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Unconventional superconductivity in heavy-fermion systems appears often near magnetic quantum critical points (QCPs). This seems to be the case also for CeRh2As2 (Tc $\approx$ 0.31 K). CeRh2As2 shows two superconducting (SC) phases, SC1 and SC2, for a magnetic field along the c axis of the tetragonal unit cell, but only the SC1 phase is observed for a field along the basal plane. Furthermore, another ordered state (phase-I) is observed below T0 $\approx$ 0.48 K whose nature is still unclear: Thermodynamic and magnetic measurements pointed to a non magnetic multipolar state, but recent $\mu$SR and NQR/NMR experiments have clearly detected antiferromagnetic (AFM) order below T0 . Also, quasi-two-dimensional AFM fluctuations were observed in NMR and neutron-scattering experiments above T0. The proximity of a QCP is indicated by non-Fermi-liquid (NFL) behavior observed above the ordered states in both specific heat $C(T)/T \propto T^{-0.6}$ and resistivity $\rho(T) \propto T^{0.5}$. These T-dependencies are not compatible with any generic AFM QCP. Because of the strong magnetic-field anisotropy of both the SC phase and phase I, it is possible to study a field-induced SC QCP as well a phase-I QCP by varying the angle $\alpha$ between the field and the c axis. Thus, by examining the behavior of the electronic specific-heat coefficient C(T)/T across these QCPs, we can determine which phase is associated with the NFL behavior. Here, we present low-temperature specific-heat measurements taken in a magnetic field as high as 21 T applied at several angles $\alpha$. We observe that the NFL behavior does very weakly depend on the field and on the angle $\alpha$, a result that is at odd with that observations in standard magnetic QCPs. This suggests a nonmagnetic origin of the quantum critical fluctuations., Comment: 10 pages, 7 figures

We present here a rare example of electronuclear quantum criticality in a metal. The compound YbCu4.6Au0.4 is located at an unconventional quantum critical point (QCP). In this material the relevant Kondo and RKKY exchange interactions are very weak, of the order of 1 K. Furthermore, there is strong competition between antiferromagnetic and ferromagnetic correlations, possibly due to geometrical frustration within the fcc Yb sublattice. This causes strong spin fluctuations which prevent the system to order magnetically. Because of the very low Kondo temperature the Yb3+ 4f-electrons couple weakly with the conduction electrons allowing the coupling to the nuclear moments of the 171Yb and 173Yb isotopes to become important. Thus, the quantum critical fluctuations observed at the QCP do not originate from purely electronic states but from entangled electronuclear states. This is evidenced by the anomalous temperature and field dependence of the specific heat at low temperatures., Comment: 10 pages, 8 figures

LuFe$_4$Ge$_2$ crystallizes in the ZrFe$_4$Si$_2$-type structure, hosting chains of Fe-tetrahedra giving rise to geometric frustration and low-dimensionality. The compound orders antiferromagnetically at around 36 K accompanied by a simultaneous structural transition from a tetragonal to an orthorhombic phase. The hydrostatic pressure dependence of the magnetic and structural transitions is investigated using electrical-transport, ac magnetic-susceptibility, ac calorimetry, M$\ddot{\rm o}$ssbauer, muon-spin relaxation ($\mu$SR), and x-ray diffraction measurements. External pressure suppresses the first-order transition to the antiferromagnetic phase (AFM1) around 1.8 GPa. The structural transition is largely unaffected by pressure and remains between 30 to 35 K for pressures up to 2 GPa. A second antiferromagnetic phase (AFM2) is observed at higher pressures. The transition from the paramagnetic to the AFM2 phase is of second-order nature and appears to be connected to the structural transition. The magnetic volume fraction obtained from $\mu$SR and M$\ddot{\rm o}$ssbauer measurements reveal that the entire sample undergoes magnetic ordering in both magnetic phases. In addition, similar low-temperature muon-precession frequencies in AFM1 and AFM2 phases point at similar ordered moments and magnetic structures in both phases. Our results further indicate enhanced magnetic fluctuations in the pressure induced AFM2 phase. The experimental observations together with density functional theory calculations suggest that the magnetic and structural order parameters in LuFe$_4$Ge$_2$ are linked by magnetic frustration, causing the simultaneous magneto-structural transition., Comment: 9 pages, 8 figures

The nature of the antiferromagnetic order in the heavy fermion metal YbRh$_2$Si$_2$, its quantum criticality, and superconductivity, which appears at low mK temperatures, remain open questions. We report measurements of the heat capacity over the wide temperature range 180 $\mu$K - 80 mK, using current sensing noise thermometry. In zero magnetic field we observe a remarkably sharp heat capacity anomaly at 1.5 mK, which we identify as an electro-nuclear transition into a state with spatially modulated electronic magnetic order of maximum amplitude 0.1$\mu_B$. We also report results of measurements in magnetic fields in the range 0 to 70 mT, applied perpendicular to the c-axis, which show eventual suppression of this order. These results demonstrate a coexistence of a large moment antiferromagnet with putative superconductivity., Comment: 12 pages, 14 figures, including the supplementary information

We report neutron depolarization measurements of the suppression of long-range ferromagnetism and the emergence of magnetic irreversibilities and spin freezing in CePd$_{1-x}$Rh$_x$ around $x^*\approx0.6$. Tracking the temperature versus field history of the neutron depolarization, we find clear signatures of long-range Ising ferromagnetism below a Curie temperature $T_{\rm C}$ for $x=0.4$ and a spin freezing of tiny ferromagnetic clusters below a freezing temperature $T_{\rm F1}$ for $x>x^*$. Under zero-field-cooling/field-heating and for $x>x^*$ a reentrant temperature dependence of the neutron depolarization between $T_{\rm F2}

CeRh$_2$As$_2$ is an unconventional superconductor with multiple superconducting phases and $T_\mathrm{c} = 0.26$ K. When $H\parallel c$, it shows a field-induced transition at $\mu_0H^* = 4$ T from a low-field superconducting state SC1 to a high-field state SC2 with a large critical field of $\mu_0H_\mathrm{c2} = 14$ T. In contrast, for $H\perp c$, only the SC1 with $\mu_0H_\mathrm{c2} = 2$ T is observed. A simple model based on the crystal symmetry was able to reproduce the phase-diagrams and their anisotropy, identifying SC1 and SC2 with even and odd parity superconducting states, respectively. However, additional orders were observed in the normal state which might have an influence on the change of the superconducting state at $H^*$. Here, we present a comprehensive study of the angle dependence of the upper critical fields using magnetic ac-susceptibility, specific heat and torque on single crystals of CeRh$_2$As$_2$. The experiments show that the state SC2 is strongly suppressed when rotating the magnetic field away from the $c$ axis and it disappears for an angle of 35$^{\circ}$. This behavior agrees perfectly with our extended model of a pseudospin triplet state with $\vec{d}$ vector in the plane and hence allows to nail down that SC2 is indeed the suggested odd-parity state., Comment: 11 pages, 9 figures

