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In a recent paper, Custers {it et al.} cite{custers} argue for the existence of a new metallic quantum critical phase at 0 K in the Ge-doped heavy-fermion system YbRh$_2$Si$_2$ in the presence of magnetic frustration. In here we discuss the consequences of this identification for the (more standard) field induced quantum critical phase.
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In Ref. 1, Schubert et al. [Phys. Rev. Research 1, 032004 (2019)] reported measurements of the isothermal magnetoresistance of Fe- and Ni-substituted YbRh$_2$Si$_2$, based on which they raised questions about the Kondo destruction description for the magnetic field-induced quantum critical point (QCP) of pristine YbRh$_2$Si$_2$. Here we make three points. Firstly, as shown by studies on pristine YbRh$_2$Si$_2$ in Paschen et al. and Friedemann et al., isothermal crossed-field and single-field Hall effect measurements are necessary to ascertain the evolution of the Fermi surface across this QCP. Because Schubert et al. did not carry out such measurements, their results on Fe- and Ni-substituted YbRh$_2$Si$_2$ cannot be used to assess the validity of the Kondo destruction picture neither for substituted nor for pristine YbRh$_2$Si$_2$. Secondly, when referring to the data of Friedemann et al. on the isothermal crossover of YbRh$_2$Si$_2$, they did not recognize the implications of the crossover width, quantified by the full width at half maximum (FWHM), being linear in temperature, with zero offset, over about $1.5$ decades in temperature, from 30 mK to 1 K. Finally, in claiming deviations of Hall crossover FWHM data of Friedemann et al. from the above linear-in-$T$ dependence they neglected the error bars of these measurements and discarded some of the data points. The claims of Schubert et al. are thus not supported by data, neither previously published nor new (Ref. 1). As such they cannot invalidate the evidence that has been reported for Kondo destruction quantum criticality in YbRh$_2$Si$_2$.
The heavy-fermion metal YbRh$_2$Si$_2$ realizes a field-induced quantum critical point with multiple vanishing energy scales $T_{rm N}(B)$ and $T^ast(B)$. We investigate their change with partial non-isoelectronic substitutions, chemical and hydrostatic pressure. Low-temperature electrical resistivity, specific heat and magnetic susceptibility of Yb(Rh$_{1-x}$T$_x$)$_2$Si$_2$ with T=Fe or Ni for $xleq 0.1$, magnetic fields $Bleq 0.3$~T (applied perpendicular to the c-axis) and hydrostatic pressure $pleq 1.5$~GPa are reported. The data allow to disentangle the combined influences of hydrostatic and chemical pressure, as well as non-isoelectronic substitution. In contrast to Ni- and Co-substitution, which enhance magnetic order, Fe-substitution acts oppositely. For $x=0.1$ it also completely suppresses the $T^ast$ crossover and eliminates ferromagnetic fluctuations. The pressure, magnetic field and temperature dependences of $T^ast$ are incompatible with its interpretation as Kondo breakdown signature.
Previously, we reported that the doping and pressure dependence of the $T^ast(B)$ crossover in YbRh$_2$Si$_2$ is incompatible with its interpretation as signature of a Kondo breakdown [M.-H. Schubert et al., Phys. Rev. Research 1, 032004(R) (2019)]. The comment by S. Wirth et al. [arXiv:1910.04108] refers to Hall measurements on undoped YbRh$_2$Si$_2$ and criticizes our study as incomplete and inconclusive. We thoroughly inspect these data and rebut the arguments of the comment.
The surprising discovery of tripling the superconducting critical temperature of KFe$_2$As$_2$ at high pressures issued an intriguing question of how the superconductivity in the collapsed tetragonal phase differs from that in the non-collapsed phases of Fe-based superconductors. Here we report $^{89}$Y nuclear magnetic resonance study of YFe$_2$Ge$_{x}$Si$_{2-x}$ compounds whose electronic structure is similar to that of iron-pnictide collapsed tetragonal phases already at ambient pressure. Fe(Ge,Si) layers show strong ferromagnetic spin fluctuations whereas layers are coupled antiferromagnetically -- both positioning the studied family close to a quantum critical point. Next, localized moments attributed either to Fe interstitial or antisite defects may account for magnetic impurity pair-breaking effects thus explaining the substantial variation of superconductivity among different YFe$_2$Ge$_2$ samples.
Measurements of low temperature transport and thermodynamic properties have been used to characterize the non-Fermi liquid state of the itinerant ferromagnet ZrZn$_2$. We observe a $T^{5/3}$ temperature dependence of the electrical resistivity at zero field, which becomes $T^2$ like in an applied field of 9 T. In zero field we also measured the thermal conductivity, and we see a novel linear in $T$ dependence of the difference between the thermal and electrical resistivities. Heat capacity measurements, also at zero field, reveal an upturn in the electronic contribution at low temperatures when the phonon term is subtracted. Taken together, we argue that these properties are consistent with a marginal Fermi liquid state which is predicted by a mean-field model of enhanced spin fluctuations on the border of ferromagnetism in three dimensions. We compare our data to quantitative predictions and establish this model as a compelling theoretical framework for understanding ZrZn$_2$.
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