Long Spin-Relaxation Times in a Transition-Metal Atom in Direct Contact to a Metal Substrate

Dissipative Spin-Wave Diode and Nonreciprocal Magnonic Amplifier

We propose an experimentally feasible dissipative spin-wave diode comprising two magnetic layers coupled via a nonmagnetic spacer. We theoretically demonstrate that the spacer mediates not only coherent interactions but also dissipative coupling. Interestingly, an appropriately engineered dissipation engenders a nonreciprocal device response, facilitating the realization of a spin-wave diode. This diode permits wave propagation in one direction alone, given that the coherent Dzyaloshinskii-Moriya (DM) interaction is balanced with the dissipative coupling. The polarity of the diode is determined by the sign of the DM interaction. Furthermore, we show that when the magnetic layers undergo incoherent pumping, the device operates as a unidirectional spin-wave amplifier. The amplifier gain is augmented by cascading multiple magnetic bilayers. By extending our model to a one-dimensional ring structure, we establish a connection between the physics of spin-wave amplification and non-Hermitian topology. Our proposal opens up a new avenue for harnessing inherent dissipation in spintronic applications.

Extending the Spin Excitation Lifetime of a Magnetic Molecule on a Proximitized Superconductor

Molecular spins on surfaces potentially used in quantum information processing and data storage require long spin excitation lifetimes. Normally, coupling of the molecular spin with the conduction electrons of metallic surfaces causes fast relaxation of spin excitations. However, the presence of superconducting pairing effects in the substrate can protect the excited spin from decaying. In this work, we show that a proximity-induced superconducting gold film can sustain spin excitations of a FeTPP-Cl molecule for more than 80 ns. This long value was determined by studying inelastic spin excitations of the S = 5/2 multiplet of FeTPP-Cl on Au films over V(100) using scanning tunneling spectroscopy. The spin lifetime decreases with increasing film thickness, along with the decrease of the effective superconducting gap. Our results elucidate the use of proximitized gold electrodes for addressing quantum spins on surfaces, envisioning new routes for tuning the value of their spin lifetime.

OsPd bimetallic dimer pushes the limit of magnetic anisotropy in atom-sized magnets for data storage

The growing gap between the volume of digital data being created and the extent of available storage capacities stimulates intensive research into surface-supported, well-ordered array of atom-sized magnets that represents the ultimate limit of magnetic data storage. Anchoring transition-metal heterodimers in vacancy defects in the graphene lattice has been identified as a vivid strategy to achieve large magnetic anisotropy energy (MAE) up to 80 meV with an easy axis aligned along the dimer bond. In this paper we have made a significant leap forward finding out MAE of 119 meV for an OsPt dimer and 170 meV for an OsPd dimer bound to a single nitrogen-decorated vacancy defect. The system with the highest MAE and with the theoretical storage density of ∼490 Tb·inch^-2pushes the current limit of theoretical blocking temperature in graphene-supported transition-metal dimers from ∼20 to ∼44 K assuming the relaxation time of 10 years. The mechanism of the enhanced MAE is discussed.

Moiré Tuning of Spin Excitations: Individual Fe Atoms on MoS_{2}/Au(111)

Magnetic adatoms on properly designed surfaces constitute exquisite systems for addressing, controlling, and manipulating single quantum spins. Here, we show that monolayers of MoS_{2} on a Au(111) surface provide a versatile platform for controllably tuning the coupling between adatom spins and substrate electrons. Even for equivalent adsorption sites with respect to the atomic MoS_{2} lattice, we observe that Fe adatoms exhibit behaviors ranging from pure spin excitations, characteristic of negligible exchange and dominant single-ion anisotropy, to a fully developed Kondo resonance, indicating strong exchange and negligible single-ion anisotropy. This tunability emerges from a moiré structure of MoS_{2} on Au(111) in conjunction with pronounced many-body renormalizations. We also find striking spectral variations in the immediate vicinity of the Fe atoms, which we explain by quantum interference reflecting the formation of Fe-S hybrid states despite the nominally inert nature of the substrate. Our work establishes monolayer MoS_{2} as a tuning layer for adjusting the quantum spin properties over an extraordinarily broad parameter range. The considerable variability can be exploited for quantum spin manipulations.

Quantum stochastic resonance of individual Fe atoms

Stochastic resonance, where noise synchronizes a system's response to an external drive, is a wide-reaching phenomenon found in noisy systems spanning from the dynamics of neurons to the periodicity of ice ages. Quantum tunneling can extend stochastic resonance to the quantum realm. We demonstrate quantum stochastic resonance for magnetic transitions in atoms by inelastic electron tunneling with a scanning tunneling microscope. Stochastic resonance is shown deep in the quantum regime, where spin-state fluctuations are driven by tunneling of the magnetization, and in a semiclassical crossover region, where thermally excited electrons drive transitions between ground and excited states. Inducing synchronization by periodically modulating transition rates provides a general mechanism to determine real-time spin dynamics ranging from milliseconds to picoseconds.

