Magnetism in semiconducting molybdenum dichalcogenides.

Transition metal dichalcogenides (TMDs) are interesting for understanding the fundamental physics of two-dimensional (2D) materials as well as for applications to many emerging technologies, including spin electronics. Here, we report the discovery of long-range magnetic order below T M = 40 and 100 K in bulk semiconducting TMDs 2H-MoTe2 and 2H-MoSe2, respectively, by means of muon spin rotation (µSR), scanning tunneling microscopy (STM), and density functional theory (DFT) calculations. The µSR measurements show the presence of large and homogeneous internal magnetic fields at low temperatures in both compounds indicative of long-range magnetic order. DFT calculations show that this magnetism is promoted by the presence of defects in the crystal. The STM measurements show that the vast majority of defects in these materials are metal vacancies and chalcogen-metal antisites, which are randomly distributed in the lattice at the subpercent level. DFT indicates that the antisite defects are magnetic with a magnetic moment in the range of 0.9 to 2.8 µB. Further, we find that the magnetic order stabilized in 2H-MoTe2 and 2H-MoSe2 is highly sensitive to hydrostatic pressure. These observations establish 2H-MoTe2 and 2H-MoSe2 as a new class of magnetic semiconductors and open a path to studying the interplay of 2D physics and magnetism in these interesting semiconductors.

Author Correction: Signatures of the topological s+- superconducting order parameter in the type-II Weyl semimetal T d -MoTe2.

The original version of this article omitted the following from the Acknowledgements: "CAM and AL were supported by the NSF MRSEC program through Columbia in the Center for Precision Assembly of Superstratic and Superatomic Solids (DMR-1420634). Additionally, this research used resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under 'Contract No. DE-AC02-05CH11231'." This has now been corrected in both the PDF and HTML versions of the article.

Signatures of the topological s +- superconducting order parameter in the type-II Weyl semimetal T d-MoTe2.

In its orthorhombic T d polymorph, MoTe2 is a type-II Weyl semimetal, where the Weyl fermions emerge at the boundary between electron and hole pockets. Non-saturating magnetoresistance and superconductivity were also observed in T d-MoTe2. Understanding the superconductivity in T d-MoTe2, which was proposed to be topologically non-trivial, is of eminent interest. Here, we report high-pressure muon-spin rotation experiments probing the temperature-dependent magnetic penetration depth in T d-MoTe2. A substantial increase of the superfluid density and a linear scaling with the superconducting critical temperature T c is observed under pressure. Moreover, the superconducting order parameter in T d-MoTe2 is determined to have 2-gap s-wave symmetry. We also exclude time-reversal symmetry breaking in the superconducting state with zero-field µSR experiments. Considering the strong suppression of T c in MoTe2 by disorder, we suggest that topologically non-trivial s +- state is more likely to be realized in MoTe2 than the topologically trivial s ++ state.

Complementary Response of Static Spin-Stripe Order and Superconductivity to Nonmagnetic Impurities in Cuprates.

We report muon-spin rotation and neutron-scattering experiments on nonmagnetic Zn impurity effects on the static spin-stripe order and superconductivity of the La214 cuprates. Remarkably, it was found that, for samples with hole doping x≈1/8, the spin-stripe ordering temperature T_{so} decreases linearly with Zn doping y and disappears at y≈4%, demonstrating a high sensitivity of static spin-stripe order to impurities within a CuO_{2} plane. Moreover, T_{so} is suppressed by Zn in the same manner as the superconducting transition temperature T_{c} for samples near optimal hole doping. This surprisingly similar sensitivity suggests that the spin-stripe order is dependent on intertwining with superconducting correlations.

Direct evidence for a pressure-induced nodal superconducting gap in the Ba0.65Rb0.35Fe2As2 superconductor.

