Quantum Griffiths effects in metallic systems

Abstract

We show that two apparently contradictory theories on the existence of Griffiths-McCoy singularities in magnetic metallic systems [1,2] are in fact mathematically equivalent. We discuss the generic phase diagram of the problem and show that there is a non-universal crossover temperature range T * < T < ω0 where power law behavior (Griffiths-McCoy behavior) is expect. For T < T * power law behavior ceases to exist due to the destruction of quantum effects generated by the dissipation in the metallic environment. We show that T * is an analogue of the Kondo temperature and is controlled by non-universal couplings. The problem of non-Fermi liquid behavior (NFL) in U and Ce intermetallics continues to attract a lot of attention due to the breakdown of Landau's Fermi liquid theory in metallic alloys [3]. NFL is often characterized by power law or logarithmic temperature behavior in physical quantities such as the magnetic susceptibility, χ(T ) and specific heat, C V (T ). Many NFL materials have as common features the closeness to a magnetic phase transition and disorder generated by the alloying [4]. It has been proposed that NFL behavior can be associated in some materials with quantum Griffiths-McCoy singularities close to a quantum critical point (QCP) [5]. These singularities are related with the tunneling, at low temperatures, of magnetic clusters with N spins generated by the percolating nature of the magnetic phase transition. As a result, the physical properties acquire non-universal power law behavior, χ(T ) ∝ C V (T )/T ∝ T −1+λ , with the exponent λ < 1 dependent on the distance from the QCP. While in its first version [5] the theory did not consider properly the dissipation coming from the electronic degrees of freedom, it was extended to include dissipation [1] with the final conclusion that power law behavior disappears below a crossover temperature T

Composition induced metal–insulator quantum phase transition in the Heusler type Fe2VAl

“…Likewise, as we previously claimed for Fe2+xV1−xAl near the paramagneticferromagnetic QCP at x  0.05 [12,21], the low-temperature enhancement in C/T that we observed at x  −0.05 and the singular temperature dependence, approximated by T −1 , can be reminiscent of a Griffiths-McCoy singularity near the QCP (Fig. 4(a)) [26]. As indicated below, there was an obvious MI transition in the vicinity of x = −0.05 and T < 0.25 K. The exponent(x) obtained from low-temperature specific heat data showed the characteristic features expected for a Griffiths phase [26]; that is,  was approximately 0 at the quantum critical point of xMIT and recovered to that of a Fermi liquid  1, with increasing distance from the QCP (Fig.…”

“…These inconsistencies with the J = 3/2 cluster model can be explained reasonably well by the fact that the antisite Fe occupying the V site facilitates the establishment of itinerant (ferromagnetic) features in Fe2+xV1−xAl at x > 0 [12] and the fact that an inhomogeneous state (Griffiths phase) that appears to consist of ferromagnetic and paramagnetic clusters emerges at 0 < x < xc m [21]. In a theoretical study, Neto et al found that a Schottky anomaly in the specific heat, due to a magnetic field, appears close to the QCP for magnetic ordering in magnetic metallic systems [26].…”

“…4(a)) [26]. As indicated below, there was an obvious MI transition in the vicinity of x = −0.05 and T < 0.25 K. The exponent(x) obtained from low-temperature specific heat data showed the characteristic features expected for a Griffiths phase [26]; that is,  was approximately 0 at the quantum critical point of xMIT and recovered to that of a Fermi liquid  1, with increasing distance from the QCP (Fig. 4(a), inset).…”

Ferromagnetic quantum singularities and small pseudogap formation in Heusler type Fe2+xV1−xAl

“…5(b)] at a temperature slightly higher than T C . It was theoretically obtained by Neto et al 28 that the low-temperature divergence is strongest at the QCP (λ = 0) and the Fermi liquid characteristics (λ = 1) are established far from the QCP. Although it would be still controversial whether the C/T upturn at the zero field is due to a distribution of magnetic anisotropies in paramagnetic clusters 3 or due to proximity to the ferromagnetic QCP, 26 Actually, at x = 0.05 resistivity, ρ(T ) shows NFL behavior: ρ − ρ 0 = A T n , with n < 2 as shown in Fig.…”

Rare region effects at classical, quantum and nonequilibrium phase transitions

“…For Ising symmetry, which is relevant for the heavy-Fermion systems as most of them have sizeable spin anisotropies, the damping causes the rare regions to freeze leading to a smeared transition rather than quantum Griffiths effects [60][61][62]. Later, Castro Neto and Jones refined their theory by including the damping [282,283]. They found that for sufficiently weak damping there will be a crossover temperature T * .…”