Session A37: Focus Session: Fe-based Superconductors: Coexistence with Magnetism

Various forms of coexistence of superconductivity and magnetism in iron-pnictide superconductors: a NMR study

Our NMR studies of iron pnictides allowed us to discover various forms of coexistence between superconductivity and magnetism. In Co-doped BaFe2As2, superconductivity and incommensurate antiferromagnetism coexist at the atomic level in an homogeneous state. In contrast, Ru isovalent doping leads to a disorderd situation where superconducting clusters appear in an antiferromagnetic background. Finally, in the 245 iron-selenide RbFeSe, antiferromagnetism and superconductivity separate in alternate layers of nanometer thickness. But in all these componds, the superconducting state remains similar in terms of local susceptibility and carrier doping. It looks as if, for superconductivity to appear, frozen Fe magnetic moments need to be small enough or far enough in distance, whatever the cause. Y. Texier et al., PRL 108, 237002 (2012); Y. Laplace et al., PRB Rapid Com 86, 020510(R) (2012); Y. Laplace, PRB Rapid Com 80, 140501 (2009)   

Nuclear magnetic resonance studies of coexisting antiferromagnetism and superconductivity in Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$

We present $^{75}$As nuclear magnetic resonance (NMR) spectra and spin lattice relaxation data from Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ for $x=$ 0.05757, 0.05898, and 0.06163, with $T_C=$ 21.5 K, 22 K, and 22.7 K respectively. The spectra become broadened below the antiferromagnetic (AFM) phase transition. Spin lattice relaxation was measured by inversion recovery at the central line with $H \perp \hat{c}$ down to 4.5 K into the coexistence region. As temperature is decreased toward the AFM phase transition, the exponential inversion recovery curve begins to deviate from the theoretical prediction. The curves were fit to a stretched exponential to characterize this deviation as a function of temperature. This behavior persists into the coexistence region and may be related to nematic fluctuations.   

Novel Phase Separation and Magnetic Volume Tuning in Underdoped NaFe$_{1-x}$Co$_x$As ($x \simeq 0.01$)

NaFeAs is a quasi-2D pnictide parent compound with a weak magnetic moment and separate structural and antiferromagnetic transitions. Because Co doping leads to a superconductor with $T_c \simeq 20$ K at a very low optimal doping of $x = 0.02$, NaFe$_{1-x}$Co$_x$As is uniquely suited to sensitive studies of the cohabitation and competition between magnetism and superconductivity. Using NMR as a local probe of both antiferromagnetic order and superconductivity, we have compared Knight shifts and relaxation rates on the Na, As, and Co nuclei. Above $T_c$, we find weak doping inhomogeneity, in the form of residual paramagnetic regions with differing $T_N$ values, and a strongly field-controlled magnetic volume. Below $T_c$, we observe a strong competition between antiferromagnetism and superconductivity, in which the temperature is the dominant control parameter, suppressing the magnetic volume fraction very significantly in favor of the superconducting one, while the external field suppresses $T_c$. Our results suggest both a microscale phase separation in real space and in reciprocal space a competition between two order parameters requiring the same electrons on the quasi-2D Fermi surface.   

$^{75}$As and $^{23}$Na NMR study in optimally Co doped NaFe$_{0.975}$Co$_{0.025}$As

The normal and superconducting state of NaFe$_{0.975}$Co$_{0.025}$As, single crystals with exceptionally narrow $^{75}$As and $^{23}$Na NMR spectra, were investigated in external magnetic fields from 6.4 T to 24 T. The Knight shift ($^{75}K$) shows an almost linear decrease in the normal state on cooling and a sharp transition to spin-singlet superconductivity below $T_c$. A temperature independent $^{75}K$ at low temperature, below 0.4 $T_c$, indicates that there are no gap nodes. The penetration depth, $\lambda_{ab}$, was found to be 456 $\pm$ 7 nm at zero temperature, after convoluting the normal state spectrum with the vortex field distribution expected from Ginzburg-Landau theory. The spin lattice relaxation rate, $1/T_1$, shows a T$^{3}$ behavior in the superconducting state at low field which becomes T$^{1.5}$ at higher fields. Additionally, the average of $1/T_1$ over the vortex unit cell at T = 4 K is linear in H$^2$.   

Structural and magnetic phase transitions in TbRuAsO and DyRuAsO

The compounds \textit{Ln}RuAsO (\textit{Ln} $=$ lanthanide) are isoelectronic, isostructural, 4$d$ transition metal analogues of the parent phases of 1111-type iron superconductors, but display markedly different behaviors. Recent results from crystallographic and physical properties measurements on TbRuAsO and DyRuAsO reveal particularly unusual properties in these materials. Analysis of low temperature x-ray and neutron powder diffraction data indicate a symmetry-lowering crystallographic phase transition in DyRuAsO at 25 K, and ordering of rare-earth magnetic moments at 7.0 and 10.5 K for TbRuAsO and DyRuAsO, respectively. The structural distortion observed in DyRuAsO (to space group P\textit{mmn}) is different than the well-known distortion that occurs in \textit{Ln}FeAsO. In addition, the findings indicate some coupling between the magnetism and the lattice, and hints of Ru magnetism are observed. A response to the structural transition is apparent in the magnetic susceptibility, and the associated heat capacity anomaly responds strongly to a magnetic field.   