The superconducting gap structure in iron-based high-temperature superconductors (Fe-HTSs) is non-universal. In contrast to other unconventional superconductors, in the Fe-HTSs both d-wave and extended s-wave pairing symmetries are close in energy. Probing the proximity between these very different superconducting states and identifying experimental parameters that can tune them is of central interest. Here we report high-pressure muon spin rotation experiments on the temperature-dependent magnetic penetration depth in the optimally doped nodeless s-wave Fe-HTS Ba0.65Rb0.35Fe2As2. Upon pressure, a strong decrease of the penetration depth in the zero-temperature limit is observed, while the superconducting transition temperature remains nearly constant. More importantly, the low-temperature behaviour of the inverse-squared magnetic penetration depth, which is a direct measure of the superfluid density, changes qualitatively from an exponential saturation at zero pressure to a linear-in-temperature behaviour at higher pressures, indicating that hydrostatic pressure promotes the appearance of nodes in the superconducting gap.

Negative oxygen isotope effect on the static spin stripe order in superconducting La(2-x)Ba(x)CuO(4) (x=1/8) observed by muon-spin rotation.

Large negative oxygen-isotope (^{16}O and ^{18}O) effects (OIEs) on the static spin-stripe-ordering temperature T_{so} and the magnetic volume fraction V_{m} were observed in La_{2-x}Ba_{x}CuO_{4}(x=1/8) by means of muon-spin-rotation experiments. The corresponding OIE exponents were found to be α_{T_{so}}=-0.57(6) and α_{V_{m}}=-0.71(9), which are sign reversed to α_{T_{c}}=0.46(6) measured for the superconducting transition temperature T_{c}. This indicates that the electron-lattice interaction is involved in the stripe formation and plays an important role in the competition between bulk superconductivity and static stripe order in the cuprates.

Nonlinear pressure dependence of TN in almost multiferroic EuTiO3.

The antiferromagnetic (AFM) phase transition temperature TN of EuTiO3 has been studied as a function of pressure p. The data reveal a nonlinear dependence of TN on p with TN increasing with increasing pressure. The exchange interactions exhibit an analogous dependence on p as TN (if the absolute value of the nearest neighbor interaction is considered) and there is evidence that the AFM transition is robust with increasing pressure. The corresponding Weiss temperature ΘW remains anomalous since it always exhibits positive values. The data are analyzed within the Bloch power law model and provide excellent agreement with experiment.

Magnetoelectric coupling in single crystal Cu2OSeO3 studied by a novel electron spin resonance technique.

The magnetoelectric (ME) coupling on spin-wave resonances in single-crystal Cu2OSeO3 was studied by a novel technique using electron spin resonance combined with electric field modulation. An external electric field E induces a magnetic field component µ0H(i)=γE along the applied magnetic field H with γ=0.7(1) µT/(V/mm) at 10 K. The ME coupling strength γ is found to be temperature dependent and highly anisotropic. γ(T) nearly follows that of the spin susceptibility J(M)(T) and rapidly decreases above the Curie temperature T(c). The ratio γ/J(M) monotonically decreases with increasing temperature without an anomaly at T(c).

Comparison of different methods for analyzing µSR line shapes in the vortex state of type-II superconductors.

A detailed analysis of muon-spin rotation (µSR) spectra in the vortex state of type-II superconductors using different theoretical models is presented. Analytical approximations of the London and Ginzburg-Landau (GL) models, as well as an exact solution of the GL model were used. The limits of the validity of these models and the reliability for extracting parameters such as the magnetic penetration depth λ and the coherence length ξ from the experimental µSR spectra were investigated. The analysis of the simulated µSR spectra showed that at high magnetic fields there is a strong correlation between λ and ξ obtained for any value of the Ginzburg-Landau parameter κ = λ/ξ. The smaller the applied magnetic field, the smaller the possibility of finding the correct value of ξ. A simultaneous determination of λ and ξ without any restrictions is very problematic, regardless of the model used to describe the vortex state. It was found that for extreme type-II superconductors and low magnetic fields, the fitted value of λ is practically independent of ξ. The second-moment method frequently used to analyze µSR spectra by means of a multi-component Gaussian fit generally yields reliable values of λ over the whole range of applied fields [Formula: see text] (H(c1) and H(c2) are the first and second critical fields, respectively). These results are also relevant for the interpretation of small-angle neutron scattering experiments on the vortex state in type-II superconductors.

