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Topological materials hosting kagome lattices have drawn considerable attention due to the interplay between topology, magnetism, and electronic correlations. The (Fe$_{1-x}$Co$_x$)Sn system not only hosts a kagome lattice but has a tunable symmetry breaking magnetic moment with temperature and doping. In this study, angle resolved photoemission spectroscopy and first principles calculations are used to investigate the interplay between the topological electronic structure and varying magnetic moment from the planar to axial antiferromagnetic phases. A theoretically predicted gap at the Dirac point is revealed in the low temperature axial phase but no gap opening is observed across a temperature dependent magnetic phase transition. However, topological surface bands are observed to shift in energy as the surface magnetic moment is reduced or becomes disordered over time during experimental measurements. The shifting surface bands may preclude the determination of a temperature dependent bulk gap but highlights the intricate connections between magnetism and topology with a surface/bulk dichotomy that can affect material properties and their interrogation., Comment: 11 pages, 4 figures

The kagome lattice is a fertile platform to explore topological excitations with both Fermi-Dirac and Bose-Einstein statistics. While relativistic Dirac Fermions and flat-bands have been discovered in the electronic structure of kagome metals, the spin excitations have received less attention. Here we report inelastic neutron scattering studies of the prototypical kagome magnetic metal FeSn. The spectra display well-defined spin waves extending up to 120 meV. Above this energy, the spin waves become progressively broadened, reflecting interactions with the Stoner continuum. Using linear spin wave theory, we determine an effective spin Hamiltonian that reproduces the measured dispersion. This analysis indicates that the Dirac magnon at the K-point remarkably occurs on the brink of a region where well-defined spin waves become unobservable. Our results emphasize the influential role of itinerant carriers on the topological spin excitations of metallic kagome magnets., 6 pages, 4 figures

High critical temperature superconductivity often occurs in systems where an antiferromagnetic order is brought near $T=0$ K by slightly modifying pressure or doping. ${\mathrm{CaKFe}}_{4}{\mathrm{As}}_{4}$ is a superconducting, stoichiometric iron-pnictide compound showing optimal superconducting critical temperature with ${T}_{c}$ as large as 35 K. Doping with Ni induces a decrease in ${T}_{c}$ and the onset of spin-vortex crystal (SVC) antiferromagnetic order, which consists of spins pointing inwards to or outwards from alternating As sites on the diagonals of the in-plane square Fe lattice. Here we study the band structure of $\mathrm{CaK}{({\mathrm{Fe}}_{0.95}{\mathrm{Ni}}_{0.05})}_{4}{\mathrm{As}}_{4}$ $({T}_{c}=10 \mathrm{K},$ ${T}_{SVC}=50 \mathrm{K})$ using quasiparticle interference with a scanning tunneling microscope and show how the SVC modifies the band structure and induces a fourfold superconducting gap anisotropy.

In the nematic state of iron-based superconductors, twin formation often obscures the intrinsic, anisotropic, in-plane physical properties. Relatively high in-plane external magnetic fields ${H}_{\mathrm{ext}}$ greater than the typical laboratory-scale magnetic fields 10--15 T are usually required to completely detwin a sample. However, recently a very small in-plane ${H}_{\mathrm{ext}}\ensuremath{\sim}0.1$ T was found to be sufficient for detwinning the nematic domains in ${\mathrm{EuFe}}_{2}{\mathrm{As}}_{2}$. To explain this behavior, a microscopic theory based on biquadratic magnetic interactions between the Eu and Fe spins has been proposed. Here, using $^{153}\mathrm{Eu}$ nuclear magnetic resonance (NMR) measurements below the ${\mathrm{Eu}}^{2+}$ ordering temperature, we show experimental evidence of the detwinning under small in-plane ${H}_{\mathrm{ext}}$. Our NMR study also reveals the evolution of the angles between the Eu and Fe spins during the detwinning process, which provides experimental evidence for the existence of biquadratic coupling in the system.

