Coherent spin control by electrical manipulation of the magnetic anisotropy

Molecular nanomagnets: a viable path toward quantum information processing?

Molecular nanomagnets (MNMs), molecules containing interacting spins, have been a playground for quantum mechanics. They are characterized by many accessible low-energy levels that can be exploited to store and process quantum information. This naturally opens the possibility of using them as qudits, thus enlarging the tools of quantum logic with respect to qubit-based architectures. These additional degrees of freedom recently prompted the proposal for encoding qubits with embedded quantum error correction (QEC) in single molecules. QEC is the holy grail of quantum computing and this qudit approach could circumvent the large overhead of physical qubits typical of standard multi-qubit codes. Another important strength of the molecular approach is the extremely high degree of control achieved in preparing complex supramolecular structures where individual qudits are linked preserving their individual properties and coherence. This is particularly relevant for building quantum simulators, controllable systems able to mimic the dynamics of other quantum objects. The use of MNMs for quantum information processing is a rapidly evolving field which still requires to be fully experimentally explored. The key issues to be settled are related to scaling up the number of qudits/qubits and their individual addressing. Several promising possibilities are being intensively explored, ranging from the use of single-molecule transistors or superconducting devices to optical readout techniques. Moreover, new tools from chemistry could be also at hand, like the chiral-induced spin selectivity. In this paper, we will review the present status of this interdisciplinary research field, discuss the open challenges and envisioned solution paths which could finally unleash the very large potential of molecular spins for quantum technologies.

Direct observation of electric field-induced magnetism in a molecular magnet

We report the direct observation of an electrically-induced magnetic susceptibility in the molecular nano- magnet [Fe₃O(O₂CPh)₆(py)₃]ClO₄·py, an Fe₃ trimer. This magnetoelectric effect results from the breaking of spatial inversion symmetry due to the spin configurations of the antiferromagnetic trimer. Both static and very low frequency electric fields were used. Fractional changes of the magnetic susceptibility of 11 ppb[Formula: see text] per kVm^-1 for the temperature range 8.5 < T < 13.5 K were observed for applied electric fields up to 62 kV m^-1. The changes in susceptibility were measured using a tunnel diode oscillator operating at liquid helium temperatures while the sample is held at a higher regulated temperature.

Spin-Electric Coupling with Anisotropy-Induced Vanishment and Enhancement in Molecular Ferroelectrics

Manipulating quantum properties by electric fields using spin-electric coupling (SEC) effects promises spatial addressability. While several studies about inorganic materials showing the SEC functionality have been reported, the vastly tunable crystal structures of molecular ferroelectrics provide a range of rationally designable materials yet to be exploited. In this work, Mn²⁺-doped molecular ferroelectrics are chosen to experimentally demonstrate the feasibility of achieving the quantum coherent SEC effect in molecular ferroelectrics for the first time. The electric field pulse applied between Hahn-echo pulses in electron paramagnetic resonance (EPR) experiments causes controllable phase shifts via manipulating of the zero-field splitting (ZFS) of the Mn(II) ions. Detailed investigations of the aMn crystal showed unexpected SEC vanishment and enhancement at different crystal orientations, which were elucidated by studying the spin Hamiltonian and magnetic anisotropy. With the enhanced SEC efficiency being achieved (0.68 Hz m/V), this work discovers an emerging material library of molecular ferroelectrics to implement coherent quantum control with selective and tunable SEC effects toward highly scalable quantum gates.

Tuning the magnetic anisotropy energy by external electric fields of CoPt dimers deposited on graphene

In the framework of first-principles calculations, we comprehensively investigate the external electric-field (EF) manipulation of the magnetic anisotropy energy (MAE) of alloyed CoPt dimers deposited on graphene. In particular, we focus on the possibility of tuning the MAE barriers under the action of external EFs and on the effects of Co-substitution. Among the various considered structures, the lowest-energy configurations were the hollow-upright and top-upright, having the Co-atom closest to the graphene layer. The optimal and higher energy configurations were related to the electronic structure through the local density of states and hybridizations between the transition-metal (TM) atoms of the dimer and graphene. In contrast to Co₂/graphene [M. Tanveer, J. Dorantes-Dávila and G. M. Pastor, Phys. Rev. B, 2017, 96(22), 224413.], the CoPt dimer having the hollow-upright ground-state configuration, exhibits a much lower value of the MAE (about |ΔE| ≃ 4.5 meV per atom) and the direction of the magnetization lies in the graphene layer. Moreover, we observe a spin-reorientation transition occurring at ε_z ≃ 0.5 V Å^-1, which opens the possibility of inducing magnetization switching by external electric fields. The microscopic origin of the changes of the MAE associated with changes in the EF has been qualitatively related to the details of the electronic structure by analyzing the local density of states and to the spin-dependent electronic densities close to the Fermi energy. Finally, the role of local environment was quantified by performing electronic structure and magnetic calculations on several higher-energy structure configurations.