Comparative study of the pressure effects on the magnetic penetration depth in electron- and hole-doped cuprate superconductors.

The effect of pressure on the magnetic penetration depth λ was tested for the hole-doped superconductor YBa(2)Cu(3)O(7-δ) and in the electron-doped one Sr(0.9)La(0.1)CuO(2) by means of magnetization measurements. Whereas a large change of λ was found in YBa(2)Cu(3)O(7-δ), confirming the non-adiabatic character of the electron-phonon coupling in hole-doped superconductors, the same quantity is not affected by pressure in electron-doped Sr(0.9)La(0.1)CuO(2), suggesting a close similarity of the latter to conventional adiabatic Bardeen-Cooper-Schrieffer superconductors. The present results imply a remarkable difference between the electronic properties of hole-doped cuprates and electron-doped Sr(0.9)La(0.1)CuO(2), giving a strong contribution to the long debated asymmetric consequences of hole and electron doping in cuprate superconductors.

Oxygen isotope effects on the superconducting transition and magnetic states within the phase diagram of Y1-xPrxBa2Cu3O7-delta.

The various phases observed in all cuprate superconductors [superconducting (SC), spin-glass (SG), and antiferromagnetic (AFM)] were investigated with respect to oxygen-isotope (16O/18O) effects, using here as a prototype system of cuprates Y1-xPrxBa2Cu3O7-delta. All phases exhibit an isotope effect which is strongest where the respective phase terminates. In addition, the isotope effects on the magnetic phases (SG and AFM) are sign reversed as compared to the one on the superconducting phase. In the coexistence regime of the SG and SC phase a two-component behavior is observed where the isotope induced decrease of the superfluid density leads to a corresponding enhancement in the SG related density.

Experimental evidence for two gaps in the high-temperature La1.83Sr0.17CuO4 superconductor.

The in-plane magnetic field penetration depth (lambda(ab)) in single-crystal La1.83Sr0.17CuO4 was investigated by muon-spin rotation (muSR). The temperature dependence of lambda(ab)(-2) has an inflection point around 10-15 K, suggesting the presence of two superconducting gaps: a large gap (Delta(1)(d)) with d-wave and a small gap (Delta(2)(s)) with s-wave symmetry. The zero-temperature values of the gaps at mu(0)H=0.02 T were found to be Delta(1)(d)(0)=8.2(1) meV and Delta(2)(s)(0)=1.57(8) meV.

Muon-spin-rotation measurements of the penetration depth of the infinite-layer electron-doped Sr0.9La0.1CuO2 cuprate superconductor.

Muon-spin-rotation (muSR) measurements of the in-plane penetration depth lambda(ab) have been performed in the infinite-layer electron-doped Sr0.9La0.1CuO2 high-T(c) superconductor (HTS). Absence of the magnetic rare-earth ions in this compound allowed us to measure for the first time the absolute value of lambda(ab)(0) in electron-doped HTSs using muSR. We found lambda(ab)(0)=116(2) nm. The zero-temperature depolarization rate sigma(0) proportional, variant 1/lambda(2)(ab)(0)=4.6(1) micros(-1) is more than 4 times higher than expected from the Uemura line. Therefore, this electron-doped HTS does not follow the Uemura relation found for hole-doped HTSs.

Pressure effects on the transition temperature and the magnetic field penetration depth in the pyrochlore superconductor RbOs2O6.

Magnetization measurements under hydrostatic pressure up to 8 kbar in the pyrochlore superconductor RbOs2O6 (T(c) approximately or equal 6.3 K at p=0) were carried out. A positive pressure effect on T(c) with dT(c)/dp=0.090(3) K/kbar was observed, whereas no pressure effect on the magnetic penetration depth lambda was detected. The pressure independent ratio 2 Delta(0)/k(B)T(c)=3.72(2) (Delta(0) is the superconducting gap at zero temperature) was found to be close to the BCS value 3.52. Magnetization and muon-spin rotation measurements of lambda(T) indicate that RbOs2O6 is an adiabatic s-wave BCS-type superconductor. The value of lambda extrapolated to zero temperature and ambient pressure was estimated to be 230(30) nm.