Abstract
The orbital angular moment of magnetic atoms adsorbed on surfaces is often quenched as a result of an anisotropic crystal field. Due to spinorbit coupling, what remains of the orbital moment typically delineates the orientation of the electron spin. These two effects limit the scope of information processing based on these atoms to essentially only one magnetic degree of freedom: the spin. In this work, we gain independent access to both the spin and orbital degrees of freedom of a single atom, inciting and probing excitations of each moment. By coordinating a single Fe atom atop the nitrogen site of the Cu_{2}N lattice, we realize a singleatom system with a large zerofield splitting—the largest reported for Fe atoms on surfaces—and an unquenched uniaxial orbital moment that closely approaches the freeatom value. We demonstrate a full reversal of the orbital moment through a singleelectron tunneling event between the tip and Fe atom, a process that is mediated by a charged virtual state and leaves the spin unchanged. These results, which we corroborate using density functional theory and firstprinciples multiplet calculations, demonstrate independent control over the spin and orbital degrees of freedom in a singleatom system.
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Introduction
Efforts to downscale information storage to the singleatom limit have largely focused on readily probing, manipulating, and engineering the spin of magnetic atoms adsorbed on surfaces^{1,2,3,4}. This is primarily a consequence of orbital quenching: the orbital angular momentum L of these systems is often diminished due to the interaction between the spinorbit coupling and the crystal field (CF) generated by the surface^{5,6}, leaving the spin S as the only viable parameter for control. Even in the case of a partially preserved orbital moment, the spinorbit interaction can act to create superpositions of the orbital angular momentum and spin states, meaning that only the total momentum L + S is preserved. In that case, independent excitations of L and S cannot occur.
Quenching of the orbital angular momentum directly affects the stability and lifetime of the atom’s magnetization^{7,8}. The viability of information processing applications based on single atoms is, however, contingent on the spin stably maintaining its direction, and thus its magnetization, over time—which necessitates a large singlesite magnetic anisotropy, as well as a slow relaxation of the magnetization. The energy barrier to flip the magnetic moment is determined by the magnetic anisotropy energy (MAE), which arises from the interplay between the CF and spinorbit coupling. Specifically, the Coulomb potential generated by the crystal breaks the spherical symmetry of the free atom, thereby lending the orbital moment a certain orientation with respect to the crystallographic axes^{5}. However, in the case of an almost fully quenched L, the spinorbit coupling only acts to higher order to produce singlesite magnetic anisotropy, which leads to MAE values far below the atomic spinorbit coupling strength. Consequently, the crystal symmetry at the atomic site—and the overlap of the atomic orbitals with the surrounding ligands—plays a crucial role in preserving the orbital angular momentum of the atom and enhancing the MAE.
Engineering the local environment of the single atom to produce an axial CF can have significant consequences on preserving the freeatom orbital moment, and consequently, increasing the magnetic anisotropy^{7,8}. 3d transition elements are particularly appealing as the magnetic atoms of choice, as, in addition to their natural abundance, they can be easily deposited on surfaces and probed locally by scanning tunneling microscopy (STM) and spectroscopy. This is illustrated by STM experiments performed on Fe and Co atoms bound to the oxygen site of the MgO/Ag(100) surface, where the local symmetry ensures a nearly axial CF. The resultant orbital moment—which is nearly preserved in the outofplane direction for the Fe atoms, and fully preserved for the Co atoms—gives rise to large zerofield splittings of, respectively, 14 meV^{7} and 58 meV^{8}. However, in both of these cases, the energy multiplets evolve under the CF and spinorbit coupling to become a mixture of S and L states, and accordingly, the transitions probed by inelastic electron tunneling spectroscopy (IETS) show that variations in L are associated with variations in S.
In this work, we present a singleatom spin system that combines a large MAE with an orbital angular moment that remains fully unquenched along the uniaxial direction. This situation is realized by placing Fe atoms atop the fourfold symmetric nitrogen binding site of the Cu_{2}N/Cu_{3}Au(100) surface, thus engendering a zerofield splitting of ∼18 meV. We demonstrate that we are able to fully rotate the preserved orbital moment via a singleelectron process between the tip and atom, without altering the spin state of the atom. Alternatively, we observe a distinct spin excitation, which does not affect the orbital moment. These finding are understood in terms of firstprinciples density functional theory (DFT) and electronic multiplet calculations.
