The trigonal compound EuSn2As2 was recently discovered to host Dirac surface states within the bulk band gap and orders antiferromagnetically below the Neel temperature TN = 24 K. Here the magnetic ground state of single-crystal EuSn2As2 and the evol
ution of its properties versus temperature T and applied magnetic field H are reported. Included are zero-field single-crystal neutron-diffraction measurements versus T, magnetization M(H,T), magnetic susceptibility chi(H,T) = M(T)/H, heat capacity Cp(H,T), and electrical resistivity rho(H,T) measurements. The neutron-diffraction and chi(T) measurements both indicate a collinear A-type antiferromagnetic (AFM) structure below TN =23.5(2) K, where the Eu{2+} spins S = 7/2 in a triangular ab-plane layer (hexagonal unit cell) are aligned ferromagnetically in the ab plane whereas the spins in adjacent Eu planes along the c axis are aligned antiferromagnetically. The chi(H{ab},T) and chi(H{c},T) data together indicate a smooth crossover between the collinear AFM alignment and an unknown magnetic structure at H ~ 0.15 T. Dynamic spin fluctuations up to 60 K are evident in the chi(T), Cp(T) and rho(H,T) measurements, a temperature that is more than twice TN. The rho(H,T) of the compound does not reflect a contribution of the topological state, but rather is consistent with a low-carrier-density metal with strong magnetic scattering. The magnetic phase diagrams for both H||c and H||ab in the H-T plane are constructed from the TN(H), chi(H,T), Cp(H,T), and rho(H,T) data.
In-plane anisotropy of electrical resistivity was studied in samples of the hole-doped Ba$_{1-x}$K$_x$Fe$_2$As$_2$ in the composition range $0.21 leq x leq 0.26$ where anisotropy changes sign. Low-temperature ($sim$20~K) irradiation with relativistic
2.5 MeV electrons was used to control the level of disorder and residual resistivity of the samples. Modification of the stress-detwinning technique enabled measurements of the same samples before and after irradiation, leading to conclusion of anisotropic character of predominantly inelastic scattering processes. Our main finding is that the resistivity anisotropy is of the same sign irrespective of residual resistivity, and remains the same in the orthorhombic $C_2$ phase above the re-entrant tetragonal transition. Unusual $T$-linear dependence of the anisotropy $Delta rho equiv rho_a(T)-rho_b(T)$ is found in pristine samples with $x=$0.213 and $x=$0.219, without similar signatures in either $rho_a(T)$ or $rho_b(T)$. We show that this feature can be reproduced by a phenomenological model of R.~M.~Fernandes {it et al.} Phys. Rev. Lett. {bf 107},217002 (2011). We speculate that onset of fluctuations of nematic order on approaching the instability towards the re-entrant tetragonal phase contributes to this unusual dependence.
The trigonal compound EuMg2Bi2 has recently been discussed in terms of its topological band properties. These are intertwined with its magnetic properties. Here detailed studies of the magnetic, thermal, and electronic transport properties of EuMg2Bi
2 single crystals are presented. The Eu{+2} spins-7/2 in EuMg2Bi2 exhibit an antiferromagnetic (AFM) transition at a temperature TN = 6.7 K, as previously reported. By analyzing the anisotropic magnetic susceptibility chi data below TN in terms of molecular-field theory (MFT), the AFM structure is inferred to be a c-axis helix, where the ordered moments in the hexagonal ab-plane layers are aligned ferromagnetically in the ab plane with a turn angle between the moments in adjacent moment planes along the c axis of about 120 deg. The magnetic heat capacity exhibits a lambda anomaly at TN with evidence of dynamic short-range magnetic fluctuations both above and below TN. The high-T limit of the magnetic entropy is close to the theoretical value for spins-7/2. The in-plane electrical resistivity rho(T) data indicate metallic character with a mild and disorder-sensitive upturn below Tmin = 23 K. An anomalous rapid drop in rho(T) on cooling below TN as found in zero field is replaced by a two-step decrease in magnetic fields. The rho(T) measurements also reveal an additional transition below TN in applied fields of unknown origin that is not observed in the other measurements and may be associated with an incommensurate to commensurate AFM transition. The dependence of TN on the c-axis magnetic field Hperp was derived from the field-dependent chi(T), Cp(T), and rho(T) measurements. This TN(Hperp) was found to be consistent with the prediction of MFT for a c-axis helix with S = 7/2 and was used to generate a phase diagram in the Hperp-T plane.
