Perspective on the muon-spin rotation/relaxation under hydrostatic pressure

Pressure, together with temperature, electric and magnetic fields, alters the system and allows to investigate the fundamental properties of the matter. Under applied pressure the interatomic distances shrink, which modify interactions between atoms and may lead to appearance of a new (sometime exotic) physical properties as, e.g., pressure induced phase transition(s); quantum critical points(s), new structural, magnetic and/or superconducting states; changes of the temperature evolution and the symmetry of the order parameter(s) etc. The muon-spin rotation/relaxation ($\mu$SR) appears to be a commonly used powerful technique allowing to study the magnetic and superconducting responses of various materials under extreme conditions. At present, $\mu$SR experiments might be performed under the high magnetic field up to $\simeq 9$ T, temperatures down to $\simeq 10-15$ mK and hydrostatic pressure up to $\simeq 2.8$ GPa. In the following Perspective paper the requirements to the $\mu$SR under pressure experiments, the existing high-pressure muon facility at the Paul Scherrer Institute (Switzerland), and selected experimental results obtained by using the $\mu$SR under pressure technique are discussed.Comment: 14 pages, 14 figure

Two-gap superconductivity in Mo8_{8}Ga41_{41} and its evolution upon the V substitution

Zero-field and transverse-field muon spin rotation/relaxation ($\mu$SR) experiments were undertaken in order to elucidate microscopic properties of a strongly-coupled superconductor Mo$_{8}$Ga$_{41}$ with $T_{\text{c}}=9.8$ K. The upper critical field extracted from the transverse-field $\mu$SR data exhibits significant reduction with respect to the data from thermodynamic measurements indicating the coexistence of two independent length scales in the superconducting state. Accordingly, the temperature-dependent magnetic penetration depth of Mo$_{8}$Ga$_{41}$ is described using the model, in which two s-wave superconducting gaps are assumed. The V for Mo substitution in the parent compound leads to the complete suppression of one superconducting gap, and Mo$_{7}$VGa$_{41}$ is well described within the single s-wave gap scenario. The reduction in the superfluid density and the evolution of the low-temperature resistivity upon the V substitution indicate the emergence of a competing state in Mo$_{7}$VGa$_{41}$ that may be responsible for the closure of one of the superconducting gaps

Superconductivity of Bi-III phase of elemental Bismuth: insights from Muon-Spin Rotation and Density Functional Theory

Using muon-spin rotation the pressure-induced superconductivity in the Bi-III phase of elemental Bismuth (transition temperature $T_{\rm c}\simeq7.05$ K) was investigated. The Ginzburg-Landau parameter $\kappa=\lambda/\xi=30(6)$ ($\lambda$ is the magnetic penetration depth, $\xi$ is the coherence length) was estimated which is the highest among single element superconductors. The temperature dependence of the superconducting energy gap [$\Delta(T)$] reconstructed from $\lambda^{-2}(T)$ deviates from the weak-coupled BCS prediction. The coupling strength $2\Delta/k_{\rm B}T_{\rm c}\simeq 4.34$ was estimated thus implying that Bi-III stays within the strong coupling regime. The Density Functional Theory calculations suggest that superconductivity in Bi-III could be described within the Eliashberg approach with the characteristic phonon frequency $\omega_{\rm ln}\simeq 5.5$ meV. An alternative pairing mechanism to the electron-phonon coupling involves the possibility of Cooper pairing induced by the Fermi surface nesting.Comment: 5 pages, 4 figure

On the superconducting nature of the Bi-II phase of elemental Bismuth

The superconductivity in the Bi-II phase of elemental Bismuth (transition temperature $T_{\rm c}\simeq3.92$ K at pressure $p\simeq 2.80$ GPa) was studied experimentally by means of the muon-spin rotation as well as theoretically by using the Eliashberg theory in combination with Density Functional Theory calculations. Experiments reveal that Bi-II is a type-I superconductor with a zero temperature value of the thermodynamic critical field $B_{\rm c}(0)\simeq31.97$~mT. The Eliashberg theory approach provides a good agreement with the experimental $T_{\rm c}$ and the temperature evolution of $B_{\rm c}$. The estimated value for the retardation (coupling) parameter $k_{\rm B}T_{\rm c}/\omega_{\rm ln} \approx 0.07$ ($\omega_{\rm ln}$ is the logarithmically averaged phonon frequency) suggests that Bi-II is an intermediately-coupled superconductor.Comment: 6 pages, 2 figure

Microscopic co-existence of superconductivity and magnetism in Ba1-xKxFe2As2

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 figure