Results
Origin of the unquenched orbital moment
The Cu_{2}N surface^{9}, in addition to providing protection to magnetic moments from electronic scattering, enables reliable and largescale atom manipulation^{10,11,12,13,14,15}. Fe atoms on the Cu_{2}N lattice preferentially bind to the Cu site, where the local C_{2v} symmetry produces a partially unquenched orbital moment resulting in inplane uniaxial magnetic anisotropy energies of ∼5 meV^{11,14}. A higher symmetry can be achieved, however, by coordinating the Fe atom atop the Nsite instead, which, in principle, could preserve the orbital moment even more, and thus lead to larger anisotropy values. Nsite adsorption on Cu_{2}N is also preferable over Cusite adsorption, in that placing an Fe atom on an Nsite requires one less atom manipulation procedure^{16}, vastly improving possibilities for building extended spin arrays. However, previous studies reported that no spinflip excitations could be resolved for Fe atoms bound to Nsites^{9}.
We use a lowtemperature STM to perform controlled singleatom manipulation and IETS. We coordinate Fe atoms, deposited on an insulating layer of Cu_{2}N that is grown on a Cu_{3}Au(100) substrate^{17}, atop the N and Cu sites of the lattice (Fig. 1a). The apparent height of the Fe atoms atop the Nsites is ∼3.1 Å, roughly 0.4 Å higher than those on Cu sites. The N binding site is fourfold symmetric (C_{4v}), with four Cu atoms as nearest neighbors, a lateral distance of 1.77 Å away (Fig. 1b). DFT calculations (see Supplementary Note 1 for additional information) indicate that the N atom atop which the magnetic atom is bound is displaced upwards by 0.3 Å with respect to the pristine surface configuration. The calculated magnetic moment for the spin of the Fe atom, considering an onsite Coulomb interactions U = 5 eV, is approximately 4.36 µ_{B}, with µ_{B} the Bohr magneton; this indicates a local spin S = 2. The DFTcalculated valence electron spin density (Fig. 1c) shows that the axial symmetry is largely intact. Thus, we can expect the orbital moment to be preserved in the outofplane direction, while it is quenched inplane. The typical overestimation of the orbital momentum quenching by DFT calculations precludes a quantitative description of L, and thus, of the resulting MAE^{18,19}.
Instead, here we adopt an alternative strategy: we carry out an electronic multiplet calculation based on a pointcharge model (PCM) description of the CF, where electron–electron repulsion between Fe delectrons, spinorbit coupling, and Zeeman contributions are considered explicitly (Supplementary Note 2)^{20,21}. The atomic positions and charges are extracted from the DFT calculations. A similar method was applied successfully to study the spin excitations of Fe on MgO^{7}.
Description of the electronic multiplet
The lowest energy levels derived from the multiplet calculations are shown in Fig. 2a. The CF contribution is separated into its axial and transverse components: the former splits off a tenfold ground state degeneracy, while the latter splits this into two quintuplets. The spinorbit coupling—where we used λ = −9.60 meV for the PCM, and −9.41 meV for the spinorbit model—partially lifts the degeneracy within the two quintuplets. Finally, the magnetic field B_{z} along the outofplane direction breaks all remaining degeneracies. At a nonzero field in the outofplane direction, the lowest two states have orbital moments L_{z} = ±1.98, closely approaching the freeatom value. Below, we will approximate these two states as L_{z} = ±2. Notably, the multiplets evolve under the CF and spinorbit coupling to become nearly pure product states of the S_{z}, L_{z} eigenstates. This separation of the spin and orbital degrees of freedom is permitted by the relative dominance of the CF over the strength of the spinorbit coupling. In fact, the use of the total angular momentum basis is not adequate here, since the magnetic anisotropy terms do not commute with the total angular momentum (\({\hat{\mathbf J}}^2\)and \({\hat{\mathbf J}}_{\it{z}}\)).