While unusual normal state properties, such as non-Fermi liquid behavior of the resistivity, are commonly associated with strong quantum fluctuations, evidence for its presence inside the superconducting dome are much scarcer. In this paper, we use s
ensitive and minimally invasive optical magnetometry based on NV-centers in diamond to probe the doping evolution of the $T=0$ penetration depth in the electron-doped iron-based superconductor Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$. A non-monotonic evolution with a pronounced peak in the vicinity of the putative magnetic QPT is found. This behavior is reminiscent to that previously seen in isovalently-substituted BaFe$_2$(As$_{1-x}$P$_x$)$_2$ compounds, despite the notable differences between these two systems. Whereas the latter is a very clean system that displays nodal superconductivity and a single simultaneous first-order nematic-magnetic transition above, and even somewhat below, $T_c$, the former is a significantly dirtier system with fully gapped superconductivity and split second-order nematic and magnetic transition above $T_c$. Thus our observation that such distinct systems display remarkably similar penetration depth peaks, combined with the theoretical result that a QPT alone does not ensure the existence of a peak, unveils a puzzling and seemingly universal manifestation of quantum fluctuations in the iron pnictides.
Low-temperature (22~K) irradiation with 2.5~MeV electrons was used to study the competition between stripe ${rm C_2}$ and tetragonal ${rm C_4}$ antiferromagnetic phases which exist in a narrow doping range around $x=$0.25 in hole-doped Ba$_{1-x}$K$_x
$Fe$_2$As$_2$. In nearby compositions outside of this range, at $x=$0.22 and $x=$0.19, the temperatures of both the concomitant orthorhombic/stripe antiferromagnetic transition $T_{rm C2}$ and the superconducting transition $T_{rm c}$ are monotonically suppressed by added disorder at similar rates of about 0.1~K/$mu Omega$cm, as revealed through using resistivity variation as an intrinsic measure of scattering rate. In a stark contrast, a rapid suppression of the ${rm C_4}$ phase at the rate of 0.24 K/$mu Omega cdot$cm is found at $x=$0.25. Moreover, this suppression of the ${rm C_4}$ phase is accompanied by unusual disorder-induced stabilization of the ${rm C_2}$ phase, determined by resistivity and specific heat measurements. The rate of the ${rm C_4}$ phase suppression is notably higher than the suppression rate of the spin-vortex phase in the Ni-doped CaKFe$_4$As$_4$ (0.16 K/$mu Omega$cm).
In-plane resistivity anisotropy was measured in strain-detwinned as-grown and partially annealed samples of isovalently-substituted $mathrm{Ba(Fe_{1-x}Ru_{x})_{2}As_{2}}$ ($0<x leq 0.125$) and the results were contrasted with previous reports on anne
al samples with low residual resistivity. In samples with high residual resistivity, detwinned with application of strain, the difference of the two components of in-plane resistivity in the orthorhombic phase, $rho_a -rho_b$, was found to obey Matthiessen rule irrespective of sample composition, which is in stark contrast with observations on annealed samples. Our findings are consistent with two-band transport model in which contribution from high mobility carriers of small pockets of the Fermi surface has negligible anisotropy of residual resistivity and is eliminated by disorder. Our finding suggests that magnetic/nematic order has dramatically different effect on different parts of the Fermi surface. It predominantly affects inelastic scattering for small pocket high mobility carriers and elastic impurity scattering for larger sheets of the Fermi surface.
In-plane resistivity measurements as a function of temperature and magnetic field up to 35~T with precise orientation within the crystallographic $ac-$plane were used to study the upper critical field, $H_{c2}$, of the hole-doped iron-based supercond
uctor Ba$_{1-x}$K$_x$Fe$_2$As$_2$. Compositions of the samples studied were spanning from underdoped $x=$0.17 ($T_c$=12~K) and $x$=0.22 ($T_c$=20~K), both in the coexistence range of stripe magnetism and superconductivity, though optimal doping $x$=0.39 ($T_c$=38.4~K), $x$=0.47 ($T_c$=37.2~K), to overdoped $x$=0.65 ($T_c$=22~K), $x$=0.83 ($T_c$=10~K). We find notable doping asymmetry of the shapes of the anisotropic $H_{c2}(T)$ suggesting important role of paramagnetic limiting effects in $H parallel a$ configuration in overdoped compositions and multi-band effects in underdoped compositions.
