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Muon spin spectroscopy ($\mu$SR) is a powerful local probe technique e.g. used for the investigation of exotic frustrated magnetism. Ab initio simulations using Density Functional Theory with the muon treated as a point-like defect (DFT+$\mu$) are commonly employed to determine the interstitial lattice positions where the muon comes to rest after implantation. These muon stopping sites are critical for accurately interpreting $\mu$SR data. For example, for the quantum spin liquid candidate Zn-Barlowite, DFT+$\mu$ simulations identify two types of muon stopping sites: a higher-energy site where the muon is located between a fluorine and a bromine atom and three similar sites near an OH group. However, our study shows that the $\mu$SR spectra of Zn-Barlowite cannot be adequately described using muon sites determined by the conventional DFT+$\mu$ approach. Instead, accurate reproduction of the $\mu$SR data requires treating the muon as a spatially extended quantum particle with a skewed wavefunction due to the anharmonicity of the surrounding electrostatic potential. The quantum nature of the muon significantly affects its lattice position and, consequently, the observed $\mu$SR spectra. Our findings highlight the potential of $\mu$SR to study the localization of quantum particles, using the muon as the probe and particle under investigation. The light mass of the muon amplifies quantum effects, enhancing the sensitivity of our measurements and enabling a detailed comparison between experimental data and theoretical calculations. These results can be directly applied to the theoretical calculations of hydrogen localization, where quantum effects, though smaller, may still be relevant in real materials.

Motivated by recent experiments on a compound {displaying Ising-like short-range correlations on the triangular lattice, we study the anisotropic easy-axis spin-$1/2$ Heisenberg model on the triangular and kagome lattice} by performing numerical calculations of finite-temperature properties, in particular of static spin structure factor and of thermodynamic quantities, on systems with up to 36 sites. On the triangular lattice, the low-temperature spin structure factor {exhibits long-range} spin correlations in the whole range of anisotropies, whereas thermodynamic quantities reveal a crossover upon increasing the anisotropy, most pronounced in the vanishing generalized Wilson ratio in the easy-axis regime. In contrast, on the kagome lattice, the spin structure factor is short-range, and thermodynamic quantities evolve steadily between the easy-axis and the isotropic case, consistent with the interpretation in terms of {a} spin liquid., Comment: 9 pages

Quasi-one-dimensional electron systems display intrinsic instability towards long-range ordered phases at sufficiently low temperatures. The superconducting orders are of particular interest as they can possess either singlet or triplet pairing symmetry and frequently compete with magnetism. Here we report on muon spin rotation and relaxation ($\mathrm{\mu}$SR) study of Rb$_2$Mo$_3$As$_3$ characterised by one of the highest critical temperatures $T_{\rm c}=10.4\ \mathrm{K}$ among quasi-one-dimensional superconductors. The transverse-field $\mathrm{\mu}$SR signal shows enhanced damping below $T_{\rm c}$ due to the formation of vortex lattice. Comparison of vortex lattice broadening against single gap $s-$, $p-$ and $d-$wave models shows the best agreement for the $s-$wave scenario but with the anomalously small superconducting gap, $\Delta_0$, to $T_{\rm c}$ ratio of $2\Delta_0/k_{\rm B}T_{\rm c}=2.74(1)$. The alternative nodal $p-$wave or $d-$wave scenarios with marginally worse goodness of fit would yield more realistic $2\Delta_0/k_{\rm B}T_{\rm c}=3.50(2)$ and $2\Delta_0/k_{\rm B}T_{\rm c}=4.08(1)$, respectively, and thus they cannot be ruled out when accounting for the superconducting state in Rb$_2$Mo$_3$As$_3$., Comment: 6 pages

Vector-chiral (VC) antiferromagnetism is a spiral-like ordering of spins which may allow ferroelectricity to occur due to loss of space inversion symmetry. In this paper we report direct experimental observation of ferroelectricity in the VC phase of $\beta$-TeVO$_4$, a frustrated spin chain system with pronounced magnetic anisotropy and a rich phase diagram. Saturation polarization is proportional to neutron scattering intensities that correspond to the VC magnetic reflection. This implies that inverse Dzyaloshinskii-Moriya mechanism is responsible for driving electric polarization. Linear magnetoelectric coupling is absent, however an unprecedented dependence of electric coercive field on applied magnetic field reveals a novel way of manipulating multiferroic information., Comment: submitted to PRB Letter, 7 pages, 4 figures