When interpreting spin excitation spectroscopy on individual magnetic atoms, it is convenient to employ an effective spin Hamiltonian^{11,12,22}. However, in this situation the unquenched orbital moment makes the effective spin framework incomplete^{23}. Instead, we use the following anisotropic spinorbit Hamiltonian^{23}:
where \(\hat O_k^q\) are the Stevens operators, which in this case are applied to the eigenstates of the orbital moment, and \(B_p^q\) are their associated coefficients. The last term represents the Zeeman energy due to an external field B. As we consider both the spin S and orbital moment L, there is no need to invoke the Landé gfactor. The results of this model, implemented with optimal fitting parameters (see Supplementary Note 3), are also depicted in Fig. 2a. Note that there is perfect agreement between the PCM and the spinorbit model presented in Eq. (1). We additionally confirm these results using electronic multiplet calculations derived using the Wannier Hamiltonian to approximate the crystal and ligand fields produced by the surface atoms (see Supplementary Note 5). This approach provides a more accurate quantitative description, and additionally accounts for charge transfer and surface polarization.
Independent spin and orbital excitations
We perform an IETS measurement with an outofplane field of 4 T, revealing a splitting of the zerofield spin excitation, with threshold voltages at 17.9 ± 0.7 meV and 19.4 ± 0.7 meV, as shown in Fig. 2b. These transitions can only be probed with a tip that is functionalized, in this case by picking up individual Fe atoms from the surface. The results of Fig. 2a allow us to uniquely assign the observed transitions to excitations between specific states. When describing these states, we choose to use product state notation since S_{z} and L_{z} are approximately good quantum numbers here. The lower energy excitations are spinonly transitions (∆S_{z} = ±1, ∆L_{z} = 0) corresponding to an excitation from the ground state \(S_z\rangle L_z\rangle =  \!\! 2\rangle  \!\! 2\rangle \equiv 0\rangle\) to \( \!\! 1\rangle  \!\! 2\rangle \equiv 2\rangle\), corresponding to an excitation threshold voltage V_{02}, as well as from the \( \!+\!2\rangle  \!+\! 2\rangle \equiv 1\rangle\) state to \( \!+\! 1\rangle  \!+\! 2\rangle \equiv 3\rangle\), with threshold V_{13} (Fig. 2d). At zero field, V_{02} = V_{13} = 18.4 ± 0.6 meV. In addition, we observe a higher energy excitation at 73.9 ± 0.8 meV (see Fig. 2b), which we denote by the threshold voltage V_{08}. This feature corresponds to an excitation from the ground state \(0\rangle\) to the excited state \( \!\! 2\rangle  \!+\! 2\rangle \equiv 8\rangle\); i.e., going from the lower spin quintuplet to the upper spin quintuplet (see Fig. 2d). A detailed analysis of the calculated transition strengths (see Supplementary Note 6) confirms that an excitation \(0\rangle \to 8\rangle\) occurs with a much larger amplitude than from other possible paths, such as transitions \(0\rangle \to 6\rangle\) or \(2\rangle \to 8\rangle\). In addition, the energy at which this transition occurs quantitatively agrees with the energy difference between the states \(0\rangle\) and \(8\rangle\) across the various models we implement, namely, the pointcharge and Wannier models (Fig. 2b and Supplementary Fig. 3).
Unlike a conventional spin excitation—in which the tunneling electron’s spin only interacts with the atom’s spin \(\left( {\Delta S_{z} \le 1} \right)\), leaving the orbital moment unchanged—we observe an independent excitation of only the orbital moment, with ∆L_{z} = 4. Although orbital excitations have been previously reported^{24,25}, here we observe a full, independent rotation of an unquenched orbital moment. These transitions are not accounted for by the usual spin exchange terms JS ⋅ σ^{26,27}, even when the orbital and spin degrees of freedom are accounted for, as in Eq. (1).