The magnetic response of $\mathrm{Ca}\mathrm{K}{({\mathrm{Fe}}_{0.949}{\mathrm{Ni}}_{0.051})}_{4}{\mathrm{As}}_{4}$ was investigated by means of the muon spin rotation/relaxation. The long-range commensurate magnetic order sets in below the N\'eel temperature ${T}_{\mathrm{N}}=50.0(5)$ K. The density-functional theory calculations have identified three possible muon stopping sites. The experimental data were found to be consistent with only one type of magnetic structure, namely, the long-range magnetic spin-vortex-crystal order with the hedgehog motif within the $ab$ plane and the antiferromagnetic stacking along the $c$ direction. The value of the ordered magnetic moment at $T\ensuremath{\approx}3$ K was estimated to be ${m}_{\mathrm{Fe}}=0.38(11){\ensuremath{\mu}}_{\mathrm{B}}$ (${\ensuremath{\mu}}_{\mathrm{B}}$ is the Bohr magneton). A microscopic coexistence of magnetic and superconducting phases accompanied by a reduction of the magnetic order parameter below the superconducting transition temperature ${T}_{\mathrm{c}}\ensuremath{\simeq}9$ K is observed. Comparison with 11, 122, and 1144 families of Fe-based pnictides points to existence of correlation between the reduction of the magnetic order parameter at $T\ensuremath{\rightarrow}0$ and the ratio of the transition temperatures ${T}_{\mathrm{c}}/{T}_{\mathrm{N}}$. Such correlations were found to be described by Machida's model for coexistence of itinerant spin-density-wave magnetism and superconductivity [K. Machida, J. Phys. Soc. Jpn. 50, 2195 (1981); S. L. Bud'ko et al., Phys. Rev. B 98, 144520 (2018)].

Quantum interference on the kagome lattice generates electronic bands with narrow bandwidth, called flat bands. Crystal structures incorporating this lattice can host strong electron correlations with nonstandard ingredients, but only if these bands lie at the Fermi level. In the six compounds with the CoSn structure type (FeGe, FeSn, CoSn, NiIn, RhPb, and PtTl) the transition metals form a kagome lattice. The two iron variants are robust antiferromagnets so we focus on the latter four and investigate their thermodynamic and transport properties. We consider these results and calculated band structures to locate and characterize the flat bands in these materials. We propose that CoSn and RhPb deserve the community's attention for exploring flat-band physics.

The upper critical field of multiband superconductors is an important quantity that can reveal details about the nature of the superconducting pairing. Here we experimentally map out the complete upper-critical-field phase diagram of a stoichiometric superconductor, ${\mathrm{CaKFe}}_{4}{\mathrm{As}}_{4}$, up to $90\phantom{\rule{0.16em}{0ex}}\mathrm{T}$ for different orientations of the magnetic field and at temperatures down to $4.2\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. The upper critical fields are extremely large, reaching values close to $\ensuremath{\sim}3\phantom{\rule{0.16em}{0ex}}{T}_{\mathrm{c}}$ at the lowest temperature, and the anisotropy decreases dramatically with temperature, leading to essentially isotropic superconductivity at $4.2\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. We find that the temperature dependence of the upper critical field can be well described by a two-band model in the clean limit with band-coupling parameters favoring intraband over interband interactions. The large Pauli paramagnetic effects together with the presence of the shallow bands is consistent with the stabilization of an FFLO state at low temperatures in this clean superconductor.

FeSn is an itinerant antiferromagnet that hosts electronic Dirac states and ordered magnetic moments lying within its Fe Kagome-lattice planes. We present magnetization measurements of single crystals of $({\mathrm{Fe}}_{1\ensuremath{-}x}{\mathrm{Co}}_{x})\text{Sn}$, revealing the evolution and suppression of this magnetic order with Co substitution. We interpret the dramatic changes in magnetic anisotropy to indicate a reorientation of the moments from perpendicular to parallel to the hexagonal $c$ axis and confirm this with neutron diffraction. It has been proposed that the Dirac nodes observed in FeSn should become gapped if the moments rotate as our data suggests. We identify Co-substituted compositions that adopt both antiferromagnetic configurations at different temperatures. This system provides a unique opportunity to study how the details of magnetic order impact Dirac electron states.