Coherent electric field manipulation of Fe3+ spins in PbTiO3

Magnetoelectrics, materials that exhibit coupling between magnetic and electric degrees of freedom, not only offer a rich environment for studying the fundamental materials physics of spin-charge coupling but also present opportunities for future information technology paradigms. We present results of electric field manipulation of spins in a ferroelectric medium using dilute ferric ion-doped lead titanate as a model system. Combining first-principles calculations and electron paramagnetic resonance (EPR), we show that the ferric ion spins are preferentially aligned perpendicular to the ferroelectric polar axis, which we can manipulate using an electric field. We also demonstrate coherent control of the phase of spin superpositions by applying electric field pulses during time-resolved EPR measurements. Our results suggest a new pathway toward the manipulation of spins for quantum and classical spintronics.

Tuning Magnetism of Metal Porphyrazine Molecules by a Ferroelectric In2Se3 Monolayer

Electric field tuning of magnetism is highly desirable for nanoelectronics, but volatility in electron spin manipulation presents a major challenge that needs urgent resolution. Here, we show by first-principles calculations that magnetism of metal porphyrazine (MPz) molecules can be effectively tuned by switching ferroelectric polarization of an adjacent In₂Se₃ monolayer. The magnetic moments of TiPz and VPz (MnPz, FePz, and CoPz) decrease (increase) at one polarization but remain unchanged at reversed polarization. This intriguing phenomenon stems from distinct metal d-orbital occupation caused by electron transfer and energy-level shift associated with the polarization switch of the In₂Se₃ monolayer. Moreover, the ferroelectric switch also tunes the underlying electronic properties, producing a metallic, half-metallic, or semiconducting state depending on polarization. These findings of robust ferroelectric tuning of magnetism and related electronic properties in MPz-adsorbed In₂Se₃ hold great promise for innovative design and implementation in advanced magnetic memory storage, sensor, and spintronic devices.

Electric field manipulation enhanced by strong spin-orbit coupling: promoting rare-earth ions as qubits

Quantum information processing based on magnetic ions has potential for applications as the ions can be modified in their electronic properties and assembled by a variety of chemical methods. For these systems to achieve individual spin addressability and high energy efficiency, we exploited the electric field as a tool to manipulate the quantum behaviours of the rare-earth ion which has strong spin-orbit coupling. A Ce:YAG single crystal was employed with considerations to the dynamics and the symmetry requirements. The Stark effect of the Ce³⁺ ion was observed and measured. When demonstrated as a quantum phase gate, the electric field manipulation exhibited high efficiency which allowed up to 57 π/2 operations before decoherence with optimized field direction. It was also utilized to carry out quantum bang-bang control, as a method of dynamic decoupling, and the refined Deutsch-Jozsa algorithm. Our experiments highlighted rare-earth ions as potentially applicable qubits because they offer enhanced spin-electric coupling which enables high-efficiency quantum manipulation.

Electric field modulation of magnetic exchange in molecular helices

The possibility to operate on magnetic materials through the application of electric rather than magnetic fields-promising faster, more compact and energy efficient circuits-continues to spur the investigation of magnetoelectric effects. Symmetry considerations, in particular the lack of an inversion centre, characterize the magnetoelectric effect. In addition, spin-orbit coupling is generally considered necessary to make a spin system sensitive to a charge distribution. However, a magnetoelectric effect not relying on spin-orbit coupling is appealing for spin-based quantum technologies. Here, we report the detection of a magnetoelectric effect that we attribute to an electric field modulation of the magnetic exchange interaction without atomic displacement. The effect is visible in electron paramagnetic resonance absorption of molecular helices under electric field modulation and confirmed by specific symmetry properties and spectral simulation.

Electric Field Control of Spins in Molecular Magnets

Coherent control of individual molecular spins in nanodevices is a pivotal prerequisite for fulfilling the potential promised by molecular spintronics. By applying electric field pulses during time-resolved electron spin resonance measurements, we measure the sensitivity of the spin in several antiferromagnetic molecular nanomagnets to external electric fields. We find a linear electric field dependence of the spin states in Cr_{7}Mn, an antiferromagnetic ring with a ground-state spin of S=1, and in a frustrated Cu_{3} triangle, both with coefficients of about 2  rad s^{-1}/V m^{-1}. Conversely, the antiferromagnetic ring Cr_{7}Ni, isomorphic with Cr_{7}Mn but with S=1/2, does not exhibit a detectable effect. We propose that the spin-electric field coupling may be used for selectively controlling individual molecules embedded in nanodevices.