Rather, this orbital transition can be understood via a cotunneling path that takes into account both the spin and the orbital momentum of the initial, intermediate, and final states, as depicted in Fig. 2c^{28,29}. Since the transition is expected to occur with similar amplitude for the hole and electron charged states, we will focus on the latter for the following discussion. In this case, the dominant channel is mediated through the negatively charged intermediate state \(S_{z} \rangle L_{z}\rangle=  3/2\rangle 0\rangle\). Accordingly, the cotunneling transition amplitude between the ground state \(0\rangle\) and the excited state \(8\rangle\) can be understood by introducing the creation and annihilation operators, \(\hat d_{\sigma _{z}\ell _{z}}^\dagger\) and \(\hat d_{\sigma _{z}\ell _{z}}\), for an electron with spin σ_{z} in an orbital with angular momentum ℓ_{z} (centered on the atom). The dominant transition amplitude between states \(0\rangle\) and \(8\rangle\) is thus proportional to^{28,29}:
This cotunneling path corresponds to a spinup electron tunneling onto the ℓ_{z} = +2 orbital, thus creating a charged virtual state with a net spin S_{z} = −3/2 and orbital moment L_{z} = 0. An electron then tunnels off the ℓ_{z} = −2 orbital, restoring the net spin to S_{z} = −2 and changing the orbital moment to L_{z} = +2, thereby completing the ∆S_{z} = 0, ∆L_{z} = 4 transition. Thus, we show independent transitions of the spin and unquenched orbital angular momenta, where we can rotate one of these atomic degrees of freedom without affecting the other.
At first sight, a ∆L_{z} = 4 transition may seem to violate conservation of total angular momentum. However, we point out that the orbital moment of a freely propagating electron is defined relative to an arbitrary origin, and can therefore, unlike the spin, assume an arbitrary value. An electron tunneling from the tip is thus free to carry an orbital moment, and inelastically excite the atomic orbital moment. Within this framework, conservation of total momentum can be understood in terms of the Einsteinde Haas effect, wherein the angular momentum of the tunneling electron is translated into an infinitesimal rotation of the macroscopic lattice^{30,31}.
We trace the evolution of the magnetic behavior of the single atom as a function of external field: in Fig. 3a–c we show IETS measurements of the spin and orbital excitations, performed for a range of discrete fields up to 5 T. In both cases, we observe the Zeeman effect as a shift toward higher threshold voltages at higher field. The measurements indicate a shift in the threshold voltage of 0.23 ± 0.04 meV/T and 0.31 ± 0.05 meV/T for the spin and orbital transitions, respectively (Fig. 3d). When expressed in terms of an effective S = 2 spin model in the absence of orbital angular momentum^{11}, the shift for the spin excitation would correspond to a Landé factor of ∼3, on par with previously reported large values^{7,8,32}.
In addition, we expect the orbital excitation to correspond to two transitions: \(0\rangle \to 8\rangle\) and \(1\rangle \to 9\rangle\), which should split as a function of magnetic field due to the Zeeman effect. We observe that the step is broadened as the field is increased, which is compatible with a splitting of V_{08} and V_{19}. We note that V_{19} is marked by a step down in the differential conductance, which is due to spinpolarized elastic conductance, combined with a reconfiguration of the occupation of states \(0\rangle\) and \(1\rangle\) around the threshold voltages.
The observed behavior is well reproduced by the transport calculations derived from the PCM. In fact, the high degree of agreement between the experimentally and theoretically derived results here is remarkable, as the pointcharge calculations are based solely on DFT results, and thereby do not have any additional fitting parameters, except for a screening factor applied to the freeatom spinorbit coupling (adjusted only to reproduce the energy of the spin excitation). However, the threshold voltage corresponding to the orbital excitation is off by ∼1.4 meV when comparing the transport calculations to the experimental data. In order to properly compare the evolution of the step, we correct for this shift in Fig. 3c. We note that the measurements shown in panels a and b are obtained on different atoms, using a different functionalized tip, than measurements shown in c and d—this causes a slight offset in the measured threshold voltages, presumably due to the tip field or variations in the local environment. We try to account for these variations, and the ambiguity in defining the threshold energy due to the unusual lineshape of the spin excitations, in the error associated with V_{02}, V_{13}, and V_{08}.
The field dependence of the threshold voltages confirms our assignation of the observed transitions to those belonging to independent excitations of the spin and orbital momentum. The ratio between the rate of change of the V_{08} and V_{02} transitions, among the various models we implement, is consistently between 1.6 and 2 (refer to Supplementary Note 7); experimentally, we observe a ratio of 1.3 ± 0.3. In contrast, the V_{06} and V_{17} transitions, which correspond to full rotations of the orbital moment along with a partial rotation of the spin, are expected to shift much faster under the effect of external field, with a rate of change three times that of V_{02}.
