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Hyperfine interaction of individual atoms on a surface

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Science  19 Oct 2018:
Vol. 362, Issue 6412, pp. 336-339
DOI: 10.1126/science.aat7047

Hyperfine spectra of surface atoms

The interaction of nuclei with nonzero spin with electron spins creates small electronic energy. With a scanning tunneling microscope tip, Willke et al. measured these hyperfine interactions for iron and titanium atoms that were manipulated on a magnesium oxide surface. The tip was also used to measure electron paramagnetic resonance spectra. The hyperfine structure of single atoms was sensitive to the binding site of the atom as well as its position relative to other magnetic atoms.

Science, this issue p. 336

Abstract

Taking advantage of nuclear spins for electronic structure analysis, magnetic resonance imaging, and quantum devices hinges on knowledge and control of the surrounding atomic-scale environment. We measured and manipulated the hyperfine interaction of individual iron and titanium atoms placed on a magnesium oxide surface by using spin-polarized scanning tunneling microscopy in combination with single-atom electron spin resonance. Using atom manipulation to move single atoms, we found that the hyperfine interaction strongly depended on the binding configuration of the atom. We could extract atom- and position-dependent information about the electronic ground state, the state mixing with neighboring atoms, and properties of the nuclear spin. Thus, the hyperfine spectrum becomes a powerful probe of the chemical environment of individual atoms and nanostructures.

The hyperfine interaction between an electron and a nuclear spin provides insight into the electronic structure and chemical bonding of atoms, molecules, and solids. It is also key to realizing quantum operations of the nuclear spin (13). Although most experiments rely on ensemble measurement, detection and control of single nuclear spins is possible for diluted molecules in crystals (4), molecules in break junctions (3, 5), ion traps (2), and defects in solids (6, 7). Nevertheless, until now, no experimental tool allowed for imaging of the atomic-scale environment of the nucleus and simultaneous resolution of the hyperfine spectrum, which crucially depends on the local electronic structure.

Atomic resolution, along with atom manipulation, has been achieved by scanning probe methods, and they have been used to study the local electronic structure of atoms and molecules. Scanning probes allow chemical identification (8) and imaging of chemical bonds (9), and they provide access to the structure (10) and dynamics (11, 12) of electron spins. The nuclear properties detected in scanning tunneling microscopy (STM) include changes in vibrational (13) and rotational (14) motion, but the hyperfine interaction has not previously been resolved owing to a limited resolution in energy (15, 16).

Combining STM with electron spin resonance (ESR), as demonstrated for individual iron (Fe) (17, 18) and titanium (Ti) atoms (19, 20), potentially provides the required energy resolution. However, no hyperfine splitting was reported so far. For atoms that have low natural abundances of magnetic nuclei (such as Fe) or multiple magnetic isotopes (such as Ti), it is necessary to study a large number of individual atoms to establish the hyperfine physics. Here we present such a study, aided by a new understanding of the tunneling parameters (21) that improve the signal-to-noise ratio compared to previous ESR-STM experiments (17, 18).

Individual Fe and Ti atoms from sources that have natural isotopic abundance were deposited on two atomic layers of MgO grown on silver (22). First, we examined Fe atoms adsorbed onto an oxygen binding site of the MgO (23) (Fig. 1A). We resonantly excited transitions between the electronic ground state (spin-up) and the first excited state (spin-down) of the Fe atom by using ESR. We used a magnetic field B = 0.9 T and a temperature T = 1.2 K, unless stated otherwise. This excitation led to a change in tunnel current ΔI when driven at the resonance frequency (17) (Fig. 1B). A magnetic tip was used for magnetoresistive readout, leading to different conductance for the two electronic states.

Fig. 1 Hyperfine interaction studied by ESR in a scanning tunneling microscope.

(A) Experimental setup showing different isotopes of single Fe atoms on a bilayer MgO film on Ag(001) in an STM (B = 0.9 T, Bz = 0.1 T, and T = 1.2 K). ESR was performed by applying a radio frequency voltage (VRF) to the tunneling junction (17, 18). SP, spin-polarized; VDC, direct current voltage. (B) ESR spectra of the change in tunnel current for different Fe isotopes (top). The blue line shows Fe that has zero nuclear spin (likely 56Fe; see main text). The orange line shows 57Fe with nuclear spin Embedded Image. Spectra were normalized to unity for 56Fe and given in arbitrary units (a.u.). Electron Zeeman energy gives the center frequency f0, here 19.89 GHz for 56Fe and 19.87 GHz for 57Fe (tunnel conditions: Iset = 12 pA, VDC = 60 mV, and VRF = 60 mV). The inset shows the peak splitting Δf for five different 57Fe atoms. The solid line indicates the error-weighted mean. Shown at the bottom are topographic images of both atoms. (C) Schematic of the energy levels E of the 56Fe atom, compared to those of 57Fe, including hyperfine interaction as a function of the external magnetic field B and the hyperfine constant A (the small nuclear Zeeman energy was neglected).

