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Evolution of nematic fluctuations in CaK(Fe$_{1-x}$Ni$_{x}$)$_{4}$As$_{4}$ with spin-vortex crystal magnetic order

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 Added by Anna B\\\"ohmer
 Publication date 2020
  fields Physics
and research's language is English




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The CaK(Fe$_{1-x}$Ni$_{x}$)$_{4}$As$_{4}$ superconductors resemble the archetypal 122-type iron-based materials but have a crystal structure with distinctly lower symmetry. This family hosts one of the few examples of the so-called spin-vortex crystal magnetic order, a non-collinear magnetic configuration that preserves tetragonal symmetry, in contrast to the orthorhombic collinear stripe-type magnetic configuration common to the 122-type systems. Thus, nematic order is completely absent from its phase diagram. To investigate the evolution of nematic fluctuations in such a case, we present elastoresistance and elastic modulus measurements in CaK(Fe$_{1-x}$Ni$_{x}$)$_{4}$As$_{4}$ ($x = 0-0.05$) combined with phenomenological modeling and density functional theory. We find clear experimental signatures of considerable nematic fluctuations, including softening of the Youngs modulus $Y_{[110]}$ and a Curie-Weiss type divergence of the B2g elastoresistance coefficient in CaK(Fe$_{0.951}$Ni$_{0.049}$)$_4$As$_4$. Overall, nematic fluctuations within this series bear strong similarities to the hole-doped Ba$_{1-x}$K$_x$Fe$_2$As$_2$ series, including a substitution-induced sign change. Our theoretical analysis addresses the effect of the specific crystal symmetry of the 1144-type structure in determining its magnetic ground state and on the nematic fluctuations.



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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.
We report neutron scattering studies on static magnetic orders and spin excitations in the Fe-based chalcogenide system Fe$_{1+delta}$Se$_{x}$Te$_{1-x}$ with different Fe and Se compositions. Short-range static magnetic order with the bicollinear spin configuration is found in all non-superconducting samples, with strong low-energy magnetic excitations near the $(0.5,0)$ in-plane wave-vector (using the two-Fe unit cell) for Se doping up to 45%. When the static order disappears and bulk superconductivity emerges, the spectral weight of the magnetic excitations shifts to the region of reciprocal space near the in-plane wave-vector $(0.5,0.5)$, corresponding to the collinear spin configuration. Our results suggest that spin fluctuations associated with the collinear magnetic structure appear to be universal in all Fe-based superconductors, and there is a strong correlation between superconductivity and the character of the magnetic order/fluctuations in
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We report measurements of the magnetic penetration depth $lambda$ in single crystals of Pr(Os$_{1-x}$Ru$_{x}$)$_{4}$Sb$_{12}$ down to 0.1 K. Both $lambda$ and superfluid density $rho_{s}$ exhibit an exponential behavior for the $x$$geq$0.4 samples, going from weak ($x$=0.4,0.6), to moderate, coupling ($x$=0.8). For the $x$$leq$0.2 samples, both $lambda$ and $rho_{s}$ vary as $T^{2}$ at low temperatures, but $rho_{s}$ is s-wave-like at intermediate to high temperatures. Our data are consistent with a three-phase scenario, where a fully-gapped phase at $T_{c1}$ undergoes two transitions: first to an unconventional phase at $T_{c2}$$lesssim$$T_{c1}$, then to a nodal low-$T$ phase at $T_{c3}$$<$$T_{c2}$, for small values of $x$.
Temperature dependent $^{57}$Fe Mossbauer spectroscopy and specific heat measurements for CaK(Fe$_{1-x}$Ni$_x$)$_4$As$_4$ with $x$ = 0, 0.017, 0.033, and 0.049 are presented. No magnetic hyperfine field (e.g. 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, $B_{hf}$, (ordered magnetic moment) below $T_c$ in CaK(Fe$_{0.967}$Ni$_{0.033}$)$_4$As$_4$ is continuously suppressed with the developing superconducting order parameter. The $B_{hf}(T)$ data for CaK(Fe$_{0.967}$Ni$_{0.033}$)$_4$As$_4$, and CaK(Fe$_{0.951}$Ni$_{0.049}$)$_4$As$_4$ can be described reasonably well by Machidas model for coexistence of itinerant spin density wave magnetism and superconductivity [K. Machida, J. Phys. Soc. Jpn. {bf 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.
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