the a-b plane. This property is illustrated in the inset of Fig. 16, where we present values of the S-6 peak temperature for fields up to 5 kOe applied parallel to the a-b plane (solid squares), and also for a constant field of 5 kOe applied at various 8 (open squares), where the field value plotted is 5 kOe cos0. We do not observe any EPR signal that we can identify with Cu + in any of the systems studied over the temperature range 2 -600 K. Possible reasons for the absence of the Cu + signal will be addressed in the analysis.
The only EPR signal we have observed and identified in these systems is that due to Gd +. We have previously reported our measurements for the system Eu2 Gd Cu04, where we found that for X=0.03 the spectra correspond to the fine structure expected for a Gd + free ion in a tetragonal host. ' For x &0.2 we found a single, broad Gd + EPR line. ' For PrGdCu04 and NdGdCu04, which do not exhibit the signatures S-1 through S-6, we also find a single Gd + EPR line with a field for resonance, H"corresponding to g -2.00 over the full temperature range, 2 -300 K. There is a small angular dependence of H" that is consistent with sample demagnetization effects.
The behavior of H" for PrGdCu04 and NdGdCu04 just summarized is in marked contrast to that which we observe for Gd-doped samples that do exhibit the S-1 to S-6 signatures. For these samples, the Gd + EPR signal above 270 K behaves exactly as that of the nonsignature samples just discussed. ' However, for temperatures below 270 K the field for resonance, H", develops an anomalous angular dependence, which we call the signature S-7. As an illustration of the large shifts of H" that are observed, we present the 35 GHz spectra shown in Fig. 17. Note that the center of the Gd + resonance signal is -2 kOe above that for the diphenylpicrylhydrazyl (DPPH} marker at g=2.00. (The midfield absorption shown in Fig. 17 is also strongly shifted to higher fields when compared to that in Fig. 10, because of the choice of field angle, temperature, and the use of a higher spec- We have made an extensive study of the temperature, frequency, and field angle dependence of the EPR signal for the sample series Euz "Gd"Cu04 (0.2~x~2 }, Tb2 "Gd"CuOz (1~x +2), and SmGdCu04. As an example of the nature of the S-7 signature, in Fig. 18 we present the shift of H" from Ha (the field corresponding to g=2.00) for a Gd2Cu04 sample as a function of the angle 0, for two temperatures and two microwave frequencies. First, we note that the behavior is independent of frequency, indicating the shift is due to the presence of an internal effective field (i.e. , not a true g shift). Second, as previously stated, above 270 K, H" is nearly independent of 0, whereas below 270 K we find that H"exhibits extreme out-of-plane anisotropy (it remains isotropic in the a bplane-). In the inset of Fig. 18 we present the temperature dependence of H, for two field angles. From these data one can readily identify TI, at which the out-of-plane anisotropy sets in, and T~, at which the anisotropy un-  Fig. 18, it goes through zero at 0-60', and then continues to extreme positive values as 8 approaches 90'. Notice that within a few degrees of the c axis, H" for 9.2 6Hz data drops sharply, although this feature is not observed in the 35 GHz data. Further evidence for an anomalous behavior close to the c axis is presented in Fig. 19 for EuGdCu04, where we present the H", peak-to-peak linewidth (b,H ), and signal peakto-peak amplitude (A ), as a function of field angle. All show a dramatic drop very close to the c axis. We tentatively interpret these data as indicative that the component of the magnetic field parallel to the planes has dropped below that value needed to "saturate" the weak ferromagnetism as illustrated in Fig. 4 and discussed under S-3.

E. S-8: specific heat
For Nd, Sm, and Gd, there is a peak in the specific heat, C~( signature S-8) that is taken to be a consequence of the antiferromagnetic ordering of their moments.