In the absence of nonequilibrium effects, inelastic spin excitations (∆S_{z} = ±1) are characterized by approximately square steps in the differential conductance^{33}, which originate from cotunneling events^{26,27}. However, additional nonlinearities may appear at the threshold voltage due to changes in the instantaneous spin state of the atom, which modify the magnetoresistance of the junction, and thus, the dI/dV lineshapes^{13,34}. The dynamical effects that we observe at the inelastic tunneling threshold voltage for the spin excitation (Fig. 4a) are indicative of relaxation times from state \(1\rangle\) longer than the average time between two tunneling electrons (∼200 ps at 1 nA).
As the presence of nonequilibrium features is attributed to dynamic processes linked to the inelastic electron transport, they are expected to be conductance dependent. We investigate this dependence by performing dI/dV measurements as a function of current setpoint, as shown in Fig. 4a, b. For this range of conductance values, we observe a decrease in the strength of the nonlinearity with increasing tunnel current^{34,35} and a shift in the inelastic steps, both of which are due to the local field from the exchange interaction between the Fe atom and the tip^{36}.
Further insight can be obtained by simulating the nonequilibrium dynamics of the local spin (Fig. 4c). This is done on two fronts: on one hand, starting from the PCM calculation, we calculate the transition rates and the nonequilibrium occupations in the weak coupling limit using a cotunneling description of transport^{28,29}. On the other, we use the spinorbit model Eq. (1) exchange coupled to the itinerant electrons. In both cases, the evolution of the occupation is accounted for by a Pauli master equation^{26,27}. Tracing the occupation of the two lowest spin states as a function of voltage (Fig. 4d) delineates that below the inelastic threshold voltage, the ground state occupation exceeds 90%. Once the applied voltage reaches the excitation threshold, spinflip excitations cause a significant drop in the occupation of \(0\rangle\).
Discussion
By coordinating a magnetic atom atop the fourfold symmetric nitrogen binding of the Cu_{2}N lattice, we have realized a singleatom system with a large magnetic anisotropy, which follows from a preserved orbital angular momentum, an ingredient that is essential to the application of magnetic atoms in magnetic storage and information processing. In this system, under the effects of the CF and spinorbit coupling, the multiplets emerge as nearly pure L and S product states, which allows us to treat these parameters as two independent degrees of freedom. We demonstrate independent control over both the spin and orbital moment, showing a full inversion of the orbital moment by means of a single electron, without affecting the spin.
As control over the orbital angular momentum shows many parallels to that of the spin momentum, we believe that this development adds a new dimension to studies on singleatom magnetism. Moreover, as Fe atoms bound to Nsites are easily manipulable, these results form a promising basis for future research on extended lattices, that can interact through both the spin and orbital angular momentum.
Methods
Experimental considerations
The experiment was conducted using a commercial low temperature, high magnetic field STM (Unisoku USM1300s). The sample was prepared in situ: monolayer insulating islands of Cu_{2}N were grown on a Cu_{3}Au(100) surface via nitrogen sputtering^{17}, and subsequently single Fe atoms were evaporated on the cold sample using electronbeam physical vapor deposition. A variable outofplane magnetic field was applied using a superconducting magnetic coil. IETS measurements were performed using standard lockin detection techniques at base operating temperature (330 mK).
Multiplet calculations for Fe/Cu_{2}N/Cu_{3}Au(100) system
For the multiplet calculations we used an archetypal value of the Hubbard repulsion U = 5.208 eV (U – J = 5 eV)^{37,38}. We have taken the atomic values of <r^{2}> = 1.393 and <r^{4}> = 4.496 atomic units^{23}. Instead of correcting the <r^{2}> and <r^{4}> parameters due to covalency and other known limitations of the point charges, we have taken the spinorbit coupling λ as a fitting parameter to reproduce the 18 meV step. The optimal fitting is found when the spinorbit coupling is screened by a factor 0.738, which translates into a (manybody) effective spinorbit coupling of –9.60 meV. The transport calculations under the cotunneling regime were carried out assuming electronhole symmetry, i.e., \(E_{0  }  E_0  E_{F} = E_{F}  E_0 + E_{0 + }\). For the surface hybridization constants, we take \(V_{k_{F},S} = 0.562\;{\mathrm{eV}}\), and for the tip hybridization \(V_{k_{F}T,d_{{z}^2}} = 0.183\;{\mathrm{eV}} = 6V_{k_{F}T,d_{{x}^2  {y}^2}} = 6V_{k_{F}T,d_{{xy}}}\).