We report combined experimental and theoretical analysis of superconductivity in $\mathrm{CaK}{({\mathrm{Fe}}_{1\ensuremath{-}x}{\mathrm{Ni}}_{x})}_{4}{\mathrm{As}}_{4}$ (CaK1144) for $x=0$, 0.017, and 0.034. To obtain the superfluid density $\ensuremath{\rho}={\left[1+\mathrm{\ensuremath{\Delta}}{\ensuremath{\lambda}}_{L}(T)/{\ensuremath{\lambda}}_{L}(0)\right]}^{\ensuremath{-}2}$, the temperature dependence of the London penetration depth $\mathrm{\ensuremath{\Delta}}{\ensuremath{\lambda}}_{L}(T)$ was measured by using a tunnel-diode resonator (TDR) and the results agreed with the microwave coplanar resonator (MWR) with the small differences accounted for by considering a three orders of magnitude higher frequency of MWR. The absolute value of ${\ensuremath{\lambda}}_{L}(T\ensuremath{\ll}{T}_{c})\ensuremath{\approx}{\ensuremath{\lambda}}_{L}(0)$ was measured by using MWR, ${\ensuremath{\lambda}}_{L}(5\phantom{\rule{4pt}{0ex}}\mathrm{K})\ensuremath{\approx}170\ifmmode\pm\else\textpm\fi{}20$ nm, which agreed well with the NV centers in diamond optical magnetometry that gave ${\ensuremath{\lambda}}_{L}(5\phantom{\rule{4pt}{0ex}}\mathrm{K})\ensuremath{\approx}196\ifmmode\pm\else\textpm\fi{}12$ nm. The experimental results are analyzed within the Eliashberg theory, showing that the superconductivity of CaK1144 is well described by the nodeless ${s}_{\ifmmode\pm\else\textpm\fi{}}$ order parameter and that upon Ni doping the interband interaction increases.

The magnetic penetration depth anisotropy $\gamma_\lambda=\lambda_{c}/\lambda_{ab}$ ($\lambda_{ab}$ and $\lambda_{c}$ are the in-plane and the out-of-plane components of the magnetic penetration depth) in a CaKFe$_4$As$_4$ single crystal sample (the critical temperature $T_{\rm c}\simeq 35$ K) was studied by means of muon-spin rotation ($\mu$SR). $\gamma_\lambda$ is almost temperature independent for $T\lesssim 20$ K ($\gamma_\lambda\simeq 1.9$) and it reaches $\simeq 3.0$ by approaching $T_{\rm c}$. The change of $\gamma_\lambda$ induces the corresponding rearrangement of the flux line lattice (FLL), which is clearly detected via enhanced distortions of the FLL $\mu$SR response. Comparison of $\gamma_\lambda$ with the anisotropy of the upper critical field ($\gamma_{H_{\rm c2}}$) studied in Phys. Rev B {\bf 94}, 064501 (2016), reveals that $\gamma_\lambda$ is systematically higher than $\gamma_{H_{\rm c2}}$ at low-temperatures and approaches $\gamma_{H_{\rm c2}}$ for $T \rightarrow T_{\rm c}$. The anisotropic properties of $\lambda$ are explained by the multi-gap nature of superconductivity in CaKFe$_4$As$_4$ and are caused by anisotropic contributions of various bands to the in-plane and the out-of-plane components of the superfluid density., Comment: 6 pages, 4 figures

