Search

Recent experiments have pointed to the formation of a new state of matter, the electron quadrupling condensate in Ba$_{1-x}$K$_x$Fe$_2$As$_2$ . The state spontaneously breaks time-reversal symmetry and is sandwiched between two critical points, separating it from the superconducting and normal metal states. The adjacent two critical points make acoustic effects a promising tool to study such states because of their sensitivity to symmetry-breaking transitions. We report a theory of the acoustic effects of systems with an electron quadrupling phase and new ultrasound velocity measurements of Ba$_{1-x}$K$_x$Fe$_2$As$_2$ single crystals. The presented theory for the electron quadrupling state gives the same type of singularities that are observed in experiment., Comment: 11 pages, 6 figures

Muon spin rotation/relaxation ($\mu$SR) and polar Kerr effect measurements provide evidence for a time-reversal symmetry breaking (TRSB) superconducting state in Sr$_2$RuO$_4$. However, the absence of a cusp in the superconducting transition temperature ($T_{\rm c}$) vs. stress and the absence of a resolvable specific heat anomaly at TRSB transition temperature ($T_{\rm TRSB}$) under uniaxial stress challenge a hypothesis of TRSB superconductivity. Recent $\mu$SR studies under pressure and with disorder indicate that the splitting between $T_{\rm c}$ and $T_{\rm TRSB}$ occurs only when the structural tetragonal symmetry is broken. To further test such behavior, we measured $T_\text{c}$ through susceptibility measurements, and $T_\text{TRSB}$ through $\mu$SR, under uniaxial stress applied along a $\langle 110 \rangle$ lattice direction. We have obtained preliminary evidence for suppression of $T_\text{TRSB}$ below $T_\text{c}$, at a rate much higher than the suppression rate of $T_\text{c}$., Comment: 9 pages, 4 figures and Appendix, accepted for publication in PRB

Theoretically, materials that break multiple symmetries allow, under certain conditions, the formation of four-fermion condensates above the superconducting critical temperature. Such states can be stabilized by phase fluctuations. Recently a fermionic quadrupling condensate that breaks the $Z_2$ time-reversal symmetry was reported in Ba$_{\rm 1-x}$K$_{\rm x}$Fe$_{2}$As$_{2}$ [V. Grinenko et al., Nat. Phys. 17, 1254 (2021)]. Evidence for the new state of matter comes from muon-spin rotation, transport, thermoelectric, and ultrasound experiments. Observing a specific heat anomaly is a very important signature of a transition to a new state of matter. However, a fluctuation-induced specific heat singularity is usually very challenging to resolve from a background of other contributions. Here, we report on detecting two anomalies in the specific heat of Ba$_{\rm 1-x}$K$_{\rm x}$Fe$_{2}$As$_{2}$ at zero magnetic field. The anomaly at the higher temperature is accompanied by the appearance of a spontaneous Nernst effect, indicating broken time-reversal ($Z_2$) symmetry. The second anomaly at the lower temperature coincides with the transition to a zero resistance state, indicating superconductivity breaking the $U(1)$ gauge symmetry. Our data provide calorimetric evidence for the $Z_2$ phase formation above the superconducting phase transition., Comment: 12 pages, 3 figures and Supplementary information

Discoveries of ordered quantum states of matter are of great fundamental interest, and often lead to unique applications. The most well known example -- superconductivity -- is caused by the formation and condensation of pairs of electrons. A key property of superconductors is diamagnetism: magnetic fields are screened by dissipationless currents. Fundamentally, what distinguishes superconducting states from normal states is a spontaneously broken symmetry corresponding to long-range coherence of fermion pairs. Here we report a set of experimental observations in hole doped Ba$_{1-x}$K$_x$Fe$_2$As$_2$ which are not consistent with conventional superconducting behavior. Our specific-heat measurements indicate the formation of fermionic bound states when the temperature is lowered from the normal state. However, for $x \sim 0.8$, instead of the standard for superconductors, zero resistance and diamagnetic screening, for a range of temperatures, we observe the opposite effect: the generation of self-induced magnetic fields measured by spontaneous Nernst effect and muon spin rotation experiments. The finite resistance and the lack of any detectable diamagnetic screening in this state exclude the spontaneously broken symmetry associated with superconducting two-fermion correlations. Instead, combined evidence from transport and thermodynamic measurements indicates that the formation of fermionic bound states leads to spontaneous breaking of time-reversal symmetry above the superconducting transition temperature. These results demonstrate the existence of a broken-time-reversal-symmetry bosonic metal state. In the framework of a multiband theory, such a state is characterized by quartic correlations: the long-range order exists only for {\it pairs} of fermion pairs., Comment: 31 pages, 11 figures, supplemental information

