Dynamical spin-susceptibility of itinerant heavy electrons with nested Fermi surface

Abstract

Heavy fermion systems frequently display non-Fermi liquid behavior due to a nearby quantum critical point. A nested Fermi surface together with the remaining interaction between the carriers after the heavy particles are formed may give rise to itinerant antiferromagnetism. The model under consideration consists of an electron pocket and a hole pocket, separated by a wave vector $\mathbf{Q}$ and Fermi momenta ${k}_{F1}$ and ${k}_{F2}$, respectively. The order can gradually be suppressed by increasing the mismatch of the Fermi momenta, defined as $2\ensuremath{\delta}={v}_{F}\ensuremath{\mid}{k}_{F1}\ensuremath{-}{k}_{F2}\ensuremath{\mid}$, and a quantum critical point is obtained as ${T}_{N}\ensuremath{\rightarrow}0$ at a mismatch value ${\ensuremath{\delta}}_{0}$. The dynamical spin susceptibility, ${\ensuremath{\chi}}^{\ensuremath{''}}(\ensuremath{\omega},\mathbf{Q}+\mathbf{q})$, which is of relevance to inelastic neutron scattering, is calculated. The mismatch of the Fermi vectors, for $\ensuremath{\delta}\ensuremath{\geqslant}{\ensuremath{\delta}}_{0}$, has the following consequences: (i) For the tuned quantum critical point (QCP), the specific heat $\ensuremath{\gamma}$ coefficient and the magnetic susceptibility increase with the logarithm of the temperature as $T$ is lowered. (ii) For the tuned QCP the linewidth of the quasiparticles is sublinear in $T$ and $\ensuremath{\omega}$. (iii) The specific heat and the linewidth display a crossover from non-Fermi liquid $(\ensuremath{\sim}T)$ to Fermi liquid $(\ensuremath{\sim}{T}^{2})$ behavior with increasing nesting mismatch and decreasing temperature. (iv) For the tuned QCP, the dynamical susceptibility has a quasielastic peak with a linewidth proportional to $T$. For small ${v}_{F}q$, the central peak becomes inelastic. (v) For noncritical Fermi vector mismatch, the peak is inelastic. (vi) In all cases for large ${v}_{F}q$, a broad quasielasticlike peak develops. (vii) While the specific heat, the homogeneous susceptibility, and the quasiparticle linewidth are only weakly dependent on the geometry of the nested Fermi surfaces, the momentum-dependent dynamical susceptibility is expected to be affected by the shape of the Fermi surface.