Pressure dependence of the superexchange interaction in antiferromagnetic La2CuO4.

Using high-pressure Raman scattering, we have directly measured the pressure dependence of the in-plane superexchange interaction J in antiferromagnetic La&CuO4 between 1 bar and 100 kbar. We find that J has a substantially weaker pressure dependence than in conventional magnets. We also show that the Hubbard-model parameters describing the low-energy electronic structure are significantly influenced by out-of-plane compositional and structural variations. Finally, we show that the relationship between J and the Neel temperature Tz is poorly described by current theory.

Using high-pressure Raman scattering, we have directly measured the pressure dependence of the inplane superexchange interaction J in antiferromagnetic La&CuO4 between 1 bar and 100 kbar. We find that Jhas a substantially weaker pressure dependence than in conventional magnets. We also show that the Hubbard-model parameters describing the low-energy electronic structure are significantly influenced by out-of-plane compositional and structural variations. Finally, we show that the relationship between Jand the Neel temperature Tz is poorly described by current theory.
One of the current challenges of condensed-matter physics is developing a better understanding of the electronic structure of the high-T, superconductors and their insulating parent compounds. The low-energy electronic structure of these materials seems to be well described by single-or multiband Hubbard models, ' incorporating hy- There is currently considerable debate ' as to how structural variations among different high-T, materials inhuence the Hubbard-model parameters. Based on spectroscopic measurements on different members of the 2:1:4 family, it has been argued that J and 5 depend predominantly on the in-plane Cu-0 spacing r. ' However, such comparisons alone cannot uniquely distinguish the effects of variations in r from those due to variations in out-of-plane composition and atomic positions. Spectroscopic measurements of J and 5 as a function of applied pressure, and their comparison with the results of material variation studies, can provide new insight into this issue. In addition, high-pressure spectroscopic measurements, in combination with electronic-structure calculations, are essential for understanding the underlying mechanisms responsible for the remarkable pressure sensitivities of the superconducting" and magnetic ordering' transitions, as well as for explaining qualitative details and trends of the electronic structure among different Cu-0 materials.
In this paper we report measurements of the pressure dependence of J in a copper oxide, focusing on antiferromagnetic LazCuO4 as the archetype of this class of compounds.
Compared to more prosaic transition-metal magnets we find that Jhas an anomalously weak pressure dependence. We also show that variations in J and 6 among different members of the 2:1:4 family are significantly influenced by out-of-plane compositional and structural variations, contrary to previous interpretations. ' Finally, we compare the pressure dependences of J and the three-dimensional (3D) magnetic ordering temperature T& and find that their relationship is poorly described by current theory. Two-magnon Raman scattering has provided a direct determination of J in a number of high-T, materials. ' However, high-pressure Raman measurements on opaque materials have been extremely limited. ' The twomagnon Raman spectrum of LazCuO4 presents particular difhculty as it is weak and very broad, necessitating the virtual elimination of the strong Raman scattering and fluorescence from the diamond anvils for an accurate determination of J. We accomplished this by developing a new diamond-anvil cell design which allows for more efticient spatial filtering of the collected light compared to previous approaches. ' Our technique' greatly expands the range of weakly scattering opaque materials accessible to high-pressure Raman scattering. The Raman-scattering measurements were performed on a single crystal of LazCuO4, grown from CuO fIux. The as-grown crystal was annealed in nitrogen at 750'C for 9 h, a procedure which reduces the oxygen doping level to yield an antiferromagnetic sample with T& of 308 K, measured by magnetic susceptibility. After mechanically polishing the sample to a thickness of 20 pm along the c axis, it was cleaved along the a and b axes with dimension of 60X 180 pm in the a-b plane. The oriented sample was loaded into the diamond-anvil cell using krypton as the pressure transmitting medium. The 7-mW incident laser beam was focused into a 50X 100 pm line on the sample. The Raman scattered light was analyzed with a Spex triple spectrometer and a charge-coupled-4657 1991 The American Physical Society device (CCD) detector. The pressure inside the cell was determined from the shift of the fluorescence peaks of a small ruby chip placed next to the sample. ' In Fig. 1 we show the room-temperature B &g symmetry Raman spectra for pressures ranging from 1 bar to 100 kbar. There was no significant scrambling of the polarizations by the strain birefringence of the diamond. The data have been corrected for the wavelength-dependent response of the collection optics, spectrometer, and detector. A linear fluorescence background from the samples has been subtracted. No pressure dependence of the resonance enhancement of the two-magnon scattering was evident, so we present results only for an incident wavelength of 4579 A.
The pressure dependence of J can be extracted' from the first and second moments M, =3.58J and Mz =0.81J of these spectra. These relations di6'er significantly from the corresponding classical ones, reflecting the strong quantum Auctuations of this two-dimensional (2D) spin--,  Numerical calculations ' of 3d-2p overlaps have found that t d--1/r" with 2. 5~n~3.0. Thus, the pressure dependence of J in these magnets arises from that of t d, while 5, U, and Ud are essentially pressure independent.
