Theoretical Analysis of Inelastic Neutron Scattering in Solid Hydrogen

The inelastic-neutron-scattering cross section of (J=1) solid hydrogen is studied and the experimental data of Stein and co-workers analyzed. The rms displacement ⟨u2⟩1/2 is deduced from the data via different methods and mutually consistent values of order 0.65 Å are obtained. The enhancement of the cross section at the libron energy due to libron-phonon interactions is found to be the same, about 40% each for both one-and two-libron processes, in agreement with the neutron scattering data. The rms splitting at the libron-phonon crossovers is found to be about 1 cm−1, somewhat smaller than found by Mertens and Biem. A sum rule for the J=1 to J=0 cross section is given which relates the average energy of this transition to the orientational internal energy. Using high-temperature expansions and experimental data for the specific heat, we obtain a qualitative fit to the neutron scattering data in the orientationally disordered phase. In the ordered phase both the sum rule and a direct calculation indicate the existence of a libron sideband above the main J=1 to J=0 line having an intensity of 10% of the main line. The energy of the main line at zero temperature is calculated including (a) tipping corrections, (b) virtual excitations with J not conserved, and (c) modified zero-point energy. The value of the electrostatic quadrupole-quadrupole coupling constant deduced from the data of Stein and co-workers using this calculation is in agreement with that obtained from other experiments

High-Temperature Expansion for the Orientational Specific Heat of Solid H\u3csub\u3e2\u3c/sub\u3e and D\u3csub\u3e2\u3c/sub\u3e

Terms up to order (Γ/kBT)5 in the high-temperature expansion of the orientational specific heat of ortho-para alloys of solid H2 or D2 are evaluated. Good agreement is obtained between theory and experiment using a Padé approximant and effective values of the quadrupolar coupling constant, Γeff/Γ0=0.83 for D2 and Γeff/Γ0=0.80 for H2, where Γ0 is the value for a rigid lattice. These values agree with other determinations of Γeff, whereas the T−2 approximation for the specific heat yields anomalously small values of Γeff

Two-Libron Spectrum of Solid H\u3csub\u3e2\u3c/sub\u3e and D\u3csub\u3e2\u3c/sub\u3e

It is shown that the two-libron lines in the Raman spectrum of solid hydrogen result from the large cubic anharmonicity of the quadrupole-quadrupole Hamiltonian. A localized picture is used to describe the interaction of two librational excitations on neighboring molecules, and dynamic interactions with other molecules are treated perturbatively. In this approximation the average single-libron energy agrees with the anharmonic calculation in the accompanying paper. Using a value of the quadrupole-coupling constant obtained from the single-libron spectrum, the resulting two-libron energies and Raman transition probabilities are in excellent agreement with the observed spectrum

Orientational Phases of Hydrogen Molecules on a Triangular Lattice

A mean-field theory for the ordering of hydrogen molecules on a triangular net is derived in terms of the quadrupole coupling constant Γ, the crystal field Vc, and the temperature T. The phase diagram consists of six regions, separated by first- and second-order transitions. For almost all values of Vc/Γ for which ordering occurs, the disordered to ordered phase transition is continuous. At T=0 K, all phases have energy gaps except for a ferrorotational phase which behaves like an XY model

Effects of Librational Anharmonicity in the Solid Hydrogens

We compare the results of the recently published anharmonic theory of librons to the best available data on the libron Raman frequencies. This allows us to deduce a refined estimate of the effective value of the intermolecular quadrupolar coupling constant Γeff for solid H2 and D2. The effect on the librons of virtual transitions to the (J=3) rotational state is included with the result that Γeff is decreased. Our estimate from the optical data is then Γeff=0.72±0.04 and 0.58±0.03 cm−1 for D2(x=1) and H2(x=1), respectively, at zero pressure, where x denotes the mole fraction of J=1 molecules. We also use the anharmonic density of states to analyze specific heat and (∂P/∂T)V data from which we obtain the average libron energy as a function of x. For D2(x=1) the result is Γeff=0.70±0.04 cm−1. Measurements of the conversion-induced pressure change in H2 give Γeff=0.56±0.03 cm−1. Both these determinations are in good agreement with the results from optical data for librons. Furthermore, it is found that there is no significant difference between Γeff(x=1) and Γeff determined from pair spectra in H2 and D2 with x≪1. The anharmonic density of states is also used to interpret the infrared absorption sideband spectrum for the creation of a vibron plus libron(s). The part of the spectrum which we attribute to one-libron processes has a width in agreement with this model and as expected there are two-libron processes resulting from cubic anharmonic libron-libron interactions. Incoherent-neutron-scattering data is also consistent with the anharmonic-libron spectrum

Possible Néel Orderings of the Kagomé Antiferromagnet

Possible Néel orderings of antiferromagnetically coupled spins on a kagomé lattice are studied using linear-spin-wave theory and high-temperature expansions. Spin-wave analysis, applied to q=0 (three spins per magnetic unit cell) and to √3 × √3 (nine spins per cell) Néel orderings yield identical excitation spectra with twofold-degenerate linear modes and a dispersionless zero-energy mode. This dispersionless mode is equivalent to an excitation localized to an arbitrary hexagon of nearest-neighbor spins. Second- (J2) and third- (J3) neighbor interactions are shown to stabilize the q=0 state for J2\u3eJ3 and the √3 × √3 state for J23. A high-temperature expansion of the spin-spin susceptibility χαβ(q) is performed to order 1/T8, for n-component, classical spins with nearest-neighbor interactions only. To order 1/T7 the largest eigenvalue of the susceptibility matrix is found to be independent of wave vector with an eigenvector that corresponds to the dispersionless mode of the ordered phase. This degeneracy is removed at order 1/T8. For n=0, the q=0 mode is favored; for n=1, the band is flat; and, for n\u3e1, the maximum susceptibility is found for a √3 × √3 excitation. Similar results are found for the three-dimensional pyrochlore lattice. The high-temperature expansion is used to interpret experimental data for the uniform susceptibility and powder-neutron-diffraction spectrum for the kagomé-lattice system SrCr8−xGa4+xO19