Microscopic Coexistence Research Articles

Two-dimensional Rashba superconductivity in Ni/Bi bilayers evidenced by nonreciprocal transport

When two different materials are brought together, a plethora of quantum phenomena and functionalities can emerge. A prominent example is the superconductivity in Ni/Bi bilayers, which arises from the artificial layered structure composed of the non-superconducting ferromagnetic and heavy metals. Although this system has been shown to exhibit unconventional superconducting properties, the underlying mechanism of the superconductivity remains elusive. Here, we provide experimental evidence of the microscopic coexistence of two-dimensional (2D) superconductivity and broken space-inversion symmetry in the Ni/Bi bilayer. The evidence is obtained from nonreciprocal transport around the superconducting transition temperature, where the resistance depends on the direction of an applied current and an external magnetic field. We find that the nonreciprocal superconducting transport is most pronounced around the Berezinskii–Kosterlitz–Thouless transition temperature. These observations support the 2D Rashba superconductivity in the Ni/Bi bilayer, which will serve as a basis for advancing the understanding of unconventional superconductivity.

Photoemission signature of the competition between magnetic order and Kondo effect in CeCoGe3

The competition between magnetic order and Kondo effect is essential for the rich physics of heavy fermion systems. Nevertheless, how such competition is manifested in the quasiparticle bands in a real periodic lattice remains elusive in spectroscopic experiments. Here we report a high-resolution photoemission study of the antiferromagnetic Kondo lattice system CeCoGe3 with a high TN1 of 21K. Our measurements reveal a weakly dispersive 4f band at the Fermi level near the Z point, arisingfrom moderate Kondo effect. The intensity of this heavy 4f band exhibits a logarithmic increase with lowering temperature and begins to deviate from this Kondo-like behavior below 25 K, just above TN1, and eventually ceases to grow below 12 K. Our work provides direct spectroscopic evidence for the competition between magnetic order and the Kondo effect in a Kondo lattice system with local-moment antiferromagnetism, indicating a distinct scenario for the microscopic coexistence and competition of these phenomena, which might be related to the real-space modulation.

Martensitic transformation in V3Si single crystal: 51V NMR evidence for coexistence of cubic and tetragonal phases

The Martensitic transformation (MT) in A15 binary-alloy superconductor V3Si, though studied extensively, has not yet been conclusively linked with a transition to superconductivity. Previous NMR studies have mainly been on powder samples and with little emphasis on temperature dependence during the transformation. Here we study a high-quality single crystal, where quadrupolar splitting of NMR spectra for 51V allowed us to distinguish between spectra from transverse chains of V as a function of temperature. Our data revealed that (1) the MT is not abrupt, but rather there is a microscopic coexistence of pre-transformed cubic phase and transformed tetragonal phase over a few K below and above Tm, while (2) no pre-transformed phase can be found at Tc, and (3) the Martensitic lengthening of one axis occurs predominantly in a plane perpendicular to the crystal growth axis, as twinned domains.

Zero-field superconducting diode effect in small-twist-angle trilayer graphene

The critical current of a superconductor can be different for opposite directions of current flow when both time-reversal and inversion symmetry are broken. %When time-reversal and inversion symmetry are simultaneously broken, the critical current of a 2D superconductor is expected to depend on the directions of current flow. Such nonreciprocal behavior in superconducting transport, which creates a superconducting diode, has recently been demonstrated experimentally by breaking these symmetries with an applied magnetic field \cite{Ando2020diodes} or by construction of a magnetic tunnel junction \cite{Diez2021magnetic}. Here we report an intrinsic superconducting diode effect which is present at zero external magnetic field in mirror symmetric twisted trilayer graphene (tTLG). Such nonreciprocal behavior, with sign that can be reversed through training with an out-of-plane magnetic field, provides direct evidence of the microscopic coexistence between superconductivity and time-reversal symmetry breaking. In addition to the magnetic-field trainability, we show that the zero-field diode effect can be controlled by varying carrier density or twist angle. In accordance with these experimental controls, a natural interpretation for the origin of the intrinsic diode effect is an imbalance in valley occupation of the underlying Fermi surface, which likely leads to finite-momentum Cooper pairing and nematicity in the superconducting phase.

