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In one-dimensional quantum materials, conducting electrons and the underlying lattices can undergo a spontaneous translational symmetry breaking, known as Peierls transition. For nearly a century, the Peierls transition has been understood within the paradigm of electron-electron interactions mediated by longitudinal acoustic phonons. This classical picture has recently been revised in topological semimetals, where transverse acoustic phonons can couple with conducting p-orbital electrons and give rise to an unconventional Fermi surface instability, dubbed the transverse Peierls transition (TPT). Most interestingly, the TPT induced lattice distortions can further break rotation or mirror/inversion symmetries, leading to nematic or chiral charge density waves (CDWs). Quantum materials that host the TPT, however, have not been experimentally established. Here, we report the experimental discovery of an incommensurate TPT in the tetragonal Dirac semimetal EuAl$_4$. Using inelastic x-ray scattering with meV resolution, we observe the complete softening of a transverse acoustic phonon at the CDW wavevector upon cooling, whereas the longitudinal acoustic phonon is nearly unchanged. Combining with first principles calculations, we show that the incommensurate CDW wavevector matches the calculated charge susceptibility peak and connects the nested Dirac bands with Al 3$p_{x}$ and 3$p_{y}$ orbitals. Supplemented by second harmonic generation measurements, we show that the CDW induced lattice distortions break all vertical and diagonal mirrors whereas the four-fold rotational symmetry is retained below the CDW transition. Our observations strongly suggest a chiral CDW in EuAl$_4$ and highlight the TPT as a new avenue for chiral quantum states., Comment: Supplementary materials are available upon request

The asymmetric distribution of chiral objects with opposite chirality is of great fundamental interests ranging from molecular biology to particle physics. In quantum materials, chiral states can build on inversion-symmetry-breaking lattice structures or emerge from spontaneous magnetic ordering induced by competing interactions. Although the handedness of a chiral state can be changed through external fields, a spontaneous chirality flipping has yet to be discovered. In this letter, we present experimental evidence of chirality flipping via changing temperature in a topological magnet EuAl$_4$, which features orthogonal spin and charge density waves (SDW/CDW). Using circular dichroism of Bragg peaks in the resonant magnetic x-ray scattering, we find that the chirality of the helical SDW flips through a first order phase transition with modified SDW wavelength. Intriguingly, we observe that the CDW couples strongly with the SDW and displays a rare commensurate-to-incommensurate transition at the chirality flipping temperature. Combining with first principles calculations and angle resolved photoemission spectroscopy, we establish the Fermi surface origin of the helical SDW with intertwined spin, charge, and lattice degrees of freedom in EuAl$_4$. Our results reveal an unprecedented spontaneous chirality flipping and lays the groundwork for a new functional manipulation of chirality through momentum dependent spin-charge-lattice interactions., Comment: Supplementary materials are available from the corresponding author upon request

Members of the CaK(Fe$_{1-x}$Mn$_{x}$)$_{4}$As$_{4}$ series have been synthesized in single crystalline form and characterized by elemental analysis, thermodynamic and transport measurements. These measurements show that the superconducting transition temperature decreases monotonically and is finally suppressed below 1.8 K. For $x$-values greater than 0.016, signatures of a magnetic transition can be detected in both thermodynamic and transport measurements in which kink-like features allow for the determination of the transition temperature, $T^*$, that increases as Mn substitution increases. A temperature-composition ($T$-$x$) phase diagram is constructed, revealing a half-dome of superconductivity with the magnetic transition temperature, $T^*$, appearing near 26 K for $x$ $\sim$ 0.017 and rising slowly up to 33 K for $x$ $\sim$ 0.036. Specific heat data are used to track the jump in specific heat at $T_c$; The CaK(Fe$_{1-x}$Mn$_x$)$_4$As$_4$ data does not follow the scaling of $\Delta$$C_{p}$ with $T_{c}^3$ as many of the other Fe-based superconducting systems do. Elastoresistivity coefficients, $2m_{66}$ and $m_{11}-m_{12}$, as a function of temperature are also measured. $2m_{66}$ and $m_{11}-m_{12}$ are qualitatively similar to CaK(Fe$_{1-x}$Ni$_x$)$_4$As$_4$. This may indicate that the magnetic order in Mn substituted system may be still the same as CaK(Fe$_{1-x}$Ni$_x$)$_4$As$_4$. A clear change in $H^\prime_{c2}$($T$)/$T_c$, where $H^\prime_{c2}$($T$) is d$H_{c2}$($T$)/d$T$, at $x$ $\sim$ 0.015 is observed and probably is related to change of the Fermi surface due to magnetic order. Coherence lengths and the London penetration depths are also calculated based on $H_{c1}$ and $H_{c2}$ data. Coherence lengths as the function of $x$ also shows the changes near $x$ = 0.015., Comment: Fig. 16 a and b were corrected

