Ubiquitous Order-Disorder Transition in the Mn Antisite Sublattice of the (MnBi2Te4)(Bi2Te3)n Magnetic Topological Insulators.

Magnetic topological insulators (TIs) herald a wealth of applications in spin-based technologies, relying on the novel quantum phenomena provided by their topological properties. Particularly promising is the (MnBi2Te4)(Bi2Te3)n layered family of established intrinsic magnetic TIs that can flexibly realize various magnetic orders and topological states. High tunability of this material platform is enabled by manganese-pnictogen intermixing, whose amounts and distribution patterns are controlled by synthetic conditions. Here, nuclear magnetic resonance and muon spin spectroscopy, sensitive local probe techniques, are employed to scrutinize the impact of the intermixing on the magnetic properties of (MnBi2Te4)(Bi2Te3)n and MnSb2Te4. The measurements not only confirm the opposite alignment between the Mn magnetic moments on native sites and antisites in the ground state of MnSb2Te4, but for the first time directly show the same alignment in (MnBi2Te4)(Bi2Te3)n with n = 0, 1 and 2. Moreover, for all compounds, the static magnetic moment of the Mn antisite sublattice is found to disappear well below the intrinsic magnetic transition temperature, leaving a homogeneous magnetic structure undisturbed by the intermixing. The findings provide a microscopic understanding of the crucial role played by Mn-Bi intermixing in (MnBi2Te4)(Bi2Te3)n and offer pathways to optimizing the magnetic gap in its surface states.

Spin-orbital Jahn-Teller bipolarons.

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 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 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 Ba2Na1-xCaxOsO6 (0 < x < 1), unveiling the formation of spin-orbital bipolarons. Polaron charge trapping, favoured by the Jahn-Teller lattice activity, converts the Os 5d1 spin-orbital Jeff = 3/2 levels, characteristic of the parent compound Ba2NaOsO6 (BNOO), into a bipolaron 5d2 Jeff = 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 d1 BNOO to d2 Ba2CaOsO6 (BCOO).

Proof-of-Concept Quantum Simulator Based on Molecular Spin Qudits.

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. Magnetic molecules 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 past decade, intense theoretical, experimental, and synthesis efforts have been devoted to develop quantum simulators based on molecular qubits and qudits. 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 toward the actual use of molecular spin qudits in quantum technologies.

Controlled coherent dynamics of [VO(TPP)], a prototype molecular nuclear qudit with an electronic ancilla.

We show that [VO(TPP)] (vanadyl tetraphenylporphyrinate) is a promising system to implement quantum computation algorithms based on encoding information in multi-level (qudit) units. Indeed, it embeds a nuclear spin 7/2 coupled to an electronic spin 1/2 by hyperfine interaction. This qubit-qudit unit can be exploited to implement quantum error correction and quantum simulation algorithms. Through a combined theoretical and broadband nuclear magnetic resonance study, we demonstrate that the elementary operations of such algorithms can be efficiently implemented on the nuclear spin qudit. Manipulation of the nuclear qudit can be achieved by resonant radio-frequency pulses, thanks to the remarkably long coherence times and the effective quadrupolar coupling induced by the strong hyperfine interaction. This approach may open new perspectives for developing new molecular qubit-qudit systems.

Radiofrequency to Microwave Coherent Manipulation of an Organometallic Electronic Spin Qubit Coupled to a Nuclear Qudit.

We report here a comprehensive characterization of a 3d organometallic complex, [V(Cp)2Cl2] (Cp = cyclopentadienyl), which can be considered as a prototypical multilevel nuclear qudit (nuclear spin I = 7/2) hyperfine coupled to an electronic qubit (electronic spin S = 1/2). By combining complementary magnetic resonant techniques, such as pulsed electron paramagnetic resonance (EPR) and broadband nuclear magnetic resonance (NMR), we extensively characterize its Spin Hamiltonian parameters and its electronic and nuclear spin dynamics. Moreover, we demonstrate the possibility to manipulate the qubit-qudit multilevel structure by resonant microwave and radiofrequency pulses, driving coherent Rabi oscillations between targeted electronuclear states. The obtained results demonstrate that this simple complex is a promising candidate for quantum computing applications.

Probing spin fluctuations in NaOsO3by muon spin rotation and NMR spectroscopy.

We have used muon spin rotation and relaxation (µSR) and23Na nuclear magnetic resonance (NMR) spectroscopic methods in the NaOsO3antiferromagnetic phase to determine the temperature evolution of the magnetic order parameter and the role of the magnetic fluctuations at the Néel temperature. Additionally, we performed muon spin relaxation measurements in the vicinity ofTA= 30 K, where the appearance of an anomaly in the electrical resistivity was suggested to be due to a progressive reduction of the Os magnetic moment associated with spin fluctuation. Our measurements suggest the absence of prominent change in the spin fluctuations frequency atTA, within the muon probing time scale and the absence of a reduction of the localized Os magnetic moment reflected by the stability within few permille of the local magnetic field strength sensed by the muons below 50 K.

Coherent Manipulation of a Molecular Ln-Based Nuclear Qudit Coupled to an Electron Qubit.

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 multilevel structure of the qudit is exploited to encode and operate a qubit with embedded basic quantum error correction.