In Table I we present the temperatures at which the peak occurs. No ordering has been observed for Pr and Eu down to 1.5 K. The specific-heat measurements of Euz, Tb Cu04 between 1.5 and 25 K for x=0.5 and 1 show an interesting behavior. In Fig. 20 we present the C as a function of temperature for EuTbCu04. The broad maximum at -3 K as shown for x=1 shifts to 1.5 K when x=0. 5, suggesting a progressive spin freezing out of local disorder. '  If all the R2Cu04 do order similarly at -270 K, the question is raised as to why some compounds show the signatures S-1 to S-7, and others do not. A possible explanation may be related to the small differences in the R ionic radii. In Fig. 21 we plot the lattice parameter, a, versus the rare-earth atomic number for compositions as indicated in the figure. The compounds studied may be divided into two groups; those that show signatures S-1 to S-7, and those that do not, as indicated by the dashed curve. The first group always contains the smaller-sized rare-earth atoms: R =Gd, Tb, or Dy. The second group contains the largest: R -=Pr, Nd, Sm, or Eu. As progressively smaller R atoms are substitutied into the R 2Cu04, a crystallographic distortion may become favorable. This may explain why the signatures S-1 and S-7 are found in Gd2Cu04 and not in EuzCu04 or Nd2Cu04. For example, when Eu and Nd are partially replaced by Tb and Dy, respectively, to form EuTbCu04 and NdDyCu04, the average ionic radii are then closer to that of Gd +, and the conditions for observing the signatures S-1 to S-7 may again become favorable.

B. Intepretation of Tz
Recent muon spin rotation and neutron scattering studies in Pr2Cu04, Nd2Cu04, and Srn2Cu04 have suggested that the copper moments order antiferrornagnetically in the plane with a Neel temperature, Tz, between 255-270 K.
We do not observe the S-1 to S-7 signatures in these pure compounds (which coincidentally are the ones which so far have been shown to become superconductors when doped with Ce or Th), ' although we do see them in the mixed NdDyCu04 and SmGdCu04 versions. From the neutron scattering experiments, and in analogy to the La2Cu04 insulating compound, we identify Tz, as discussed in Sec. III, with a threedimensional (3D) Neel transition, Tz. Even though we do not observe the signature anomalies identifying T& in all the R2Cu04 compounds shown in Table I, we expect that all versions undergo a 3D antiferromagnetic transition with their Tz close to 270 K. The S-1, S-3, S-4, S-5, and S-7 signatures are typically fully established a few degrees below -270 K, and their properties are basically independent of temperature down to TL. A common feature found in signatures S-1 to S-7 is a large out-ofplane anisotropy (not found in any signal above Tz), which further supports the basic 2D nature of the Cu02 planes.
As noted, all combinations of rare earths studied gave almost the same value of T"(when observed). However, we found that when Gd is replaced by Ce or Th, or Cu is replaced by Ni, Tz is depressed.

C. The meaning of TI
In contrast to Tz, the value of TL depends on the rare earths used. At TL dramatic changes occur in most signatures. For example, the large changes in the H"of Gd + (signature S-7) shown in the inset of Fig. 18 correlate with the rapid changes observed in the dc and ac magnetization at TL. A plausible explanation for the behavior seen at TL is that the exchange interaction between the Cu and R ions is sufficient to cause the Cu to undergo a spontaneous spin reorientation, similar to that observed in the orthoferrites. nar, since in crystals with true tetragonal symmetry, the antisymmetric coupling cancels, and the Dzyaloshinsky-Moriya interaction is no longer effective.
If the canted component were ordered it would produce an internal field at the R site in the direction of the a-b plane. Following Cooke et al. , we can estimate the canted copper moment, Mc"by writing the measured magnetization as M =Mc"+C~(H; +H, )/( T+8R ), where C~i s the Curie constant for the rare-earth, e~i s the Curie-Weiss temperature, and H, the applied field.
The common intersection point for the curves in Fig. 5 gives Mc"~10+10 emu/mol, which is equivalent to -2+2X 10 'p~/Cu. Unfortunately, there is a large uncertainty in this result, but the sign of the Mc" is such that the ferromagnetic component of Cu is in the direction of the applied field. The average value of Mc" is similar to the weak ferromagnetic moment, -3 X 10 p&/Cu reported in La2Cu04.
