Anomalous quantum criticality in an itinerant ferromagnet

Abstract

The dynamics of continuous phase transitions is governed by the dynamic scaling exponent relating the correlation length and correlation time. For transitions at finite temperature, thermodynamic critical properties are independent of the dynamic scaling exponent. In contrast, at quantum phase transitions where the transition temperature becomes zero, static and dynamic properties are inherently entangled by virtue of the uncertainty principle. Consequently, thermodynamic scaling equations explicitly contain the dynamic exponent. Here we report on thermodynamic measurements (as a function of temperature and magnetic field) for the itinerant ferromagnet Sr 1 À x Ca x RuO 3 where the transition temperature becomes zero for x ¼ 0.7. We find dynamic scaling of the magnetization and specific heat with highly unusual quantum critical dynamics. We observe a small dynamic scaling exponent of 1.76 strongly deviating from current models of ferromagnetic quantum criticality and likely being governed by strong disorder in conjunction with strong electron-electron coupling.

Quantum-critical scale invariance in a transition metal alloy

“…QC behavior in disordered 3d FM has been well explained by the Belitz-Kirkpatrick-Vojta theory, predicting critical exponents ν = 1 and z = 3 for the asymptotic limit, and ν = 0.25 and z = 6 for the preasymptotic limit 37,38 , neither of which is in agreement with our observation. Experimentally, previously measured exponents in QC materials, such as YbNi 4 31 , YFe 2 Al 10 (layered QC metal, d/z = 1, νz = 0.59) 32 , and Sr 0.3 Ca 0.7 RuO 3 (disordered FM QCP, z = 1.76) 41 are also incompatible with the measured dynamical exponent.…”

Quantum critical behavior in the asymptotic limit of high disorder in the medium entropy alloy NiCoCr0.8

“…22,24 All of the magnetization data from the NiCoCr 0.8 single crystals should collapse onto a single curve when M=T β T is plotted vs. H/T γ T þβ T . Since γ T and β T for NiCoCr 0.8 are found experimentally to have the values of γ T ≈ 0.5, and β T ≈ 1, this implies that if M(T, H)/ T is plotted vs. H/ T 1.5 , all of the magnetization data should fall on one curve.…”

Quantum Critical Scaling in the Disordered Itinerant Ferromagnet UCo1−xFexGe

“…The data are displayed in a log-log plot so that the slope of each curve corresponds to 1/δ. We note that for the determination of 1/δ, the data for H 0.1 T, where scaling is not expected because of domain effects, were omitted [21]. The resulting temperature dependence of 1/δ for each of the three concentrations is shown in Fig.…”

“…Single crystals of UCo 1−x Fe x Ge are grown via the Czochralski method, which typically leads to concentration gradients that would be detrimental for the determination of critical exponents. Finally, it has been demonstrated that the use of polycrystalline samples does not affect the ability to reliably determine scaling exponents of phase transitions [20,21].…”