Parameters of the anisotropic spinorbit Hamiltonian
The parameters \(B_p^q\) and λ_{SO} of the spinorbit Hamiltonian (Eq. (1)) were obtained by fitting the corresponding energy spectrum to the results of the multiorbital electronic Hamiltonian at zero magnetic field. The best fit was obtained for \(B_2^0 =  1.404\;{\mathrm{eV}}\), \(B_4^0 = 0.188\;{\mathrm{eV}}\), and \(B_4^4 = 0.16\;{\mathrm{meV}}\), which indicates an almost pure uniaxial easy axis system. The value obtained for the spinorbit coupling is λ_{SO} = −9.41 meV. Details regarding the fitting procedure are delineated in Supplementary Note 3. In addition, the coupling to the surface was taken to be (ρJ_{K,S}) = 0.25, where ρ is the density of states at the Fermi energy and J_{K,S} is the Kondo exchange coupling with the surface, while (ρJ_{K,T}) = 0.0484 for the tip. In addition, a direct tunneling term of (ρT) = 0.25 was also assumed (we have assumed the same density of states for the surface and the tip).
Data availability
All data presented in this work are publicly available with identifier (DOI) https://doi.org/10.5281/zenodo.3959042.
References
Loth, S., Baumann, S., Lutz, C. P., Eigler, D. M. & Heinrich, A. J. Bistability in atomicscale sntiferromagnets. Science 335, 196–199 (2012).
Khajetoorians, A. A., Wiebe, J., Chilian, B. & Wiesendanger, R. Realizing allspinbased logic operations atom by atom. Science 332, 1062–1064 (2011).
Natterer, F. D. et al. Reading and writing singleatom magnets. Nature 543, 226–228 (2017).
Donati, F. et al. Magnetic remanence in single atoms. Science 352, 318–321 (2016).
Khomskii, D. I. Transition Metal Compounds (Cambridge University Press, Cambridge, 2014).
Eriksson, O., Johansson, B., Albers, R. C., Boring, A. M. & Brooks, M. S. S. Orbital magnetism in Fe, Co, and Ni. Phys. Rev. B 42, 2707–2710 (1990).
Baumann, S. et al. Origin of perpendicular magnetic anisotropy and large orbital moment in Fe atoms on MgO. Phys. Rev. Lett. 115, 237202 (2015).
Rau, G. et al. Reaching the magnetic anisotropy limit of a 3d metal atom. Science 344, 988–992 (2014).
Choi, T. & Gupta, J. A. Building blocks for studies of nanoscale magnetism: adsorbates on ultrathin insulating Cu_{2}N. J. Phys. Condens. Mat. 26, 394009 (2014).
Hirjibehedin, C. F., Lutz, C. P. & Heinrich, A. J. Spin coupling in engineered atomic structures. Science 312, 1021–1024 (2006).
Hirjibehedin, C. F. et al. Large magnetic anisotropy of a single atomic spin embedded in a surface molecular network. Science 317, 1199–1203 (2007).
Otte, A. F. et al. The role of magnetic anisotropy in the Kondo effect. Nat. Phys. 4, 847–850 (2008).
Loth, S. et al. Controlling the state of quantum spins with electric currents. Nat. Phys. 6, 340–344 (2010).
Bryant, B., Spinelli, A., Wagenaar, J. J. T., Gerrits, M. & Otte, A. F. Local control of single atom magnetocrystalline anisotropy. Phys. Rev. Lett. 111, 127203 (2013).
Spinelli, A., Bryant, B., Delgado, F., FernándezRossier, J. & Otte, A. F. Imaging of spin waves in atomically designed nanomagnets. Nat. Mater. 13, 782–785 (2014).
Spinelli, A., Rebergen, M. P. & Otte, A. F. Atomically crafted spin lattices as model systems for quantum magnetism. J. Phys. Condens. Mat. 27, 243203 (2015).
Gobeil, J., Coffey, D., Wang, S.J. & Otte, A. F. Large insulating nitride islands on Cu_{3}Au as a template for atomic spin structures. Surf. Sci. 679, 202–206 (2019).
Błoński, P. et al. Magnetocrystalline anisotropy energy of Co and Fe adatoms on the (111) surfaces of Pd and Rh. Phys. Rev. B 81, 104426 (2010).