Large magnetic anisotropy in an OsIr dimer anchored in defective graphene

Single-atom magnets represent the ultimate limit of magnetic data storage. The identification of substrates that anchor atom-sized magnets firmly and, thus, prevent their diffusion and large magnetic anisotropy has been at the centre of intense research efforts for a long time. Using density functional theory we show the binding of transition metal (TM) atoms in defect sites in the graphene lattice: single vacancy and double vacancy, both pristine and decorated by pyridinic nitrogen atoms, are energetically more favourable than away from the centre of defects, which could be used for engineering the position of TMs with atomic precision. Relativistic calculations revealed magnetic anisotropy energy (MAE) of ∼10 meV for Ir@NSV with an easy axis parallel to the graphene plane. MAE can be remarkably boosted to 50 meV for OsIr@NSV with the easy axis perpendicular to the graphene plane, which paves the way to the storage density of ∼490 Tb/inch²with the blocking temperature of 14 K assuming the relaxation time of 10 years. Magnetic anisotropy is discussed based on the relativistic electronic structures. The influence of an orbital-dependent on-site Coulomb repulsionUand a non-local correlation functional optB86b-vdW on MAE is also discussed.

Precise Spin Manipulation of Single Molecule Positioning on Graphene by Coordination Chemistry

Precise spin manipulation of single molecules is crucial for future molecular spintronics. However, it has been a formidable challenge due to the complexities of the strong molecule-substrate coupling as well as the response of the molecule to external stimulus. Here we demonstrate by density functional theory calculations that precise spin manipulation can be achieved by extra CO and NO molecules coordination to transition metal phthalocyanine (TMPc) (TM = Co, Fe, Mn) molecules deposited on metal-supported graphene; the spins of TMPc molecules are switched from S to S - ¹/₂ (|S - 1|) after NO (CO) coordination. With the aid of a combination of molecular orbitals (MO) theory and recently developed principal interacting spin-orbital (PISO) analysis, the impacts of NO and CO coordinations on both adsorption configuration and spin polarization of TMPc are well elucidated. We reveal the different coordination geometries that CO always coordinates axially to the TM center with a linear geometry, while NO prefers a bent geometry, which can be attributed to the competition between the σ- and π-type interactions according to the PISO analysis. Particularly, the NO-MnPc complex adopts a bent geometry deviating from the prediction by the existing Enemark-Feltham formalism. In addition, MO analysis suggests that during the CO coordination, the simultaneous existence of σ-donation and π-back-donation promotes electrons flowing from the d_z² to partially occupied d_π (d_xz and d_xz) orbitals with subsequent reordering of the TM d-orbitals, resulting in the spin transition of S → |S - 1|. In comparison, given that NO is regarded as NO^- when it adopts a bent geometry coordinating to the TM center, the complete (CoPc) or partial (FePc and MnPc) quenching of the molecular spins caused by NO coordination is attributed to the electron transfer from TM to NO. These theoretical findings provide important insights into relevant experiments and offer an effective design strategy to realize underlying single-molecular spintronics devices integrated with two-dimensional materials.

Sensing the Spin of an Individual Ce Adatom

The magnetic moment of rare earth elements originates from electrons in the partially filled 4f orbitals. Accessing this moment electrically by scanning tunneling spectroscopy is hampered by shielding of outerlying orbitals. Here, we show that we can detect the magnetic moment of an individual Ce atom adsorbed on a Cu_{2}N ultrathin film on Cu(100) by using a sensor tip that has its apex functionalized with a Kondo screened spin system. We calibrate the sensor tip by deliberately coupling it to a well characterized Fe atom. Subsequently, we use the splitting of the tip's Kondo resonance when approaching a spectroscopically dark Ce atom to sense its magnetic moment.

Reversible spin storage in metal oxide-fullerene heterojunctions

We show that hybrid MnO_x/C₆₀ heterojunctions can be used to design a storage device for spin-polarized charge: a spin capacitor. Hybridization at the carbon-metal oxide interface leads to spin-polarized charge trapping after an applied voltage or photocurrent. Strong electronic structure changes, including a 1-eV energy shift and spin polarization in the C₆₀ lowest unoccupied molecular orbital, are then revealed by x-ray absorption spectroscopy, in agreement with density functional theory simulations. Muon spin spectroscopy measurements give further independent evidence of local spin ordering and magnetic moments optically/electronically stored at the heterojunctions. These spin-polarized states dissipate when shorting the electrodes. The spin storage decay time is controlled by magnetic ordering at the interface, leading to coherence times of seconds to hours even at room temperature.

Stabilizing spin systems via symmetrically tailored RKKY interactions

Spins of single atoms adsorbed on substrates are promising building blocks for spintronics and quantum computation schemes. To process spin information and for increased magnetic stability, these spins have to be coupled to arrays. For a single atom, a high symmetry of the environment increases its spin stability. However, little is known about the role of the symmetry of the magnetic couplings in the arrays. Here, we study arrays of atomic spins coupled via Ruderman−Kittel−Kasuya−Yosida interaction, focusing on Dzyaloshinskii−Moriya and symmetric anisotropic exchange. We show that the high spin stability of a trimer can be remotely detected by a nearby atom, and how the Dzyaloshinskii−Moriya interaction leads to its destabilization. Adding more nearby atoms further destabilizes the trimer, due to a non-local effective transverse anisotropy originating in the symmetric anisotropic exchange. This transverse anisotropy can be quenched for highly symmetric structures, where the spin lifetime of the array increases drastically.

