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The discovery of chiral helical magnetism (CHM) in Cr$_{1/3}$NbS$_2$ and the stabilization of a chiral soliton lattice (CSL) has attracted considerable interest in view of their potential technological applications. However, there is an ongoing debate regarding whether the sister compound, Mn$_{1/3}$NbS$_2$, which shares the same crystal structure, exhibits similar nontrivial properties which rely on the stabilization of the lack of inversion symmetry at the magnetic ion. In this study, we conduct a comprehensive investigation of the magnetically ordered states of both compounds, using $^{53}$Cr, $^{55}$Mn and $^{93}$Nb nuclear magnetic resonance. Our results, supported by density functional calculations, detect in a high-quality single crystal of Cr$_{1/3}$NbS$_2$ all the signatures of the monoaxial CHM in a magnetic field, identifying it as a textbook NMR case. The detailed understanding of this prototypic behavior provides a reference for Mn$_{1/3}$NbS$_2$. Despite the much larger density of specific defects in this second single crystal, we confirm the presence of a CHM phase in the Mn compound, characterized by a very large critical field for the forced ferromagnetic phase ($\approx 5$ T for H$\parallel\hat c$)., Comment: 10 pages, 7 figures, Supplemental MAterial

Positive muon spin rotation and relaxation spectroscopy is a well established experimental technique for studying materials. It provides a local probe that generally complements scattering techniques in the study of magnetic systems and represents a valuable alternative for materials that display strong incoherent scattering or neutron absorption. Computational methods can effectively quantify the microscopic interactions underlying the experimentally observed signal, thus substantially boosting the predictive power of this technique. Here, we present an efficient set of algorithms and workflows devoted to the automation of this task. In particular, we adopt the so-called DFT+{\mu} procedure, where the system is characterised in the density functional theory (DFT) framework with the muon modeled as a hydrogen impurity. We devise an automated strategy to obtain candidate muon stopping sites, their dipolar interaction with the nuclei, and hyperfine interactions with the electronic ground state. We validate the implementation on well-studied compounds, showing the effectiveness of our protocol in terms of accuracy and simplicity of use

The use of $d$-level qudits instead of two-level qubits can largely increase the power of quantum logic for many applications, ranging from quantum simulations to quantum error correction. Molecular Nanomagnets are ideal spin systems to realize these large-dimensional qudits. Indeed, their Hamiltonian can be engineered to an unparalleled extent and can yield a spectrum with many low-energy states. In particular, in the last decade intense theoretical, experimental and synthesis efforts have been devoted to develop quantum simulators based on Molecular Nanomagnets. However, this remarkable potential is practically unexpressed, because no quantum simulation has ever been experimentally demonstrated with these systems. Here we show the first prototype quantum simulator based on an ensemble of molecular qudits and a radiofrequency broadband spectrometer. To demonstrate the operativity of the device, we have simulated quantum tunneling of the magnetization and the transverse-field Ising model, representative of two different classes of problems. These results represent an important step towards the actual use of molecular spin qudits in quantum technologies.

Polarons and spin-orbit (SO) coupling are distinct quantum effects that play a critical role in charge transport and spin-orbitronics. Polarons originate from strong electron-phonon interaction and are ubiquitous in polarizable materials featuring electron localization, in particular $\mathrm{3d}$ transition metal oxides (TMOs). On the other hand, the relativistic coupling between the spin and orbital angular momentum is notable in lattices with heavy atoms and develops in $\mathrm{5d}$ TMOs, where electrons are spatially delocalized. Here we combine ab initio calculations and magnetic measurements to show that these two seemingly mutually exclusive interactions are entangled in the electron-doped SO-coupled Mott insulator $\mathrm{Ba_2Na_{1-x}Ca_xOsO_6}$ ($0< x < 1$), unveiling the formation of spin-orbital bipolarons. Polaron charge trapping, favoured by the Jahn-Teller lattice activity, converts the Os $\mathrm{5d^1}$ spin-orbital $\mathrm{J_{eff}=3/2}$ levels, characteristic of the parent compound $\mathrm{Ba_2NaOsO_6}$ (BNOO), into a bipolaron $\mathrm{5d^2}$ $\mathrm{J_{eff}=2}$ manifold, leading to the coexistence of different J-effective states in a single-phase material. The gradual increase of bipolarons with increasing doping creates robust in-gap states that prevents the transition to a metal phase even at ultrahigh doping, thus preserving the Mott gap across the entire doping range from $\mathrm{d^1}$ BNOO to $\mathrm{d^2}$ $\mathrm{Ba_2CaOsO_6}$ (BCOO).