We report on the observation of superconductivity in LaRh$_2$As$_2$, which is the analogue without $f$-electrons of the heavy-fermion system with two superconducting phases CeRh$_2$As$_2$. A zero-resistivity transition, a specific-heat jump and a drop in magnetic ac susceptibility consistently point to a superconducting transition at a transition temperature of $T_c = 0.28$\,K. The magnetic field-temperature superconducting phase diagrams determined from field-dependent ac-susceptibility measurements reveal small upper critical fields $\mu_{\mathrm{0}}H_{c2} \approx 12$\,mT for $H\parallel ab$ and $\mu_{\mathrm{0}}H_{c2} \approx 9$\,mT for $H\parallel c$. The observed $H_{c2}$ is larger than the estimated thermodynamic critical field $H_c$ derived from the heat-capacity data, suggesting that LaRh$_2$A$s_2$ is a type-II superconductor with Ginzburg-Landau parameters $\kappa^{ab}_{GL} \approx 1.9$ and $\kappa^{c}_{GL}\approx 2.7$. The microscopic Eliashberg theory indicates superconductivity to be in the weak-coupling regime with an electron-phonon coupling constant $\lambda_{e-ph} \approx 0.4$. Despite a similar $T_c$ and the same crystal structure as the Ce compound, LaRh$_2$As$_2$ displays conventional superconductivity, corroborating the substantial role of the 4$f$ electrons for the extraordinary superconducting state in CeRh$_2$As$_2$., Comment: 11 pages, 8 figures

CeRh2As2 has recently been reported to be a rare case of multi-phase unconventional superconductor [S. Khim et al., arXiv:2101.09522] close to a quantum critical point (QCP). Here, we present a comprehensive study of its normal state properties and of the phase (I) below To ~ 0.4 K which preempts superconductivity at Tc = 0.26 K. The 2nd-order phase transition at To presents signatures in specific heat and thermal expansion, but none in magnetization and ac-susceptibility, indicating a non-magnetic origin of phase I. In addition, an upturn of the in-plane resistivity at To points to a gap opening at the Fermi level in the basal plane. Thermal expansion indicates a strong positive pressure dependence of To , dTo/dp = 1.5 K/GPa, in contrast to the strong negative pressure coefficient observed for magnetic order in Ce-based Kondo lattices close to a QCP. Similarly, an in-plane magnetic field shifts To to higher temperatures and transforms phase I into another non-magnetic phase (II) through a 1st-order phase transition at about 9 T. Using renormalized band structure calculations, we found that the Kondo effect (TK ~ 30 K) leads to substantial mixing of the excited crystalline-electric-field (CEF) states into the ground state. This allows quadrupolar degrees of freedom in the resulting heavy bands at the Fermi level which are prone to nesting. The huge sensitivity of the quadrupole moment on hybridization together with nesting would cause an unprecedented case of phase transition into a quadrupole-density-wave (QDW) state at a temperature To << TK , which would explain the nature of phase I and II., Comment: 11 pages, 10 figures

We report on the synthesis and physical properties of cm-sized CoGeO$_3$ single crystals grown in a high pressure mirror furnace at pressures of 80~bar. Direction dependent magnetic susceptibility measurements on our single crystals reveal highly anisotropic magnetic properties that we attribute to the impact of strong single ion anisotropy appearing in this system with T$_N$~$\sim$~33.5~K. Furthermore, we observe effective magnetic moments that are exceeding the spin only values of the Co ions which reveals the presence of sizable orbital moments in CoGeO$_3$.

We report the discovery of two-phase unconventional superconductivity in CeRh$_2$As$_2$. Using thermodynamic probes, we establish that the superconducting critical field of its high-field phase is as high as 14 T, remarkable in a material whose transition temperature is 0.26 K. Furthermore, a $c$-axis field drives a transition between two different superconducting phases. In spite of the fact that CeRh$_2$As$_2$ is globally centrosymmetric, we show that local inversion-symmetry breaking at the Ce sites enables Rashba spin-orbit coupling to play a key role in the underlying physics. More detailed analysis identifies the transition from the low- to high-field states to be associated with one between states of even and odd parity.

In the iron-pnictide material CeFeAsO not only the Fe moments, but also the local 4f moments of the Ce order antiferromagnetically at low temperatures. We elucidate on the peculiar role of the Ce on the emergence of superconductivity. While application of pressure suppresses the iron SDW ordering temperature monotonously up to 4 GPa, the Ce-4f magnetism is stabilized, until both types of magnetic orders disappear abruptly and a narrow SC dome develops. With further increasing pressure characteristics of a Kondo-lattice system become more and more apparent in the electrical resistivity. This suggests a connection of the emergence of superconductivity with the extinction of the magnetic order and the onset of Kondo-screening of the Ce-4f moments., Comment: 6 pages, 3 figures + supplemental material

The Fe sublattice in the compound ZrFe$_4$Si$_2$ features geometrical frustration and quasi-one-dimensionality. We therefore investigated the magnetic behavior in ZrFe$_4$Si$_2$ and its evolution upon substituting Ge for Si and under the application of hydrostatic pressure using structural, magnetic, thermodynamic, and electrical-transport probes. Magnetic measurements reveal that ZrFe$_4$Si$_2$ holds paramagnetic Fe moments with an effective moment $\mu_{\rm eff}= 2.18~\mu_{B}$. At low temperatures the compound shows a weak short-range magnetic order below 6 K. Our studies demonstrate that substituting Ge for Si increases the unit-cell volume and stabilizes the short-range order into a long-range spin-density wave type magnetic order. On the other hand, hydrostatic pressure studies using electrical-resistivity measurements on ZrFe$_4$(Si$_{0.88}$Ge$_{0.12}$)$_2$ indicate a continuous suppression of the magnetic ordering upon increasing pressure. Therefore, our combined chemical substitution and hydrostatic pressure studies suggest the existence of a lattice-volume-controlled quantum critical point in ZrFe$_4$Si$_2$., Comment: 9 pages, 7 figures, Published version with new title and extended discussion