Exploration of the atomic spin interactions promises next generation information technologies. Here the authors show the observation and understanding of the Dzyaloshinskii−Moriya and symmetric anisotropic exchange interactions controlled spin dynamics and stability in Fe cluster-adatom complexes on Pt surfaces.

Electronic and magnetic properties of CoPc and FePc molecules on graphene: the substrate, defect, and hydrogen adsorption effects

Transition metal phthalocyanines (TMPcs) are particularly appealing for spintronic processing and data storage devices due to their structural simplicity and functional flexibility. To realize effective control of the spins in TMPc-based systems, it is necessary to quantify how the structural and chemical environment of the molecule affects its spin center. Herein we perform a detailed investigation of the electronic and spintronic properties of vertically stacked heterostructures formed by CoPc or FePc adsorbed on a monolayer of graphene under the influences of the gold substrate, vacancies in graphene, and extra atomic hydrogen coordination on the TMPc. By using density functional theory (DFT), we reveal that both the TMPc molecules prefer the carbon-top position on graphene, and the existence of the Au substrate enhances the stability of the adsorption, while this enhanced adsorption will not modify the molecular magnetism, keeping it the same value as in the free standing case. Moreover, with the aid of a combination of DFT and ab initio wavefunction-based calculations, our results indicate that the magnetic anisotropy of the FePc-graphene complex can be actively tuned by the Au substrate. Our calculations also show that defects in graphene including single and double vacancies can modify the magnetism of these heterostructures. In particular, the spin state of FePc can be tuned from S = 1 to S = 2 with such defect engineering. Further spin state tunability can be achieved from a hydrogenation process, with the coordination of one extra hydrogen on the Co-top site for CoPc and the pyridinic N site for FePc, respectively, tuning their spin states from S = 1/2 to S = 0 and from S = 1 to S = 2. These findings may prove to be instrumental for rational design of future molecular spintronics devices integrated with two-dimensional materials.

Enhanced quantum coherence in exchange coupled spins via singlet-triplet transitions

Manipulation of spin states at the single-atom scale underlies spin-based quantum information processing and spintronic devices. These applications require protection of the spin states against quantum decoherence due to interactions with the environment. While a single spin is easily disrupted, a coupled-spin system can resist decoherence by using a subspace of states that is immune to magnetic field fluctuations. Here, we engineered the magnetic interactions between the electron spins of two spin-1/2 atoms to create a "clock transition" and thus enhance their spin coherence. To construct and electrically access the desired spin structures, we use atom manipulation combined with electron spin resonance (ESR) in a scanning tunneling microscope. We show that a two-level system composed of a singlet state and a triplet state is insensitive to local and global magnetic field noise, resulting in much longer spin coherence times compared with individual atoms. Moreover, the spin decoherence resulting from the interaction with tunneling electrons is markedly reduced by a homodyne readout of ESR. These results demonstrate that atomically precise spin structures can be designed and assembled to yield enhanced quantum coherence.

Spin-fluctuation and spin-relaxation effects of single adatoms from first principles

Single adatoms offer an exceptional playground for studying magnetism and its associated dynamics at the atomic scale. Here we review recent results on single adatoms deposited on metallic substrates, based on time-dependent density functional theory. First we analyze quantum zero-point spin-fluctuations (ZPSF) as calculated from the fluctuation-dissipation theorem, and show how they affect the magnetic stability by modifying the magnetic anisotropy energy. We also assess the impact of ZPSF in the limit of small hybridization to the substrate characteristic of semi-insulating substrates, connecting to recent experimental investigations where magnetic stability of a single adatom was achieved for the first time. Secondly, we inspect further the dynamics of single adatoms by considering the longitudinal and transverse spin-relaxation processes, whose time-scales are analyzed and related to the underlying electronic structure of both the adatom and the substrate. Thirdly, we analyze spin-fluctuation modes of paramagnetic adatoms, i.e. adatoms where the Stoner criterion for magnetism is almost fulfilled. Interestingly, such modes can develop well-defined peaks in the meV range, their main characteristics being determined by two fundamental electronic properties, namely the Stoner parameter and the density of states at the Fermi level. Furthermore, simulated inelastic scanning tunneling spectroscopy curves reveal that these spin-fluctuation modes can be triggered by tunneling electrons, opening up potential applications also for paramagnetic adatoms. Lastly, an overview of the outstanding issues and future directions is given.

Manipulation of spin and magnetic anisotropy in bilayer magnetic molecular junctions

The Kondo effect and magnetic anisotropy in bilayer TMPc/TMPc/Pb(111) junctions can be actively tuned by changing the intermediate decoupling layer.