Quantum decoherence dynamics of divacancy spins in silicon carbide

Long coherence times are key to the performance of quantum bits (qubits). Here, we experimentally and theoretically show that the Hahn-echo coherence time of electron spins associated with divacancy defects in 4H-SiC reaches 1.3 ms, one of the longest Hahn-echo coherence times of an electron spin in a naturally isotopic crystal. Using a first-principles microscopic quantum-bath model, we find that two factors determine the unusually robust coherence. First, in the presence of moderate magnetic fields (30 mT and above), the ²⁹Si and ¹³C paramagnetic nuclear spin baths are decoupled. In addition, because SiC is a binary crystal, homo-nuclear spin pairs are both diluted and forbidden from forming strongly coupled, nearest-neighbour spin pairs. Longer neighbour distances result in fewer nuclear spin flip-flops, a less fluctuating intra-crystalline magnetic environment, and thus a longer coherence time. Our results point to polyatomic crystals as promising hosts for coherent qubits in the solid state.

Generation of constant-amplitude radio-frequency sweeps at a tunnel junction for spin resonance STM

We describe the measurement and successful compensation of the radio-frequency transfer function of a scanning tunneling microscope over a wide frequency range (15.5-35.5 GHz) and with high dynamic range (>50 dB). The precise compensation of cabling resonances and attenuations is critical for the production of constant-voltage frequency sweeps for electric-field driven electron spin resonance (ESR) experiments. We also demonstrate that a well-calibrated tunnel junction voltage is necessary to avoid spurious ESR peaks that can arise due to a non-flat transfer function.

Electron paramagnetic resonance of individual atoms on a surface

We combined the high-energy resolution of conventional spin resonance (here ~10 nano-electron volts) with scanning tunneling microscopy to measure electron paramagnetic resonance of individual iron (Fe) atoms placed on a magnesium oxide film. We drove the spin resonance with an oscillating electric field (20 to 30 gigahertz) between tip and sample. The readout of the Fe atom's quantum state was performed by spin-polarized detection of the atomic-scale tunneling magnetoresistance. We determine an energy relaxation time of T1 ≈ 100 microseconds and a phase-coherence time of T2 ≈ 210 nanoseconds. The spin resonance signals of different Fe atoms differ by much more than their resonance linewidth; in a traditional ensemble measurement, this difference would appear as inhomogeneous broadening.

Coherence and organisation in lanthanoid complexes: from single ion magnets to spin qubits

Molecular magnetism is reaching a degree of development that will allow for the rational design of sophisticated systems.

Coherent interaction with two-level fluctuators using near field scanning microwave microscopy

Near field Scanning Microwave Microscopy (NSMM) is a scanning probe technique that non-invasively can obtain material properties on the nano-scale at microwave frequencies. While focus has been on developing room-temperature systems it was recently shown that this technique can potentially reach the quantum regime, opening up for applications in materials science and device characterization in solid state quantum information processing. In this paper we theoretically investigate this new regime of NSMM. Specifically we show that interaction between a resonant NSMM probe and certain types of two-level systems become possible when the NSMM probe operates in the (sub-) single photon regime, and we expect a high signal-to-noise ratio if operated under the right conditions. This would allow to detect single atomic material defects with energy splittings in the GHz range with nano-scale resolution, provided that individual defects in the material under study are well enough separated. We estimate that this condition is fulfilled for materials with loss tangents below tan δ ∼ 10(-3) which holds for materials used in today's quantum circuits and devices where typically tan δ < 10(-5). We also propose several extensions to a resonant NSMM that could improve sensitivity and functionality also for microscopes operating in a high power regime.

Coherent Precession of an Individual 5/2 Spin

We present direct observation of a coherent spin precession of an individual Mn^{2+} ion, having both electronic and nuclear spins equal to 5/2, embedded in a CdTe quantum dot and placed in a magnetic field. The spin state evolution is probed in a time-resolved pump-probe measurement of absorption of the single dot. The experiment reveals subtle details of the large-spin coherent dynamics, such as nonsinusoidal evolution of states occupation, and beatings caused by the strain-induced differences in energy levels separation. Sensitivity of the large-spin impurity on the crystal strain opens the possibility of using it as a local strain probe.

Quantum information processing with hybrid spin-photon qubit encoding

We introduce a scheme to perform quantum information processing that is based on a hybrid spin-photon qubit encoding. The proposed qubits consist of spin ensembles coherently coupled to microwave photons in coplanar waveguide resonators. The quantum gates are performed solely by shifting the resonance frequencies of the resonators on a nanosecond time scale. An additional cavity containing a Cooper-pair box is exploited as an auxiliary degree of freedom to implement two-qubit gates. The generality of the scheme allows its potential implementation with a wide class of spin systems.