Our attempts to observe the antiferromagnetic resonance (AFMR) modes in La2Cu04+~in both single-crystal and small-particle forms have been unsuccessful. An argument based on a magnetic-susceptibility sum rule shows that the resonance previously identified with the AFMR in polycrystalline La2Cu04+~[R. T. Collins et al. , Phys. Rev. B 37, 5817 (1988)l is too strong to be compatible with a magnetic spin-wave mode. No evidence of an AFMR mode is found in our single-crystal La2Cu04+~transmission measurements versus magnetic field. Additional measurements on small particles show that the broad resonant feature observed around 8 cm ' is produced by an electric-dipole-active superconducting sphere resonance of the La2CuOq+~particles. The recent discovery of superconductivity' at temperatures above 30 K in La2 -"Ba,Cu04+~has brought much attention to the parent compound La2Cu04+y. Early magnetic susceptibility measurements on La2Cu04+s howed anomalies around 250 K which suggested antiferromagnetism in this compound. The antiferromagnetic ordering on the Cu sites was confirmed by elastic neutron scattering. Moreover, inelastic neutron scattering and two-magnori Raman-scattering measurements showed that the intraplanar antiferromagnetic exchange interaction in La2Cu04+~, as well as in YBaqCu306+y, is quite strong. Collins et a/. have reported a very broad antiferromagnetic resonance (AFMR) feature at 9 cm '. Using neutron scattering together with the results of Ref. 6, Peters eta/.reported in-plane and out-of-plane spinwave excitations at energies of 8+ 2 and 20+ 4 cm ', respectively. The identification of the modes would appear complete were it not for the fact that we find the measured strength of the reported AFMR mode to be more than an order of magnitude larger than the value required by the measured dc susceptibility. In this paper, we first show that the far-infrared line strength of the reported AFMR in powder samples is not consistent with the measured dc magnetic susceptibility. Next we demonstrate with single-crystal samples that an absorption line of the same strength is not observed. To identify the origin of the observed resonance we have made additional far-infrared measurements on LaqCu-04+~, in small particle form. Our study shows that the resonant feature observed by Collins et al. is most likely a superconducting sphere resonance similar to that previously observed in La2 -"Sr"Cu04+y.To show that the resonance feature reported by Collins et a/. is not consistent with AFMR, we use a susceptibility sum rule which relates the magnetic absorption strength of the AFMR to the dc magnetic susceptibility for linearly polarized light, namely j~h , a;ay~; (0) =, ", ' dto . n "p co Here g~;(0) is the contribution to the dc magnetic susceptibility in emu/cm produced by the ac response of magnetic mode i Both A. tt; and to are given in cm, and n is the low-frequency index of refraction produced by the electric dipole active TO modes of the lattice vibration spectrum; n is assumed to be a constant over the FIR frequen...

Sum rules and causality are used to obtain a general relation connecting the dynamic and static properties of any dielectric system which supports polarization waves. The Lyddane-Sachs-Teller relation appears as a special limiting case. Inhomogeneous media provide illustrative examples. PACS numbers: 42.20.Dd, 63.50.+X, 77.80.-eThe Lyddane-Sachs-Teller (LST) relation 1 remains a and corner stone in the understanding of displacive ferroelectricity. Frohlich 2 and Cochran 3 first recognized the connection between the static and dynamic properties of ferroelectrics because the LST relation for a simple homogeneous dielectric, 60/^oo-WM 2(1) provided a connection between the transverse and longitudinal frequencies, co t and coi, and the dc and optical dielectric constants, 6o and 6«>, in the dielectric response function. Equation (1) has been generalized to cubic crystals with more than two atoms per unit cell 3 and also to include the case of damping. 4 In addition, Barker 5 found that Eq. (1) could be obtained from a causality argument if the response approximated a ^-function mode at co t . All of these extensions treat single crystals. With sum-rule and causality arguments we show that for any nonconductor the ratio of the static and highfrequency dielectric constants equals the ratio of second moments of the longitudinal and transverse loss. By simulation this general relation is shown to describe exactly the connection between the dynamic and static properties of inhomogeneous media in the long-wavelength limit for two distinct topologies.Consider a nonmagnetic linear isotropic dielectric system which is described by the dielectric function eico) -Ree"(] while the corresponding irrotational loss function is Im[ -eoo/eico)].One way to identify characteristic frequencies of this arbitrary system is using a moment representation. 6 With the LST relation in mind, we define a weighted second moment of the solenoidal and irrotational loss peaks as (a> 2 ) t = f ^x 2 Im Jo dx X e(x) r •Jo dx Im £00 i -i (2) / = r^x Jo v X Im -e» e(x) Jo dx Im e-Oc) -l (3) using an obvious notation. Next we make use of a general sum-rule result that 7,8 JT* xlm -6* e(x) J 9 OO o dx xlm c(x)Each of the integrals involved is an "/-sum rule" which can be obtained from a Kramers-Kronig relation plus the requirement that in the high-frequency limit the response is free-particle-like. Therefore, the numerator in Eq. (3) is equal to the numerator in Eq. (2) and the ratio of the two equations simplifies to <0) 2 )/ Jo > (dx/x)lml€(x)/€oo] (co 2 )t "/o°(rfx/x)Im[-6ooMx)] (5) A Kramers-Kronig integral connecting the real and imaginary parts of the solenoidal response function is 9 K J 0 xIm[c"(x)/6oo] *Re f(o>) -1 which when evaluated at co ""0 reduces to i_ r°°dx KJO x Im e-(x) *0 -1. (6) (7) In a similar manner one can ev...

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We have measured the spectral dependence of the diffuse reflectivity of polished sintered pellets of YBa2Cu307y La2 -Sr"Cu04y and related superconducting and nonsuperconducting oxides between 500 and 5000 cm ' at room temperature. The growth in ir scattering with decreasing frequency is qualitatively explained by the anisotropic conductivity of these materials. Even at its peak ir value the effect is too small to alter significantly the optical constants obtained from specular reflectivity measurements.Since no additional scattering occurs near 0.5 eV, the absorption observed in sintered pellets at that energy cannot be associated with an anisotropic electronic excitation.