Geometrical frustration describes situations where interactions are incompatible with the lattice geometry and stabilizes exotic phases such as spin liquids. Whether geometrical frustration of magnetic interactions in metals can induce unconventional
quantum critical points is an active area of research. We focus on the hexagonal heavy fermion metal CeRhSn where the Kondo ions are located on distorted kagome planes stacked along the c axis. Low-temperature specific heat, thermal expansion and magnetic Gruneisen parameter measurements prove a zero-field quantum critical point. The linear thermal expansion, which measures the initial uniaxial pressure derivative of the entropy, displays a striking anisotropy. Critical and noncritical behaviors along and perpendicular to the kagome planes, respectively, prove that quantum criticality is driven by geometrical frustration. We also discovered a spin-flop-type metamagnetic crossover. This excludes an itinerant scenario and suggests that quantum criticality is related to local moments in a spin-liquid like state.
We report low-temperature thermal conductivity $kappa$ of pyrochlore Yb$_2$Ti$_2$O$_7$, which contains frustrated spin-ice correlations with significant quantum fluctuations. In the disordered spin-liquid regime, $kappa(H)$ exhibits a nonmonotonic ma
gnetic field dependence, which is well explained by the strong spin-phonon scattering and quantum monopole excitations. We show that the excitation energy of quantum monopoles is strongly suppressed from that of dispersionless classical monopoles. Moreover, in stark contrast to the diffusive classical monopoles, the quantum monopoles have a very long mean free path. We infer that the quantum monopole is a novel heavy particle, presumably boson, which is highly mobile in a three-dimensional spin liquid.
When magnetic order is suppressed by frustrated interactions, spins form a highly correlated fluctuating spin liquid state down to low temperatures. Magnetic order of local moments can also be suppressed when they are fully screened by conduction ele
ctrons through the Kondo effect. Thus, the combination of strong geometrical frustration and Kondo screening may lead to novel types of quantum phase transitions. We report low-temperature thermodynamic measurements on the frustrated Kondo lattice Pr$_2$Ir$_2$O$_7$, which displays a chiral spin liquid state below 1.5 K due to the frustrated interaction between Ising 4f local moments and their interplay with Ir conduction electrons. Our results provide a first clear example of zero-field quantum critical scaling that emerges in a spin liquid state of a highly frustrated metal.
Bicritical points, at which two distinct symmetry-broken phases become simultaneously unstable, are typical for spin-flop metamagnetism. Interestingly, the heavy-fermion compound YbAgGe also possesses such a bicritical point (BCP) with a low temperat
ure T_BCP ~ 0.3 K at a magnetic field of mu_0 H_BCP ~ 4.5 T. In its vicinity, YbAgGe exhibits anomalous behavior that we attribute to the influence of a quantum bicritical point (QBCP), that is close in parameter space yet can be reached by tuning T_BCP further to zero. Using high-resolution measurements of the magnetocaloric effect, we demonstrate that the magnetic Grueneisen parameter Gamma_H indeed both changes sign and diverges as required for quantum criticality. Moreover, Gamma_H displays a characteristic scaling behavior but only on the low-field side, H < H_BCP, indicating a pronounced asymmetry with respect to the critical field. We speculate that the small value of T_BCP is related to the geometric frustration of the Kondo-lattice of YbAgGe.
Quantum criticality in the normal and superconducting state of the heavy-fermion metal CeCoIn$_5$ is studied by measurements of the magnetic Gr{u}neisen ratio, $Gamma_H$, and specific heat in different field orientations and temperatures down to 50 m
K. Universal temperature over magnetic field scaling of $Gamma_H$ in the normal state indicates a hidden quantum critical point at zero field. Within the superconducting state the quasiparticle entropy at constant temperature increases upon reducing the field towards zero, providing additional evidence for zero-field quantum criticality.
The interplay between superconductivity and Eu$ ^{2+}$ magnetic moments in EuFe$_2$(As$_{1-x}$P$_x$)$_2$ is studied by electrical resistivity measurements under hydrostatic pressure on $x=0.13$ and $x=0.18$ single crystals. We can map hydrostatic pre
ssure to chemical pressure $x$ and show, that superconductivity is confined to a very narrow range $0.18leq x leq 0.23$ in the phase diagram, beyond which ferromagnetic (FM) Eu ordering suppresses superconductivity. The change from antiferro- to FM Eu ordering at the latter concentration coincides with a Lifshitz transition and the complete depression of iron magnetic order.
The heavy-fermion superconductor CeCoIn$_5$ displays an additional transition within its superconducting (SC) state, whose nature is characterized by high-precision studies of the isothermal field dependence of the entropy, derived from combined spec
ific heat and magnetocaloric effect measurements at temperatures $Tgeq 100$ mK and fields $Hleq 12$ T aligned parallel, perpendicular and $18^circ$ off the tetragonal [100] direction. For any of these conditions, we do not observe an additional entropy contribution upon tuning at constant temperature by magnetic field from the homogeneous SC into the presumed Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) SC state. By contrast, for $Hparallel [100]$ a negative isothermal entropy contribution, compatible with spin-density-wave (SDW) ordering, is found. Our data exclude the formation of a FFLO state in CeCoIn$_5$ for out-of-plane field directions, where no SDW order exists.
We report low-temperature specific heat measurements in magnetic fields up to 12 T applied parallel and perpendicular to the tetragonal c-axis of the heavy fermion superconductor Ce$_2$PdIn$_8$. In contrast to its quasi-two-dimensional (2D) relative
CeCoIn$_5$, the system displays an almost isotropic upper critical field. While there is no indication for a FFLO phase in Ce$_2$PdIn$_8$, the data suggest a smeared weak first-order superconducting transition close to $H_{c2}approx 2$ T. The normal state electronic specific heat coefficient displays logarithmically divergent behavior, comparable to CeCoIn$_5$ and in agreement with 2D quantum criticality of spin-density-wave type.
We investigated the effect of electron and hole doping on the high-field low-temperature superconducting state in CeCoIn$_5$ by measuring specific heat of CeCo(In$_{rm 1-x}$M$_{rm x}$)$_5$ with M=Sn, Cd and Hg and $x$ up to 0.33% at temperatures down
to 0.1,K and fields up to 14,T. Although both Cd- and Hg-doping (hole-doping) suppresses the zero-field $T_c$ monotonically, $H_{c2}$ increases with small amounts of doping and has a maximum around $x$=0.2% (M=Cd). On the other hand, with Sn-doping (electron-doping) both zero-field $T_c$ and $H_{c2}$ decrease monotonically. The critical temperature for the high-field low-temperature superconducting state (so called {it Q}-state) correlates with $H_{c2}$ and $T_c$, which we interpret in support of the superconducting origin of this state.