Interplay of magnetism and superconductivity in 2D extended Hubbard model

The interplay between magnetic and superconducting states on a square lattice is studied using the extended Hubbard model, which takes into account the attraction of electrons located at nearest neighbor sites. Ferro-, antiferro-, and spiral magnetic states with all possible sets of spiral wave vectors, as well as singlet superconducting states with s-wave and d-wave pairing order parameters, are considered. Formation of a state with the intermediate s+id-symmetry and phase separation between different phases are allowed. The results of the Hartree–Fock and slave boson approximations are compared in order to study the role of correlation effects. Both macroscopic phase separation and microscopic coexistence of the superconducting and magnetic phases are found under certain model parameters.

Possible unconventional pairing in (Ca,Sr)3(Ir,Rh)4Sn13 superconductors revealed by controlling disorder

We study the evolution of temperature-dependent resistivity with controlled point-like disorder induced by 2.5 MeV electron irradiation in stoichiometric compositions of the "3-4-13" stannides, $(\text{Ca,Sr})_{3}(\text{Ir,Rh})_{4}\text{Sn}_{13}$.Three of these cubic compounds exhibit a microscopic coexistence of charge-density wave (CDW) order and superconductivity (SC), while $\text{Ca}_{3}\text{Rh}_{4}\text{Sn}_{13}$ does not develop CDW order. As expected, the CDW transition temperature, $T_{\text{CDW}}$, is universally suppressed by irradiation in all three compositions. The superconducting transition temperature, $T_{c}$, behaves in a more complex manner. In $\text{Sr}_{3}\text{Rh}_{4}\text{Sn}_{13}$, it increases initially in a way consistent with a direct competition of CDW and SC, but quickly saturates at higher irradiation doses. In the other three compounds, $T_{c}$ is monotonically suppressed by irradiation. The strongest suppression is found in $\text{Ca}_{3}\text{Rh}_{4}\text{Sn}_{13}$, which does not have CDW order. We further examine this composition by measuring the London penetration depth, $\lambda(T)$, from which we derive the superfluid density. The result unambiguously points to a weak-coupling, full single gap, isotropic superconducting state. Therefore, we must explain two seemingly incompatible experimental observations: a single isotropic superconducting gap and a significant suppression of $T_{c}$ by non-magnetic disorder. We conduct a quantitative theoretical analysis based on a generalized Anderson theorem which points to an unconventional multiband $s^{+-}$-pairing state where the sign of the order parameter is different on one (or a small subset) of the smaller Fermi surface sheets, but remains overall fully-gapped.

Interplay of Magnetism and Superconductivity in 2d Extended Hubbard Model

The interplay between magnetic and superconducting states on a square lattice is studied using the extended Hubbard model, which takes into account the attraction of electrons located at nearest neighbor sites. Ferro-, antiferro-, and spiral magnetic states with all possible sets of spiral wave vectors, as well as singlet superconducting states with s-wave and d-wave pairing order parameters, are considered. Formation of a state with the intermediate s+id-symmetry and phase separation between different phases are allowed. The results of the Hartree-Fock and slave boson approximations are compared in order to study the role of correlation effects. Both macroscopic phase separation and microscopic coexistence of the superconducting and magnetic phases are found under certain model parameters.

Anomaly of longitudinal spin susceptibility at a superconducting instability inside a magnetic phase

We study the longitudinal spin susceptibility inside a magnetically ordered phase, which exhibits a superconducting instability leading to a coexistence of the two ordered phases. Inside the magnetic phase, the superconducting gap acquires a linear term in a magnetic field applied along the direction of the magnetic moment. We find that such a linear term generates a jump of the longitudinal spin susceptibility when the superconducting instability occurs via a continuous phase transition. This anomaly at the superconducting instability is a thermodynamic signature of the microscopic coexistence of superconductivity and magnetism and can be a general feature associated with the breaking of spin rotational symmetry inside the magnetic phase.