Temperature dependent $^{57}\mathrm{Fe}$ M\"ossbauer spectroscopy and specific heat measurements for $\mathrm{CaK}{({\mathrm{Fe}}_{1\ensuremath{-}x}{\mathrm{Ni}}_{x})}_{4}{\mathrm{As}}_{4}$ with $x=0$, 0.017, 0.033, and 0.049 are presented. No magnetic hyperfine field (i.e., no static magnetic order) down to 5.5 K was detected for $x=0$ and 0.017 in agreement with the absence of any additional feature below superconducting transition temperature ${T}_{c}$ in the specific heat data. The evolution of magnetic hyperfine field with temperature was studied for $x=0.033$ and 0.049. The long-range magnetic order in these two compounds coexists with superconductivity. The magnetic hyperfine field ${B}_{\text{hf}}$ (ordered magnetic moment) below ${T}_{c}$ in $\mathrm{CaK}{({\mathrm{Fe}}_{0.967}{\mathrm{Ni}}_{0.033})}_{4}{\mathrm{As}}_{4}$ is continuously suppressed with the developing superconducting order parameter. The ${B}_{\text{hf}}(T)$ data for $\mathrm{CaK}{({\mathrm{Fe}}_{0.967}{\mathrm{Ni}}_{0.033})}_{4}{\mathrm{As}}_{4}$ and $\mathrm{CaK}{({\mathrm{Fe}}_{0.951}{\mathrm{Ni}}_{0.049})}_{4}{\mathrm{As}}_{4}$ can be described reasonably well by Machida's model for coexistence of itinerant spin density wave magnetism and superconductivity [K. Machida, J. Phys. Soc. Jpn. 50, 2195 (1981)]. We demonstrate directly that superconductivity suppresses the spin density wave order parameter if the conditions are right, in agreement with the theoretical analysis.

We employ polarization-resolved Raman spectroscopy to study the multiband stoichiometric ${T}_{c}=35$ K superconductor ${\mathrm{CaKFe}}_{4}{\mathrm{As}}_{4}$. We do not detect Pomeranchuk-like electronic nematic fluctuations which were universally observed in the $XY\phantom{\rule{4pt}{0ex}}({B}_{2g})$ symmetry Raman response for most families of the Fe-based superconductors. In the superconducting state we observe, consistent with a nodeless order parameter, a full spectral weight suppression at low energies and the emergence of a composite pair-breaking coherence feature at energies between 12 and 20 meV. We analyze the superconductivity-induced phonon self-energy effects and give an estimation for the electron-phonon coupling constant ${\ensuremath{\lambda}}^{\mathrm{\ensuremath{\Gamma}}}=0.0015$ which is insufficient to provide attraction for high-${T}_{c}$ pairing.

We report inelastic light scattering results on the stoichiometric and fully ordered superconductor ${\mathrm{CaKFe}}_{4}{\mathrm{As}}_{4}$ as a function of temperature and light polarization. In the energy range between 10 and 315 ${\mathrm{cm}}^{\ensuremath{-}1}$ (1.24 and 39.1 meV) we observe the particle-hole continuum above and below the superconducting transition temperature ${T}_{c}$ and seven of the eight Raman active phonons. The main focus is placed on the analysis of the electronic excitations. Below ${T}_{c}$ all three symmetries projected with in-plane polarizations display a redistribution of spectral weight characteristic for superconductivity. The energies of the pair-breaking peaks in ${A}_{1g}$ and ${B}_{2g}$ symmetry are in approximate agreement with the results from photoemission studies. In ${B}_{1g}$ symmetry the difference between the normal and superconducting state is most pronounced, and the feature is shifted downwards with respect to those in ${A}_{1g}$ and ${B}_{2g}$ symmetry. The maximum peaking at 134 ${\mathrm{cm}}^{\ensuremath{-}1}$ (16.6 meV) has a substructure on the high-energy side. We interpret the peak at 134 ${\mathrm{cm}}^{\ensuremath{-}1}$ in terms of a collective Bardasis-Schrieffer (BS) mode and the substructure as a remainder of the pair-breaking feature on the electron bands. There is a very weak peak at 50 ${\mathrm{cm}}^{\ensuremath{-}1}$ (6.2 meV) which is tentatively assigned to another BS mode.

The magnetic order in CaK(Fe[1-x]Ni[x])4As4 (1144) single crystals (x = 0.051 and 0.033) has been studied by neutron diffraction. We observe magnetic Bragg peaks associated to the same propagation vectors as found for the collinear stripe antiferromagnetic (AFM) order in the related BaFe2As2 (122) compound. The AFM state in 1144 preserves tetragonal symmetry and only a commensurate, non-collinear structure with a hedgehog spin-vortex crystal (SVC) arrangement in the Fe plane and simple AFM stacking along the c direction is consistent with our observations. The SVC order is promoted by the reduced symmetry in the FeAs layer in the 1144 structure. The long-range SVC order coexists with superconductivity, however, similar to the doped 122 compounds, the ordered magnetic moment is gradually suppressed with the developing superconducting order parameter. This supports the notion that both collinear and non-collinear magnetism and superconductivity are competing for the same electrons coupled by Fermi surface nesting in iron arsenide superconductors.