Destructive interference of electron hopping on the frustrated kagome lattice generates Dirac nodes, saddle points, and flat bands in the electronic structure. The latter provides the narrow bands and a peak in the density of states that can generate correlated electron behavior when the Fermi level lies within them. In the kagome metal CoSn, this alignment is not realized, and the compound is a Pauli paramagnet. Here we show that replacing part of the tin with indium (CoSn1-xInx) moves the Fermi energy into the flat band region, with support from band structure calculations, heat capacity measurements, and angle resolved photoemission spectroscopy. The associated instability results in the emergence of itinerant antiferromagnetism with a Neel temperature up to 30K. Long range magnetic order is confirmed by neutron diffraction measurements, which indicate an ordered magnetic moment of 0.1-0.2 Bohr magnetons per Co (for x = 0.4). Thus, CoSn1-xInx provides a rare example of an itinerant antiferromagnet with a small ordered moment. This work provides clear evidence that flat bands arising from frustrated lattices in bulk crystals represent a viable route to new physics, evidenced here by the emergence of magnetic order upon introducing a non-magnetic dopant into a non-magnetic kagome metal.

Kagom${\'e}$ lattice is a fertile platform for topological and intertwined electronic excitations. Recently, experimental evidence of an unconventional charge density wave (CDW) is observed in a Z2 kagom${\'e}$ metal AV$_{3}$Sb$_{5}$ (A= K, Cs, Rb). This observation triggers wide interests on the interplay between frustrated crystal structure and Fermi surface instabilities. Here we analyze the lattice effect and its impact on CDW in AV$_{3}$Sb$_{5}$. Based on published experimental data, we show that the CDW induced structural distortions is consistent with the theoretically predicted inverse star-of-David pattern, which preserves the $D_{6h}$ symmetry in the kagom${\'e}$ plane but breaks the sixfold rotational symmetry of the crystal due to the phase shift between kagom${\'e}$ layers. The coupling between the lattice and electronic degrees of freedom yields a weak first order structural transition without continuous change of lattice dynamics. Our result emphasizes the fundamental role of lattice geometry in proper understanding of unconventional electronic orders in AV$_{3}$Sb$_{5}$.

CoSn is a Pauli paramagnet with relatively flat d-bands centered about 100 meV below the Fermi energy Ef. Single crystals of CoSn lightly doped with Fe, In, or Ni are investigated using x-ray and neutron scattering, magnetic susceptibility and magnetization, ac susceptibility, specific heat and resistivity measurements. Within the rigid band approximation, hole doping with a few percent of Fe or In should move the flat bands closer to Ef, whereas electron doping with Ni should move the flat bands further away from Ef. We provide evidence that this indeed occurs. Fe and In doping drive CoSn toward magnetism, while Ni doping suppresses CoSn's already weak magnetic response. The resulting ground state is different for Fe versus In doping. For Fe-doped crystals, Co1-xFexSn, with 0.02 < x < 0.27, the magnetic and specific heat data are consistent with the formation of a spin glass, with a glass transition temperature, Tg, ranging from 1 K for x=0.02 to 10 K for x= 0.27. Powder and single crystal neutron diffraction found no evidence of long-range magnetic order below Tg with x = 0.17. For In-doped crystals, CoSn1-yIny, both the magnetic susceptibility and the Sommerfeld coefficient, gamma, increase substantially relative to pure CoSn, but with no clear indication of a magnetic transition for 0.05 < y < 0.2. CoSn crystals doped with Ni (Co0.93Ni0.07Sn) have a significantly smaller magnetic susceptibility and gamma than pure CoSn, consistent with the flat bands further from Ef., Comment: 20 pages, 10 figures

