Dimensional crossover in quantum critical metallic magnets (original) (raw)
Quantum critical singularities in two-dimensional metallic XY ferromagnets
Physical Review B, 2018
An important problem in contemporary physics concerns quantum-critical fluctuations in metals. A scaling function for the momentum, frequency, temperature and magnetic field dependence of the correlation function near a 2D-ferromagnetic quantum-critical point (QCP) is constructed, and its singularities are determined by comparing to the recent calculations of the correlation functions of the dissipative quantum XY model (DQXY). The calculations are motivated by the measured properties of the metallic compound YFe 2 Al 10 , which is a realization of the DQXY model in 2D. The frequency, temperature and magnetic field dependence of the scaling function as well as the singularities measured in the experiments are given by the theory without adjustable exponents. The same model is applicable to the superconductor-insulator transitions, classes of metallic AFM-QCPs, and as fluctuations of the loop-current ordered state in hole-doped cuprates. The results presented here lend credence to the solution found for the 2D-DQXY model, and its applications in understanding quantum-critical properties of diverse systems.
Quantum-critical phase from frustrated magnetism in a strongly correlated metal
Nature Physics, 2019
Strange-metal phenomena often develop at the border of antiferromagnetic order in strongly correlated metals. It has been well established that they can originate from the fluctuations anchored by the point of continuous quantum phase transition out of the antiferromagnetic order, i.e., a quantum critical point. What has been unclear is how these phenomena can be associated with a potential new phase of matter at zero temperature. Here we show that magnetic frustration of the 4f-local moments in the distorted Kagome intermetallic compound CePdAl gives rise to such a paramagnetic quantum-critical phase. Moreover, we demonstrate that this phase turns into a Fermi liquid through a Mott-like crossover; in a two-dimensional parameter space of pressure and magnetic field, this crossover is linked to a line of zero-temperature 4f-electron localization-delocalization phase transitions at low and moderate pressures. Our discovery motivates a new design principle for strongly correlated metallic states with unconventional excitations that may underlie the development of such effects as high temperature superconductivity. Geometrical frustration in quantum-spin systems gives rise to quantum fluctuations which may suppress long-range magnetic order and cause a quantum-spin-liquid ground state [1]. This notion is traditionally associated with insulating magnets only. There has been increasing recognition, however, that geometrical frustration is also important to bad metals that host local moments, such as strongly correlated f-electron metals [2-7], which provide a prototype setting
Cubic interactions and quantum criticality in dimerized antiferromagnets
Physical Review B, 2011
In certain Mott-insulating dimerized antiferromagnets, triplet excitations of the paramagnetic phase can decay into the two-particle continuum. When such a magnet undergoes a quantum phase transition into a magnetically ordered state, this coupling becomes part of the critical theory provided that the lattice ordering wavevector is zero. One microscopic example is the staggered-dimer antiferromagnet on the square lattice, for which deviations from O(3) universality have been reported in numerical studies. Using both symmetry arguments and microscopic calculations, we show that a non-trivial cubic term arises in the relevant order-parameter quantum field theory, and assess its consequences using a combination of analytical and numerical methods. We also present finite-temperature quantum Monte Carlo data for the staggered-dimer antiferromagnet which complement recently published results. The data can be consistently interpreted in terms of critical exponents identical to that of the standard O(3) universality class, but with anomalously large corrections to scaling. We argue that the two-particle decay of critical triplons, although irrelevant in two spatial dimensions, is responsible for the leading corrections to scaling due to its small scaling dimension.
Approaching quantum criticality in a partially geometrically frustrated heavy-fermion metal
In the antiferromagnetic (AF) heavy-fermion system CePdAl the magnetic Ce ions form a network of equilateral triangles in the (001) plane, similar to the kagomé lattice, with one third of the Ce moments not participating in the long-range order. The Néel temperature T N = 2.7 K is reduced upon replacing Pd by Ni in CePd 1−x Ni x Al, with T N → 0 for x = 0.144, where the specific heat C exhibits a C/T ∝ − log T dependence. Within the Hertz-Millis-Moriya model of quantum criticality, this behavior might indicate 2D critical antiferromagnetic fluctuations arising from the decoupling of 3D magnetic order by frustration. On the other hand, the simultaneous presence of Kondo effect and geometric frustration might entail a different route to quantum criticality.
EPL (Europhysics Letters), 2008
Quantum critical points exist at zero temperature, yet, experimentally their influence seems to extend over a large part of the phase diagram of systems such as heavy-fermion compounds and high-temperature superconductors. Theoretically, however, it is generally not known over what range of parameters the physics is governed by the quantum critical point. We answer this question for the spin-density wave to Fermi-liquid quantum critical point in the twodimensional Hubbard model. This problem is in the d =2,z= 2 universality class. We use the two-particle self-consistent approach, which is accurate from weak to intermediate coupling, and whose critical behavior is the same as for the self-consistent-renormalized approach of Moriya. Despite the presence of logarithmic corrections, numerical results demonstrate that quantum critical scaling for the static magnetic susceptibility can extend up to very high temperatures but that the commensurate to incommensurate crossover leads to deviations to scaling.