Revisiting the phase diagram of LaFe1−xCoxAsO in single crystals by thermodynamic methods

In this work we revisit the phase diagram of Co-doped LaFeAsO using single crystals and thermodynamic methods. From magnetic susceptibility studies we track the doping evolution of the antiferromagnetic phase, revealing a continuous suppression of $T_\mathrm{N}$ up to 5$\%$ Co doping. In order to study the evolution of the so-called nematic phase, the temperature dependence of the lengths changes along the $a$ and $b$ orthorhombic directions, $\Delta L/L_0$, was determined by high-resolution capacitance dilatometry. The results clearly show a gradual reduction of the orthorhombic distortion $\delta$ and of $T_\mathrm{S}$ with increasing Co content up to 4.5$\%$, while it is completely suppressed for 7.5$\%$ Co. Bulk superconductivity was found in a small doping region around 6$\%$ Co content, while both $T_\mathrm{c}$ and the superconducting volume fraction rapidly drop in the neighbouring doping regime. Ultimately, no microscopic coexistence between the superconducting and magnetic phases can be assessed within our resolution limit, in sharp contrast with other iron-pnictide families, e.g., electron- and hole-doped BaFe$_2$As$_2$.

Magnetism and its coexistence with superconductivity in CaK(Fe0.949Ni0.051)4As4 : Muon spin rotation/relaxation studies

The magnetic response of CaK(Fe$_{0.949}$Ni$_{0.051}$)$_4$As$_4$ was investigated by means of the muon-spin rotation/relaxation. The long-range commensurate magnetic order sets in below the N\'{e}el temperature $T_{\rm N}= 50.0(5)$~K. The density-functional theory calculations have identified three possible muon stopping sites. The experimental data were found to be consistent with only one type of magnetic structure, namely, the long-range magnetic spin-vortex-crystal order with the hedgehog motif within the $ab-$plane and the antiferromagnetic stacking along the $c-$direction. The value of the ordered magnetic moment at $T\approx3$ K was estimated to be $m_{\rm Fe}=0.38(11)$ $\mu_{\rm B}$ ($\mu_{\rm B}$ is the Bohr magneton). A microscopic coexistence of magnetic and superconducting phases accompanied by a reduction of the magnetic order parameter below the superconducting transition temperature $T_{\rm c}\simeq 9$ K is observed. Comparison with 11, 122, and 1144 families of Fe-based pnictides points to existence of correlation between the reduction of the magnetic order parameter at $T\rightarrow 0$ and the ratio of the transition temperatures $T_{\rm c}/T_{\rm N}$. Such correlations were found to be described by Machida's model for coexistence of itinerant spin-density wave magnetism and superconductivity [Machida, J. Phys. Soc. Jpn. 50, 2195 (1981) and Bud'ko et al., Phys. Rev. B 98, 144520 (2018)].

Rotation of reflectivity anisotropy due to uniaxial strain along [110]tetr in the electron-doped Fe-based superconductor Ba(Fe0.955Co0.045)2As2

We present a strain-dependent time-resolved reflectometry experiment on $\mathrm{Ba}{({\mathrm{Fe}}_{0.955}{\mathrm{Co}}_{0.045})}_{2}{\mathrm{As}}_{2}$ in the nematic state. Uniaxial external pressure has usually been applied to obtain a single nematic domain. However, reflectivity with and without pumping under uniaxial strain along ${[110]}_{\text{tetr}}$ reveals an unexpected nematicity of which ${C}_{4}$ symmetry-breaking orientation is rotated by ${20}^{\ensuremath{\circ}}$. Our observation suggests a microscopic coexistence of ${B}_{2g}$ and ${B}_{1g}$ nematicity under uniaxial strain and possibly of an $XY$-type nematic order in the electron-doped iron pnictide.

Microscopic Distribution and Coexistence States of Tramp Elements and Valuable Metals in Recycled Steel Material by a Statistical Analysis

Microscopic Distribution and Coexistence States of Tramp Elements and Valuable Metals in Recycled Steel Material by a Statistical Analysis

Extended Magnetic Dome Induced by Low Pressures in Superconducting FeSe_{1-x}S_{x}.

