Session Y2: Invited Session: Magnetism and non-Fermi Liquid in Heavy Fermion Metals

Dimensionality and quantum criticality in heavy fermion metals

Heavy fermion compounds are at the forefront of research on quantum criticality. This is due to the fact that many of these materials can be tuned to a quantum critical point (QCP) by readily accessible values of the control parameters magnetic field, pressure or substitution/doping. In recent years efforts are being made to classify the different kinds of quantum critical behavior experimentally observed, to test the extent to which heavy fermion quantum criticality is universal. We have identified a cubic heavy fermion material, Ce$_3$Pd$_{20}$Si$_6$, as exhibiting a field-induced quantum phase transition as the lower of two consecutive phase transitions is suppressed to zero. This transition is accompanied by an abrupt change of Fermi surface [1], reminiscent of what happens across the field-induced antiferromagnetic to paramagnetic transition in tetragonal YbRh$_2$Si$_2$ [2]. In Ce$_3$Pd$_{20}$Si$_6$, the QCP separates two different ordered phases. In fact, a Kondo destruction QCP [3] has been theoretically predicted to exist in the ordered portion of a global phase diagram for quantum critical heavy fermion compounds [4]. We conclude that dimensionality is an effective way to tune through such a global phase diagram and that the cubic material studied here is situated in the barely explored three-dimensional portion of this phase diagram. We believe that this finding will guide the search for further experimental anchoring points in the global phase diagram, and for a unified theoretical description.\\[0.2cm] Work done in collaboration with J. Custers, J. Larrea J., K.- A. Lorenzer, M. M\"{u}ller, A. Prokofiev, A. Sidorenko, H. Winkler, A. M. Strydom, Y. Shimura, T. Sakakibara, R. Yu and Q. Si.\\[4pt] [1] J. Custers, K.-A. Lorenzer, M. M\"{u}ller, A. Prokofiev, A. Sidorenko, H. Winkler, A. M. Strydom, Y. Shimura, T. Sakakibara, R. Yu, Q. Si, and S. Paschen, Nature Materials 11, 189 (2012).\\[0pt] [2] S. Paschen et al., Nature 432, 881 (2004). S. Friedemann et al., Proc. Natl. Acad. Sci. 107, 14547 (2010).\\[0pt] [3] Q. Si et al. Nature 413, 804 (2001). P. Coleman et al., J. Phys. Condens. Matter 13, R723 (2001). T. Senthil et al., Phys. Rev. B 69, 035111 (2004).\\[0pt] [4] Q. Si, Physica B 378-380, 23 (2006). Q. Si, Phys. Status Solidi B 247, 476 (2010).   

From incommensurate correlations to mesoscopic spin resonance in YbRh2Si2

Spin fluctuations are reported near the magnetic field driven quantum critical point in YbRh2Si2 [1]. On cooling, ferromagnetic fluctuations evolve into incommensurate correlations with a characteristic in-plane wave vector of $q_m = (\delta,\delta)$ with $\delta=0.14 \pm 0.04$ r.l.u. At low temperatures, an in plane magnetic field induces a sharp intra doublet resonant excitation at an energy $g\mu_B\mu_0H$ with $g=3.8\pm 0.2$. The intensity is localized at the zone center and has a width in momentum space indicating precession of spin density extending $\xi = 6 \pm 2$ \AA\ beyond the 4f site.\\[4pt] [1] C. Stock, C. Broholm, F. Demmel, J. Van Duijn, J. W. Taylor, H.J. Kang, R. Hu, and C. Petrovic, Phys. Rev. Lett. {\bf 109}, 127201 (2012).   