The anomalous apparent dependence of J on the superexchange path length in La2Cu04 suggests either that 5 and/or t d may have anomalous path-length dependence, or that they do not depend exclusively on the Cu-0 spacing, but also on the interplanar structure. Addressing the first possibility, high-pressure reAectivity measurements find that b, depends only weakly on r, varying as 1/r" with n =0.4+0.4. Using Eq. (1) to combine the measured apparent dependence of J and 6 on r with constrained LDA band-structure estimates for U and Ud, we find that t d --1/r" with n = 1.8+0.2. In contrast, tight-binding fits to LAPW band structures for La2Cu04 at two different lattice constants, as well as atomic overlap calculations predict the much stronger dependence t d -1/r" with 2. 5 n 3.0. This discrepancy may reAect the inadequacy of mean-field density functional calculations for fully including correlation effects.
However, we note that LDA estimates of t d = 1.3 eV and 6 =3.6 eV do not satisfy tpd &&6, so the perturbation theory expression for J may itself be invalid. Exact diagonalization studies of small Cu-0 clusters qualitatively support this conclusion, giving a significantly weaker dependence of J on t d than Eq. (1). Constrained LDA band-structure calculations at several lattice spacings combined with exact diagonalization studies of larger clusters are required to definitively rule out an anomalously weak path-length dependence for t d.
The second possibility is that the Hubbard-model parameters are sensitive to variations in interplanar structure. Comparing the apparent dependences of Jand 6 on Cu-0 spacing extracted from pressure measurements with those deduced from measurements ' on different 2:1:4compounds supports this possibility. For example, the material variation studies of Cooper et al. deduced that J-1/r" with n =4+2, in mild disagreement with the apparent dependence derived from our pressure measurements of n =6.4+0.8. Furthermore, the weak apparent dependence of 6 on Cu-0 spacing deduced from pressure measurements on LazCu04, is in dramatic contrast to the very strong apparent dependence of 1/r" with n =6+2 found in material variation studies.
Applying pressure or varying the out-of-plane composition and atomic positions both result in simultaneous changes in the intraand interplanar distances, albeit in different ways. Nevertheless, if the in-plane Cu-0 spacing is the single relevant length scale for determining low-energy electronic structure, then J(r ) and b, ( r) should be identical for the pressure and material studies.
The extent of the disagreement demonstrated here clearly indicates that this is not the case. While a Hubbardmodel description involving Cu and O orbitals originating in the plane seems to be a valid simplification of the low-energy electronic structure, our results indicate that the Hubbard-model parameters depend on the full 3D structure of the material. Although our data do not provide an indication of what the most important out-ofplane structural features are, we note that recent theoretical work ' has found for a large number of high-T, materials that the Madelung potential contributions to 6 depend significantly on the out-of-plane structure.
Measurements of the pressure dependence of J can be combined with high-pressure neutron-diffraction measurements' of TN to estimate the dependence of the effective interplanar coupling J~o n the interplanar spacing R. As a result of the interlayer coupling, domains in adjacent layers order in 3D at a Neel temperature TN, which is a function of the domain size g, the reduced moment M and Jy given self-consistently by T~=J~M g (Tz) . (2) The temperature dependence of the 2D correlation length g has the form 27Tps g(T&) =C&a exp B TN (3) where a is the lattice constant, C& =0. 5, and the spinwave stiffness 2~p, =0.94J.
The pressure dependence of J~i s extracted from Eqs.
(2) and (3) by combining our measurements of J(P) with those of Tz(P) (Ref. 12) and ambient pressure M2, 29 both measured by neutron scattering on samples of La2CuO4 with a somewhat higher oxygen doping level and lower TN than our sample. The calculated J~i s extraordinarily sensitive to pressure, increasing about a factor of 20 in 100 kbar. While J~s hould increase as R decreases, we regard the extracted pressure dependence to be unphysically strong. It is likely instead that Eq. (2)  significantly influenced by the out-of-plane composition and atomic positions. Finally, we conclude that the existing selfconsistent theory does not adequately describe the 3D magnetic ordering in LazCu04. The improvements in high-pressure Raman-scattering techniques reported here allow the application of these powerful pressure studies to a substantially wider class of materials than has been possible previously. Ohta, Tohyarna, and Maekawa recently reported a theoretical analysis of the material dependence of Jand 5 which supports our conclusions. However, we do not agree with their suggestion that the weak-pressure dependence of J results from a cancellation of the pressure dependencies of t d and A. instead, we believe, as discussed above, that it arises because either (a) the large value of t~d /b leads to a reduction in y from the perturbation theory result that y =4, where Ithor (b) t d has an anomalously weak dependence on te Cu-0 spacing.
Part of this work was performed while M.C.A. was at Los Alamos National Laboratory, Los Alamos, New Mexico, and S.B.D. at AT%T Bell Laboratories, Murray Hill, New York. M.C.A. is grateful to the Superconductivity Pilot Center, Los Alamos National Laboratory for travel assistance. Work at Los Alamos was performed under the auspices of the U.S. Department of Energy. P. W. Anderson, Science, 235, 1196; V. J. Emery, Phys.