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The mixed valence Cr compound NaCr$_2$O$_4$, synthesized using a high-pressure technique, offers a unique playground for investigating unconventional physical properties in condensed matter. In the present study, muon spin rotation/relaxation ($\mu^+$SR) and high-resolution neutron powder diffraction (NPD) measurements were carried out to clarify the true magnetic ground state of this interesting compound. Our detailed study brings new insight, allowing us to confirm the existence of a commensurate antiferromagnetic order (C-AFM) and to extract its ordered Cr moment $\mu^{\rm C}_{\rm Cr}=(4.30\pm0.01)\mu_B$. Such a value of the ordered moment is in fact compatible with the existence of high-spin Cr sites. Further, the value of the canting angle of the Cr spin axial vector is refined as $\theta_{\rm c}=(8.8\pm0.5)^{\circ}$. Employing high-quality samples in combination with time-of-flight NPD, a novel magnetic supercell was also revealed. Such supercell display an incommensurate (IC)-AFM propagation vector (0~0~${\textstyle \frac{1}{2}-}\delta$), having an ordered moment $\mu^{\rm IC}_{\rm Cr}=(2.20\pm0.03)\mu_B$. It is suggested that the C-AFM and IC-AFM modulations are due to itinerant and localized contributions to the magnetic moment, respectively. Finally, the direct measurement of the magnetic order parameter provided a value of the critical exponent $\beta = 0.245 \approx \frac{1}{4}$, suggesting a non conventional critical behavior for the magnetic phase transition in NaCr$_2$O$_4$.

The magnetism of double perovskites is a complex phenomenon, determined from intra- or interatomic magnetic moment interactions, and strongly influenced by geometry. We take advantage of the complementary length and time scales of the muon spin rotation, relaxation and resonance ($\mu^+$SR) microscopic technique and bulk AC/DC magnetic susceptibility measurements to study the magnetic phases of the LaCaNiReO$_6$ double perovskite. As a result we are able to discern and report a newly found dynamic phase transition and the formation of magnetic domains below and above the known magnetic transition of this compound at T$_N$ = 103 K. $\mu^+$SR, serving as a local probe at crystallographic interstitial sites, reveals a transition from a metastable ferrimagnetic ordering below T = 103 K to a stable one below T = 30 K. The fast and slow collective dynamic state of this system are investigated. Between 103 K < T < 230 K, the following two magnetic environments appear, a dense spin region and a static-dilute spin region. The paramagnetic state is obtained only above T > 270 K. An evolution of the interaction between Ni and Re magnetic sublattices in this geometrically frustrated fcc perovskite structure, is revealed as a function of temperature and magnetic field, through the critical behaviour and thermal evolution of microscopic and macroscopic physical quantities.

The silver ruthenium oxide AgRuO$_3$ consists of honeycomb [Ru$_2^{5+}$O$_6^{2-}$] layers, and can be considered an analogue of SrRu$_2$O$_6$ with a different intercalation stage. We present measurements of magnetic susceptibility and specific heat on AgRuO$_3$ single crystals which reveal a sharp antiferromagnetic transition at 342(3)K. The electrical transport in single crystals of AgRuO$_3$ is determined by a combination of activated conduction over an intrinsic semiconducting gap of $\approx$ 100 meV and carriers trapped and thermally released from defects. From powder neutron diffraction data a N\'eel-type antiferromagnetic structure with the Ru moments along the $c$ axis is derived. Raman and muon spin rotation spectroscopy measurements on AgRuO$_3$ powder samples indicate a further weak phase transition or a crossover in the temperature range 125-200 K. The transition does not show up in magnetic susceptibility and its origin is argued to be related to defects but cannot be fully clarified. The experimental findings are complemented by DFT-based electronic structure calculations. It is found that the magnetism in AgRuO$_3$ is similar to that of SrRu$_2$O$_6$, however with stronger intralayer and weaker interlayer magnetic exchange interactions., Comment: 13 pages, 16 figures, includes supplement 3 pages, 3 figures

We present a combination of thermodynamic and dynamic experimental signatures of a disorder driven dynamic cooperative paramagnet in a 50% site diluted triangular lattice spin-1/2 system, Y$_2$CuTiO$_6$. Magnetic ordering and spin freezing are absent down to 50 mK, far below the Curie Weiss scale of ~-134 K. We observe scaling collapses of the magnetic field- and temperature-dependent magnetic heat capacity and magnetisation data, respectively, in conformity with expectations from the random singlet physics. Our experiments establish the suppression of any freezing scale, if at all present, by more than three orders of magnitude, opening a plethora of interesting possibilities such as disorder-stabilized long range quantum entangled ground states., Comment: 18 pages, 9 figures, published in Physical Review Letters