CeCoSi is an intermetallic antiferromagnet with a very unusual temperature-pressure phase diagram: at ambient pressure it orders below $T_{\mathrm{N}} = 8.8$ K, while application of hydrostatic pressure induces a new magnetically ordered phase with exceptionally high transition temperature of $\sim40$ K at 1.5 GPa. We studied the magnetic properties and the pressure-induced magnetic phase of CeCoSi by means of elastic and inelastic neutron scattering (INS) and heat capacity measurements. At ambient pressure CeCoSi orders into a simple commensurate AFM structure with a reduced ordered moment of only $m_{\mathrm{Ce}} = 0.37(6)$ $\mu_{\mathrm{B}}$. Specific heat and low-energy INS indicate a significant gap in the low-energy magnon excitation spectrum in the antiferromagnetic phase, with the CEF excitations located above 10 meV. Hydrostatic pressure gradually shifts the energy of the magnon band towards higher energies, and the temperature dependence of the magnons measured at 1.5 GPa is consistent with the phase diagram. Moreover, the CEF excitations are also drastically modified under pressure., Comment: 8 pages, 11 figures

A very strong magnetoelastic effect in the CeCo$_{1-x}$Fe$_{x}$Si alloys is reported. The strength of the magnetostrictive effect can be tuned upon changing $x$. The moderate low-temperature linear magnetostriction observed at low Fe concentrations becomes very large ($\frac {\Delta L}{L} \left(16 T,2 K\right) =$ 3$\times$10$^{-3}$) around the critical concentration ($x_c \approx$ 0.23) at which the long-range antiferromagnetic order vanishes. Upon increasing doping through the non-magnetic region ($x > x_c$), the magnetostriction strength gradually weakens again. Remarkably the low-temperature magnetostriction at the critical concentration shows a pronounced $S$-like shape (centered at $B_m \sim$ 6 T) resembling other well-known Ce-based metamagnetic systems like CeRu$_2$Si$_2$ and CeTiGe. Unlike what is observed in these compounds, however, the field dependence of the magnetization shows only a minor upturn around $B_m$ vaguely resembling a metamagnetic behavior. The subtle interplay between magnetic order and the Kondo screening seems to originate an enhanced valence susceptibility slightly changing the Ce ions valence, ultimately triggering the large magnetostriction observed around the critical concentration., Comment: 6 pages, 6 figures

We present thermopower measurements on Yb(Rh$_{1-x}$Co$_x$)$_2$Si$_2$. Upon Co substitution the Kondo temperature is decreasing and the single large thermopower minimum observed for YbRh$_2$Si$_2$ splits into two minima. Simultaneously, the absolute thermopower values are strongly reduced due to a weaker exchange coupling between the $4f$ and the conduction electron states with increasing $x$. Pure YbCo$_2$Si$_2$ is considered a stable, trivalent system. Nevertheless, we still observe two minima in the thermopower indicative of weak residual Kondo scattering. This is in line with results from photo emission spectroscopy revealing a tiny contribution from Yb$^{2+}$. The value at the high-$T$ minimum in $S(T)$ is found to be proportional to the Sommerfeld coefficient for the whole series. This unexpected finding is discussed in relation to recent measurements of the valence and Fermi surface evolution with temperature., Comment: 13 pages, 4 figures

Nuclear magnetic resonance measurements were performed on CeCu$_{2}$Si$_{2}$ in the presence of a magnetic field close to the upper critical field $\mu_{0} H_{\rm c2}$ in order to investigate its superconducting (SC) properties near pair-breaking fields. In lower fields, the Knight shift and nuclear spin-lattice relaxation rate divided by temperature $1/T_1T$ abruptly decreased below the SC transition temperature $T_{\rm c}(H)$, a phenomenon understood within the framework of conventional spin-singlet superconductivity. In contrast, $1/T_1T$ was enhanced just below $T_{\rm c}(H)$ and exhibited a broad maximum when magnetic fields close to $\mu_0H_{\rm c2}(0)$ were applied parallel or perpendicular to the $c$ axis, although the Knight shift decreased just below $T_{\rm c}(H)$. This enhancement of $1/T_1T$, which was recently observed in the organic superconductor $\kappa$-(BEDT-TTF)$_{2}$Cu(NCS)$_{2}$, suggests the presence of high-density Andreev bound states in the inhomogeneous SC region, a hallmark of the Fulde-Ferrell-Larkin-Ovchinnikov phase., Comment: 5 pages, 3 figures

Polycrystalline samples of Ce(Cu$_{1-x}$Co$_x$)$_2$Ge$_2$ were investigated by means of electrical resistivity $\rho$($T$), magnetic susceptibility $\chi$($T$), specific heat $C$$_p$($T$) and thermo electric power $S$($T$) measurements. The long-range antiferromagnetic (AFM) order, which set in at $T$$_N$ = 4.1 K in CeCu$_2$Ge$_2$, is suppressed by non-iso-electronic cobalt (Co) doping at a critical value of the concentration $x$$_c$ = 0.6, accompanied by non-Fermi liquid (NFL) behavior inferred from the power law dependence of heat capacity and susceptibility i.e. $C$($T$)/$T$ and $\chi$($T$) $\propto$ $T$$^{-1+\lambda}$ down to 0.4 K, along with a clear deviation from $T$$^2$ behavior of the electrical resistivity. However, we have not seen any superconducting phase in the quantum critical regime down to 0.4 K., Comment: 8 pages, 11 figures

Yb(Rh1-xCox)2Si2 is a model system to address two challenging problems in the field of strongly correlated electron systems: The first is the intriguing competition between ferromagnetic (FM) and antiferromagnetic (AFM) order when approaching a magnetic quantum critical point (QCP). The second is the occurrence of magnetic order along a very hard crystalline electric field (CEF) direction, i.e. along the one with the smallest available magnetic moment. Here, we present a detailed study of the evolution of the magnetic order in this system from a FM state with moments along the very hard c direction at x = 0.27 towards the yet unknown magnetic state at x = 0. We first observe a transition towards an AFM canted state with decreasing x and then to a pure AFM state. This confirms that the QCP in YbRh2Si2 is AFM, but the phase diagram is very similar to those observed in some inherently FM systems like NbFe2 and CeRuPO, which suggests that the basic underlying instability might be FM. Despite the huge CEF anisotropy the ordered moment retains a component along the c-axis also in the AFM state. The huge CEF anisotropy in Yb(Rh1-xCox)2Si2 excludes that this hard-axis ordering originates from a competing exchange anisotropy as often proposed for other heavy-fermion systems. Instead, it points to an order-by-disorder based mechanism., Comment: 6 pages, 4 figures