We report muon spin rotation and magnetization measurements under pressure on Fe_{1+δ}Se_{1-x}S_{x} with x≈0.11. Above p≈0.6 GPa we find a microscopic coexistence of superconductivity with an extended dome of long range magnetic order that spans a pressure range between previously reported separated magnetic phases. The magnetism initially competes on an atomic scale with the coexisting superconductivity leading to a local maximum and minimum of the superconducting T_{c}(p). The maximum of T_{c} corresponds to the onset of magnetism while the minimum coincides with the pressure of strongest competition. A shift of the maximum of T_{c}(p) for a series of single crystals with x up to 0.14 roughly extrapolates to a putative magnetic and superconducting state at ambient pressure for x≥0.2.

Coexistence of superconductivity and antiferromagnetism in the Hubbard model for cuprates

Antiferromagnetism and $d$-wave superconductivity are the most important competing ground-state phases of cuprate superconductors. Using cellular dynamical mean-field theory (CDMFT) for the Hubbard model, we revisit the question of the coexistence and competition of these phases in the one-band Hubbard model with realistic band parameters and interaction strengths. With an exact diagonalization solver, we improve on previous works with a more complete bath parametrization which is carefully chosen to grant the maximal possible freedom to the hybridization function for a given number of bath orbitals. Compared with previous incomplete parametrizations, this general bath parametrization shows that the range of microscopic coexistence of superconductivity and antiferromagnetism is reduced for band parameters for NCCO, and confined to electron-doping with parameters relevant for YBCO.

Correlated Partial Disorder in a Weakly Frustrated Quantum Antiferromagnet.

Partial disorder-the microscopic coexistence of long-range magnetic order and disorder-is a rare phenomenon that has been experimentally and theoretically reported in some Ising- or easy plane-spin systems, driven by entropic effects at finite temperatures. Here, we present an analytical and numerical analysis of the S=1/2 Heisenberg antiferromagnet on the sqrt[3]×sqrt[3]-distorted triangular lattice, which shows that its quantum ground state has partial disorder in the weakly frustrated regime. This state has a 180° Néel ordered honeycomb subsystem coexisting with disordered spins at the hexagon center sites. These central spins are ferromagnetically aligned at short distances, as a consequence of a Casimir-like effect originated by the zero-point quantum fluctuations of the honeycomb lattice.

Disentangling superconducting and magnetic orders in NaFe1−xNixAs using muon spin rotation

Muon spin rotation and relaxation studies have been performed on a "111" family of iron-based superconductors NaFe_1-xNi_xAs. Static magnetic order was characterized by obtaining the temperature and doping dependences of the local ordered magnetic moment size and the volume fraction of the magnetically ordered regions. For x = 0 and 0.4 %, a transition to a nearly-homogeneous long range magnetically ordered state is observed, while for higher x than 0.4 % magnetic order becomes more disordered and is completely suppressed for x = 1.5 %. The magnetic volume fraction continuously decreases with increasing x. The combination of magnetic and superconducting volumes implies that a spatially-overlapping coexistence of magnetism and superconductivity spans a large region of the T-x phase diagram for NaFe_1-xNi_xAs . A strong reduction of both the ordered moment size and the volume fraction is observed below the superconducting T_C for x = 0.6, 1.0, and 1.3 %, in contrast to other iron pnictides in which one of these two parameters exhibits a reduction below TC, but not both. The suppression of magnetic order is further enhanced with increased Ni doping, leading to a reentrant non-magnetic state below T_C for x = 1.3 %. The reentrant behavior indicates an interplay between antiferromagnetism and superconductivity involving competition for the same electrons. These observations are consistent with the sign-changing s-wave superconducting state, which is expected to appear on the verge of microscopic coexistence and phase separation with magnetism. We also present a universal linear relationship between the local ordered moment size and the antiferromagnetic ordering temperature TN across a variety of iron-based superconductors. We argue that this linear relationship is consistent with an itinerant-electron approach, in which Fermi surface nesting drives antiferromagnetic ordering.