We report a muon spin rotation ($\mu^{+}$SR) study of the magnetic properties of the double perovskite compound LaSrNiReO$_{6}$. Using the unique length and time scales of the $\mu^{+}$SR technique, we successfully clarify the magnetic ground state of LaSrNiReO$_{6}$, which was previously deemed as a spin glass state. Instead, our $\mu^{+}$SR results point towards a long-range dynamically ordered ground state below $T_{\rm C}= 23$ K, for which a static limit is foreseen at $T=0$. Furthermore, between 23 K$250$ K) state. Our results reveal how two separate, yet intertwined magnetic lattices interact within the unique double perovskite structure and the importance of using complementary experimental techniques to obtain a complete understanding of the microscopic magnetic properties of complex materials., Comment: 11 pages (with references), 11 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

The Dirac semimetal PdTe$_2$ was recently reported to be a type-I superconductor with $T_c = 1.64$ K and a critical field $\mu_0H_c = 13.6$ mT. Since type-I superconductivity is unexpected for binary compounds, we have conducted muon spin rotation experiments to probe the superconducting phase on the microscopic scale via its intermediate state. For crystals with a finite demagnetization factor, $N$, the intermediate state forms in applied fields $(1-N)H_c < H_a < H_c$. We have carried out transverse field muon spin rotation measurements on a thin disk-like crystal with the field perpendicular to ($N_{\perp}=0.86$) and in the plane ($N_{\parallel}=0.08$) of the disk. By analysing the $\mu$SR signal we find that the volume fraction of the normal domains grows quasi-linearly with applied field at the expense of the Meissner domain fraction. This then provides solid evidence for the intermediate state and type-I superconductivity in the bulk of PdTe$_2$.

Nodal-line semimetals are topologically non-trivial states of matter featuring band crossings along a closed curve, i.e. nodal-line, in momentum space. Through a detailed analysis of the electronic structure, we show for the first time that the normal state of the superconductor NaAlSi, with a critical temperature of $T_{\rm c} \approx$ 7 K, is a nodal-line semimetal, where the complex nodal-line structure is protected by non-symmorphic mirror crystal symmetries. We further report on muon spin rotation experiments revealing that the superconductivity in NaAlSi is truly of bulk nature, featuring a fully gapped Fermi-surface. The temperature-dependent magnetic penetration depth can be well described by a two-gap model consisting of two $s$-wave symmetric gaps with $\Delta_1 =$ 0.6(2) meV and $\Delta_2 =$ 1.39(1) meV. The zero-field muon experiment indicates that time-reversal symmetry is preserved in the superconducting state. Our observations suggest that notwithstanding its topologically non-trivial band structure, NaAlSi may be suitably interpreted as a conventional London superconductor, while more exotic superconducting gap symmetries cannot be excluded. The intertwining of topological electronic states and superconductivity renders NaAlSi a prototypical platform to search for unprecedented topological quantum phases.

Single-crystal x-ray diffraction, density-functional band-structure calculations, and muon spin relaxation ($\mu$SR) are used to probe pressure evolution of the triangular spin-liquid candidate YbMgGaO$_4$. The rhombohedral crystal structure is retained up to at least 10 GPa and shows a nearly uniform compression along both in-plane and out-of-plane directions, whereas local distortions caused by the random distribution of Mg$^{2+}$ and Ga$^{3+}$ remain mostly unchanged. The $\mu$SR data confirm persistent spin dynamics up to 2.6 GPa and down to 250 mK with no change in the muon relaxation rate. Longitudinal-field $\mu$SR reveals power-law behavior of the spin-spin autocorrelation function, both at ambient pressure and upon compression., Comment: published version

We report on magnetization $M(H)$, dc/ac magnetic susceptibility $\chi(T)$, specific heat $C_{\mathrm{m}}(T)$ and muon spin relaxation ($\mu$SR) measurements of the Kitaev honeycomb iridate Cu$_2$IrO$_2$ with quenched disorder. In spite of the chemical disorders, we find no indication of spin glass down to 260~mK from the $C_{\mathrm{m}}(T)$ and $\mu$SR data. Furthermore, a persistent spin dynamics observed by the zero-field muon spin relaxation evidences an absence of static magnetism. The remarkable observation is a scaling relation of $\chi[H,T]$ and $M[H,T]$ in $H/T$ with the scaling exponent $\alpha=0.26-0.28$, expected from bond randomness. However, $C_{\mathrm{m}}[H,T]/T$ disobeys the predicted universal scaling law, pointing towards the presence of low-lying excitations in addition to random singlets. Our results signify an intriguing role of quenched disorder in a Kitaev spin system in creating low-energy excitations possibly pertaining to Z$_2$ fluxes.

Identifying the symmetry of the wave function describing the Cooper pairs is pivotal in understanding the origin of high-temperature superconductivity in iron-based superconductors. Despite nearly a decade of intense investigation, the answer to this question remains elusive. Here we use the muon spin rotation/relaxation (muSR) technique to investigate the underlying symmetry of the pairing state of the FeSe superconductor, the basic building block of all iron-chalcogenide superconductors. Contrary to earlier muSR studies on powders and crystals, we show that while the superconducting gap is most probably anisotropic but nodeless along the crystallographic c-axis, it is nodal in the ab-plane, as indicated by the linear increase of the superfluid density at low temperature. We further show that the superconducting properties of FeSe display a less pronounced anisotropy than expected., Comment: 13 Pages, 8 figures (Accepted in PRB Rapid)