The magnetic properties of rare earth compounds are usually well captured by assuming a fully localized f shell and only considering the Hund's rule ground state multiplet split by a crystal electrical field (CEF). Currently, the standard technique for probing CEF excitations in lanthanides is inelastic neutron scattering. Here we show that with the recent leap in energy resolution, resonant inelastic soft X-ray scattering has become a serious alternative for looking at CEF excitations with some distinct advantages compared to INS. As an example we study the CEF scheme in CeRh2Si2, a system that has been intensely studied for more than two decades now but for which no consensus has been reached yet as to its CEF scheme. We used two new features that have only become available very recently in RIXS, high energy resolution of about 30 meV as well as polarization analysis in the scattered beam, to find a unique CEF description for CeRh2Si2. The result agrees well with previous INS and magnetic susceptibility measurements. Due to its strong resonant character, RIXS is applicable to very small samples, presents very high cross sections for all lanthanides, and further benefits from the very weak coupling to phonon excitation. The rapid progress in energy resolution of RIXS spectrometers is making this technique increasingly attractive for the investigation of the CEF scheme in lanthanides.

Strong electron correlations can give rise to extraordinary properties of metals with renormalized quasiparticles which are at the basis of Landau's Fermi liquid theory. Near a quantum critical point, these quasiparticles can be destroyed and non-Fermi liquid behavior ensues. YbRh$_2$Si$_2$ is a prototypical correlated metal as it exhibits quasiparticles formation, formation of Kondo lattice coherence and quasiparticle destruction at a field-induced quantum critical point. Here we show how, upon lowering the temperature, the Kondo lattice coherence develops and finally gives way to non-Fermi liquid electronic excitations. By measuring the single-particle excitations through scanning tunneling spectroscopy down to 0.3 K, we find the Kondo lattice peak emerging below the Kondo temperature $T_{\rm K} \sim$ 25 K, yet this peak displays a non-trivial temperature dependence with a strong increase around 3.3 K. At the lowest temperature and as a function of an external magnetic field, the width of this peak is minimized in the quantum critical regime. Our results provide a striking demonstration of the non-Fermi liquid electronic excitations in quantum critical metals, thereby elucidating the strange-metal phenomena that have been ubiquitously observed in strongly correlated electron materials., Comment: 7 pages, 5 figures

We have performed $^{63}$Cu nuclear magnetic resonance/nuclear quadrupole resonance measurements to investigate the magnetic and superconducting (SC) properties on a "superconductivity dominant" ($S$-type) single crystal of CeCu$_2$Si$_2$. Although the development of antiferromagnetic (AFM) fluctuations down to 1~K indicated that the AFM criticality was close, Korringa behavior was observed below 0.8~K, and no magnetic anomaly was observed above $T_{\rm c} \sim$ 0.6 K. These behaviors were expected in $S$-type CeCu$_2$Si$_2$. The temperature dependence of the nuclear spin-lattice relaxation rate $1/T_1$ at zero field was almost identical to that in the previous polycrystalline samples down to 130~mK, but the temperature dependence deviated downward below 120~mK. In fact, $1/T_1$ in the SC state could be fitted with the two-gap $s_{\pm}$-wave rather than the two-gap $s_{++}$-wave model down to 90~mK. Under magnetic fields, the spin susceptibility in both directions clearly decreased below $T_{\rm c}$, indicative of the formation of spin singlet pairing. The residual part of the spin susceptibility was understood by the field-induced residual density of states evaluated from $1/T_1T$, which was ascribed to the effect of the vortex cores. No magnetic anomaly was observed above the upper critical field $H_{c2}$, but the development of AFM fluctuations was observed, indicating that superconductivity was realized in strong AFM fluctuations., Comment: 10 pages, 8 figures

A key aspect of unconventional pairing by the antiferromagnetic spin-fluctuation mechanism is that the superconducting energy gap must have opposite sign on different parts of the Fermi surface. Recent observations of non-nodal gap structure in the heavy-fermion superconductor CeCu$_2$Si$_2$ were then very surprising, given that this material has long been considered a prototypical example of a superconductor where the Cooper pairing is magnetically mediated. Here we present a study of the effect of controlled point defects, introduced by electron irradiation, on the temperature-dependent magnetic penetration depth $\lambda(T)$ in CeCu$_2$Si$_2$. We find that the fully-gapped state is robust against disorder, demonstrating that low-energy bound states, expected for sign-changing gap structures, are not induced by nonmagnetic impurities. This provides bulk evidence for $s_{++}$-wave superconductivity without sign reversal., Comment: 5 pages, 4 figures + Supplemental Material (1 page, 1 figure). Will appear in Phys. Rev. Lett

We investigated the anisotropic magnetic properties of CePd$_2$As$_2$ by magnetic, thermal and electrical transport studies. X-ray diffraction confirmed the tetragonal ThCr$_2$Si$_2$-type structure and the high-quality of the single crystals. Magnetisation and magnetic susceptibility data taken along the different crystallographic directions evidence a huge crystalline electric field (CEF) induced Ising-type magneto-crystalline anisotropy with a large $c$-axis moment and a small in-plane moment at low temperature. A detailed CEF analysis based on the magnetic susceptibility data indicates an almost pure $\langle\pm5/2 \rvert$ CEF ground-state doublet with the dominantly $\langle\pm3/2 \rvert$ and the $\langle\pm1/2 \rvert$ doublets at 290 K and 330 K, respectively. At low temperature, we observe a uniaxial antiferromagnetic (AFM) transition at $T_N=14.7$ K with the crystallographic $c$-direction being the magnetic easy-axis. The magnetic entropy gain up to $T_N$ reaches almost $R\ln2$ indicating localised $4f$-electron magnetism without significant Kondo-type interactions. Below $T_N$, the application of a magnetic field along the $c$-axis induces a metamagnetic transition from the AFM to a field-polarised phase at $\mu_0H_{c0}=0.95$ T, exhibiting a text-book example of a spin-flip transition as anticipated for an Ising-type AFM., Comment: 9 Pages, 8 figures

The anisotropy of magnetic properties commonly is introduced in textbooks using the case of an antiferromagnetic system with Ising type anisotropy. This model presents huge anisotropic magnetization and a pronounced metamagnetic transition and is well-known and well-documented both, in experiments and theory. In contrast, the case of an antiferromagnetic $X$-$Y$ system with weak in-plane anisotropy is only poorly documented. We studied the anisotropic magnetization of the compound GdRh$_2$Si$_2$ and found that it is a perfect model system for such a weak-anisotropy setting because the Gd$^{3+}$ ions in GdRh$_2$Si$_2$ have a pure spin moment of S=7/2 which orders in a simple AFM structure with ${\bf Q} = (001)$. We observed experimentally in $M(B)$ a continuous spin-flop transition and domain effects for field applied along the $[100]$- and the $[110]$-direction, respectively. We applied a mean field model for the free energy to describe our data and combine it with an Ising chain model to account for domain effects. Our calculations reproduce the experimental data very well. In addition, we performed magnetic X-ray scattering and X-ray magnetic circular dichroism measurements, which confirm the AFM propagation vector to be ${\bf Q} = (001)$ and indicate the absence of polarization on the rhodium atoms.