For 3.4% of Fe atoms (5 out of 147, see inset in Fig. 1B) investigated, the ESR peak was split by Δf = 231 ± 5 MHz, where f is the frequency of the applied radio frequency voltage. We attributed this splitting to the presence of a nuclear moment Embedded Image for 57Fe (2.1% natural abundance). By contrast, the I = 0 isotopes, predominantly 56Fe, showed no splitting. We could not distinguish different I = 0 isotopes and thus label them 56Fe for simplicity. Because the hyperfine splitting Δf is much smaller than the thermal energy kBT/h ≈ 25 GHz, where kB is the Boltzmann constant and h is the Planck constant, the two nuclear states Embedded Image are occupied with equal probability. Thus, the 57Fe peaks each had half the ESR peak height of the single peak observed for 56Fe. Moreover, the simultaneous presence of two peaks indicates that the nuclear spin relaxation time was here much shorter than the time scale of the measurement (~1 ms) (22).

For the magnetic field used here, the electronic Zeeman energy is large compared to the hyperfine interaction. Because the Fe atom on MgO shows a large out-of-plane magnetic anisotropy, the electron spin is quantized along the out-of-plane direction z (23). Thus, the nuclear spin was quantized along z as well, leading to the spin Hamiltonian (24)H = gzμBBzSz + AzIzSz(1)where μB is the Bohr magneton and Sz and Iz are the z-axis spin operators for the electron and nuclear spin, respectively. Parameters gz and Az are the z components of the electron g-factor and the hyperfine coupling constant, respectively. Bz is the z component of the magnetic field. The very small nuclear Zeeman energy is neglected here.

When determining the eigenstates of Eq. 1, the spins can either be aligned or anti-aligned with the magnetic field to give product states Embedded Image, where mS and mI are the electron and nuclear quantum numbers (Fig. 1C). Transitions occurred between the mS = ±2 electronic states (ΔmS = 4) (17) and left the nuclear spin state unchanged (ΔmI = 0), leading to one resonance peak for 56Fe. The spectra were centered at frequency f0 given by the Zeeman energy hf0 = gzμBBzΔmS. The two frequencies observed for 57Fe in Fig. 1B differed because of the relative alignment of the electron and nuclear spin, to give a peak splitting Δf = ΔmSΔmIAz = 4Az, where ΔmI = 1 (24).

In contrast to that of Fe, the hyperfine interaction of Ti atoms was more complex and reflected changes in the local electronic environment (24). The Ti atoms studied here were hydrogenated (19), resulting in an electronic spin of Embedded Image that lacked magnetic anisotropy. Thus, to good approximation, the electron spin followed the magnetic-field direction (19, 20). The hyperfine spectra for Ti located on a bridge binding site (TiB) of MgO (20) (Fig. 2) showed 2I + 1 peaks, one for each nuclear spin state, resulting in six peaks for 47Ti (Embedded Image, 7.4% natural abundance), eight peaks for 49Ti (Embedded Image, 5.4%), and a single peak for the nuclear spin–free isotopes, predominantly 48Ti (I = 0, 73.7%). We found a splitting Δf between adjacent peaks of ~47 MHz for both 47Ti and 49Ti, implying that their nuclear gyromagnetic ratios were equal [see section 2 in (22)]. For all investigated atoms, we found no appreciable dependence of the hyperfine splitting on the magnetic field caused by the proximity of the tip (19) nor on the local electric field induced by the dc bias voltage.

Fig. 2 Hyperfine interaction for titanium on a bridge binding site.

On the left are ESR spectra for 48Ti (blue, nuclear spin I = 0), 47Ti (orange, Embedded Image) and 49Ti (yellow, Embedded Image). The inset shows the bridge binding site. On the right are STM images for each atom. Experimental conditions for 48Ti: f0 = 23.03 GHz, Iset = 8 pA, VDC = 40 mV, and VRF = 30 mV; for 47Ti: f0 = 22.99 GHz, Iset = 8 pA, VDC = 40 mV, and VRF = 30 mV; and for 49Ti: f0 = 22.69 GHz, Iset = 20 pA, VDC = 60 mV, and VRF = 40 mV.

In contrast to ensemble measurements, the binding site of individual atoms could be determined from STM images, and the atom could be moved among binding sites by using atom manipulation. We moved a 47Ti atom to different binding sites (Fig. 3A). We observed a pronounced reduction of the splitting Δf to ~10 MHz (Fig. 3B) when the Ti atom was moved from a bridge to an oxygen site (TiO). The larger splitting was restored by moving the same atom back to a bridge binding site. In Fig. 3C, we show the exact position of the atoms obtained from Fig. 3A and show density functional theory (DFT) calculations (22) of the respective electronic ground state. The statistics for different atoms on the same type of binding site (Fig. 3D) revealed a small, but reproducible, difference in Δf for the two inequivalent bridge binding sites. This difference was caused by different values of gxgy and AxAy (resulting from the low symmetry of the bridge binding site) along with a magnetic field direction BxBy [Fig. 3C and section 1 in (22)].