Observation of Crossover to 4-Dimensional Critical Behaviour
The critical behaviour of the d-dimensional Ising model in a transverse field H_perp at temperatures near T = 0 and for H_perp --> Hc_perp, are predicted to be the same as for a (d +1)-dimensional Ising model in zero field as a function of temperature for T --> Tc. We present evidence for such a dimensionality cross-over by studying the field-dependent critical behaviour of the staggered magnetization of the d = 3 Ising-type antiferromagnet MnCl2.4H20 at low temperatures.
Reports on Progress in Physics, 2016
The anomalous transport and thermodynamic properties in the quantum-critical region, in the cuprates, and in the quasi-two dimensional Fe-based superconductors and heavy-fermion compounds, have the same temperature dependences. This can occur only if, despite their vast microscopic differences, a common statistical mechanical model describes their phase transitions. The antiferromagnetic (AFM)-ic models for the latter two, just as the loop-current model for the cuprates, map to the dissipative XY model. The solution of this model in 2+1 D reveals that the critical fluctuations are determined by topological excitations, vortices and a variety of instantons, and not by renormalized spin-wave theories of the Landau-Ginzburg-Wilson type, adapted by Moriya, Hertz and others for quantum-criticality. The absorptive part of the fluctuations is a separable function of momentum q, measured from the ordering vector, and of the frequency ω and the temperature T which scale as tanh(ω/2T) at criticality. Direct measurements of the fluctuations by neutron scattering in the quasi-two-dimensional heavy fermion and Fe-based compounds, near their antiferromagnetic quantum critical point, are consistent with this form. Such fluctuations, together with the vertex coupling them to fermions, lead to a marginal fermi-liquid, with the imaginary part of the self-energy ∝ max(ω, T) for all momenta, a resistivity ∝ T , a T ln T contribution to the specific heat, and other singular fermi-liquid properties common to these diverse compounds, as well as to d-wave superconductivity. This is explicitly verified, in the cuprates, by analysis of the pairing and the normal self-energy directly extracted from the recent high resolution angle resolved photoemission measurements. This reveals, in agreement with the theory, that the frequency dependence of the attractive irreducible particle-particle vertex in the d-wave channel is the same as the irreducible particle-hole vertex in the full symmetry of the lattice.
Strong-coupling theory of heavy-fermion criticality
Physical Review B, 2014
We present a theory of the scaling behavior of the thermodynamic, transport and dynamical properties of a three-dimensional metal at an antiferromagnetic (AFM) critical point. We show how the critical spin fluctuations at the AFM wavevector q = Q induce energy fluctuations at small q, giving rise to a diverging quasiparticle effective mass over the whole Fermi surface. The coupling of the fermionic and bosonic degrees of freedom leads to a self-consistent relation for the effective mass, which has a strong coupling solution in addition to the well-known weak-coupling spin-densitywave solution. We use the recently-introduced concept of critical quasiparticles, employing a scaledependent effective mass ratio m * /m and quasiparticle weight factor Z. We adopt a scale-dependent vertex correction that boosts the coupling of fermions and spin fluctuations. The ensuing spin fluctuation spectrum obeys ω/T -scaling. Our results are in good agreement with experimental data on the heavy fermion compounds YbRh2Si2 and CeCu6-xAux for 3D and 2D spin fluctuations, respectively.
Quantum criticality in heavy-fermion metals
Nature Physics, 2008
Quantum criticality describes the collective fluctuations of matter undergoing a second-order phase transition at zero temperature. Heavy-fermion metals have in recent years emerged as prototypical systems to study quantum critical points. There have been considerable efforts, both experimental and theoretical, that use these magnetic systems to address problems that are central to the broad understanding of strongly correlated quantum matter. Here, we summarize some of the basic issues, including the extent to which the quantum criticality in heavy-fermion metals goes beyond the standard theory of order-parameter fluctuations, the nature of the Kondo effect in the quantum-critical regime, the non-Fermi-liquid phenomena that accompany quantum criticality and the interplay between quantum criticality and unconventional superconductivity.
Scaling of Magnetic Fluctuations near a Quantum Phase Transition
Physical Review Letters, 1998
We use inelastic neutron scattering to measure the magnetic fluctuations in a single crystal of the heavy fermion alloy CeCu5.9Au0.1 close to the antiferromagnetic quantum critical point. The energy(E)-, wavevector(q)-and temperature(T)-dependent spectra obey E/T scaling at Q near (1,0,0). The neutron data and earlier bulk susceptibility are consistent with the form χ −1 ∼ f (Q) + (−iE + aT) α , with an anomalous exponent α ≈ 0.8 = 1. We confirm the earlier observation of quasi-low dimensionality and show how both the magnetic fluctuations and the thermodynamics can be understood in terms of a quantum Lifshitz point.