Inelastic neutron spin waves

Inelastic neutron scattering(INS) measurements probe directly the imaginary part of the dynamical spin susceptibility. Therefore, it is of interest to analyze the role played by the electronic correlations in connection with the resonance peak seen by INS[3], This feature is well understood using various approaches[20, 21] as a result of the spin density wave(SDW) collective mode formation at co = coreSt i.e. when the denominator of the RPA spin susceptibility at the antiferromagnetic wave vector Q is close to zero. 

The results of two inelastic neutron scattering experiments on U2Zn17 are rather controversial (Walter et al. 1987, Broholm et al. 1987a). Common features shared by both works are the absence of spin-wave excitations and the presence of a broad Lorentzian quasi-elastic line with T of the order of 10 meV, persisting across Tn. 

The same study (Neville et al. 1996) also reports on inelastic neutron scattering measurements. They show spin wave excitation at low temperatures which, however, collapse into a diffusive response at 10 K (see in this connection also the discussion on USb). The 10 K point is clearly a special temperature but its exact nature remains enigmatic. But without doubt, this Kondo material exhibits most imusual spin d3mamical properties. Further studies are called for. 

There have been attempts to calculate the spin wave contribution to the heat capacity from inelastic neutron scattering data for Tb and Gd (Sedaghat and Cracknell, 1971 Stevens and Krukewich, 1973). The former found the power of T to increase with increasing temperature for gadolinium from n = 1.56 to n = 2.3, but no simple power law above 14 K. The latter investigators found n 1.5 for terbium and gadolinium. Wells et al. (1974) have confirmed that for... 

Well below T, in the zero-temperature limit, the excitations out of the antifer-romagnetically ordered ground state of eq. (2) are spin waves. Neglecting interlayer coupling, conventional spin-wave theory in the classical (large-5) limit predicts a dynamic susceptibility (as measured ly inelastic neutron scattering) of the form... 

Elementary excitations ( dynamics ) in condensed matter systems maybe studied by inelastic neutron scattering. A large proportion of solid-state physics concerns dynamical phenomena ( collective excitations ) in crystalline materials, such as lattice vibrations (phonons), or spin waves (magnons) (see, e.g., Aschroft and Mermin 1976). These phenomena have been... 

Recent detailed study of the spin-wave dispersion by Bohn et al. (1980) in a single crystal of EuS (enriched with Eu) by inelastic neutron scattering technique (fig. 6a) confirms previous assumptions that the range of the exchange interactions is essentially limited to the second nearest neighbors = 0.220 K and 2/ 6 "... 

Fig. 6. (a) Spin-wave dispersion in EuS, measured by inelastic neutron scattering at 7 =1.3K (T = 16.6 K). The solid lines represent the best fit using up to fifth neighbors exchange interactions. The arrows indicate the boundary of the first Brillouin zone in the various symmetry directions (from Bohn et al. 1980). (b) Dependence of the exchange interactions, /, and /j, on the Eu-Eu distance in the Eu-chal-cogenides. 

Certainly the clearest conclusion from the examples of this chapter is the total absence of sharp features in the inelastic response function of anomalous lanthanide and metallic actinide materials. This contrasts strongly with the sharp dispersionless crystal-field excitations observed in most lanthanide compounds, in which the exchange interactions are weak (fig, 2), and with the sharp spin-wave excitations found in systems with strong exchange interactions. In many of the early studies with neutron inelastic scattering, for example of the heavy lanthanides or transition metals and their compounds, the width of the excitations was never an issue. It was almost always limited by the instrumental resolution, although it should be stressed that this resolution is relatively poor compared to that obtained by optical techniques. However, the situation is completely different in the materials discussed in this chapter. Now the dominant factor is often the width indeed in some materials the width of the over-damped response function is almost the only remaining parameter with which to characterize the response. 

In a recent critical analysis Dietrich et al. (1975) compare these experiments and argue that specific heat and NMR at temperatures less than about jTc sample only spin waves with low wave vector. In that region the spin wave energy depends only on the stiffness constant, being proportional to the sum of (Ji + J2) and thus Ji and I2 cannot be determined individually. On the other hand, inelastic neutron scattering determines the dispersion of the spin waves over the entire Brillouin zone and the best fit of spin wave theory to these data yield /i and I2 separately and J2 is shown to be positive. The recommended values for 7i,2 of EuO and EuS are also collected in table 19.2. 

The mechanism responsible for the formation of Cooper pairs in the superconductive state remains unsolved. Extensive spin-polarized inelastic neutron-scattering experiments have revealed a 41 meV resonance in the spin-excitation spectrum of the superconductive copper oxides that has caught theoretical attention [317]. Carbotte et al. [318] have noted that if these spin excitations are strongly coupled to the charge carriers, they should also be seen as a peak in the optical conductivity. They therefore calculated a((o) for a d-wave superconductor with inelastic scattering from the neutron data. Comparison with a-axis optical-conductivity data [319] showed that the... 

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