$\beta$-TeVO$_4$ is a frustrated spin 1/2 zig-zag chain system,where spin-density-wave (SDW), vector chiral (VC)and an exotic dynamic spin-stripe phase compete at low temperatures. Here we use torque magnetometry to study the anisotropy of these phases in magnetic fields of up to 5 T. Our results show that the magnetic-field-induced spin reorientation occurs in the SDW and in the spin stripe phases for $\mu_0 H \geq 2$~T. The observed spin reorientation is a new element of the anisotropic phase diagram for the field directions in the $ac$ and $a^*b$ crystallographic planes. The presented results should help establishing the model of anisotropic magnetic interactions, which are responsible for the formation of complex magnetic phases in $\beta$-TeVO$_4$ and similar quantum systems., Comment: Accepted for publication in Physical Review B

The layered {\beta}-NaMnO2, a promising Na-ion energy-storage material has been investigated for its triangular lattice capability to promote complex magnetic configurations that may release symmetry restrictions for the coexistence of ferroelectric and magnetic orders. The complexity of the neutron powder diffraction patterns underlines that the routinely adopted commensurate structural models are inadequate. Instead, a single-phase superspace symmetry description is necessary, demonstrating that the material crystallizes in a compositionally modulated q= (0.077(1), 0, 0) structure. Here, Mn3+ Jahn-Teller distorted MnO6 octahedra form corrugated layer stacking sequences of the {\beta}-NaMnO2 type, which are interrupted by flat sheets of the {\alpha}-like oxygen topology. Spontaneous long-range collinear antiferromagnetic order, defined by the propagation vector k= (1/2, 1/2, 1/2), appears below TN1= 200 K. Moreover, a second transition into a spatially modulated proper-screw magnetic state (k+-q) is established at TN2= 95 K, with an antiferromagnetic order parameter resembling that of a two-dimensional (2D) system. The evolution of 23Na NMR spin-lattice relaxation identifies a magnetically inhomogene-ous state in the intermediate T-region (TN2

The existence of a quantum spin liquid (QSL) in which quantum fluctuations of spins are sufficiently strong to preclude spin ordering down to zero temperature was originally proposed theoretically more than 40 years ago, but its experimental realisation turned out to be very elusive. Here we report on an almost ideal spin liquid state that appears to be realized by atomic-cluster spins on the triangular lattice of a charge-density wave (CDW) state of 1T-TaS$_2$. In this system, the charge excitations have a well-defined gap of $\sim 0.3$ eV, while nuclear magnetic quadrupole resonance and muon spin relaxation experiments reveal that the spins show gapless quantum spin liquid dynamics and no long range magnetic order down to 70~mK. Canonical $T^{2}$ power-law temperature dependence of the spin relaxation dynamics characteristic of a QSL is observed from 200~K to $T_f= 55$ K. Below this temperature we observe a new gapless state with reduced density of spin excitations and high degree of local disorder signifying new quantum spin order emerging from the QSL., Comment: 15 pages, 4 figures, submitted for a publication

Using local-probe magnetic-characterization techniques of muon spin relaxation ($\mu$SR) and electron spin resonance (ESR) we have investigated the Mn-induced magnetism of the wide-bandgap perovskite SrTiO$_3$. Our results clearly demonstrate that this diluted magnetic oxide (DMO) remains paramagnetic down to low temperatures for both doping cases, i.e., when Mn substitutes for Sr or Ti. In addition, both experimental techniques have unveiled that the distribution of individual Mn$^{2+}$ and Mn$^{4+}$ ions is nonrandom, as these ions partially aggregate into nanosized clusters., Comment: a few minor changes were made

Phase inhomogeneity of otherwise chemically homogenous electronic systems is an essential ingredient leading to fascinating functional properties, such as high-$T_c$ superconductivity in cuprates, colossal magnetoresistance in manganites, and giant electrostriction in relaxors. In these materials distinct phases compete and can coexist due to intertwined ordered parameters. Charge degrees of freedom play a fundamental role, although phase-separated ground states have been envisioned theoretically also for pure spin systems with geometrical frustration that serves as a source of phase competition. Here we report a paradigmatic magnetostructurally inhomogenous ground state of the geometrically frustrated $\alpha$-NaMnO$_2$ that stems from the system's aspiration to remove magnetic degeneracy and is possible only due to the existence of near-degenerate crystal structures. Synchrotron X-ray diffraction, nuclear magnetic resonance and muon spin relaxation show that the spin configuration of a monoclinic phase is disrupted by magnetically short-range ordered nanoscale triclinic regions, thus revealing a novel complex state of matter., Comment: version equivalent to the one published in Nature Communications, freely available at http://www.nature.com/ncomms/2014/140129/ncomms4222/full/ncomms4222.html