Structural and magnetic properties of Ba$_{1-x}$Na$_x$Fe$_2$As$_2$

Iron pnictides have attracted significant intrigue because of their astonishing superconducting properties in a large number of materials that support chemical substitutions at literally every site. Of particular interest is AFe2As2 (A$=$ Ba, Sr, Ca) in which hole or electron-doping is achieved by chemical substitution of alkaline or transition metal elements at the Ba and Fe sites, respectively. Nominally isovalent P substitutions for As have also been achieved producing a phase diagram remarkably similar to the electron- or hole-doped diagrams. A universal picture has emerged: a spin density wave region is stable at low substitution levels in which the Fe magnetic moments are aligned antiferromagnetically along the a- and c-axes and ferromagnetically in the direction of the b-axis. With increased substitution, the magnetic structure progressively loses strength to a point where it's suppressed in favor of superconductivity usually extending over a broad substitution range to form a superconducting dome. In these 122 systems, samples with compositions in the crossover region have been demonstrated by neutron diffraction and other techniques to allow the microscopic coexistence of both magnetism and superconductivity. I will present insights on the structural and magnetic properties of the Ba$_{1-x}$Na$_{x}$Fe$_{2}$As$_{2}$ system and discuss the results in a general context.   

Synthesis, structure and magnetic properties of BaFe$_{2}$(As$_{\mathrm{1-x}}$P$_{\mathrm{x}}$)$_{2}$ as determined by elastic and inelastic neutron scattering

Unconventional superconductivity and microscopic phase coexistence have been demonstrated in a narrow compositional region of the122 system between two competing spin density wave and superconducting order parameters. Quantum critical fluctuations induced by the suppression of the antiferromagnetic order have been proposed to mediate pairing in analogy with the role played by phonons in conventional cuprates. Establishing unambiguous conclusions concerning the pairing mechanism has proven difficult in the pnictides due to the complexity of the electronic structures. Recent reports have shown that isovalent P substitution for As in BaFe$_{2}$As$_{2}$ suppresses the structural and magnetic transitions and lead to superconductivity similar to hole or electron doping. From the chemical point-of-view, there is no net change in the electron-to-hole ratio in this charge compensated system. I will briefly discuss synthesis details of high quality pnictides and BaFe$_{2}$(As$_{\mathrm{1-x}}$P$_{\mathrm{x}}$)$_{2}$ samples and present structural results obtained by neutron diffraction. Inelastic neutron measurements will also be discussed.   

The phase diagram of BaFe$_2$(As$_{\mathrm{1-x}}$P$_{x})_2$ as determined by neutron diffraction

The iron-arsenides are a now famous family of high-$T_{\mathrm{c}}$ superconductors where the superconducting state is stabilized by suppressing a magnetic ground state in a parent compound. The phenomenon is quite robust, and BaFe$_{2}$As$_{2}$, for example, can be made superconducting either by applying pressure or by electron, hole, or isovalent doping. The isovalently doped BaFe$_{2}$(As$_{\mathrm{1-x}}$P$_{x})_{2}$ materials are particularly interesting because it is not obvious what is driving the suppression of the SDW and enhancing $T_{\mathrm{c}}$. The driving force has been variously ascribed to chemical pressure, changes in polarity of the Fe-(As,P) bond, and other even more subtle chemical effects. Moreover, reports on various general features in the iron-arsenide phase diagram---such as short-range nematic order and the separation of the N\'{e}el transition ($T_{\mathrm{N}})$ and the structural transition ($T_{\mathrm{s}})$---remain contradictory and underexplored. We have undertaken a detailed neutron diffraction study of the phase diagram in order to clarify some of the ambiguities. We find that $T_{\mathrm{s}} =$ $T_{\mathrm{N}}$ and that the superconducting dome rises more sharply than for the aliovalently doped materials. Moreover, the $T$ dependence of the structural and magnetic order parameters and a discontinuous increase in $c$/$a$ below $T_{\mathrm{N}}$ suggest a first order phase transition.   