The pressure dependence of the magnetic and superconducting transitions and that of the superconducting upper critical field are reported for $\mathrm{CaK}{({\mathrm{Fe}}_{1\ensuremath{-}x}{\mathrm{Ni}}_{x})}_{4}{\mathrm{As}}_{4}$, the first example of an Fe-based superconductor with spin-vortex-crystal-type magnetic ordering. Resistance measurements were performed on single crystals with two substitution levels $(x=0.033,0.050)$ under hydrostatic pressures up to 5.12 GPa and in magnetic fields up to 9 T. Our results show that, for both compositions, magnetic transition temperatures ${T}_{\mathrm{N}}$ are suppressed upon applying pressure; the superconducting transition temperatures ${T}_{\mathrm{c}}$ are suppressed by pressure as well, except for $x=0.050$ in the pressure region where ${T}_{\mathrm{N}}$ and ${T}_{\mathrm{c}}$ cross. Furthermore, the pressure associated with the crossing of the ${T}_{\mathrm{N}}$ and ${T}_{\mathrm{c}}$ lines also coincides with a minimum in the normalized slope of the superconducting upper critical field, consistent with a likely Fermi-surface reconstruction associated with the loss of magnetic ordering. Finally, at $p\ensuremath{\sim}4$ GPa, both Ni-substituted $\mathrm{CaK}{({\mathrm{Fe}}_{1\ensuremath{-}x}{\mathrm{Ni}}_{x})}_{4}{\mathrm{As}}_{4}$ samples likely go through a half-collapsed-tetragonal phase transition, similar to the parent compound ${\mathrm{CaKFe}}_{4}{\mathrm{As}}_{4}$.

Controlled pointlike disorder introduced by 2.5-MeV electron irradiation was used to probe the superconducting state of single crystals of $\mathrm{CaK}{({\mathrm{Fe}}_{1\ensuremath{-}x}{\mathrm{Ni}}_{x})}_{4}{\mathrm{As}}_{4}$ superconductor at $x=0$ and 0.05 doping levels. Both compositions show an increase of the residual resistivity and a decrease of the superconducting transition temperature, ${T}_{c}$, at the rate of $d{T}_{c}/d\ensuremath{\rho}({T}_{c})\ensuremath{\approx}0.19$ K/($\ensuremath{\mu}\mathrm{\ensuremath{\Omega}}\phantom{\rule{0.16em}{0ex}}\mathrm{cm}$) for $x=0$ and 0.38 K/($\ensuremath{\mu}\mathrm{\ensuremath{\Omega}}\phantom{\rule{0.16em}{0ex}}\mathrm{cm}$) for $x=0.05$, respectively. In the Ni-doped compound ($x=0.05$), the coexisting spin-vortex crystal (SVC) magnetic phase is suppressed at the rate of $d{T}_{N}/d\ensuremath{\rho}({T}_{N})\ensuremath{\approx}$ 0.16 K/($\ensuremath{\mu}\mathrm{\ensuremath{\Omega}}\phantom{\rule{0.16em}{0ex}}\mathrm{cm}$). The low-temperature variation of London penetration depth is well approximated by the power-law function, $\mathrm{\ensuremath{\Delta}}\ensuremath{\lambda}(T)=A{T}^{n}$, with $n\ensuremath{\approx}\phantom{\rule{0.16em}{0ex}}2.5$ for $x=0$ and $n\ensuremath{\approx}\phantom{\rule{0.16em}{0ex}}1.9$ for $x=0.05$ in the pristine state. Detailed analysis of $\ensuremath{\lambda}(T)$ and ${T}_{c}$ evolution with disorder is consistent with two effective nodeless energy gaps in the density of states due to robust ${s}_{\ifmmode\pm\else\textpm\fi{}}$ pairing. Overall the behavior of $\mathrm{CaK}{({\mathrm{Fe}}_{1\ensuremath{-}x}{\mathrm{Ni}}_{x})}_{4}{\mathrm{As}}_{4}$ at $x=0$ is similar to a slightly overdoped ${\mathrm{Ba}}_{1\ensuremath{-}y}{\mathrm{K}}_{y}{\mathrm{Fe}}_{2}{\mathrm{As}}_{2}$ at $y\ensuremath{\approx}$ 0.5, and at $x=0.05$ to an underdoped composition at $y\ensuremath{\approx}$ 0.2.