Magnetostriction drives a rhombohedral distortion in the cubic rock salt antiferromagnet MnO at the N\'eel temperature $T_{N}=118$ K. As an unexpected consequence we show that this distortion acts to localize the site of an implanted muon due to the accompanying redistribution of electron density. This lifts the degeneracy between equivalent sites, resulting in a single observed muon precession frequency. Above $T_{N}$, the muon instead becomes delocalized around a network of equivalent sites. Our first-principles simulations based on Hubbard-corrected density-functional theory and molecular dynamics are consistent with our experimental data and help to resolve a long-standing puzzle regarding muon data on MnO, as well as having wider applicability to other magnetic oxides., Comment: 7 pages, 3 figures

The recently discovered vanadium-based kagome metals AV$_3$Sb$_5$ (A = K, Rb, Cs) offer the possibility to study the interplay between competing electronic orderings, such as charge density order and superconductivity. We focus on the former and provide a comprehensive set of $^{51}$V, $^{87}$Rb, and $^{121}$Sb magnetic resonance measurements on an RbV$_3$Sb$_5$ single crystal. Elucidating the symmetries and properties of the CDW phase is essential to understanding the unconventional electronic orderings occurring in this material. We establish the structure of the $2\times 2 \times 2$ superlattice that describes the system below the charge density wave transition by combining both experimental and computational methods, with a methodology that can be readily applied to the remaining compounds of the same family. Our results give compelling evidence that the CDW structure occurring below 103 K for RbV$_3$Sb$_5$ is the so-called Inverse Start of David pattern $\pi$-shifted along the c axis (also known as staggered tri-hexagonal).

We report on the first example of quantum coherence between the spins of muons and quadrupolar nuclei. We observe this effect in vanadium intermetallic compounds which adopt the A15 crystal structure, and whose members include all technologically dominant superconductors. The entangled states are extremely sensitive to the local structural and electronic environments through the electric field gradient at the quadrupolar nuclei. This case-study demonstrates that positive muons can be used as a quantum sensing tool to probe also structural and charge related phenomena in materials, even in the absence of magnetic order.

We present a detailed study of the electronic and magnetic interactions of Ba2CoO4, structurally very uncommon because of the isolated CoO4 distorted tetrahedral coordination. We show the presence of Co(d)-O(p) hybridized states characterized by spin polarized oxygen atoms, with their magnetic moments parallel to that on Co. The calculated isotropic exchange interaction parameters, which include the contributions from ligand spins, demonstrate the presence of a 3D network of magnetic couplings, that are partially frustrated in the identified magnetic ground state. Our results indicate that the dominant indirect exchange mechanism responsible for this ground state is mediated by O atoms along the Co-O...O-Co path., Comment: 5 pages, 3 figures, 3 tables and supplemental information

We show that [VO(TPP)] (vanadyl tetraphenylporphyrinate) is a promising system suitable to implement quantum computation algorithms based on encoding information in multi-level (qudit) units. Indeed, it embeds an electronic spin 1/2 coupled through hyperfine interaction to a nuclear spin 7/2, both characterized by remarkable coherence. We demonstrate this by an extensive broadband nuclear magnetic resonance study, which allow us to characterize the nuclear spin-Hamiltonian and to measure the spin dephasing time as a function of the magnetic field. In addition, we combine targeted measurements and numerical simulations to show that nuclear spin transitions conditioned by the state of the electronic qubit can be individually addressed and coherently manipulated by resonant radio-frequency pulses, thanks to the remarkably long coherence times and the effective quadrupolar coupling induced by the strong hyperfine coupling. This approach may open new perspectives for developing new molecular qubit-qudit systems.

Fe$_2$P alloys have been identified as promising candidates for magnetic refrigeration at room-temperature and for custom magnetostatic applications. The intent of this study is to accurately characterize the magnetic ground state of the parent compound, Fe$_2$P, with two spectroscopic techniques, $\mu$SR and NMR, in order to provide solid bases for further experimental analysis of Fe$_2$P-type transition metal based alloys. We perform zero applied field measurements using both techniques below the ferromagnetic transition $T_C=220~\mathrm K$. The experimental results are reproduced and interpreted using first principles simulations validating this approach for quantitative estimates in alloys of interest for technological applications., Comment: 10 pages, 2 figures

We demonstrate that the [Yb(trensal)] molecule is a prototypical coupled electronic qubit-nuclear qudit system. The combination of noise-resilient nuclear degrees of freedom and large reduction of nutation time induced by electron-nuclear mixing enables coherent manipulation of this qudit by radio-frequency pulses. Moreover, the multi-level structure of the qudit is exploited to encode and operate a qubit with embedded basic quantum error correction.