Magnetic neutron diffraction study of BaFe$_{2(1-x)}$Co$_{2x}$As$_{2}$ critical exponents through the tricritical doping

We present temperature dependent magnetic neutron diffraction measurements of BaFe$_{2(1-x)}$Co$_{2x}$As$_{2}$ for x~=~0.039, 0.022, and 0.021 as-grown single crystals. We are motivated to investigate the magnetic tricritical point in the (x,T) plane near x$^{m}_{tr}$$\approx$0.022,[1] as well as to systematically probe the character of the magnetic phase transition across a range of dopings. All samples show long range antiferromagnetic order that may be described near the transition by $I\propto(1-T/T_N )^{2\beta}$ with $\beta$~=~0.291 for x~=~0.039, $\beta$~=~0.208 for x~=~0.022, and $\beta$~=~0.198 for x~=~0.021, showing a monotonic increase from the parent BaFe$_{2}$As$_{2}$ compound, $\beta$~=~0.103.[2] We will discuss the results based on theoretical predictions for the behavior of the order parameter in the vicinity of a tricritical point.\\[4pt] [1] M.G. Kim, R.M. Fernandes, A. Kreyssig, J.W. Kim, A. Thaler, S.L. Bud'ko, P.C. Canfield, R.J. McQueeney, J. Schmalian, and A.I. Goldman, Phys. Rev. B 83, 134522 (2011). \newline [2] S.D. Wilson, Z. Yamani, C.R. Rotundu, B. Freelon, E. Bourret-Courchesne, and R.J. Birgeneau, Phys. Rev. B 79, 184519 (2009).   

First order quantum phase transition under the superconducting dome of Ba(Fe$_{\mathrm{1-x}}$Co$_{\mathrm{x}})_{2}$As$_{2}$

We present the results of magnetoresistivity and magnetization measurements performed under pressure (P) on single crystals of Ba(Fe$_{\mathrm{1-x}}$Co$_{\mathrm{x}})_{2}$As$_{2}$ (x $=$ 0, 0.042, 0.06, 0.08). Our results show that the antiferromagnetic phase macroscopically coexists with the superconducting phase and can be induced by the magnetic field locally nucleated in the vortex core for the x $=$ 0.06 sample. In addition, the diamagnetic signal of the x $=$ 0.06 sample shows a huge jump around P $=$ 0.5~GPa, where the superconducting transition temperature displays a maximum. This suggests that a first order antiferromagnetic quantum phase transition (QPT) is present inside the superconducting dome, and that the superconductivity in this system is closely related to this QPT. A magnetic tricritical point is observed inside the superconducting dome, and no quantum critical point is expected in zero magnetic field.   

Intermediate orthorhombic phases in Ba-122 Iron Arsenides

Despite widespread interest, there are details of the tetragonal-orthorhombic structural phase transition in the iron arsenide superconductors that remain controversial. We have revisited the transition in three characteristic compositions of the canonical ``122'' family Ba(Fe/Co)$_2$(As/P)$_2$ using single crystal synchrotron x-ray diffraction. In the parent compound, we confirm previous observations of a sequence of structural transitions which are closely spaced in temperature, and uncover pronounced magnetoelastic effects in the intermediate orthorhombic phase. Modification of the structural transitions by doping is observed to differ significantly depending on whether the dopant is Co or P.   

Effects of the adjacent antiferromagnetic layer on superconductivity for the case of K$_{y}$Fe$_{2-x}$Se$_{2}$

A mesoscopic phase separation of superconductivity and antiferromagnetism has been recently reported as a prominence in ternary iron selenides. The iron vacancy is free in the superconducting (SC) segment, but clusters and forms order in the antiferromagnetic (AFM) segment. In this report we use a two-orbital model of one AFM layer coupled with another vacancy-free layer for superconductivity and study the effects of the interlayer coupling and the AFM order on SC instability. The SC instability is evaluated by solving the Bethe-Salpeter equation within a local pairing model. Since two individual layers have different Fermi surface (FS) structures, when coupled the FS topography will change depending on the interlayer coupling and the AFM order. We demonstrate that the superconductivity is more stable when FS sheets are disconnected. Interlayer coupling will deteriorate superconductivity and its effect becomes weak when the AFM moment is saturated. Due to lack of reflection symmetry, the SC gap is highly anisotropic and the presence of accidental nodes on disconnected FS sheets of d-wave superconductivity is possible.   

Resonance peak of neutron scattering in iron-based superconductors

Recently, nematic electronic states had been discovered in various strongly correlated metals such as iron-based superconductors, Sr$_{\mathrm{3}}$Ru$_{\mathrm{2}}$O$_{\mathrm{7}}$ and heavy fermions. These phenomena originate from the electron-electron correlation, since the lattice distortions are very small. Interestingly, many of these materials exhibit unconventional superconductivity, suggesting that the fluctuations of the nematic order parameter would cause the superconductivity. The origin of the nematic states had been unsolved since they cannot be explained by the mean-field approximation. Here, we study this issue beyond the mean-field approximation. We calculate the vertex correction (VC) for the irreducible susceptibility in various multiorbital Hubbard models, and derive the spin and orbital fluctuations self-consistently [1,2]. Near the magnetic quantum critical point, it is found that strong ferro- and antiferro-orbital fluctuations are induced by the VC in both iron-based superconductors and Sr$_{\mathrm{3}}$Ru$_{\mathrm{2}}$O$_{\mathrm{7}}$. The divergence of the ferro-orbital fluctuations presents the orbital nematic state in these materials. [1] S. Onari and H. Kontani, Phys. Rev. Lett. 109, 137001 (2012). [2] Y. Ohno, M. Tsuchiizu, S. Onari, and H. Kontani, arXiv:1209.3629.