The iron-based high temperature superconductors exhibit a rich phase diagram reflecting a complex interplay between spin, lattice, and orbital degrees of freedom. The nematic state observed in these ...compounds epitomizes this complexity, by entangling a real-space anisotropy in the spin fluctuation spectrum with ferro-orbital order and an orthorhombic lattice distortion. A subtle and less-explored facet of the interplay between these degrees of freedom arises from the sizable spin-orbit coupling present in these systems, which translates anisotropies in real space into anisotropies in spin space. We present nuclear magnetic resonance studies, which reveal that the magnetic fluctuation spectrum in the paramagnetic phase of BaFe2As2 acquires an anisotropic response in spin-space upon application of a tetragonal symmetry-breaking strain field. Our results unveil an internal spin structure of the nematic order parameter, indicating that electronic nematic materials may offer a route to magneto-mechanical control.
Abstract
TmVO
4
exhibits ferroquadrupolar order of the Tm 4f electronic orbitals at low temperatures, and is a model system for Ising nematicity. A magnetic field oriented along the
c
-axis ...constitutes a transverse effective field for the quadrupolar order parameter, continuously tuning the system to a quantum phase transition as the field is increased from zero. In contrast, in-plane magnetic fields couple to the order parameter only at second order, such that orienting along the primary axes of the quadrupole order results in an effective longitudinal field, whereas orienting at 45 degrees results in a second effective transverse field. Not only do in-plane fields engender a marked in-plane anisotropy of the critical magnetic and quadrupole fluctuations above the ferroquadrupolar ordering temperature, but in-plane transverse fields initially enhance the ferroquadrupolar order, before eventually suppressing it, an effect that we attribute to admixing of the higher crystalline electric field levels.
We report 77Se NMR data in the normal and superconducting states of a single crystal of FeSe for several different field orientations. The Knight shift is suppressed in the superconducting state for ...in-plane fields, but does not vanish at zero temperature. For fields oriented out of the plane, little or no reduction is observed below Tc. These results reflect spin-singlet pairing emerging from a nematic state with large orbital susceptibility and spin-orbit coupling. The spectra and spin-relaxation rate data reveal electronic inhomogeneity that is enhanced in the superconducting state, possibly arising from enhanced density of states in the vortex cores. Despite the spin polarization of these states, there is no evidence for antiferromagnetic fluctuations.
Nuclear magnetic resonance provides a wealth of information about the magnetic and nematic degrees of freedom in the iron-based superconductors. A striking observation is that the spin lattice ...relaxation rate is inhomogeneous with a standard deviation that correlates with the nematic susceptibility. Moreover, the spin lattice relaxation is strongly affected by uniaxial strain, and in doped samples it depends sensitively upon the history of the applied strain. These observations suggest that quenched strain fields associated with doping atoms induce a nematic glass in the iron pnictide materials.
The electric field gradient (EFG) tensor at the As75 site couples to the orbital occupations of the As p orbitals and is a sensitive probe of local nematicity in BaFe2As2. We use nuclear magnetic ...resonance to measure the nuclear quadrupolar splittings and find that the EFG asymmetry responds linearly to the presence of a strain field in the paramagnetic phase. We extract the nematic susceptibility from the slope of this linear response as a function of temperature and find that it diverges near the structural transition, in agreement with other measures of the bulk nematic susceptibility. Our work establishes an alternative method to extract the nematic susceptibility which, in contrast to transport methods, can be extended inside the superconducting state.
We report the experimental details of how mechanical detwinning can be implemented in tandem with high-sensitivity nuclear magnetic resonance measurements and use this setup to measure the in-plane ...anisotropy of the spin-lattice relaxation rate in underdoped Ba(Fe1−xCox)2As2 with x=0.048. The anisotropy reaches a maximum of 30% at TN, and the recovery data reveal that the glassy behavior of the spin fluctuations present in the twinned state persist in the fully detwinned crystal. A theoretical model is presented to describe the spin-lattice relaxation rate in terms of anisotropic nematic spin fluctuations.
URu2Si2 exhibits an anomalous peak in the nonlinear magnetic susceptibility at the hidden order transition. In order to investigate this anomaly, we conducted direct magnetization measurements and ...investigated the detailed angular dependence of the Si29 nuclear magnetic resonance Knight shift tensor. We find that the nonlinear magnetization is smaller than previously reported, and the analogous nonlinear Knight shift tensor is below the detection limit. Our results suggest that the magnitude of the anomalous peak is sample dependent.
We report P31 and Si29 NMR in single crystals of URu2Si2−xPx for x=0.09 and x=0.33. The spectra in the x=0.33 sample are consistent with a homogenous commensurate antiferromagnetic phase below TN∼37 ...K. The Knight shift exhibits an anomaly at the coherence temperature T* that is slightly enhanced with P doping. Spin-lattice-relaxation rate data indicate that the density of states is suppressed for x=0.09 below 30 K, similar to the undoped compound, but there is no evidence of long-range order at this concentration. Our results suggest that Si substitution provides chemical pressure and electronic tuning mediated by filling of the s/p shells with minimal electronic inhomogeneity.
We present evidence for nuclear spin-lattice relaxation driven by glassy nematic fluctuations in isovalent P-doped BaFe2As2 single crystals. Both the 75As and 31P sites exhibit a ...stretched-exponential relaxation similar to the electron-doped systems. By comparing the hyperfine fields and the relaxation rates at these sites we find that the As relaxation cannot be explained solely in terms of magnetic spin fluctuations. We demonstrate that nematic fluctuations couple to the As nuclear quadrupolar moment and can explain the excess relaxation. Finally, these results suggest that glassy nematic dynamics are a common phenomenon in the ironbased superconductors.
The iron-based high temperature superconductors exhibit a rich phase diagram reflecting a complex interplay between spin, lattice, and orbital degrees of freedom. The nematic state observed in these ...compounds epitomizes this complexity, by entangling a real-space anisotropy in the spin fluctuation spectrum with ferro-orbital order and an orthorhombic lattice distortion. A subtle and less-explored facet of the interplay between these degrees of freedom arises from the sizable spin-orbit coupling present in these systems, which translates anisotropies in real space into anisotropies in spin space. We present nuclear magnetic resonance studies, which reveal that the magnetic fluctuation spectrum in the paramagnetic phase of BaFe2As2 acquires an anisotropic response in spin-space upon application of a tetragonal symmetry-breaking strain field. Lastly, our results unveil an internal spin structure of the nematic order parameter, indicating that electronic nematic materials may offer a route to magneto-mechanical control.
PDF