In exotic superconductors including high-$T_c$ copper-oxides, the interactions mediating electron Cooper-pairing are widely considered to have a magnetic rather than the conventional electron-phonon origin. Interest in such exotic pairing was initiated by the 1979 discovery of heavy-fermion superconductivity in CeCu$_2$Si$_2$, which exhibits strong antiferromagnetic fluctuations. A hallmark of unconventional pairing by anisotropic repulsive interactions is that the superconducting energy gap changes sign as a function of the electron momentum, often leading to nodes where the gap goes to zero. Here, we report low-temperature specific heat, thermal conductivity and magnetic penetration depth measurements in CeCu$_2$Si$_2$, demonstrating the absence of gap nodes at any point on the Fermi surface. Moreover, electron-irradiation experiments reveal that the superconductivity survives even when the electron mean free path becomes substantially shorter than the superconducting coherence length. This indicates that superconductivity is robust against impurities, implying that there is no sign change in the gap function. These results show that, contrary to long-standing belief, heavy electrons with extremely strong Coulomb repulsions can condense into a fully-gapped s-wave superconducting state, which has an on-site attractive pairing interaction., Comment: 8 pages, 5 figures + Supplement (3 pages, 5 figures)

The Kondo model predicts that both the valence at low temperatures and its temperature dependence scale with the characteristic energy T_K of the Kondo interaction. Here, we study the evolution of the 4f occupancy with temperature in a series of Yb Kondo lattices using resonant X-ray emission spectroscopy. In agreement with simple theoretical models, we observe a scaling between the valence at low temperature and T_K obtained from thermodynamic measurements. In contrast, the temperature scale T_v at which the valence increases with temperature is almost the same in all investigated materials while the Kondo temperatures differ by almost four orders of magnitude. This observation is in remarkable contradiction to both naive expectation and precise theoretical predictions of the Kondo model, asking for further theoretical work in order to explain our findings. Our data exclude the presence of a quantum critical valence transition in YbRh2Si2.

Unusual phases and phase transitions are seen at the magnetic-nonmagnetic boundary in Ce, Eu and Yb-based compounds. EuNi$_2$P$_{2}$ is a very unusual valence fluctuating Eu system, because at low temperatures the Eu valence stays close to 2.5 instead of approaching an integer value. Eu valence and thus the magnetic property in this system can be tuned by Ge substitution in P site as EuNi$_2$Ge$_{2}$ is known to exhibit antiferromagnetc (AFM) ordering of divalent Eu moments with $T_N$ = 30 K. We have grown EuNi$_2$(P$_{1-x}$Ge$_x$)$_2$ (0.0 $\leq$ $x$ $\leq$ 0.5) single crystals and studied their magnetic, thermodynamic and transport properties. Increasing Ge doping to $x >$ 0.4 results in a well-defined AFM ordered state with $T_N$ = 12 K for $x$ = 0.5. Moreover, the reduced value of magnetic entropy for $x$ = 0.5 at $T_N$ suggests the presence of valance fluctuation/ Kondo effect in this compound. Interestingly, the specific heat exhibits an enhanced Sommerfeld coefficient upon Ge doping. Subsequently, electronic structure calculations lead to a non-integral valence in EuNi$_2$P$_{2}$ but a stable divalent Eu state in EuNi$_2$Ge$_{2}$ which is in good agreement with experimental results., Comment: 7 pages, 8 figures

We report on the results of powder and single crystal neutron diffraction to investigate the magnetic order in YbCo$_2$Si$_2$ below the N\'eel temperature $T_{\rm N} = 1.7~$K in detail. Two different magnetically ordered phases can clearly be distinguished. At lowest temperatures a commensurate magnetic structure with a propagation vector ${\bf k}_1 = (0.25~ 0.25~ 1)$ is found, while the intermediate phase ($T > 0.9~$K) is characterized by an incommensurate magnetic structure with ${\bf k}_2 = (0.25~ 0.086~ 1)$. The magnetic structure in YbCo$_2$Si$_2$ is in marked contrast to all other known RCo$_2$Si$_2$ compounds (R = rare earth element) likely due to some itineracy of the Yb 4f states being responsible for the magnetism., Comment: 9 pages, 7 figures, accepted for publication in Phys. Rev. B

We report a detailed study of the magnetic properties of CeCo$_{0.85}$Fe$_{0.15}$Si under high magnetic fields (up to 16 Tesla) measuring different physical properties such as specific heat, magnetization, electrical resistivity, thermal expansion and magnetostriction. CeCo$_{0.85}$Fe$_{0.15}$Si becomes antiferromagnetic at $T_N \approx$ 6.7 K. However, a broad tail (onset at $T_X \approx$ 13 K) in the specific heat precedes that second order transition. This tail is also observed in the temperature derivative of the resistivity. However, it is particularly noticeable in the thermal expansion coefficient where it takes the form of a large bump centered at $T_X$. A high magnetic field practically washes out that tail in the resistivity. But surprisingly, the bump in the thermal expansion becomes a well pronounced peak fully split from the magnetic transition at $T_N$. Concurrently, the magnetoresistance also switches from negative to positive just below $T_X$. The magnetostriction is considerable and irreversible at low temperature ($\frac {\Delta L}{L} \left(16 T\right) \sim$ 4$\times$10$^{-4}$ at 2 K) when the magnetic interactions dominate. A broad jump in the field dependence of the magnetostriction observed at low $T$ may be the signature of a weak ongoing metamagnetic transition. Taking altogether, the results indicate the importance of the lattice effects in the development of the magnetic order in these alloys., Comment: 5 pages, 6 figures