Critical quasi-particle theory and scaling near a Quantum Critical Point of Heavy Fermion metals

We recently developed a theory of the critical properties of a heavy fermion metal near an antiferromagnetic (AFM) quantum phase transition governed by three-dimensional spin fluctuations. The critical spin fluctuations induce critical behavior of the electron quasi-particles (qp) as seen in a diverging effective mass, leading, e.g., to a diverging specific heat coefficient. This in turn gives rise to a modification of the spin excitation spectrum [1]. We use that the concept of electron quasi-particles is well-defined as long as the qp width is less than their excitation energy, which is still the case in the so-called non-Fermi liquid regime. Impurity scattering [1,2] and/or higher order loop processes in the clean system [3] cause a redistribution of the critical scattering at the hot lines all over the Fermi surface, leading to a weakly momentum dependent critical self-energy. We derive a self-consistent equation for the qp effective mass which allows for two physical solutions: the usual weak coupling spin density wave solution and a strong coupling solution featuring a power law divergence of the effective mass as a function of energy scale. The resulting spin excitation spectrum obeys E/T scaling with dynamical exponent z$=$4 and correlation length exponent $\nu =$1/3, in excellent agreement with data for YbRh$_2$Si$_2$ [1,2]. Results of our theory applied to three-dimensional metals featuring quasi-two-dimensional spin fluctuations will be presented with the aim of explaining the observed properties of the AFM quantum critical point of CeCu$_{\mathrm{6-x}}$Au$_{\mathrm{x}}$, in particular the E/T scaling exhibited by inelastic neutron scattering data. In that case we find z$=$8/3 and $\nu =$3/7 [3]. Finally, the microscopic underpinning of our theory will be addressed, including the issues of qp renormalization, vertex corrections, interaction of bosonic fluctuations in the renormalization group sense, and higher loop corrections [3].\\[4pt] [1] P. W\"{o}lfle, and E. Abrahams, Phys. Rev. B \textbf{84}, 041101 (2011); Ann. Phys. (Berlin) \textbf{523}, 591 (2011); Phys. Rev. B \textbf{80}, 235112 (2009).\\[0pt] [2] E. Abrahams and P. W\"{o}lfle, PNAS \textbf{109}, 3228 (2012).\\[0pt] [3] E. Abrahams, J. Schmalian, and P. W\"{o}lfle, to be published.   

Ferromagnetic quantum criticality in heavy fermion systems

Heavy fermion (HF) systems are metals where the weak hybridisation between nearly localized $f$-electrons and the mobile conduction electrons, i.e. the Kondo effect, leads to a Fermi liquid (FL) ground state with narrow bands and quasiparticles with strongly enhanced effective electronic masses. When the magnetic RKKY interaction becomes comparable to the Kondo interaction, magnetic order can appear, mostly at very low $T$. The magnetic order can be suppressed by an external parameter, e.g. pressure or magnetic field, inducing a quantum phase transition (QPT) at $T = 0$. If this QPT is continuous, the associated quantum critical point (QCP) is surrounded by a non-FL regime of quantum critical fluctuations where unconventional superconductivity or novel phases of matter may arise [1]. The unambiguous observation of antiferromagnetic (AFM) QCPs in HF systems [2] has led to an increasing number of theoretical and experimental works in order to understand QPTs as deeply as their classical counterpart. Although it has been demonstrated that in antiferromagnets QCPs exist, in ferromagnets there is still no clear evidence. Intensive investigations have shown that metallic ferromagnets are inherently unstable [3,4] and do not exhibit a FM QCP. However, in the recently discovered HF system YbNi$_{4}$P$_{2}$, a quasi-1D ferromagnet with a remarkably-low $T_{C} = 0.15$\,K [5], the $T$-divecgence in the Gr\"uneisen ratio points to the presence of a FM QCP. I will present a general overview of the state of the art of FM quantum criticality in HF systems, discussing in particular the cases of YbNi$_{4}$P$_{2}$, CeFePO, CePd$_{1-x}$Rh$_{x}$ as well as the AFM system YbRh$_{2}$Si$_{2}$ where FM order is induced by chemical pressure.\\[4pt] [1] H. Q. Yuan \textit{et al.}, Science \textbf{302} 2104 (2003)\\[0pt] [2] J. Custers \textit{et al.}, Nature \textbf{424} 524 (2003)\\[0pt] [3] D. Belitz \textit{et al.}, Phys. Rev. Lett. \textbf{82} 4707 (1999)\\[0pt] [4] M. Uhlarz \textit{et al.}, Phys. Rev. Lett. \textbf{93} 256404 (2004)\\[0pt] [5] C. Krellner \textit{et al.}, New J. Phys. \textbf{13} 103014 (2011)