In muon spin rotation experiments the positive implanted muon vibrates with large zero point amplitude by virtue of its light mass. Quantum mechanical calculations of the host material usually treat the muon as a point impurity, ignoring this large vibrational amplitude. As a first order correction, the muon zero point motion is usually described within the harmonic approximation, despite the large anharmonicity of the crystal potential. Here we apply the stochastic self-consistent harmonic approximation, a quantum variational method devised to include strong anharmonic effects in total energy and vibrational frequency calculations, in order to overcome these limitations and provide an accurate ab initio description of the quantum nature of the muon. We applied this full quantum treatment to the calculation of the muon contact hyperfine field in textbook-case metallic systems, such as Fe, Ni, Co including MnSi and MnGe, significantly improving agreement with experiments. Our results show that muon vibrational frequencies are strongly renormalized by anharmonicity. Finally, in contrast to the harmonic approximation, we show that including quantum anharmonic fluctuations, the muon stabilizes at the octahedral site in bcc Fe., Comment: 10 pages

In positive muon spin rotation and relaxation spectroscopy it is becoming nowadays customary to take advantage of Density Functional Theory (DFT) based computational methods to aid the experimental data analysis. DFT aided muon site determination is especially useful for measurements performed in magnetic materials, where large contact hyperfine interactions may arise. Here we present a systematic analysis of the accuracy of the ab initio estimation of muon's hyperfine contact field on elemental transition metals, performing state of the art spin-polarized plane wave DFT and using the projector augmented pseudopotential approach, which allows to include the core state effects due to the spin ordering. We further validate this method in not-so-simple, non-centrosymmetric metallic compounds, presently of topical interest for their spiral magnetic structure giving rise to skyrmion phases, such as MnSi and MnGe. The calculated hyperfine fields agree with experimental values in all cases, provided the spontaneous spin magnetization of the metal is well reproduced within the approach. To overcome the known limits of the conventional mean field approximation of DFT on itinerant magnets, we adopt the so-called reduced Stoner theory [L. Ortenzi et al.,Phys. Rev. B 86, 064437 (2012)]. We establish the accuracy of the estimated muon contact field in metallic compounds with DFT and our results show improved agreement with experiments compared to those of earlier publications., Comment: 8 pages, 4 figures

Muon spin rotation and relaxation studies have been performed on a "111" family of iron-based superconductors NaFe_1-xNi_xAs. Static magnetic order was characterized by obtaining the temperature and doping dependences of the local ordered magnetic moment size and the volume fraction of the magnetically ordered regions. For x = 0 and 0.4 %, a transition to a nearly-homogeneous long range magnetically ordered state is observed, while for higher x than 0.4 % magnetic order becomes more disordered and is completely suppressed for x = 1.5 %. The magnetic volume fraction continuously decreases with increasing x. The combination of magnetic and superconducting volumes implies that a spatially-overlapping coexistence of magnetism and superconductivity spans a large region of the T-x phase diagram for NaFe_1-xNi_xAs . A strong reduction of both the ordered moment size and the volume fraction is observed below the superconducting T_C for x = 0.6, 1.0, and 1.3 %, in contrast to other iron pnictides in which one of these two parameters exhibits a reduction below TC, but not both. The suppression of magnetic order is further enhanced with increased Ni doping, leading to a reentrant non-magnetic state below T_C for x = 1.3 %. The reentrant behavior indicates an interplay between antiferromagnetism and superconductivity involving competition for the same electrons. These observations are consistent with the sign-changing s-wave superconducting state, which is expected to appear on the verge of microscopic coexistence and phase separation with magnetism. We also present a universal linear relationship between the local ordered moment size and the antiferromagnetic ordering temperature TN across a variety of iron-based superconductors. We argue that this linear relationship is consistent with an itinerant-electron approach, in which Fermi surface nesting drives antiferromagnetic ordering., Comment: 20 pages, 14 figures, Correspondence should be addressed to Prof. Yasutomo Uemura: tomo@phys.columbia.edu

The temperature-pressure phase diagram of the ferromagnet LaCrGe$_3$ is determined for the first time from a combination of magnetization, muon-spin-rotation and electrical resistivity measurements. The ferromagnetic phase is suppressed near $2.1$~GPa, but quantum criticality is avoided by the appearance of a magnetic phase, likely modulated, AFM$_Q$. Our density functional theory total energy calculations suggest a near degeneracy of antiferromagnetic states with small magnetic wave vectors $Q$ allowing for the potential of an ordering wave vector evolving from $Q=0$ to finite $Q$, as expected from the most recent theories on ferromagnetic quantum criticality. Our findings show that LaCrGe$_3$ is a very simple example to study this scenario of avoided ferromagnetic quantum criticality and will inspire further study on this material and other itinerant ferromagnets.