CeRuPO is a rare example of a ferromagnetic (FM) Kondo-lattice system. External pressure suppresses the ordering temperature to zero at about $p_c\approx3$ GPa. Our ac-susceptibility and electrical-resistivity investigations evidence that the type of magnetic ordering changes from FM to antiferromagnetic (AFM) at about $p^*\approx0.87$ GPa. Studies in applied magnetic fields suggest that ferromagnetic and antiferromagnetic correlations compete for the ground state at $p>p^*$, but finally the AFM correlations win. The change in the magnetic ground-state properties is closely related to the pressure evolution of the crystalline-electric-field level (CEF) scheme and the magnetic Ruderman-Kittel-Kasuya-Yosida (RKKY) exchange interaction. The N\'{e}el temperature disappears abruptly in a first-order-like fashion at $p_c$, hinting at the absence of a quantum critical point. This is consistent with the low-temperature transport properties exhibiting Landau-Fermi-liquid (LFL) behavior in the whole investigated pressure range up to 7.5 GPa., Comment: 12 figures

The highest antiferromagnetic (AFM) temperature in Ce based compounds has been reported for CeScGe with Tn=47K, but its local or itinerant nature was not deeply investigated yet. In order to shed more light into this unusually high ordering temperature we have investigated structural, magnetic, transport and thermal properties of CeTi{1-x}Sc{x}Ge alloys within the range of stability of the CeScSi-type structure: 0.25

We report on the crystal structure, physical properties, and electronic structure calculations for the ternary pnictide compound EuCr2As2. X-ray diffraction studies confirmed that EuCr2As2 crystalizes in the ThCr2Si2-type tetragonal structure (space group I4/mmm). The Eu ions are in a stable divalent state in this compound. Eu moments in EuCr2As2 order magnetically below Tm = 21 K. A sharp increase in the magnetic susceptibility below Tm and the positive value of the paramagnetic Curie temperature obtained from the Curie-Weiss fit suggest dominant ferromagnetic interactions. The heat capacity exhibits a sharp {\lambda}-shape anomaly at Tm, confirming the bulk nature of the magnetic transition. The extracted magnetic entropy at the magnetic transition temperature is consistent with the theoretical value Rln(2S+1) for S = 7/2 of the Eu2+ ion. The temperature dependence of the electrical resistivity \r{ho}(T) shows metallic behavior along with an anomaly at 21 K. In addition, we observe a reasonably large negative magneto-resistance (~ -24%) at lower temperature. Electronic structure calculations for EuCr2As2 reveal a moderately high density of states of Cr-3d orbitals at the Fermi energy, indicating that the nonmagnetic state of Cr is unstable against magnetic order. Our density functional calculations for EuCr2As2 predict a G-type AFM order in the Cr sublattice. The electronic structure calculations suggest a weak interlayer coupling of the Eu moments., Comment: 9 pages, 7 figures

Most of magnetic transitions related to Ce ordering are found below T_ord~12K. Among the few cases exceeding that temperature, two types of behaviors can be distinguished. One of them is related to the rare cases of Ce binary compounds formed in BCC structures, with a quartet ground state, whose degeneracy is reduced by undergoing different types of transitions mostly structural. The other group shows evidences of itinerant character with the outstanding example of CeRh_3B_2 showing the highest T_ord=115K. The second highest ordering temperature has been reported for CeScGe with T_ord=47K, but the nature of this magnetic state has not been investigated very deeply. In order to shed more light into this unusual high temperature ordering we studied the structural, magnetic, transport and thermal properties of CeTi_1-xSc_xGe alloys in the stability range of the CeScSi-type structure 0.250.65, the magnetic phase boundary splits into two transitions, with an intermediate phase presenting incommensurate spin density waves features., Comment: 8 pages, 10 figures

Physical properties of polycrystalline CeCrGe$_{3}$ and LaCrGe$_{3}$ have been investigated by x-ray absorption spectroscopy, magnetic susceptibility $\chi(T)$, isothermal magnetization M(H), electrical resistivity $\rho(T)$, specific heat C($T$) and thermoelectric power S($T$) measurements. These compounds are found to crystallize in the hexagonal perovskite structure (space group \textit{P6$_{3}$/mmc}), as previously reported. The $\rho(T)$, $\chi(T)$ and C($T$) data confirm the bulk ferromagnetic ordering of itinerant Cr moments in LaCrGe$_{3}$ and CeCrGe$_{3}$ with $T_{C}$ = 90 K and 70 K respectively. In addition a weak anomaly is also observed near 3 K in the C($T$) data of CeCrGe$_{3}$. The T dependences of $\rho$ and finite values of Sommerfeld coefficient $\gamma$ obtained from the specific heat measurements confirm that both the compounds are of metallic character. Further, the $T$ dependence of $\rho$ of CeCrGe$_{3}$ reflects a Kondo lattice behavior. An enhanced $\gamma$ of 130 mJ/mol\,K$^{2}$ together with the Kondo lattice behavior inferred from the $\rho(T)$ establish CeCrGe$_{3}$ as a moderate heavy fermion compound with a quasi-particle mass renormalization factor of $\sim$ 45., Comment: 7 pages, 7 figures. Accepted by Journal of Physics: Condensed Matter

Carrying a large, pure spin magnetic moment of 7 $\mu$bohr/atom in the half-filled 4f shell, divalent europium is an outstanding element for assembling novel magnetic devices in which a two-dimensional electron gas (2DEG) is polarized due to exchange interaction with an underlying magnetically-active Eu layer, even in the absence of a magnetic field. A natural example for such geometry is the intermetallic layered material EuRh$_2$Si$_2$, in which magnetically active layers of Eu are well separated from each other by non-magnetic Si-Rh-Si trilayers. Applying angle-resolved photoelectron spectroscopy (ARPES) to this system, we discovered a large spin splitting of a Shockley-type surface state formed by itinerant electrons of the Si-Rh-Si surface related trilayer. ARPES shows that the splitting sets in below approx. 32.5K and quickly saturates to around 150meV upon cooling. Interestingly, this temperature is substantially higher than the order temperature of the Eu 4f moments (approx. 24.5K) in the bulk. Our results clearly show that the magnetic exchange interaction between the surface state and the buried 4f moments in the 4th subsurface layer is the driving force for the formation of itinerant ferromagnetism at the surface. We demonstrate that the observed spin splitting of the surface state, reflecting properties of 2DEG, is easily controlled by temperature. Such a splitting may also be induced into states of functional surface layers deposited onto the surface of EuRh$_2$Si$_2$ or similarly ordered magnetic materials with metallic or semiconducting properties., Comment: 5 pages, 3 figures

