The search for quantum critical scaling in a classical system

Abstract

Order-disorder phase transitions in magnetic metals that occur at zero temperature have been studied in great detail. Theorists have advanced scenarios for these quantum critical systems in which the unusual response can be seen to evolve from a competition between ordering and disordering tendencies, driven by quantum fluctuations. Unfortunately, there is a potential disconnect between the real systems that are being studied experimentally, and the idealized systems that theoretical scenarios are based upon. Here we discuss how disorder introduces a change in morphology from a three-dimensional system to a collection of magnetic clusters, and we present neutron scattering data on a classical system, Li͓Mn Quantum fluctuations can be strong enough to prevent a system from ordering, even at 0 K. In metals that possess atomic magnetic moments, one can tweak the strength of the magnetic interactions compared to the disordering quantum fluctuations in such a way that the system orders exactly at 0 K. Such a system is said to be at the quantum critical point ͑QCP͒. The interest in such systems is easy to understand. One can expect a new type of ordering behavior because the spatial and temporal dimensions are no longer independent at 0 K.1 Also, one can expect new physics to emerge. After all, when a system is on the verge of ordering at 0 K, the degrees of freedom that prevent the system from ordering also provide a channel for the system to adopt a new, lower energy ground state. An example is the observed superconducting state 1 that forms close to the QCP with quasiparticles consisting of some admixture of magnetic moments and conduction electrons.The question that has attracted most attention is "what exactly happens at the QCP?" On the one hand, 2 it could be that all moments will become fully shielded at some finite temperature, with the residual interaction between the resulting heavy quasiparticles driving the system toward ordering ͓Fig. 1͑a͔͒. On the other hand, 2 the QCP could be the point in the phase diagram where vestiges of moments can survive all the way down to 0 K upon cooling without being completely screened though the Kondo effect, resulting in long-range order ͓Fig. 1͑b͔͒. Unfortunately, the experimental situation is much murkier than a simple choice between these two possible answers.To drive a system to a QCP, one tweaks the interaction between moments by changing the degree of overlap between the local atomic orbitals and the extended conduction electron bands. Ideally, one simply applies hydrostatic pressure to a system without any intrinsic disorder, and all magnetic moments will undergo the same temperature evolution. This is the situation that most theoretical efforts have focused on ͓Ref. 1͔. In some experiments however, one cannot attain the high pressures required and one results to applying chemical pressure. Here, some elements are substituted with different sized ones so as to achieve lattice expansion/ contraction at the cost of introducing some disorder. However, it was generally...

Magnetic excitations in the spinel compoundLix[Mn1.96Li0.04]Heitmann1, Schmets2, Gaddy3 et al. 2010Phys. Rev. BSelf Cite9040View full textAdd to dashboardCite

“…͑1͒, independent of the value of q. Thus, similar to the fully lithiated case, 28 the dynamics for all x do not show any length scale dependence ͑see Fig. 7͒, at least in the range 0.5Ͻ q =2 / Ͻ1.8 Å −1 .…”

“…To do so, we study the classical spinel system Li x ͓Mn 1.96 Li 0.04 ͔O 4 ͑x = 0.2, 0.6, 0.8, 1.0͒ by means of inelastic neutron-scattering experiments. This is an extension of the work of Lamsal et al 28 who investigated the possibility of E / T scaling in the x = 1.0 compound. We show that the dynamics of the magnetic clusters that are present in these systems 29 below ϳ70 K do indeed mimic E / T-scaling behavior for all concentrations x; these concentrations cover geometrically frustrated short-range magnetism ͑x = 1.0͒ to long-range magnetic ordering ͑x = 0.2͒.…”

“…Lamsal et al 28 have shown that the data taken in the pilot experiment 38 on the fully lithiated compound ͑x = 1.0͒ display what looks like E / T scaling for T = 30, 50, and 70 K. We extend these observations to all concentrations x in order to show that the mimicking of E / T-scaling behavior is present for all x, even when long-range order is present at low temperatures ͑x = 0.2͒. To demonstrate this, we plot the full response for T = 24, 33, 41, and 100 K as a function of E / T for all four concentrations x in Fig.…”

Universality, Scaling, and Collapse in Supercritical Fluids

“…Finally, it is worth pointing that the Widom delta in Fig. 1(a-b) is akin to the "fan-shaped" quantum critical region found near metal-insulator transitions, where universality and scaling are expected 18,19,25,26 .…”

Magnetic ordering in the spinel compound Li[Mn2−xLix]O4(x=,0.04)

“…As to the latter, if the structural units were indeed that small, we should expect to see a difference in the quasielastic scattering between when the units are probed on a length scale smaller than or larger than their size L, around q =2 / L ϳ 1.2 Å −1 . However, the quasielastic scattering 4,9 displays no length scale dependence, as shown in Fig. 2.…”