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 $H_{\rm ext}$ greater than the typical lab-scale magnetic fields 10--15 T are usually required to completely detwin a sample. However, recently a very small in-plane $H_{\rm ext} \sim$ 0.1 T was found to be sufficient for detwinning the nematic domains in EuFe$_2$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 $^{153}$Eu nuclear magnetic resonance (NMR) measurements below the Eu$^{2+}$ ordering temperature, we show experimental evidence of the detwinning under small in-plane $H_{\rm ext}$. Our NMR study also reveals the evolution of the angles between the Eu and Fe spins during the detwinning process, which provides the first experimental evidence for the existence of biquadratic coupling in the system., Comment: 5 pages, 3 figures, accepted for publication in Phys. Rev. B rapid communication

We report combined experimental and theoretical analysis of superconductivity in CaK(Fe$_{1-x}$Ni$_x$)$_4$As$_4$ (CaK1144) for $x=$0, 0.017 and 0.034. To obtain the superfluid density, $\rho=\left(1+\Delta \lambda_L(T)/\lambda_L(0) \right)^{-2}$, the temperature dependence of the London penetration depth, $\Delta \lambda_L (T)$, was measured by using 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 $\lambda_L (T \ll T_c) \approx \lambda_L(0)$ was measured by using MWR, $\lambda_L (\mathrm{5~K}) \approx 170 \pm 20$ nm, which agreed well with the NV-centers in diamond optical magnetometry that gave $\lambda_L (\mathrm{5~K}) \approx 196 \pm 12$ nm. The experimental results are analyzed within the Eliashberg theory, showing that the superconductivity of CaK1144 is well described by the nodeless s$_{\pm}$ order parameter and that upon Ni doping the interband interaction increases., Comment: 8 pages, 5 figures

Two ordering states, antiferromagnetism and nematicity, have been observed in most iron-based superconductors (SCs). In contrast to those SCs, the newly discovered SC CaK(Fe$_{1-x}$Ni$_x$)$_4$As$_4$ exhibits an antiferromagnetic (AFM) state, called hedgehog spin-vortex crystal structure, without nematic order, providing the opportunity for the investigation into the relationship between spin fluctuations and SC without any effects of nematic fluctuations. Our $^{75}$As nuclear magnetic resonance studies on CaK(Fe$_{1-x}$Ni$_x$)$_4$As$_4$ (0$\le x\le$ 0.049) revealed that CaKFe$_4$As$_4$ is located close to a hidden hedgehog SVC AFM quantum-critical point (QCP). The magnetic QCP without nematicity in CaK(Fe$_{1-x}$Ni$_x$)$_4$As$_4$ highlights the close connection of spin fluctuations and superconductivity in iron-based SCs. The advantage of stoichiometric composition also makes CaKFe$_4$As$_4$ an ideal platform for further detailed investigation of the relationship between magnetic QCP and superconductivity in iron-based SCs without disorder effects., Comment: 6 pages, 5 figures, accepted for publication in Phys. Rev. Lett

The lower critical magnetic field, $H_{c1}$, of superconductors is measured by using ensembles of NV-centers-in-diamond optical magnetometry. The technique is minimally invasive, and has sub-gauss field sensitivity and sub-$\mu$m spatial resolution, which allow for accurate detection of the vector field at which the vortices start penetrating the sample from the corners. Aided by the revised calculations of the effective demagnetization factors of actual cuboid - shaped samples, $H_{c1}$ and the London penetration depth, $\lambda$, derived from $H_{c1}$ can be obtained. We apply this method to three well-studied superconductors: optimally doped Ba(Fe$_{1-x}$Co$_{x}$)$_2$As$_2$, stoichiometric CaKFe$_4$As$_4$, and high-$T_c$ cuprate YBa$_2$Cu$_3$O$_{7-\delta}$. Our results are well compared with the values of $\lambda$ obtained using other techniques, thus adding another non-destructive and sensitive method to measure these important parameters of superconductors.

