Muon spin rotation measurements supported by magnetization experiments have been carried out in a stoichiometric high-$T_c$ parent compound La$_2$CuO$_4$ in %the a temperature range from 2~K to 340~K and in transverse magnetic fields up to 5~T. Along
with the antiferromagnetic local field, muon spin rotation spectra indicate presence of an additional source of magnetic field on the muon. The characteristic splitting of about 45~G coming from this additional magnetic field is consistent with spontaneous circulating currents model of Varma.
The spontaneous expulsion of applied magnetic field, the Meissner effect, is a defining feature of superconductors; in Type-II superconductors above the lower critical field, this screening takes the form of a lattice of magnetic flux vortices. Using
implanted spin-1/2 positive muons, one can measure the vortex lattice field distribution through the spin precession and deduce key parameters of the superconducting ground state, and thereby fundamental properties of the superconducting pairing. Muon spin rotation/relaxation ($mu$SR) experiments have indeed revealed much interesting physics in the underdoped cuprates, where superconductivity is closely related to, or coexistent with, disordered or fluctuating magnetic and charge excitations. Such complications should be absent in overdoped cuprates, which are believed to exhibit conventional Fermi liquid behaviour. These first transverse field (TF)-$mu^+$SR experiments on heavily-overdoped single crystals reveal a superfluid density exhibiting a clear inflection point near 0.5$T_c$, with a striking doping-independent scaling. This reflects hitherto unrecognized physics intrinsic to $d$-wave vortices, evidently generic to the cuprates, and may offer fundamentally new insights into their still-mysterious superconductivity.
In strongly correlated materials, cooperative behavior of the electrons causes a variety of quantum ordered states that may, in some cases, coexist. It has long been believed, however, that such coexistence among ferromagnetic ordering, superconducti
vity and heavy-fermion behavior is impossible, as the first supports parallel spin alignment while the conventional understanding of the latter two phenomena assumes spin-singlet or anti-parallel spins. This understanding has recently been challenged by an increasing number of observations in uranium systems (UGe2, URhGe, UIr and UCoGe) in which superconductivity is found within a ferromagnetic state and, more fundamentally, both ordering phenomena are exhibited by the same set of heavy 5f electrons. Since the coexistence of superconductivity and ferromagnetism is at odds with the standard theory of phonon-mediated spin-singlet superconductivity, it requires an alternative pairing mechanism, in which electrons are bound into spin-triplet pairs by spin fluctuations. Within the heavy-fermion scenario, this alternative mechanism assumes that the magnetism has a band character and that said band forms from heavy quasiparticles composed of f electrons. This band is expected to be responsible for all three phenomena although its nature and the nature of those heavy quasiparticles still remains unclear. Here we report spectroscopic evidence for the formation in UGe2 of subnanometer-sized spin polarons whose dynamics we follow into the paramagnetic and ferromagnetic phases. These spin polarons behave as heavy carriers and thus may serve as heavy quasiparticles made of 5f electrons; once coherence is established, they form a narrow spin-polaron band which thus provides a natural reconciliation of itinerant ferromagnetism with spin-triplet superconductivity and heavy-fermion behavior.
We present transverse field muon spin rotation/relaxation measurements on single crystals of the spin-1/2 kagome antiferromagnet Herbertsmithite. We find that the spins are more easily polarized when the field is perpendicular to the kagome plane. We
demonstrate that the difference in magnetization between the different directions cannot be accounted for by Dzyaloshinksii-Moriya type interactions alone, and that anisotropic axial interaction is present.
Muon spin rotation/relaxation spectroscopy %(supported by magnetization measurements) has been employed to study electron localization around a donor center - the positive muon - in the 3d magnetic spinel semiconductor CdCr$_2$Se$_4$ at temperatures
from 2 to 300 K in magnetic fields up to 7 T. A bound state of an electron around a positive muon - a magnetic polaron - is detected far above the ferromagnetic transition up to 300 K. Electron localization into a magnetic polaron occurs due to its strong exchange interaction with the magnetic 3d electrons of local Cr$^{3+}$ ions, which confines its wave function within Rapprox 0.3 nm, allowing significant overlap with both the nearest and next nearest shells of Cr ions.