Single Crystal Growth and Study of the Ferromagnetic Superconductor RbEuFe4As4

RbEuFe4As4 exhibits both superconducting order in the FeAs layers and ferromagnetic order in the Eu layers, providing a good platform to study the interaction and microscopic coexistence of these two traditionally incompatible orders. Growing high-quality RbEuFe4As4 single crystals is essential to investigate these phenomena at a deeper level. Here we report the successful growth of the RbEuFe4As4 single crystals with millimeter-size dimensions using a RbAs flux. The high-quality crystals were characterized via resistivity, magnetization, and heat capacity measurements. Single crystal X-ray diffraction data refinements reveal almost regular FeAs4 tetrahedra (As1–Fe–As1 = 108.60(7)°, As2–Fe–As2 = 109.01(8)°, and As1–Fe–As2 = 109.81(2)°) in RbEuFe4As4, providing structural support for the highest superconducting transition temperature (Tc = 36.8 K) among all known AAeFe4As4 (A = K, Rb, Cs; Ae = Ca, Sr, Eu) compounds. Our flux method using RbAs can also be employed to grow other desired transition metal comp...

Phase separation and local lattice distortions analysis of charge-ordered manganese films La1-xCaxMnO3-δ by Raman spectroscopy

Polycrystalline films La1-xCaxMnO3-δ (LCMO) deposited on (001) MgO substrates for three different Ca concentrations (x = 0.67, 0.75, 0.85) were studied by Raman spectroscopy, X-ray diffraction and scanning electron microscope (SEM). Images of the surface and cross-section (edge) of samples of all compositions were obtained using SEM with high (up to 1 nm) spatial resolution. It was demonstrated that changes occur in the morphology and the formation of preferential orientation films x = 0.75, 0.85 relative to the substrate. It was founded that with an increase in the quantity of calcium there occurs a decrease in parameter pseudocubic unit cell. We have investigated the temperature (80K-350K) dependence of the Raman spectra of LCMO films. We have shown that Raman response of polycrystalline films below 150K corresponds to the microscopic coexistence of isostructural phases, with crystallographic symmetry Pnma. Detailed analysis of spectra allows to detect the occurrence of several different local lattice distortions: structural phases that have weak Jahn–Teller or/and spin crossover induced structural distortions with distorted octahedra Mn3+O6 and symmetric or nearly symmetric Mn4+O6 octahedra and the octahedral tilts in charge-ordered manganese films LCMO with x = 0.67, 0.75 at low temperature. Our results confirm the coexistence of charge–ordered antiferromagnetic state and ferromagnetic metallic phases with the competition between super-exchange and double-exchange interactions.

NMR study of the new magnetic superconductor CaK(Fe0.951Ni0.049)4As4 : Microscopic coexistence of the hedgehog spin-vortex crystal and superconductivity

Coexistence of a new-type antiferromagnetic (AFM) state, the so-called hedgehog spin-vortex crystal (SVC), and superconductivity (SC) is evidenced by $^{75}$As nuclear magnetic resonance study on single-crystalline CaK(Fe$_{0.951}$Ni$_{0.049}$)$_4$As$_4$. The hedgehog SVC order is clearly demonstrated by the direct observation of the internal magnetic induction along the $c$ axis at the As1 site (close to K) and a zero net internal magnetic induction at the As2 site (close to Ca) below an AFM ordering temperature $T_{\rm N}$ $\sim$ 52 K. The nuclear spin-lattice relaxation rate 1/$T_1$ shows a distinct decrease below $T_{\rm c}$ $\sim$ 10 K, providing also unambiguous evidence for the microscopic coexistence. Furthermore, based on the analysis of the 1/$T_1$ data, the hedgehog SVC-type spin correlations are found to be enhanced below $T$ $\sim$ 150 K in the paramagnetic state. These results indicate the hedgehog SVC-type spin correlations play an important role for the appearance of SC in the new magnetic superconductor.

Neutron scattering study of spin density wave and weak ferromagnetic orders in [formula omitted

Microscopic coexistence between weak ferromagnetism (WFM) and superconductivity (SC) in Tb0.47Y0.53Ni211B2C was investigated. Magnetization measurements indicate that antiferromagnetic (AFM), WFM and SC transitions occur in this material. Unpolarized neutron diffraction experiments revealed that the AFM order is best described by a longitudinal spin density wave with a propagation vector of q=0.550a∗. Polarized neutron diffraction experiments further confirmed that the WFM order is originated in Tb0.47Y0.53Ni211B2C.