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The authors reply to the Comment arXiv:2104.03770 by P. Canfield et. al.

The partial (up to 7 %) substitution of Cd for Zn in the Yb-based heavy-fermion material YbFe$_2$Zn$_{20}$ is known to induce a slight ($\sim 20$ %) reduction of the Sommerfeld specific heat coefficient $\gamma$ and a huge (up to two orders of magnitude) reduction of the $T^2$ resistivity coefficient $A$, corresponding to a drastic and unexpected reduction of the Kadowaki-Woods ratio $A/\gamma ^2$. Here, Yb $L_{3}$-edge X-ray absorption spectroscopy shows that the Yb valence state is close to $3+$ for all $x$, whereas X-ray diffraction reveals that Cd replace the Zn ions only at the $16c$ site of the $Fd\bar{3}m$ cubic structure, leaving the $48f$ and $96g$ sites with full Zn occupation. Ab-initio electronic structure calculations in pure and Cd-doped materials, carried out without considering correlations, show multiple conduction bands with only minor modifications of the band dispersions near the Fermi level and therefore do not explain the resistivity drop introduced by Cd substitution. We propose that the site-selective Cd substitution introduces light conduction bands with substantial contribution of Cd($16c$) $5p$ levels that have weak coupling to the Yb$^{3+}$ $4f$ moments. These light fermions coexist with heavy fermions originated from other conduction bands with larger participation of Zn($48f$ and $96g$) $4p$ levels that remain strongly coupled with the Yb$^{3+}$ local moments., Comment: 9 pages, 4 figures, to appear in Phys. Rev. B

A fast and automated scheme for general polarization transformations holds great value in adaptive optics, quantum information, and virtually all applications involving light-matter and light-light interactions. We present an experiment that uses a liquid crystal on silicon spatial light modulator (LCOS-SLM) to perform polarization transformations on a light field. We experimentally demonstrate the point-by-point conversion of uniformly polarized light fields across the wave front to realize arbitrary, spatially varying polarization states. Additionally, we demonstrate that a light field with an arbitrary spatially varying polarization can be transformed to a spatially invariant (i.e., uniform) polarization., Comment: 16 pages, 10 figures

Temperature dependent magnetization, muon spin rotation and $^{57}$Fe M\"ossbauer spectroscopy experiments performed on crystals of intermetallic FeGa$_{3-y}$Ge$_{y}$ ($y=0.11,0.14,0.17,0.22,0.27$, $0.29,0.32$) are reported. Whereas at $y=0.11$ even a sensitive magnetic microprobe such as $\mu$SR does not detect magnetism, all other samples display weak ferromagnetism with a magnetic moment of up to 0.22 $\mu_B$ per Fe atom. As a function of doping and of temperature a crossover from short range to long range magnetic order is observed, characterized by a broadly distributed spontaneous internal field. However, the $y=0.14$ and $y=0.17$ remain in the short range ordered state down to the lowest investigated temperature. The transition from short range to long range order appears to be accompanied by a change of the character of the spin fluctuations, which exhibit spin wave excitations signature in the LRO part of the phase diagram. M\"ossbauer spectroscopy for $y=0.27$ and 0.32 indicates that the internal field lies in the plane perpendicular to the crystallographic $c$ axis. The field distribution and its evolution with doping suggest that the details of the Fe magnetic moment formation and the consequent magnetic state are determined not only by the dopant concentration but also by the way the replacement of the Ga atoms surrounding the Fe is accomplished.