Peters, L. et al. Correlation effects and orbital magnetism of Co clusters. Phys. Rev. B 93, 224428 (2016).
Ferrón, A., Delgado, F. & FernándezRossier, J. Derivation of the spin Hamiltonians for Fe in MgO. N. J. Phys. 17, 033020 (2015).
Lado, J. L., Ferrón, A. & FernándezRossier, J. Exchange mechanism for electron paramagnetic resonance of individual adatoms. Phys. Rev. B 96, 205420 (2017).
Donati, F. et al. Magnetic moment and anisotropy of individual Co atoms on graphene. Phys. Rev. Lett. 111, 236801 (2013).
Abragam, A. & Bleaney, B. Electron Paramagnetic Resonance of Transition Ions (Clarendon Press, Oxford, 1986).
Bryant, B. et al. Controlled complete suppression of singleatom inelastic spin and orbital cotunneling. Nano Lett. 15, 6542–6546 (2015).
Kiraly, B. et al. An orbitally derived singleatom magnetic memory. Nat. Commun. 9, 3904 (2018).
Ternes, M. Probing magnetic excitations and correlations in single and coupled spin systems with scanning tunneling spectroscopy. Prog. Surf. Sci. 92, 83–115 (2017).
Delgado, F. & FernándezRossier, J. Spin decoherence of magnetic atoms on surfaces. Prog. Surf. Sci. 92, 40–82 (2017).
Delgado, F. & FernándezRossier, J. Cotunneling theory of atomic spin inelastic electron tunneling spectroscopy. Phys. Rev. B 84, 045439 (2011).
Gálvez, J. R., Wolf, C., Delgado, F. & Lorente, N. Cotunneling mechanism for allelectrical electron spin resonance of single adsorbed atoms. Phys. Rev. B 100, 035411 (2019).
Chudnovsky, E. M. & Garanin, D. A. Rotational states of a nanomagnet. Phys. Rev. B 81, 214423 (2010).
Bloembergen, N., Shapiro, S., Pershan, P. S. & Artman, J. O. Crossrelaxation in spin systems. Phys. Rev. 114, 445–459 (1959).
Chilian, B. et al. Anomalously large g factor of single atoms adsorbed on a metal substrate. Phys. Rev. B 84, 212401 (2011).
Ternes, M. Spin excitations and correlations in scanning tunneling spectroscopy. N. J. Phys. 17, 063016 (2015).
RolfPissarczyk, S. et al. Dynamical negative differential resistance in antiferromagnetically coupled fewatom spin chains. Phys. Rev. Lett. 119, 217201 (2017).
Grundmann, M. The Physics of Semiconductors (SpringerVerlag, Heidelberg, 2006).
Yan, S., Choi, D.J., Burgess, J. A. J., RolfPissarczyk, S. & Loth, S. Control of quantum magnets by atomic exchange bias. Nat. Nanotechnol. 10, 40–45 (2014).
Mazurenko, V. V. et al. Correlation effects in insulating surface nanostructures. Phys. Rev. B 88, 085112 (2013).
Ferrón, A., Lado, J. L. & FernándezRossier, J. Electronic properties of transition metal atoms on Cu_{2}N/Cu(100). Phys. Rev. B 92, 174407 (2015).
Acknowledgements
The authors thank the Netherlands Organisation for Scientific Research (NWO) and the European Research Council (ERC Starting Grant 676895 “SPINCAD”). F.D. acknowledges financial support from Basque Government, grant IT98616 and Canary Islands program Viera y Clavijo (Ref. 2017/0000231). J.W.G. acknowledges financial support from FONDECYT: Iniciación en Investigación 2019 grant N. 11190934 (Chile).
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R.R., D.C., and A.F.O. conceived the experiment, R.R., D.C., and J.G. acquired the data. R.R. analyzed the data. J.W.G. and F.D. performed theoretical calculations. R.R., F.D., and A.F.O. wrote the paper, with considerable contributions from all listed authors. A.F.O. supervised the experimental work.
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Rejali, R., Coffey, D., Gobeil, J. et al. Complete reversal of the atomic unquenched orbital moment by a single electron. npj Quantum Mater. 5, 60 (2020). https://doi.org/10.1038/s4153502000262w
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DOI: https://doi.org/10.1038/s4153502000262w
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