Within the experimental error, we never detect a magnetic remanence. Instead, there is a sharp increase of the initial magnetization with applied magnetic field, as seen in Figs. 3 -5. It seems that a small, but finite, magnetic field is necessary to "turn on" the mechanism that leads to the observed anisotropic properties. One possibility is that there are basically antiferromagnetic domains, but with slightly canted Cu moments that can be aligned by a sma11 magnetic field. Such a picture could also explain the strong dependence on applied magnetic field of S-1 or S-5. The broad shoulder, found above S-1 in the ac susceptibility ( Fig. 9), may also be indicative of short-range order. A similar dependence on the magnetization was recently reported for a-T1MnC13.
In the description of the S-3 data in Sec. III A we mention that in GdzCu04 the magnetization is nearly independent of field orientation in the plane, while for EuTbCu04 there is a large anisotropy. One possible explanation is that for EuTbCu04 there is additional symmetry breaking induced by magnetoelastic stress placed on the lattice by the copper ordering process. ' Such a small distortion could be consistent with the absence of any observed difference in the ratio of lattice parameters (a, b) at temperatures well below T~, as measured by x rays.
K. Angular anisotropy D. The consequences of a distortion from tetragonal symmetry A possible interpretation of the S-3 signature, i.e. , the weak ferromagnetism that depends only on the component of the magnetic field in the plane, is that there is a canting of the copper moments away from strictly antiferromagnetic alignment. A similar interpretation was invoked in the orthoferrites by Cooke et al. The origin of the spin canting is attributed to an antisymmetric exchange interaction, as discussed by Dzyaloshinsky and Moriya. Implicit in this interpretation is the assumption that the Cu-0 coordination is no longer square pla-Independent of the mechanism responsible for H, , data similar to that illustrated in Figs. 4 and 5 may be analyzed at all temperatures between TI, and TL to yield an H; with a value of -800 Oe, nearly independent of R. A feature common to several signatures is that they only depend on the component of field in the a-b plane. This is illustrated by the data shown in Figs. 13 -15, 18, and 19. These data exhibit a K/cosO dependence that may be interpreted as requiring an applied field at any angle 8, of such a magnitude that the component of field in the plane has the constant value K.
Additional examples of anisotropy are the field required to reach the linear portion of the M versus H curve for the signature S-3 as shown in Fig. 7, or the field required to produce a peak at a given temperature in the magnetoabsorption signal S-6 as shown in Fig. 16.

F. EPR of Gd +
The only EPR signal observed and identified is for Gd +, which has an S7&2 ground state. For systems where the S-1 through S-6 signatures are not present, as in Pr (or Nd) GdCu04, the Gd + resonance field, H", and the linewidth, AHpp are essentially independent of angle at any temperature.
Apparently, the Gd + resonance does not reflect the antiferromagnetic ordering at -270 K found by the neutron and muon studies.
In contrast, in the group of compounds where the other signatures are present, the H" for Gd + has an unexpected angular dependence below T&. At temperatures above T&, H", as corrected for sample demagnetization, is essentially independent of 8, as illustrated for T=300 K in Fig.   18. As further illustrated in Figs. 18 and 19, at all temperatures between Tz and TL the shift in H" from H0 is very anisotropic. Since the magnitude of this shift is basically independent of frequency, it reflects an internal field, and not a change in g value. The amount the shift in H" is about 500 Oe at 8=0, which is in the correct direction, but is significantly smaller than the -800 Oe deduced for H;(0) from the Md, data. As previously mentioned, if the only mechanism which contributes to the shift were the one associated with H;, one would expect H"-H0 to go to zero at 8=90'. Instead, as is seen in Figs. 18 and 19, it goes through zero at 8-60', and then continues to extreme positive values as 8 approaches 90'. We try to represent the angular dependence of H" with the following expression: presumably reflecting the incomplete "setting" of the field in the plane noted earlier.