The temperature dependence of the in-plane magnetic penetration depth ($\lambda_{ab}$) in an extensively characterized sample of superconducting CaKFe$_4$As$_4$ ($T_{\rm c}\simeq35$ K) was investigated using muon-spin rotation ($\mu$SR). A comparison of $\lambda_{ab}^{-2}(T)$ measured by $\mu$SR with the one inferred from ARPES data confirms the presence of multiple gaps at the Fermi level. An agreement between $\mu$SR and ARPES requires the presence of additional bands, which are not resolved by ARPES experiments. These bands are characterized by small supercondcting gaps with an average zero-temperature value of $\Delta_{0} =$ 2.4(2) meV. Our data suggest that in CaKFe$_4$As$_4$ the $s^\pm$ order parameter symmetry acquires a more sophisticated form by allowing a sign change not only between electron and hole pockets, but also within pockets of similar type., Comment: 6 pages, 4 figures. Accpeted for publication in Phys.Rev.B (Rapid)

We use a scanning tunneling microscope to study the superconducting density of states and vortex lattice of single crystals of ${\mathrm{CaKFe}}_{4}{\mathrm{As}}_{4}$. This material has a critical temperature of ${T}_{c}=35$ K, one of the highest among stoichiometric iron based superconductors (FeBSCs), and is comparable to ${T}_{c}$ found near optimal doping in other FeBSCs. We observe quasiparticle scattering from defects with a pattern related to interband scattering between zone centered hole sheets. We measure the tunneling conductance in vortex cores and find a peak due to Caroli--de Gennes--Matricon bound states. The peak is located above the Fermi level, showing that ${\mathrm{CaKFe}}_{4}{\mathrm{As}}_{4}$ is a clean superconductor with vortex core bound states close to the so-called extreme quantum limit. We identify locations where the superconducting order parameter is strongly suppressed due to pair breaking. Vortices are pinned at these locations, and the length scale of the suppression of the order parameter is of order of the vortex core size. As a consequence, the vortex lattice is disordered up to 8 T.

The coexistence of a new-type antiferromagnetic (AFM) state, the so-called hedgehog spin-vortex crystal (SVC), and superconductivity (SC) is evidenced by an $^{75}\mathrm{As}$ nuclear magnetic resonance study on single-crystalline $\mathrm{CaK}{({\mathrm{Fe}}_{0.951}{\mathrm{Ni}}_{0.049})}_{4}{\mathrm{As}}_{4}$. The hedgehog SVC order is clearly demonstrated by the direct observation of internal magnetic induction along the $c$ axis at the As1 site (close to K) and a zero net internal magnetic induction at the As2 site (close to Ca) below an AFM ordering temperature ${T}_{\mathrm{N}}\ensuremath{\sim}52$ K. The nuclear spin-lattice relaxation rate $1/{T}_{1}$ shows a distinct decrease below ${T}_{\mathrm{c}}\ensuremath{\sim}10$ K, providing also unambiguous evidence for the microscopic coexistence. Furthermore, based on the analysis of the $1/{T}_{1}$ data, the hedgehog SVC-type spin correlations are found to be enhanced below $T\ensuremath{\sim}150$ K in the paramagnetic state. These results indicate the hedgehog SVC-type spin correlations play an important role for the appearance of SC in the new magnetic superconductor.