We develop a generalized pseudo-fermion functional renormalization group (PFFRG) approach that can be applied to arbitrary Heisenberg models with spins ranging from the quantum case $S=1/2$ to the classical limit $S\rightarrow\infty$. Within this framework, spins of magnitude $S$ are realized by implementing $M=2S$ copies of spin-1/2 degrees of freedom on each lattice site. We confirm that even without explicitly projecting onto the highest spin sector of the Hilbert space, ground states tend to select the largest possible local spin magnitude. This justifies the average treatment of the pseudo fermion constraint in previous spin-1/2 PFFRG studies. We apply this method to the antiferromagnetic $J_1$-$J_2$ honeycomb Heisenberg model with nearest neighbor $J_1>0$ and second neighbor $J_2>0$ interactions. Mapping out the phase diagram in the $J_2/J_1$-$S$ plane we find that upon increasing $S$ quantum fluctuations are rapidly decreasing. In particular, already at $S=1$ we find no indication for a magnetically disordered phase. In the limit $S\rightarrow\infty$, the known phase diagram of the classical system is exactly reproduced. More generally, we prove that for $S\rightarrow\infty$ the PFFRG approach is identical to the Luttinger-Tisza method., Comment: 14 pages, 13 figures

We study the three-dimensional Kasteleyn transition in both nearest neighbours and dipolar spin ice models using an algorithm that conserves the number of excitations. We first limit the interactions range to nearest neighbours to test the method in the presence of a field applied along $[100]$, and then focus on the dipolar spin ice model. The effect of dipolar interactions, which is known to be greatly self screened at zero field, is particularly strong near full polarization. It shifts the Kasteleyn transition to lower temperatures, which decreases $\approx 0.4 K$ for the parameters corresponding to the best known spin ice materials, $Dy_2Ti_2O_7$ and $Ho_2Ti_2O_7$. This shift implies effective dipolar fields as big as $0.05$ tesla opposing the applied field, and thus favoring the creation of "strings" of reversed spins. We compare the reduction in the transition temperature with results in previous experiments, and study the phenomenon quantitatively using a simple molecular field approach. Finally, we relate the presence of the effective residual field to the appearance of string-ordered phases at low fields and temperatures, and we check numerically that for fields applied along $[100]$ there are only three different stable phases at zero temperature., Comment: Accepted for publication in Journal of Physics: Condensed Matter

A detailed microscopic and quantitative description of the electronic and magnetic properties of Gd$^{3+}$-doped YCo$_{2}$Zn$_{20}$ single crystals (Y$_{1-x}$Gd$_{x}$Co$_{2}$Zn$_{20}$: (0.002 $\lesssim x \leq $ 1.00) is reported through a combination of temperature-dependent electron spin resonance (ESR), heat capacity and $dc$ magnetic susceptibility experiments, plus first-principles density functional theory (DFT) calculations. The ESR results indicate that this system features an \emph{exchange bottleneck} scenario wherein various channels for the spin-lattice relaxation mechanism of the Gd$^{3+}$ ions can be identified via exchange interactions with different types of conduction electrons at the Fermi level. Quantitative support from the other techniques allow to extract the exchange interaction parameters between the localized magnetic moments of the Gd$^{3+}$ ions and the different types of conduction electrons present at the Fermi level ($J_{fs}$, $J_{fp}$ and $J_{fd}$). Despite the complexity of the crystal structure, our combination of experimental and electronic structure data establish GdCo$_{2}$Zn$_{20}$ as a model RKKY system by predicting a Curie-Weiss temperature $\theta_{C} = -1.2(2)$~K directly from microscopic parameters, in very good agreement with the bulk value from magnetization data. The successful microscopic understanding of the electronic structure and behavior for the two end compounds YCo$_{2}$Zn$_{20}$ and GdCo$_{2}$Zn$_{20}$ means they can be used as references to help describe the more complex electronic properties of related materials., Comment: Phys. Rev. B (accepted)

FeGa$_3$ is an unusual intermetallic semiconductor that presents intriguing magnetic responses to the tuning of its electronic properties. When doped with Ge, the system evolves from diamagnetic to paramagnetic to ferromagnetic ground states that are not well understood. In this work, we have performed a joint theoretical and experimental study of FeGa$_{3-x}$Ge$_x$ using Density Functional Theory and magnetic susceptibility measurements. For low Ge concentrations we observe the formation of localized moments on some Fe atoms and, as the dopant concentration increases, a more delocalized magnetic behavior emerges. The magnetic configuration strongly depends on the dopant distribution, leading even to the appearance of antiferromagnetic interactions in certain configurations., Comment: See "Note added to arXiv version" in text