The spin wave excitations emerging from the chiral helically modulated 120$^{\circ}$ magnetic order in a langasite Ba$_3$NbFe$_3$Si$_2$O$_{14}$ enantiopure crystal were investigated by unpolarized and polarized inelastic neutron scattering. A dynamical fingerprint of the chiral ground state is obtained, singularized by (i) spectral weight asymmetries answerable to the structural chirality and (ii) a full chirality of the spin correlations observed over the whole energy spectrum. The intrinsic chiral nature of the spin waves elementary excitations is shown in absence of macroscopic time reversal symmetry breaking.

A study of an impurity driven phase-transition into a magnetically ordered state in the spin-liquid Haldane chain compound PbNi2V2O8 is presented. Both, macroscopic magnetization as well as 51V nuclear magnetic resonance (NMR) measurements reveal that the spin nature of dopants has a crucial role in determining the stability of the induced long-range magnetic order. In the case of nonmagnetic (Mg2+) doping on Ni2+ spin sites (S=1) a metamagnetic transition is observed in relatively low magnetic fields. On the other hand, the magnetic order in magnetically (Co2+) doped compounds survives at much higher magnetic fields and temperatures, which is attributed to a significant anisotropic impurity-host magnetic interaction. The NMR measurements confirm the predicted staggered nature of impurity-liberated spin degrees of freedom, which are responsible for the magnetic ordering. In addition, differences in the broadening of the NMR spectra and the increase of nuclear spin-lattice relaxation in doped samples, indicate a diverse nature of electron spin correlations in magnetically and nonmagnetically doped samples, which begin developing at rather high temperatures with respect to the antiferromagnetic phase transition., Comment: 10 pages, 7 figures

A comprehensive study of impurity-induced magnetism in nonmagnetically (Mg${}^{2+}$) and magnetically (Co${}^{2+}$) doped PbNi${}_{2}$V${}_{2}$O${}_{8}$ compounds is given, using both macroscopic dc susceptibility and local-probe electron spin resonance (ESR) techniques. Magnetic coupling between impurity-liberated spins is estimated from a linewidth of low-temperature ESR signal in Mg-doped samples. In addition, in the case of magnetic cobalt dopants the impurity-host magnetic exchange is evaluated from the Co-induced contribution to the linewidth in the paramagnetic phase. The experimentally observed severe broadening of the ESR lines in the magnetically doped compounds with respect to nonmagnetic doping is attributed to a rapid spin-lattice relaxation of the Co${}^{2+}$ ions, which results in a bottleneck-type of temperature dependence of the induced linewidth. The exchange parameters obtained from the ESR analysis offer a satisfactory explanation of the observed low-temperature magnetization in doped samples., Comment: 8 pages, 6 figures

X-band ESR measurements on a single crystal of SrCu$_2$(BO$_3$)$_2$ system in a temperature range between 10 K and 580 K are presented. The temperature and angular dependence of unusually broad ESR spectra can be explained by the inclusion of antisymmetric Dzyaloshinsky-Moriya (DM) interaction, which yields by far the largest contribution to the linewidth. However, the well-accepted picture of only out-of-plane interdimer DM vectors is not sufficient for explanation of the observed angular dependence. In order to account for the experimental linewidth anisotropy we had to include sizable in-plane components of interdimer as well as intradimer DM interaction in addition to the out-of-plane interdimer one. The nearest-neighbor DM vectors lie perpendicular to crystal anisotropy c-axis due to crystal symmetry. We also emphasize that above the structural phase transition occurring at 395 K dynamical mechanism should be present allowing for instantaneous DM interactions. Moreover, the linewidth at an arbitrary temperature can be divided into two contributions; namely, the first part arising from spin dynamics governed by the spin Hamiltonian of the system and the second part due to significant spin-phonon coupling. The nature of the latter mechanism is attributed to phonon-modulation of the antisymmetric interaction, which is responsible for the observed linear increase of the linewidth at high temperatures., Comment: 17 pages, 4 figures, submitted to PRB