We have studied the temperature-pressure phase diagram of CeCoSi by electrical-resistivity experiments under pressure. Our measurements revealed a very unusual phase diagram. While at low pressures no dramatic changes and only a slight shift of the Ne\'{e}l temperature $T_N$ ($\approx 10$ K) are observed, at about 1.45 GPa a sharp and large anomaly, indicative of the opening of a spin-density-wave (SDW) gap, appears at a comparatively high temperature $T_S \approx 38$ K. With further increasing pressure $T_S$ shifts rapidly to low temperatures and disappears at about 2.15 GPa, likely continuously in a quantum critical point, but without evidence for superconductivity. Even more surprisingly, we observed a clear shift of $T_S$ to higher temperatures upon applying a magnetic field. We discuss two possible origins for $T_S$, either magnetic ordering of Co or a meta-orbital type of transition of Ce., Comment: 6 pages, 5 figures

Detailed $^{195}$Pt- and $^{171}$Yb nuclear magnetic resonance (NMR) studies on the heterogeneous mixed valence system YbPtGe$_2$ are reported. The temperature dependence of the $^{195}$Pt-NMR shift $^{195}K(T)$ indicates the opening of an unusual magnetic gap below 200\,K. $^{195}K(T)$ was analyzed by a thermal activation model which yields an isotropic gap $\Delta/k_B \approx 200$\,K. In contrast, the spin-lattice relaxation rate $^{195}$($1/T_1$) does not provide evidence for the gap. Therefore, an intermediate-valence picture is proposed while a Kondo-insulator scenario can be excluded. Moreover, $^{195}$($1/T_1$) follows a simple metallic behavior, similar to the reference compound YPtGe$_2$. A well resolved NMR line with small shift is assigned to divalent $^{171}$Yb. This finding supports the proposed model with two sub-sets of Yb species (di- and trivalent) located on the Yb2 and Yb1 site of the YbPtGe$_2$ lattice., Comment: Submitted in Physical Review B (Rapid Communication)

A quantum critical point (QCP) arises at a continuous transition between competing phases at zero temperature. Collective excitations at magnetic QCPs give rise to metallic properties that strongly deviate from the expectations of Landau's Fermi liquid description, the standard theory of electron correlations in metals. Central to this theory is the notion of quasiparticles, electronic excitations which possess the quantum numbers of the bare electrons. Here we report measurements of thermal and electrical transport across the field-induced magnetic QCP in the heavy-fermion compound YbRh$_2$Si$_2$. We show that the ratio of the thermal to electrical conductivities at the zero-temperature limit obeys the Wiedemann-Franz (WF) law above the critical field, $B_c$. This is also expected at $B < B_c$, where weak antiferromagnetic order and a Fermi liquid phase form below 0.07 K ($B = 0$). However, at the critical field the low-temperature electrical conductivity suggests a non-Fermi-liquid ground state and exceeds the thermal conductivity by about 10%. This apparent violation of the WF law provides evidence for an unconventional type of QCP at which the fundamental concept of Landau quasiparticles breaks down. These results imply that Landau quasiparticles break up, and that the origin of this disintegration is inelastic scattering associated with electronic quantum critical fluctuations. Our finding brings new insights into understanding deviations from Fermi-liquid behaviour frequently observed in various classes of correlated materials., Comment: 16 pages, 4 figures, and supplemental information

We study the effect of magnetic fields up to 15 T on the heavy fermion state of YbRh$_2$Si$_2$ via Hall effect and magnetoresistance measurements down to 50 mK. Our data show anomalies at three different characteristic fields. We compare our data to renormalized band structure calculations through which we identify Lifshitz transitions associated with the heavy fermion bands. The Hall measurements indicate that the de-renormalization of the quasiparticles, {\it i.e} the destruction of the local Kondo singlets, occurs smoothly while the Lifshitz transitions occur within rather confined regions of the magnetic field., Comment: 7 pages, 5 figures

The spin dynamics of the layered square-lattice vanadate Pb2VO(PO4)2 is investigated by electron spin resonance at various magnetic fields and at temperatures above magnetic ordering. The linewidth divergence towards low temperatures seems to agree with isotropic Heisenberg-type spin exchange suggesting that the spin relaxation in this quasi-two dimensional compound is governed by low-dimensional quantum fluctuations. However, a weak easy- plane anisotropy of the g factor points to the presence of a planar XY type of exchange. Indeed, we found that the linewidth divergence is described best by XY-like spin fluctuations which requires a single parameter only. Therefore, ESR-probed spin dynamics could establish Pb2VO(PO4)2 as the first frustrated square lattice system with XY-inherent spin topological fluctuations., Comment: 5 pages, 3 figures

Structural, magnetic and thermal measurements performed on CeCo{1-x}Fe{x}Si alloys are reported. Three regions can be recognized: i) Co-rich (x < 0.20) with a decreasing long range antiferromagnetic order which vanishes at finite temperature, ii) an intermediate region (0.20 < x < 0.30) showing a broad magnetic anomaly (C_A) in specific heat and iii) the non-magnetic region progressively changing from a non-Fermi-liquid type behavior towards a Fermi liquid one as Fe concentration increases. The C_A anomaly emerges as an incipient contribution above T_N already at x = 0.10, which indicates that this contribution is related to short range correlations likely of quasi-two dimensional type. Both, T_N transition and C_A anomaly are practically not affected by applied magnetic field up to B ~ 10 Tesla., Comment: 5 pages, 5 figures, research in progress

We report on the valence fluctuation of Ce in CeMo$_{2}$Si$_{2}$C as studied by means of magnetic susceptibility $\chi(T)$, specific heat $C(T)$, electrical resistivity $\rho(T)$ and x-ray absorption spectroscopy. Powder x-ray diffraction revealed that CeMo$_{2}$Si$_{2}$C crystallizes in CeCr$_{2}$Si$_{2}$C-type layered tetragonal crystal structure (space group \textit{P4/mmm}). The unit cell volume of CeMo$_{2}$Si$_{2}$C deviates from the expected lanthanide contraction, indicating non-trivalent state of Ce ions in this compound. The observed weak temperature dependence of the magnetic susceptibility and its low value indicate that Ce ions are in valence fluctuating state. The formal $L_{III}$ Ce valence in CeMo$_{2}$Si$_{2}$C $<$$\widetilde{\nu}$$>$ = 3.11 as determined from x-ray absorption spectroscopy measurement is well bellow the value $<$$\widetilde{\nu}$$> \simeq$ 3.4 in tetravalent Ce compound CeO$_{2}$. The temperature dependence of specific heat does not show any anomaly down to 1.8 K which rules out any magnetic ordering in the system. The Sommerfeld coefficient obtained from the specific heat data is $\gamma$ = 23.4 mJ/mol\,K$^{2}$. The electrical resistivity follows the $T{^2}$ behavior in the low temperature range below 35 K confirming a Fermi liquid behavior. Accordingly both the Kadowaki Wood ratio $A/\gamma^{2}$ and the Sommerfeld Wilson ratio $\chi(0)/\gamma$ are in the range expected for Fermi-liquid systems. In order to get some information on the electronic states, we calculated the band structure within the density functional theory, eventhough this approach is not able to treat 4f electrons accurately. The non-$f$ electron states crossing the Fermi level have mostly Mo 4d character. They provide the states with which the 4f sates are strongly hybridized, leading to the intermediate valent state., Comment: 18 pages, 10 figures Submitted to Journal of Alloys and Compounds