G. Mid6eld absorption
The midfield absorption, S-4, is the most pervasive of all the signatures listed in Table I. If any of the other signatures are present, it is always observed and it is the only signature found in pure Eu2Cu04. Note that in Fig.  21 the lattice parameter for Eu2Cu04 is close enough to the dashed boundary that one might expect signatures to be present in this compound. The addition of only 1 at. % of Gd is sufficient for other signatures, e.g. , S-l, to appear. ' The intensity of the midfield absorption corresponds to a large effective moment per formula unit, between 3 and 100p~. The larger values imply a cooperative response within the spin system. This suggests that we may be observing the resonance of spin clusters or domains that in turn feel an internal field due to the anisotropic exchange interactions.  (2), with K'=300 Oe represents the data fairly well until a few degrees from the c axis, at which point H"(for the 9.2 GHz) data drops sharply, a feature not contained in Eq. (2). We attribute the sharp drop to be a consequence of there no longer being a large enough component of the applied field in the a-b plane to fully "set" the weak ferromagnetism as required from the data in Fig. 4. We infer that this feature is not observed in the 35 GHz data because we cannot align the crystal accurately enough to the c axis to achieve a small enough projected component of the field in the plane, as the magnitude of the applied field necessary to observe the Gd + resonance is -3.5 times larger than at 9.2 GHz.
As seen in Fig. 19 Fig. 15) have been found in other 1D and 2D systems where the EPR line is associated with spincluster resonances.
The field for resonance of the midfield absorption is a function of frequency, which is further evidence for it being some form of spin resonance. However, we note that the signal does not go to zero when the rf magnetic field is parallel to the dc field.

H. Low-field absorption
The low-field absorption, S-5, is the most difficult signature to fully characterize because it appears at very low fields (where it is may overlap S-4), and because it appears to evolve in a complex way with temperature near TL and T&. However, at temperatures where it is well resolved, the field at which the signal peaks depends on the angle, 8, of the dc field to the a-b plane as 1/cos8.

I. Ordering of the R moments
Both the specific-heat and magnetic-susceptibility measurements of R2Cu04 indicate antiferromagnetic order at about 1.5, 6, and 6.5 K, for R =Nd, Sm, and Gd, respectively.
We cannot associate TL with the incipient antiferromagnetic ordering of the R moments, because Nd2Cu04 and Sm2Cu04, which do not show any of the signatures, both order, whereas EuTbCu04, which exhibits all of the signatures, does not. Notice that the specific heat of EuTbCu04 shown in Fig. 20 has a broad Schottky type of maximum that strongly depends on the concentration of Tb. This behavior can be interpreted as a progressive freezing of the spins out of local disorder, where there is a spread of magnetic exchange constants, including those beyond nearest-neighbor interactions between the Tb ions. ' J. The Cu + moment problem 1. The Ck magnetization For layered magnetic systems one expects significant deviations from free-ion magnetic behavior for temperatures less than -3T~. ' We can seek to determine the contribution of the Cu + ions to Md, in this temperature range, but unfortunately the large Md, of the R ions makes this quite difficult. If, at the highest temperature measured, -700 K, the Cu + contributed with a full S= -, ' moment, they would consitute -5% of the total Md, for the Gd and 25%%uo for the Pr or Nd compounds.
As can be seen, the inverse susceptibility data for Pr2Cu04 and Nd2Cu04 presented in Fig. 1 are linear, and between 100 and 700 K can be well fit with p ff 3.66+0. 05p~, 0"--65 K for Pr, and p ff 3.56+0. 05pz, Oz --60 K for Nd. From these data we conclude that the contribution of Cu + in the Pr or Nd compounds is~0.4+0.2pz/Cu. The small moment of Sm + in Sm2Cu04, -0. 5p~/ion, suggests that it might be the optimum system to determine the contribution of Cu + to the magnetization. However, a similar analysis for Sm2Cu04 is complicated because Sm + has a J = -, ' level as a ground state, spIit into three doublets by the tetragonal crystal field. As a result of the large admixture with low-lying J multiplets (as also frequently seen in other Sm compounds), it is necessary to take into account the populations of levels other than the ground state. These levels are all split by crystal-field effects, and one must also include second order Zeeman terms. As a consequence of these effects it is more difficult to determine the effective Cu + moment from the Sm compound magnetization data than would at first appear.
2. The eQeet of a Cu + dipolar field on the Gd EPR The EPR data for dilute Gd in Eu2, Gd"Cu04 (x=0.03) may be interpreted to set a limit on the magnitude of the ordered Cu moment by the following analysis.
