Paramagnon

Fig. 3.18 Reciprocal of paramagnetic mass susceptibility x 1 of Ni 00 - Gax for various compositions near Ni3Ga as a function of T (de Boer et al 1969). Note the behaviour, here ascribed to paramagnons, at compositions 73 and 73.5 at the lowest temperature.

Perhaps the most sensitive test for the presence of paramagnons is the predicted large T2 term in the resistivity if this occurs without a correspondingly large increase in y then paramagnons rather than Baber scattering are indicated. Figure 3.20 (from Tari and Coles 1971) shows the behaviour of the constant A in Pd-Ni, where... 

Fig. 3.19 Expected effect on susceptibility due to paramagnons (schematic) (a) without enhancement (b) with Stoner enhancement (c) effect of paramagnons.

This kind of enhancement, which occurs for a half-full band near the point where an antiferromagnetic lattice forms, is quite different from the Stoner enhancement for nearly ferromagnetic metals described in Chapter 3, Section 11. The latter occurs for non-integral occupation of a d-band, and enhances the Pauli susceptibility only, not the specific heat, apart from probably small paramagnon effects. 

Paramagnon energy is connected with antiferromagnetic correlation length ... 

Other features of a Fermi liquid emerge when a perturbation that is slowly varying in space and time is coupled either to spin or charge degrees of freedom. The mean-field that wraps up each quasi-particle in a Fermi liquid acts as a coherent restoring force that leads to a collective response of the system as a whole. One then finds two types of collective or sound modes, namely the charge (or the plasmons for a metal) and the spin (paramagnons) modes [52]. 

Consider for example the paramagnons of an anisotropic 2D Fermi liquid as described by the one-electron spectrum (2) with = 0 the imaginary part of the retarded spin response function at low frequency is found to be... 

The absence of pole on the real axis in this expression indicates - as is the case for isotropic Fermi liquid [52] - strong damping of paramagnons. Nonetheless, the spectral weight shows a peak at... 

It should be noted here that the expression for the relaxation rate slightly differs when paramagnons induce weak ferromagnetism. In this case, (TD varies as a power of the spin... 

The presence of a delta function in this expression indicates the absence of damping for paramagnons in a Luttinger liquid - in contrast to a Fermi liquid (see Eq. 9) - this also indicates that spin collective excitations are exact eigenstates of the system in one dimension (similar conclusions also hold for the charge part). Now close to q = 2k% one can use the following expression [118] ... 

The paramagnon contribution to the specific heat has been evaluated by Doniach and Engelsberg (1966) and Brinkman and Engelsberg (1968). It yields an enhancement of the linear electronic term, which can be conceived as an enhancement of the effective mass of the electrons. It can be written as... 

This quite general concept is used to specify any shift (in time and space) between the instantaneous value of magnetic moments and dieir mean value given by flie molecular field approximation and the Boltzmann statistics. Spin fluctuations can be individual and/or collective. In the latter case processes such as spin waves or paramagnons are considered and many models have been developed to interprete experiments with these concepts. 

Fig. 17.36. Excitation spectrum of the coupled electron-ion system. The dashed line indicates the paramagnon pole.

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