We investigate the magnetic field dependent thermopower, thermal conductivity, resistivity and Hall effect in the heavy fermion metal YbRh2Si2. In contrast to reports on thermodynamic measurements, we find in total three transitions at high fields, rather than a single one at 10 T. Using the Mott formula together with renormalized band calculations, we identify Lifshitz transitions as their origin. The predictions of the calculations show that all experimental results rely on an interplay of a smooth suppression of the Kondo effect and the spin splitting of the flat hybridized bands., Comment: 5 pages, 4 figures

Journal ref.: J. Phys.: Condens. Matter 25, 065602 (2013): We investigated the optical reflectivity of the heavy-fermion metal CeCu2Si2 in the energy range 3 meV - 30 eV for temperatures between 4K - 300K. The results for the charge dynamics indicate a behavior that is expected for the formation of a coherent heavy quasiparticle state: Upon cooling the spectra of the optical conductivity indicate a narrowing of the coherent response. Below temperatures of 30 K a considerable suppression of conductivity evolves below a peak structure at 13 meV. We assign this gap-like feature to strong electron correlations due to the 4f-conduction electron hybridization., Comment: 7 pages, 3 figures

Many-body interactions in crystalline solids can be conveniently described in terms of quasiparticles with strongly renormalized masses as compared to those of non-interacting particles. Examples of extreme mass renormalization are on the one hand graphene, where the charge carriers obey the linear dispersion relation of massless Dirac fermions, and on the other hand heavy-fermion materials where the effective electron mass approaches the mass of a proton. Here we show that both extremes, Dirac fermions like they are found in graphene and extremely-heavy quasiparticles characteristic for Kondo materials, may not only coexist in a solid but can undergo strong mutual interactions. Using the example of EuRh2Si2 we explicitly demonstrate that these interactions can take place at the surface and in the bulk. The presence of the linear dispersion is imposed solely by the crystal symmetry while the existence of heavy quasiparticles is caused by the localized nature of the 4f states., Comment: 4 pages, 4 figures

Cerium 4f electronic spin dynamics in single crystals of the heavy-fermion system CeFePO is studied by means of ac-susceptibility, specific heat and muon-spin relaxation ($\mu$SR). Short-range static magnetism occurs below the freezing temperature Tg ~ 0.7 K, which prevents the system from accessing the putative ferromagnetic quantum critical point. In the $\mu$SR, the sample-averaged muon asymmetry function is dominated by strongly inhomogeneous spin fluctuations below 10 K and exhibits a characteristic time-field scaling relation expected from glassy spin dynamics, strongly evidencing cooperative and critical spin fluctuations. The overall behavior can be ascribed neither to canonical spin glasses nor other disorder-driven mechanisms., Comment: 5 pages, 4 figures, accepted for publication in Physical Review Letters, Link: http://prl.aps.org/accepted/6207bYdaGef1483c419928305372ce2d4419eb96f

We present the discovery of ferromagnetism in single crystalline Yb(Rh$_{0.73}$Co$_{0.27}$)$_{2}$Si$_{2}$ below $T_{C} = 1.30\,$K with a spontaneous magnetic moment of $0.1\,\mu_{B}$/Yb along the crystallographic c-axis. This is shown by the huge c-susceptibility peak, the hysteresis in magnetization as well as by the field-dependent susceptibility and specific heat data. This discovery motivates the reinvestigation of the magnetic order in Yb(Rh$_{1-x}$Co$_{x}$)$_{2}$Si$_{2}$ with $x < 0.27$ and in pure YbRh$_{2}$Si$_{2}$ under small pressures with field along the $c$-direction to look for low-lying ferromagnetic order., Comment: 5 pages, 4 figures

We carried out a combined P-substitution and hydrostatic pressure study on CeFeAs_1-xP_xO single crystals in order to investigate the peculiar relationship of the local moment magnetism of Ce, the ordering of itinerant Fe moments, and their connection with the occurrence of superconductivity. Our results evidence a close relationship between the weakening of Fe magnetism and the change from antiferromagnetic to ferromagnetic ordering of Ce moments at p*=1.95 GPa in CeFeAs_0.78P_0.22O. The absence of superconductivity in CeFeAs_0.78P_0.22O and the presence of a narrow and strongly pressure sensitive superconducting phase in CeFeAs_0.70P_0.30O and CeFeAs_0.65P_0.35O indicate the detrimental effect of the Ce magnetism on superconductivity in P-substituted CeFeAsO., Comment: 5 pages, 4 figures

Superconductivity in lanthanide- and actinide-based heavy-fermion metals can have different microscopic origins. Among others, Cooper pair formation based on fluctuations of the valence, of the quadrupole moment or of the spin of the localized 4f/5f shell have been proposed. Spin-fluctuation mediated superconductivity in CeCu2Si2 was demonstrated by inelastic neutron scattering to exist in the vicinity of a spin-density-wave quantum critical point. The isostructural HF compound YbRh2Si2 which is prototypical for a Kondo-breakdown quantum critical point has so far not shown any sign of superconductivity down to approximately 10mK. In contrast, results of de-Haas-van-Alphen experiments by Shishido et al. (J. Phys. Soc. Jpn. 74, 1103 (2005)) suggest superconductivity in CeRhIn5 close to an antiferromagnetic quantum critical point beyond the spin-density-wave type, at which the Kondo effect breaks down. For the related compound CeCoIn5 however, a field-induced quantum critical point of spin-density-wave type is extrapolated to exist inside the superconducting phase., Comment: invited paper at the Materials & Mechanisms of Superconductivity (M2S) 2012