The break-up of heavy electrons at a quantum critical point

Abstract

The point at absolute zero where matter becomes unstable to new forms of order is called a quantum critical point (QCP). The quantum fluctuations between order and disorder 1-5 that develop at this point induce profound transformations in the finite temperature electronic properties of the material. Magnetic fields are ideal for tuning a material as close as possible to a QCP, where the most intense effects of criticality can be studied. A previous study 6 on theheavy-electron material Y bRh 2 Si 2 found that near a field-induced quantum critical point electrons move ever more slowly and scatter off one-another with ever increasing probability, as indicated by a divergence to infinity of the electron effective mass and cross-section. These studies could not shed light on whether these properties were an artifact of the applied field 7,8 , or a more general feature of field-free QCPs. Here we report that when Germanium-doped Y bRh 2 Si 2 is tuned away from a chemically induced quantum critical point by magnetic fields there is a universal behavior in the temperature dependence of the specific heat and resistivity: the characteristic kinetic energy of electrons is directly proportional to the strength of the applied field. We infer that all ballistic motion of electrons vanishes at a QCP, forming a new class of conductor in which individual 1 electrons decay into collective current carrying motions of the electron fluid.Recent work 6 on the heavy electron material YbRh 2 Si 2 9 has demonstrated that a magnetic field can be used to probe the heavy electron quantum critical point. This material exhibits a small antiferromagnetic (AFM) ordering temperature T N = 70 mK (Fig. 1a) that is driven to zero by a critical magnetic field B c = 0.66 T (if the field is applied parallel to the crystallographic c-axis, perpendicular to the easy magnetic plane) 6 . For 2 Past experience 7,8 suggested that a finite field quantum critical point has properties which are qualitatively different to a zero field transition, shedding doubt on the reliability of these measurements as an indicator of the physics of a quantum phase transition at zero field. However, the zero-field properties of YbRh 2 (Si 1−x Ge x ) 2 above T ≈ 70 mK for the undoped (x = 0) and doped (x = 0.05) crystals are essentially identical (Fig. 2a), suggesting that by suppressing the critical field we are still probing the same quantum critical point.In both compounds, the ac-susceptibility follows a temperature dependence χ −1 ∝ T α from 0.3 K to ≤ T ≤ 1.5 K, with α = 0.75 14 , and the coefficient of the electronic specific heat, C el (T )/T , exhibits 9 a logarithmic divergence between 0.3 K and 10 K. However, in the low-T paramagnetic regime, i. e. , T N < T < ∼ 0.3 K, the ac-susceptibility follows a CurieWeiss law (inset of Fig. 2a) with a Weiss temperature Θ W ≈ 0.3 K, and a surprisingly large effective moment µ eff ≈ 1.4µ B /Yb 3+ , indicating the emergence of coupled, unquenched spins at the quantum critical point. The electronic specific heat coefficient, C e...

Scaling of the magnetic entropy and magnetization in

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