We have an enduring interest in understanding how magnetic order occurs in metallic systems. Over the years, two different scenarios have been developed. In one limit, the magnetic moments are localized on certain ions, which are magnetic due to partially full d or f shells. The moments are coupled by the itinerant conduction electrons, and two outcomes are possible, depending on the strength of this exchange coupling J. If J is small, then magnetic order is expected at an onset temperature which increases with J. If J becomes large, then the spins of the conduction electrons suppress the magnetic moments via the Kondo effect. In this way, magnetic order is not possible if the exchange interaction is too large. These observations are summarized in the Doniach Phase Diagram, shown at the right.

The Doniach phase diagram shows the temperatures and intermoment coupling strengths J

Since the exchange interaction J depends on the details of the system: the properties of the conduction electrons and the nature of the magnetic moments which they are exchange coupled to, the Doniach phase diagram implies that there are materials having a critical value of J=J_C which are literally poised at the interface of magnetic and nonmagnetic behaviors, i.e. they undergo magnetic order exactly at zero temperature. While there may be some materials which occur naturally at the quantum critical composition (J=J_C), in general it is necessary to tune a system to the quantum critical point (QCP) through compositional variation, or the application of high pressures or high magnetic fields. Much interest is currently concentrated on understanding the properties of the magnetic moments near the QCP, and whether we can regard it as resulting from a suppression of localized magnetic moments, or from a breakdown in coupling between the moments themselves. Our view is that there is no universal answer to this question, and that examples of both sorts of instabilities exist among the materials studied so far.

The dynamical susceptibility of Ce(Ru1-xFex)2Ge2 for x=xc=0.76 can be scaled to a universal expression, shown here. The temperature scale ?(q) vanishes at the antiferromagnetic q=0.4 A-1. A similar measurement on the paramagnetic composition x=0.85 reveals that this scaling collapse only occurs at the QCP.

The properties of a system tuned to be near a QCP are very unusual. We have used neutron scattering measurements to study how spatial and temporal correlations develop near antiferromagnetic QCPs in several different systems. Our early studies on UCu4Pd showed that the fundamental magnetic excitations have no characteristic energy scale, other than the system temperature itself, for a large range of excitation energies and sample temperatures. Further, we found that the magnetic correlations in this system never extend outside the unit cell, and that there is no characteristic propagation wave vector for the nascent magnetic order. Indeed, the only susceptibility in the system which diverges as TY0 is the local susceptibility. It follows that the same sort of dynamical critical behavior is found on every length scale. In contrast to UCu₄Pd, where local physics is responsible for the unusual critical behavior, a very different scenario is found in the system Ce(Ru_1-xFex)₂Ge₂, where Fe doping drives CeRu₂Ge₂ from ferromagnet, to modulated antiferromagnetic order, and ultimately to paramagnetic behavior via a quantum critical point at x=0.76 and T=0. Here, our neutron scattering measurements find that the QCP is driven by a T=0 divergence in the antiferromagnetic correlations, accompanied by the E/T scaling of the dynamical response as was initially found in UCu₄Pd. We have proposed here a phenomenological expression for the dynamical susceptibility which encompasses both the spatial and temporal criticality, and the scaling collapse of the dynamical susceptibility, determined experimentally at more than 12,000 different wave vectors, energies, and temperatures is demonstrated here. More recently, similar measurements on the paramagnetic concentration x=0.85 finds a very different sort of non-critical behavior, which reinforces the general result that the non-Fermi liquid phenomena found near the QCP originate with the anomalous critical fluctuations of a zero temperature phase transition.

Currently, we seek to broaden our understanding of the critical phenomena associated with zero temperature phase transitions by studying ferromagnets as well as antiferromagnets, including local moment and itinerant systems. By analogy to finite temperature transitions, we expect that the spatial dimensionality of the host system may play an important role, and that disorder is very important for limiting the range and lifetime of magnetic fluctuations. Consequently, we are very interested in using continuous variables such as pressure or magnetic field to control proximity to the QCP.