There is considerable evidence that the superconducting state of Sr$_2$RuO$_4$ breaks time reversal symmetry. In the experiments showing time reversal symmetry breaking its onset temperature, $T_\text{TRSB}$, is generally found to match the critical temperature, $T_\text{c}$, within resolution. In combination with evidence for even parity, this result has led to consideration of a $d_{xz} \pm id_{yz}$ order parameter. The degeneracy of the two components of this order parameter is protected by symmetry, yielding $T_\text{TRSB} = T_\text{c}$, but it has a hard-to-explain horizontal line node at $k_z=0$. Therefore, $s \pm id$ and $d \pm ig$ order parameters are also under consideration. These avoid the horizontal line node, but require tuning to obtain $T_\text{TRSB} \approx T_\text{c}$. To obtain evidence distinguishing these two possible scenarios (of symmetry-protected versus accidental degeneracy), we employ zero-field muon spin rotation/relaxation to study pure Sr$_2$RuO$_4$ under hydrostatic pressure, and Sr$_{1.98}$La$_{0.02}$RuO$_4$ at zero pressure. Both hydrostatic pressure and La substitution alter $T_\text{c}$ without lifting the tetragonal lattice symmetry, so if the degeneracy is symmetry-protected $T_\text{TRSB}$ should track changes in $T_\text{c}$, while if it is accidental, these transition temperatures should generally separate. We observe $T_\text{TRSB}$ to track $T_\text{c}$, supporting the hypothesis of $d_{xz} \pm id_{yz}$ order., Comment: 14 pages, 8 Figures

We present a piezoelectric-driven uniaxial pressure cell that is optimized for muon spin relaxation and neutron scattering experiments, and that is operable over a wide temperature range including cryogenic temperatures. To accommodate the large samples required for these measurement techniques, the cell is designed to generate forces up to 1000 N, and to minimize the background signal the space around the sample is kept as open as possible. We demonstrate here that by mounting plate-like samples with epoxy, a uniaxial stress exceeding 1 GPa can be achieved in an active volume of 5 mm3. We show that for practical operation it is important to monitor both the force and displacement applied to the sample. Also, because time is critical during facility experiments, samples are mounted in detachable holders that can be rapidly exchanged. The piezoelectric actuators are likewise contained in an exchangeable cartridge., Comment: Review of Scientific Instruments accepted for publication Oct 2020, 9 pages, 8 figures

Among unconventional superconductors, Sr$_2$RuO$_4$ has become a benchmark for experimentation and theoretical analysis because its normal-state electronic structure is known with exceptional precision, and because of experimental evidence that its superconductivity has, very unusually, a spontaneous angular momentum, i.e. a chiral state. This hypothesis of chirality is however difficult to reconcile with recent evidence on the spin part of the order parameter. Measurements under uniaxial stress offer an ideal way to test for chirality, because under uniaxial stress the superconducting and chiral transitions are predicted to split, allowing the empirical signatures of each to be identified separately. Here, we report zerofield muon spin relaxation (ZF-$\mu$SR) measurements on crystals placed under uniaxial stresses of up to 1.05 GPa. We report a clear stress-induced splitting between the onset temperatures of superconductivity and time-reversal symmetry breaking, consistent with qualitative expectations for chiral superconductivity. We also report the appearance of unexpected bulk magnetic order under a uniaxial stress of ~ 1.0 GPa in clean Sr$_2$RuO$_4$., Comment: 28 pages, 12 figures

We present a detailed investigation of the electronic properties of CeFeAsO under chemical (As by P substitution) and hydrostatic pressure by means of in-house and synchrotron M\"ossbauer spectroscopy. The Fe magnetism is suppressed due to both pressures and no magnetic order was observed above a P-substitution level of 40% or 5.2 GPa hydrostatic pressure. We compared both pressures and found that the isovalent As by P substitution change the crystallographic and electronic properties differently than hydrostatic pressure., Comment: supplement is included in the pdf file

We present a detailed investigation of the magnetic and superconducting properties of Ca1-xNaxFe2As2 single crystals with x = 0.00, 0.35, 0.50, and 0.67 by means of the local probe techniques Moessbauer spectroscopy and muon spin relaxation experiments. With increasing Na substitution level, the magnetic order parameter as well as the magneto-structural phase transition are suppressed. For x = 0.50 we find a microscopic coexistence of magnetic and superconducting phases accompanied by a reduction of the magnetic order parameter below the superconducting transition temperature Tc. A systematic comparison with other 122 pnictides reveals a square-root correlation between the reduction of the magnetic order parameter and the ratio of the transition temperatures, Tc/TN, which can be understood in the framework of a Landau theory. In the optimally doped sample with Tc = 34 K, diluted magnetism is found and the temperature dependence of the penetration depth and superfluid density are obtained, proving the presence of two superconducting s-wave gaps, Comment: 14 pages, 14 figures

We present our results of a local probe study on EuFe$_{2}$(As$_{1-x}$P$_{x}$)$_{2}$ single crystals with $x$=0.13, 0.19 and 0.28 by means of muon spin rotation and ${}^{57}$Fe M\"ossbauer spectroscopy. We focus our discussion on the sample with $x$=0.19 viz. at the optimal substitution level, where bulk superconductivity ($T_{\text{SC}}=28$ K) sets in above static europium order ($T^{\text{Eu}}=20$K) but well below the onset of the iron antiferromagnetic (AFM) transition ($\sim$100 K). We find enhanced spin dynamics in the Fe sublattice closely above $T_{\text{SC}}$ and propose that these are related to enhanced Eu fluctuations due to the evident coupling of both sublattices observed in our experiments., Comment: Contribution to the 13th International Conference on Muon Spin Rotation, Relaxation and Resonance (MuSR2014)