The thermal conductivity kappa of the iron-arsenide superconductor Ba1-xKxFe2As2 was measured for heat currents parallel and perpendicular to the tetragonal c axis at temperatures down to 50 mK and in magnetic fields up to 15 T. Measurements were per
formed on samples with compositions ranging from optimal doping (x = 0.34; Tc = 39 K) down to dopings deep into the region where antiferromagnetic order coexists with superconductivity (x = 0.16; Tc = 7 K). In zero field, there is no residual linear term in kappa(T) as T goes to 0 at any doping, whether for in-plane or inter-plane transport. This shows that there are no nodes in the superconducting gap. However, as x decreases into the range of coexistence with antiferromagnetism, the residual linear term grows more and more rapidly with applied magnetic field. This shows that the superconducting energy gap develops minima at certain locations on the Fermi surface and these minima deepen with decreasing x. We propose that the minima in the gap structure arise when the Fermi surface of Ba1-xKxFe2As2 is reconstructed by the antiferromagnetic order.
We report $^{75}$As nuclear magnetic resonance (NMR) measurements of single-crystalline Ca(Fe$_{1-x}$Co$_x$)$_2$As$_2$ ($x$ = 0.023, 0.028, 0.033, and 0.059) annealed at 350~$^{circ}$C for 7 days. From the observation of a characteristic shape of $^{
75}$As NMR spectra in the stripe-type antiferromagnetic (AFM) state, as in the case of $x$ = 0 ($T_{rm N}$ = 170 K), clear evidence for the commensurate AFM phase transition with the concomitant structural phase transition is observed in $x$ = 0.023 ($T_{rm N}$ = 106 K) and $x$ = 0.028 ($T_{rm N}$ = 53 K). Through the temperature dependence of the Knight shifts and the nuclear spin lattice relaxation rates (1/$T_1$), although stripe-type AFM spin fluctuations are realized in the paramagnetic state as in the case of other iron pnictide superconductors, we found a gradual decrease of the AFM spin fluctuations below a crossover temperature $T^*$ which was nearly independent of Co-substitution concentration, and is attributed to a pseudogap-like behavior in the spin excitation spectra of these systems. The $T^*$ feature finds correlation with features in the temperature-dependent inter-plane resistivity, $rho_c(T)$, but not with the in-plane resistivity $rho _a (T)$. The temperature evolution of anisotropic stripe-type AFM spin fluctuations are tracked in the paramagnetic and pseudogap phases by the 1/$T_1$ data measured under magnetic fields parallel and perpendicular to the $c$ axis. Based on our NMR data, we have added a pseudogap-like phase to the magnetic and electronic phase diagram of Ca(Fe$_{1-x}$Co$_x$)$_2$As$_2$.
The in-plane London penetration depth, $Deltalambda(T)$, was measured using a tunnel diode resonator technique in single crystals of Ba$_{1-x}$K$_{x}$Fe$_{2}$As$_{2}$ with doping levels $x$ ranging from heavily underdoped, $x$=0.16 ($T_{c}$=7~K) to n
early optimally doped, $x$= 0.34 ($T_{c}=$39 K). Exponential saturation of $Deltalambda(T)$ in the $Tto0$ limit is found in optimally doped samples, with the superfluid density $rho_{s}(T)equiv(lambda(0)/lambda(T))^{2}$ quantitatively described by a self-consistent $gamma$-model with two nodeless isotropic superconducting gaps. As the doping level is decreased towards the extreme end of the superconducting dome at $x$=0.16, the low-temperature behavior of $Deltalambda(T)$ becomes non-exponential and best described by the power-law $Deltalambda(T)propto T^{2}$, characteristic of strongly anisotropic gaps. The change between the two regimes happens within the range of coexisting magnetic/nematic order and superconductivity, $x<0.25$, and is accompanied by a rapid rise in the absolute value of $Deltalambda(T)$ with underdoping. This effect, characteristic of the competition between superconductivity and other ordered states, is very similar to but of significantly smaller magnitude than what is observed in the electron-doped Ba(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$ compounds. Our study suggests that the competition between superconductivity and magnetic/nematic order in hole-doped compounds is weaker than in electron-doped compounds, and that the anisotropy of the superconducting state in the underdoped iron pnictides is a consequence of the anisotropic changes in the pairing interaction and in the gap function promoted by both magnetic and nematic long-range order.