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., Comment: (5 pages, 5 figures)

We employ polarization-resolved Raman spectroscopy to study multi-band stoichiometric superconductor CaKFe$_4$As$_4$. The B$_{2g}$ symmetry Raman response shows no signatures of Pomeranchuk-like electronic nematic fluctuations which is observed for many other Fe-based superconductors. In the superconducting state, we identify three pair-breaking peaks at 13.8, 16.9 and 21 meV and full spectral weight suppression at low energies. The pair-breaking peak energies in Raman response are about 20% lower than twice the gap energies as measured by single-particle spectroscopy, implying a sub-dominant $d$-wave symmetry interaction. We analyze the superconductivity induced phonon self-energy effects and give an estimation of weak electron-phonon coupling constant $\lambda^\Gamma$=0.0015.

Controlled point-like disorder introduced by 2.5 MeV electron irradiation was used to probe the superconducting state of single crystals of \CaKx\ 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 $dT_c/d\rho(T_c) \approx$ 0.19 K(\textmu$\Omega$cm)$^{-1}$ for $x=0$ and 0.38 K(\textmu$\Omega$cm)$^{-1}$ for $x=\:$0.05, respectively. In Ni - doped, $x = 0.05$, compound the coexisting spin-vortex crystal (SVC) magnetic phase is suppressed at the rate of $dT_N/d\rho(T_N)\approx$ 0.16 K(\textmu$\Omega$cm)$^{-1}$. Low - temperature variation of London penetration depth is well approximated by the power law, $\Delta \lambda (T) = AT^n$ with $n\approx\,$2.5 for $x=0$ and $n\approx\,$1.9 for $x=0.05$ in the pristine state. Electron irradiation leads to the exponent $n$ increase above 2 in $x=0.05$ suggesting superconducting gap with significant anisotropy that is smeared by the disorder scattering. Detailed analysis of $\lambda (T)$ and \(T_{c}\) evolution with disorder is consistent with two effective nodeless superconducting energy gaps due to robust s$_{\pm}$ pairing. Overall the behavior of \CaKx\ at $x = 0$ is similar to a slightly overdoped \BaK\ at $y \approx$ 0.5 and at $x= 0.05$ to an underdoped composition at $y \approx$ 0.2.

Coexistence of a new-type antiferromagnetic (AFM) state, the so-called hedgehog spin-vortex crystal (SVC), and superconductivity (SC) is evidenced by $^{75}$As nuclear magnetic resonance study on single-crystalline CaK(Fe$_{0.951}$Ni$_{0.049}$)$_4$As$_4$. The hedgehog SVC order is clearly demonstrated by the direct observation of the 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 $T_{\rm N}$ $\sim$ 52 K. The nuclear spin-lattice relaxation rate 1/$T_1$ shows a distinct decrease below $T_{\rm c}$ $\sim$ 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 $T$ $\sim$ 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., Comment: 5 pages, 4 figures, accepted for publication in Phys. Rev. B rapid communication

Non-invasive magnetic field sensing using optically - detected magnetic resonance of nitrogen-vacancy (NV) centers in diamond was used to study spatial distribution of the magnetic induction upon penetration and expulsion of weak magnetic fields in several representative superconductors. Vector magnetic fields were measured on the surface of conventional, Pb and Nb, and unconventional, LuNi$_2$B$_2$C, Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$, Ba(Fe$_{0.93}$Co$_{0.07}$)$_2$As$_2$, and CaKFe$_4$As$_4$, superconductors, with diffraction - limited spatial resolution using variable - temperature confocal system. Magnetic induction profiles across the crystal edges were measured in zero-field-cooled (ZFC) and field-cooled (FC) conditions. While all superconductors show nearly perfect screening of magnetic fields applied after cooling to temperatures well below the superconducting transition, $T_c$, a range of very different behaviors was observed for Meissner expulsion upon cooling in static magnetic field from above $T_c$. Substantial conventional Meissner expulsion is found in LuNi$_2$B$_2$C, paramagnetic Meissner effect (PME) is found in Nb, and virtually no expulsion is observed in iron-based superconductors. In all cases, good correlation with macroscopic measurements of total magnetic moment is found. Our measurements of the spatial distribution of magnetic induction provide insight into microscopic physics of the Meissner effect.

