arXiv:1503.01844v1 [cond-mat.str-el] 6 Mar 2015 Inhomogeneous glassy nematic fluctuations in iron arsenide superconductors A. P. Dioguardi, 1 M. M. Lawson, 1 B. T. Bush, 1 J. Crocker, 1 K. R. Shirer, 1 D. M. Nisson, 1 T. Kissikov, 1 S. Ran, 2 S. L. Bud’ko, 2 P. C. Canfield, 2 S. Yuan, 3 P. L. Kuhns, 3 A. P. Reyes, 3 H.-J. Grafe, 4 and N. J. Curro 1 1 Department of Physics, University of California, Davis, California 95616, USA 2 Ames Laboratory U.S. DOE and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA 3 National High Magnetic Field Laboratory, Florida State University, Tallahassee, Florida 32310, USA 4 IFW Dresden, Institute for Solid State Research, P.O. Box 270116, D-01171 Dresden, Germany (Dated: March 11, 2015) The iron arsenide superconductors exhibit multiple phase transitions upon doping, including antiferromagnetism, unconventional superconductivity, and electronically- driven nematic ordering that breaks C4 rotation symmetry. Orthorhombic distortions of the lattice in the nematic phase form perpendicular twin domains, and strong cou- pling between the spin and orbital degrees of freedom ensure that the antiferromagnet- ically ordered Fe spins lie along either of these two orthogonal directions. Upon doping, the nematic and antiferromagnetic ordering temperatures are suppressed, yet strong antiferromagnetic and nematic fluctuations persist in the paramagnetic state beyond optimal doping, even in the absence of long range order. Here we demonstrate that these fluctuations are inhomogeneous and glassy, reflecting a broad distribution of lo- cally frustrated domains. This behavior arises because the dopants introduce quenched random fields that couple to the nematic order. These results suggest that disorder- induced frustration plays a significant role in suppressing long-range antiferromagnetic order and in the emergence of superconductivity. Nuclear magnetic resonance (NMR) has played a cen- tral role in the investigation of spin fluctuations in the iron arsenide superconductors. The 75 As nuclei (I =3/2, 100% abundant) experience a strong hyperfine coupling to the neighboring Fe spins [1], thus the spin lattice re- laxation rate, T -1 1 , is a sensitive probe of the dynam- ical spin susceptibility of the Fe spins [2]. In the para- magnetic state of a homogeneous material, critical spin fluctuations exhibit a characteristic time scale, τ c , that diverges as a power law at the phase transition temper- ature, τ c ∝ (T − T N ) -α . Consequently, the NMR re- laxation rate T -1 1 ∝ τ c exhibits a sharp divergence at T N . NMR studies of T -1 1 in Ba(Fe 1-x Co x ) 2 As 2 and BaFe 2 (As 1-x P x ) 2 revealed the presence of spin fluctua- tions over a broad range of doping and temperature, with a quantum phase transition at a critical doping level, x c , that lies close to the maximal T c [3, 4]. Several recent experimental studies have reported a deviation from the expected power law divergence of T -1 1 [5–8]. In LaFeAsO 1-x F x , Ba(Fe 1-x Rh x ) 2 As 2 , and Ba(Fe 1-x Co x ) 2 As 2 , the characteristic time scale of the antiferromagnetic fluctuations grows progressively slower over a broad temperature range, the spin-lattice recov- ery function exhibits stretched exponential behavior, and the NMR signal intensity is suppressed (wipeout). These features point to dynamical inhomogeneity, a character- istic of disordered spin glasses indicative of a distribution of relaxation rates, in which some fraction of the nuclei relax too quickly to be observed [9, 10]. Similar behav- ior has been observed in the cluster spin-glass phase of the underdoped high T c cuprates [11–13]. The cuprates, however, are doped Mott insulators, and the glassy be- havior was attributed to intrinsic frustration between the competing effects of Coulomb repulsion and charge segre- gation [14, 15]. The iron arsenides do not exhibit charge ordering and thus a different mechanism must be driving the glassy dynamics. In order to quantify the distribution of relaxation rates, we fit the 75 As magnetization recovery to a distribution: M (t)=  P (W 1 )f (W 1 t)dW 1 , where P (W 1 ) describes the relaxation rate distribution, and the relaxation function f (x) is described in the Methods section. For a homoge- neous system P (W 1 ) is a delta function centered at T -1 1 and thus M (t) ∼ f (t/T 1 ). If the distribution has a finite width, then the recovery function is more complex, typ- ically exhibiting stretched behavior. For example, if the relaxation function f (x)= e -x , then M (t) ∼ e -(t/T1) β , where β ≤ 1 is the stretching exponent [9]. Previous studies have reported stretched recovery, however the dis- tribution function for general β can only be expressed as an infinite series. Here we assume a log-normal distri- bution P (W 1 ) with median T -1 1 and standard deviation σ 1 , and fit the magnetization recovery directly. This ap- proach enables us to extract the width of the dynamical distribution, a quantity that sheds important light on the glassy behavior. Fig. 1 shows the temperature dependence of the distri- bution P (W 1 ), T -1 1 , and σ 1 as a function of temperature for Ba(Fe 1-x Co x ) 2 As 2 . The data reveal a progressive broadening of the distribution below 100K, as well as an increase in both T -1 1 and σ 1 reaching a peak at a temperature that coincides with the onset of long-range antiferromagnetic order at T N . The peak temperature is strongly doping dependent, reflecting the suppression of T N with doping concentration. The width σ 1 increases by