We report $^{75}\mathrm{As}$ nuclear magnetic resonance (NMR) studies on a new iron-based superconductor, ${\mathrm{CaKFe}}_{4}{\mathrm{As}}_{4}$, with ${T}_{\mathrm{c}}\phantom{\rule{0.28em}{0ex}}=\phantom{\rule{0.28em}{0ex}}35$ K. $^{75}\mathrm{As}$ NMR spectra show two distinct lines corresponding to the As(1) and As(2) sites close to the K and Ca layers, respectively, revealing that K and Ca layers are well ordered without site inversions. We found that nuclear quadrupole frequencies ${\ensuremath{\nu}}_{\mathrm{Q}}$ of the As(1) and As(2) sites show an opposite temperature $T$ dependence. Nearly $T$ independent behavior of the Knight shifts $K$ is observed in the normal state, and a sudden decrease in $K$ in the superconducting (SC) state suggests spin-singlet Cooper pairs. $^{75}\mathrm{As}$ spin-lattice relaxation rates $1/{T}_{1}$ show a power-law $T$ dependence with different exponents for the two As sites. The isotropic antiferromagnetic spin fluctuations characterized by the wave vector $\mathbf{q}\phantom{\rule{0.28em}{0ex}}=\phantom{\rule{0.28em}{0ex}}(\ensuremath{\pi},\phantom{\rule{0.28em}{0ex}}0)$ or $(0,\phantom{\rule{0.28em}{0ex}}\ensuremath{\pi})$ in the single-iron Brillouin zone notation are revealed by $1/{T}_{1}T$ and $K$ measurements. Such magnetic fluctuations are necessary to explain the observed temperature dependence of the $^{75}\mathrm{As}$ quadrupole frequencies, as evidenced by our first-principles calculations. In the SC state, $1/{T}_{1}$ shows a rapid decrease below ${T}_{\mathrm{c}}$ without a Hebel-Slichter peak and decreases exponentially at low $T$, consistent with an ${s}^{\ifmmode\pm\else\textpm\fi{}}$ nodeless two-gap superconductor.

Single crystals of $R{\mathrm{Mg}}_{2}{\mathrm{Cu}}_{9}$ ($R=\mathrm{Y}$, Ce-Nd, Gd-Dy, Yb) were grown using a high-temperature solution growth technique and were characterized by measurements of room-temperature x-ray diffraction, temperature-dependent specific heat, and temperature- and field-dependent resistivity and anisotropic magnetization. ${\mathrm{YMg}}_{2}{\mathrm{Cu}}_{9}$ is a non-local-moment-bearing metal with an electronic specific heat coefficient, $\ensuremath{\gamma}\ensuremath{\sim}15$ mJ/mol ${\mathrm{K}}^{2}$. Yb is divalent and basically non-moment-bearing in ${\mathrm{YbMg}}_{2}{\mathrm{Cu}}_{9}$. Ce is trivalent in ${\mathrm{CeMg}}_{2}{\mathrm{Cu}}_{9}$ with two magnetic transitions being observed at 2.1 K and 1.5 K. ${\mathrm{PrMg}}_{2}{\mathrm{Cu}}_{9}$ does not exhibit any magnetic phase transition down to 0.5 K. The other members being studied ($R=\mathrm{Nd}$, Gd-Dy) all exhibit antiferromagnetic transitions at low temperatures ranging from 3.2 K for ${\mathrm{NdMg}}_{2}{\mathrm{Cu}}_{9}$ to 11.9 K for ${\mathrm{TbMg}}_{2}{\mathrm{Cu}}_{9}$. Whereas ${\mathrm{GdMg}}_{2}{\mathrm{Cu}}_{9}$ is isotropic in its paramagnetic state due to zero angular momentum ($L=0)$, all the other local-moment-bearing members manifest an anisotropic, planar magnetization in their paramagnetic states. To further study this planar anisotropy, detailed angular-dependent magnetization was carried out on magnetically diluted (${\mathrm{Y}}_{0.99}{\mathrm{Tb}}_{0.01}$)${\mathrm{Mg}}_{2}{\mathrm{Cu}}_{9}$ and (${\mathrm{Y}}_{0.99}{\mathrm{Dy}}_{0.01}$)${\mathrm{Mg}}_{2}{\mathrm{Cu}}_{9}$. Despite the strong, planar magnetization anisotropy, the in-plane magnetic anisotropy is weak and field-dependent. A set of crystal electric field parameters are proposed to explain the observed magnetic anisotropy.