We report $^{75}$As nuclear magnetic resonance (NMR) studies on a new iron-based superconductor CaKFe$_4$As$_4$ with $T_{\rm c}$ = 35 K. $^{75}$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 $\nu_{\rm Q}$ of the As(1) and As(2) sites show an opposite temperature ($T$) dependence. Nearly $T$ independent behavior of the Knight shifts $K$ are observed in the normal state, and a sudden decrease in $K$ in the superconducting (SC) state clearly evidences spin-singlet Cooper pairs. $^{75}$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 wavevector ${\bf q}$ = ($\pi$, 0) or (0, $\pi$) in the single-iron Brillouin zone notation are revealed by 1/$T_1T$ and $K$ measurements. Such magnetic fluctuations are necessary to explain the observed temperature dependence of the $^{75}$As quadrupole frequencies, as evidenced by our first-principles calculations. In the SC state, 1/$T_1$ shows a rapid decrease below $T_{\rm c}$ without a Hebel-Slichter peak and decreases exponentially at low $T$, consistent with an $s^{\pm}$ nodeless two-gap superconductor., Comment: 9 pages, 6 figures, accepted for publication in Phys.Rev. B

Magnetism is widely considered to be a key ingredient of unconventional superconductivity. In contrast to cuprate high-temperature superconductors, antiferromagnetism in Fe-based superconductors (FeSCs) is characterized by a pair of magnetic propagation vectors. Consequently, three different types of magnetic order are possible. Of theses, only stripe-type spin-density wave (SSDW) and spin-charge-density wave (SCDW) orders have been observed. A realization of the proposed spin-vortex crystal (SVC) order is noticeably absent. We report a magnetic phase consistent with the hedgehog variation of SVC order in Ni- and Co-doped CaKFe4As4 based on thermodynamic, transport, structural and local magnetic probes combined with symmetry analysis. The exotic SVC phase is stabilized by the reduced symmetry of the CaKFe4As4 structure. Our results suggest that the possible magnetic ground states in FeSCs have very similar energies, providing an enlarged configuration space for magnetic fluctuations to promote high-temperature superconductivity., Comment: Updated version including supplemental material

Measurements of the anisotropic properties of single crystals play a crucial role in probing the physics of new materials. Determining a growth protocol that yields suitable high-quality single crystals can be particularly challenging for multi-component compounds. Here we present a case study of how we refined a procedure to grow single crystals of CaKFe$_{4}$As$_{4}$ from a high temperature, quaternary liquid solution rich in iron and arsenic ("FeAs self-flux"). Temperature dependent resistance and magnetization measurements are emphasized, in addition to the x-ray diffraction, to detect inter-grown CaKFe$_{4}$As$_{4}$, CaFe$_{2}$As$_{2}$ and KFe$_{2}$As$_{2}$ within, what appear to be, single crystals. Guided by the rules of phase equilibria and these data, we adjusted growth parameters to suppress formation of the impurity phases. The resulting optimized procedure yielded phase-pure single crystals of CaKFe$_{4}$As$_{4}$. This optimization process offers insight into the growth of quaternary compounds and a glimpse of the four-component phase diagram in the pseudo-ternary FeAs-CaFe$_{2}$As$_{2}$-KFe$_{2}$As$_{2}$ system., Comment: 9 Pages 6 Figures

We study the superconducting density of states and vortex lattice of single crystals of CaKFe$_4$As$_4$ using a scanning tunneling microscope (STM). This material has a critical temperature of $T_c= 35\,$ K, which is one of the highest among stoichiometric iron based superconductors (FeBSC) and is comparable to $T_c$ found near optimal doping in other FeBSC. Using quasi-particle interference we identify the hole sheets around the zone center and find that two superconducting gaps open in these sheets. The scattering centers are small defects that can be localized in the surface topography and just produce quasiparticle interference, without suppressing the superconducting order parameter. This shows that sign inversion is not within hole bands, but between hole and the electron bands. Vortex core bound states show electron-hole asymmetric bound states due to proximity of the top of one of the hole bands to the Fermi level $E_F$. This places CaKFe$_4$As$_4$ in a similar situation as FeSe or related materials, with a superconducting gap $\Delta$ just a few times smaller than $E_F$. On the other hand, we also identify locations showing strong suppression of the superconducting order parameter. Their size is of order of the vortex core size and vortices are pinned at these locations, leading to a disordered vortex lattice., Comment: 7 figures