We present a detailed investigation of the electronic phase diagram of effectively charge compensated Ba1-xKx(Fe1-yCoy)2As2 with x/2 = y. Our experimental study by means of x-ray diffraction, M\"ossbauer spectroscopy, muon spin relaxation and ac susceptibility measurements on polycrystalline samples is complemented by density functional electronic structure calculations. For low substitution levels of x/2 = y \< 0.13, the system displays an orthorhombically distorted and antiferromagnetically ordered ground state. The low temperature structural and magnetic order parameters are successively reduced with increasing substitution level. We observe a linear relationship between the structural and the magnetic order parameter as a function of temperature and substitution level for x/2 = y \< 0.13. At intermediate substitution levels in the range between 0.13 and 0.19, we find superconductivity with a maximum Tc of 15 K coexisting with static magnetic order on a microscopic length scale. For higher substitution levels x/2 = y \> 0.25 a tetragonal non-magnetic ground state is observed. Our DFT calculations yield a signifcant reduction of the Fe 3d density of states at the Fermi energy and a strong suppression of the ordered magnetic moment in excellent agreement with experimental results. The appearance of superconductivity within the antiferromagnetic state can by explained by the introduction of disorder due to non-magnetic impurities to a system with a constant charge carrier density. Our experimental study by means of x-ray diffraction, M\"ossbauer spectroscopy, muon spin relaxation and ac susceptibility measurements on polycrystalline samples is complemented by density functional electronic structure calculations., Comment: 16 pages, 14 figures

We present a study of the structural and physical properties of directly hole doped LaFe1-xMnxAsO (x = 0.0-0.2) and the influence of charge compensation / electron-doping by additional F doping in LaFe0.9Mn0.1AsO1-yFy (y = 0.1-0.5). High quality polycrystalline samples were prepared using a solid state metathesis reaction. The unit cell increases upon Mn doping, but decreases again when additional F is inserted. The semiconducting character of LaFe1-xMnxAsO decreases with additional F doping. Muon spin relaxation (muSR) measurements reveal short range magnetic order in LaFe1-xMnxAsO and a suppression of magnetism by additional electron-doping with fluoride in LaFe0.9Mn0.1AsO1-yFy. Superconductivity remains absent even though the electronic preconditions are fulfilled in electron-doped LaFe0.9Mn0.1AsO1-yFy at x > 0.1, which is suggestive of effective pair breaking by Mn in this system., Comment: 16 pages, 6 figures

We have studied the structural and electronic phase diagrams of CeFeAsO1-xFx and SmFeAsO1-xFx by a detailed analysis of muon spin relaxation experiments, synchrotron X-ray diffraction, M\"ossbauer spectroscopy, electrical resistivity, specific heat, and magnetic susceptibility measurements (Full abstract in the main document).

We study the interplay of magnetic and superconducting order in single crystalline hole doped Ba1-xNaxFe2As2 using muon spin relaxation. We find microscopic coexistence of magnetic order and superconductivity. In a strongly underdoped specimen the two forms of order coexist without any measurable reduction of the ordered magnetic moment by superconductivity, while in a nearly optimally doped sample the ordered magnetic moment is strongly suppressed below the superconducting transition temperature. This coupling can be well described within the framework of an effective two-band model incorporating inter- and intra-band interactions. In optimally doped Ba1-xNaxFe2As2 we observe no traces of static or dynamic magnetism and the temperature dependence of the superfluid density is consistent with two s-wave gaps without nodes.

It is widely believed that, in contrast to its electron doped counterparts, the hole doped compound Ba1-xKxFe2As2 exhibits a mesoscopic phase separation of magnetism and superconductivity in the underdoped region of the phase diagram. Here, we report a combined high-resolution x-ray powder diffraction and volume sensitive muon spin rotation study of underdoped Ba1-xKxFe2As2 (0 \leq x \leq 0.25) showing that this paradigm is wrong. Instead we find a microscopic coexistence of the two forms of order. A competition of magnetism and superconductivity is evident from a significant reduction of the magnetic moment and a concomitant decrease of the magneto-elastically coupled orthorhombic lattice distortion below the superconducting phase transition., Comment: 4 pages, 4 figures

Measurements of the in-plane magnetic field penetration depth \lambda_{ab} in Fe-based superconductors with the nominal composition SmFeAsO_0.85 (T_c\simeq52K) and NdFeAsO_0.85 (T_c\simeq51K) were carried out by means of muon-spin-rotation. The absolute values of \lambda_{ab} at T=0 were found to be 189(5)nm and 195(5)nm for Sm and Nd substituted samples, respectively. The analysis of the magnetic penetration depth data within the Uemura classification scheme, which considers the correlation between the superconducting transition temperature T_c and the effective Fermi temperature T_F, reveal that both families of Fe-based superconductors (with and without fluorine) falls to the same class of unconventional superconductors., Comment: 5 pages, 4 figures