The rapid developments of computational quantum chemistry methods and supercomputing facilities motivate the renewed interest in the analysis of the muon/electron interactions in $\mu$SR experiments with \emph{ab initio} approaches. Modern simulation methods seem to be able to provide the answers to the frequently asked questions of many $\mu$SR experiments: where is the muon? Is it a passive probe? What are the interaction parameters governing the muon-sample interaction? In this review we describe some of the approaches used to provide quantitative estimations of the aforementioned quantities and we provide the reader with a short discussion on the current developments in this field.

The discovery of a superconducting dome in the proximity of the magnetic to paramagnetic transition in the electronic phase diagram of MnP as a function of hydrostatic pressure has renewed the interest in the magnetic properties of this binary pnictide. Here we present an ab initio study obtained with Density Functional Theory (DFT) simulations as a function of pressure. We show that the itinerant-electron magnetism of MnP is well characterized by the mean-field Kohn-Sham method which correctly describes the ambient pressure magnetic states, the anomalous trend of the lattice parameters as a function of pressure and the critical pressure for the disappearance of the magnetic order. We are finally able to confirm the nature of the new helical structure observed at high pressure.

Neutron diffraction and muon spin relaxation measurements are used to obtain a detailed phase diagram of Pr(Fe,Ru)AsO. The isoelectronic substitution of Ru for Fe acts effectively as spin dilution, suppressing both the structural and magnetic phase transitions. The temperature of the tetragonal-orthorhombic structural phase transition decreases gradually as a function of x. Slightly below the transition temperature coherent precessions of the muon spin are observed corresponding to static magnetism, possibly reflecting a significant magneto-elastic coupling in the FeAs layers. Short range order in both the Fe and Pr moments persists for higher levels of x. The static magnetic moments disappear at a concentration coincident with that expected for percolation of the J1-J2 square lattice model.

We present an accurate and efficient method to calculate the effect of random fluctuations of the local field at the muon, for instance in the case muon diffusion, within the framework of the strong collision approximation. The method is based on a reformulation of the Markovian process over a discretized time base, leading to a summation equation for the muon polarization function which is solved by discrete Fourier transform. The latter is formally analogous, though not identical, to the integral equation of the original continuous-time model, solved by Laplace transform. With real-case parameter values, the solution of the discrete-time strong collision model is found to approximate the continuous-time solution with excellent accuracy even with a coarse-grained time sampling. Its calculation by the fast Fourier transform algorithm is very efficient and suitable for real time fitting of experimental data even on a slow computer., Comment: 7 pages, 3 figures. Submitted to Journal of Physics: Condensed Matter

We investigate the effect of external pressure on magnetic order in undoped LnFeAsO (Ln = La, Ce, Pr, La) by using muon-spin relaxation measurements and ab-initio calculations. Both magnetic transition temperature $T_m$ and Fe magnetic moment decrease with external pressure. The effect is observed to be lanthanide dependent with the strongest response for Ln = La and the weakest for Ln = Sm. The trend is qualitatively in agreement with our DFT calculations. The same calculations allow us to assign a value of 0.68(2) $\mu_B$ to the Fe moment, obtained from an accurate determination of the muon sites. Our data further show that the magnetic lanthanide order transitions do not follow the simple trend of Fe, possibly as a consequence of the different $f$-electron overlap., Comment: 16 pages, 11 figures

The effect of isoelectronic substitutions on the microscopic properties of LaFe1-xRuxAsO, for 0< x< 0.8, has been investigated by means of muSR and 139La NMR. It was found that Ru substitution causes a progressive reduction of the N\`eel temperature (T_N) and of the magnetic order parameter without leading to the onset of superconductivity. The temperature dependence of 139La nuclear spin-lattice relaxation rate 1/T_1 can be suitably described within a two-band model. One band giving rise to the spin density wave ground-state, while the other one is characterized by weakly correlated electrons. Fe for Ru substitution yields to a progressive decrease of the density of states at the Fermi level close to the one derived from band structure calculations. The reduction of T_N with doping follows the predictions of the J_1-J_2 model on a square lattice, which appears to be an effective framework to describe the magnetic properties of the spin density wave ground-state., Comment: 6 pages, 8 figures