Measurements of the London penetration depth and tunneling conductance in single crystals of the recently discovered stoicheometric, iron - based superconductor, CaKFe$_4$As$_4$ (CaK1144) show nodeless, two effective gap superconductivity with a larger gap of about 6-9 meV and a smaller gap of about 1-4 meV. Having a critical temperature, $T_{c,onset}\approx$35.8 K, this material behaves similar to slightly overdoped Ba$_{1-x}$K$_x$)Fe$_2$As$_2$ (e.g. $x=$0.54, $T_c \approx$ 34 K)---a known multigap $s_{\pm}$ superconductor. We conclude that the superconducting behavior of stoichiometric CaK1144 demonstrates that two-gap $s_{\pm}$ superconductivity is an essential property of high temperature superconductivity in iron - based superconductors, independent of the degree of substitutional disorder.

Single crystalline, single phase CaKFe$_{4}$As$_{4}$ has been grown out of a high temperature, quaternary melt. Temperature dependent measurements of x-ray diffraction, anisotropic electrical resistivity, elastoresistivity, thermoelectric power, Hall effect, magnetization and specific heat, combined with field dependent measurements of electrical resistivity and field and pressure dependent measurements of magnetization indicate that CaKFe$_{4}$As$_{4}$ is an ordered, stoichiometric, Fe-based superconductor with a superconducting critical temperature, $T_c$ = 35.0 $\pm$ 0.2 K. Other than superconductivity, there is no indication of any other phase transition for 1.8 K $\leq T \leq$ 300 K. All of these thermodynamic and transport data reveal striking similarities to that found for optimally- or slightly over-doped (Ba$_{1-x}$K$_x$)Fe$_2$As$_2$, suggesting that stoichiometric CaKFe$_4$As$_4$ is intrinsically close to what is referred to as "optimal-doped" on a generalized, Fe-based superconductor, phase diagram. The anisotropic superconducting upper critical field, $H_{c\text{2}}(T)$, of CaKFe$_{4}$As$_{4}$ was determined up to 630 kOe. The anisotropy parameter $\gamma(T)=H_{c\text{2}}^{\perp}/H_{c\text{2}}^{\|}$, for $H$ applied perpendicular and parallel to the c-axis, decreases from $\simeq 2.5$ at $T_c$ to $\simeq 1.5$ at 25 K which can be explained by interplay of paramagnetic pairbreaking and orbital effects. The slopes of $dH_{c\text{2}}^{\|}/dT\simeq-44$ kOe/K and $dH_{c\text{2}}^{\perp}/dT \simeq-109$ kOe/K at $T_c$ yield an electron mass anisotropy of $m_{\perp}/m_{\|}\simeq 1/6$ and short Ginzburg-Landau coherence lengths $\xi_{\|}(0)\simeq 5.8 \text{\AA}$ and $\xi_{\perp}(0)\simeq 14.3 \text{\AA}$. The value of $H_{c\text{2}}^{\perp}(0)$ can be extrapolated to $\simeq 920$ kOe, well above the BCS paramagnetic limit., Comment: 13 pages, 15 figures, part of arXiv:1606.02241 is included

Information on the lattice parameter of single crystals with known crystallographic structure allows for estimations of sample quality and composition. In many cases it is suffcient to determine one lattice parameter or the lattice spacing along a certain, high-symmetry direction, e.g. in order to determine the composition in a substitution series by taking advantage of Vegard's rule. Here we present a guide to accurate measurements of single crystals with dimensions ranging from 200 $\mu$m up to several millimeter using a standard powder diffractometer in Bragg-Brentano geometry. The correction of the error introduced by the sample height and the optimization of the alignment are discussed in detail. In particular for single crystals with a plate-like habit, the described procedure allows for measurement of the lattice spacings normal to the plates with high accuracy on a timescale of minutes., Comment: 9 pages, 4 figures