If the Cu moments are ordered antiferromagnetically in the plane, and have a full moment expected for S= -, ', there will be a net static dipolar magnetic field at alternating R sites of -+800 Oe. (Since the field alternates direction at the R sites, it cannot be responsible for the H; of S-3). If the dipolar field was parallel to the applied field it would result in a splitting of the Gd + EPR signal of about 1600 Oe. From the observed spectra we conclude that if the fields are parallel, then the effective magnetic moment is &0.3 of that expected for a spin -, '. If the fields were perpendicular, however, there would primarily be a small reduction in H"(-100 Oe) with a greatly reduced splitting due only to any angular anisotropy of the resonance, in which case our data would not set a meaningful limit.
3. Why is the EPR of the Cu + ion not observed' The nature of EPR in 2D antiferromagnetic compounds has been studied in several systems, and in most cases an EPR signa) is observed only well above Tz. ' At temperatures of -3T& the linewidth decreases slowly as the temperature is reduced, passing through a minimum at -2T&, and subsequently increases anomalously when approaching TN from above.
Since we believe that the 3D ordering temperature is of the order of Th for the R2Cu04 system, the fact that we do not observe any Cu EPR signal at temperatures up to 600 K in these compounds suggests that the 2D antiferromagnetic correlations are strong even for T~2T&, or there are other mechanisms operative that broaden the Cu EPR signal beyond detectable limits.
We note that the typical observation of the narrowest EPR signal at -2T~for many 2D antiferromagnetic systems clearly does not seem to be obeyed in the other copper-oxide superconducting systems. (The absence of a Cu + EPR signal has been reported previously by us and other authors for the other copper-oxide superconductors and their parent compounds, La2Cu04 and RBazCu306. ' ) That is, when the La or 1:2:3 versions are doped to suppress the Neel temperatures, one still does not observe a Cu + EPR signal at any temperature, including those in the vicinity of 2T~. Thus, this "rule of thumb" based on other systems is not appropriate. One explanation may be that the intraplanar exchange is really much larger than that inferred from the observed Tz, and that other conditions, such as hole doping, reduce the observed 3D ordering temperature, but not the underlying 2D spin correlations in an equivalent manner.
U. CONCLUSIONS From our data and recent neutron-diffraction and muon precession measurements, ' we conclude that all the R2Cu04 compounds studied here order antiferromagnetically in a quasi-two-dimensional arrangement at -270 K with the Cu moments strongly coupled within the Cu02 layers. The presence of long-range 2D antiferromagnetic spin correlations, well above T~, is supported by the negligible contribution of the Cu moments to the dc magnetization,~0.4ps/Cu, and the total absence of a Cu + EPR signal up to 600 K. This behavior is similar to that reported for La2Cu04, which is also a 2D antiferromagnetic insulator below 300 K.
Below Tz -270 K, the compounds can be divided into two groups, one where the signatures S-1 to S-7 as described are present, and the other where they are not.
The presence of these signatures may be due to a distortion of the tetragonal arrangement of the Cu ions, which in turn produces an internal field at the R sites. Such a distortion may also induce the formation of spin-canted antiferrornagnetic domains that may be aligned by a small external field. This picture could explain the presence of the weak ferromagnetism (S-3), the midfield absorption (S-4), and the magnetic field dependence of the S-1 peak.
A common feature of the diverse signatures is their unusual dependence on the angle and magnitude of the applied magnetic field. It appears that, for those samples that exhibit the S-1 to S-7 signatures, there is a minimum component of field needed in the a-b plane to fully establish their character. Equation (2) at least provides an empirical description for the angular dependence of the Gd + EPR signal, however, the physical origin of the several terms describing the shift in H, is not known. TI is tentatively attributed to a spontaneous spin reorientation of the canted Cu ions. In contrast to Tz, TL depends on the R used, but it does not appear to be directly associated with any antiferromagnetic ordering that may occur at lower temperatures.
We suggest that further investigation of the complex magnetic properties of the R2Cu04 compounds and their doped superconducting versions is warranted, and that once clarified, the signatures described herein will be useful monitors to further our understanding of the role of magnetism in the high-temperature superconducting copper oxides.