Fig. 3 Binding site dependence of the hyperfine spectrum of titanium.

(A) By using atom manipulation, a 47Ti atom on a bridge site (site 1, red, TiB) was moved to an oxygen binding site (site 2, green, TiO) and subsequently to a different bridge binding site (site 3, blue). White lines indicate the MgO lattice, with the intercepts corresponding to the positions of oxygen atoms. (B) ESR spectra for the binding sites in (A) (site 1: Iset = 10 pA, VDC = 40 mV, VRF = 40 mV, and f0 = 22.89 GHz; site 2: Iset = 10 pA, VDC = 60 mV, VRF = 7 mV, and f0 = 22.91 GHz; and site 3: Iset = 10 pA, VDC = 40 mV, VRF = 40 mV, and f0 = 22.69 GHz). (C) Sketches (left) show the binding site. Calculated spin density (right) of the binding configurations obtained by DFT. (D) Statistics of the hyperfine splitting Δf for the different binding sites (horizontal bridge site in red, Δf = 44.9 ± 0.5 MHz; vertical bridge site in blue, Δf = 48.1 ± 0.3 MHz; and oxygen site in green, Δf = 10.8 ± 0.7 MHz. For the latter, Δf was obtained by neglecting electric quadrupole interaction which leads to unequal spacing of the peaks). (E) High-resolution ESR spectra for 47Ti (top, Iset = 1.5 pA, VDC = 60 mV, VRF = 25 mV, T = 0.6 K, and f0 = 22.49 GHz) and 49Ti (bottom, Iset = 2.5 pA, VDC = 60 mV, VRF = 25 mV, T = 0.6 K, and f0 = 22.49 GHz) on an oxygen binding site. Black lines are fits to the data, including the anisotropic hyperfine and nuclear electric quadrupole interaction (see main text).

Hyperfine spectra for both isotopes of TiO are shown in high resolution in Fig. 3E. In addition to the strong decrease in Δf compared with that for TiB, the interval between peaks as well as their amplitudes were nonuniform. To describe the spectra, we generalize the hyperfine Hamiltonian in Eq. 1 toH = HEZ + HHF + HNQ(2)Here, the electron Zeeman term Embedded Image and the hyperfine term Embedded Image were generalized to include the x and y spin components, needed for electronic spins lacking strong anisotropy (19), and the hyperfine interaction was allowed to have anisotropy. Moreover, Embedded Image is the nuclear electric quadrupole interaction, caused by the electric field gradient at the position of the nucleus (24), where Pi are the components of the nuclear electric quadrupole tensor (22). This quadrupole term is irrelevant for Embedded Image systems, as in the case of Fe (24). Using the known symmetry of the system, only three fit parameters, Az, Ax = Ay, and Pz were required to give good fits to the complex hyperfine spectrum of TiO (22). Simulated ESR spectra of the experimental data obtained by using EasySpin (25) are superimposed on the data in Fig. 3E. The fits reflect that the hyperfine and the nuclear quadrupole interaction have comparable energies for TiO, resulting in peaks that are irregularly spaced because they are not well approximated by eigenstates of either operator alone. Furthermore, these measurements allowed us to determine the ratio of the nuclear quadrupole moments of 49Q/47Q ≈ 0.79. The excellent agreement with ensemble measurements [49Q/47Q = 0.82 (26)] shows the fidelity of the model and that good accuracy was obtained with this limited number of fit parameters.

Although the electric quadrupole interaction changed the peak intensities and spacings for TiO, the overall reduction in Δf compared to that for TiB was caused by the reduction in the hyperfine coupling constant A. We consider here two contributions (24). The first is the isotropic Fermi contact term originating from a finite spin density of unpaired s electrons at the nucleus induced by interaction with the d electrons. The second is the anisotropic magnetic dipolar interaction of the nuclear spin with the surrounding d electrons, which depends on the orbital symmetry (27). The observed changes in Δf for the different binding sites of Ti were caused by the occupation of different orbitals in the magnetic ground state of the atom (Fig. 3C). We found a larger Fermi contact contribution for TiB (+50 MHz) compared with that for TiO (+19 MHz), presumably caused by a difference in covalency (24) [section 2 in (22)].

More importantly, the three spatial components of the dipolar contribution changed in magnitude and sign for the different binding sites. Because the magnetic field was applied nearly in-plane (Fig. 1A), the in-plane components Ax and Ay contributed the most to Δf. In the case of TiB, the dipolar contribution added to the Fermi contact part for one of the two components (Ax ≈ +61 MHz; Ay ≈ +29 MHz). By contrast, for TiO, both in-plane directions opposed the Fermi contact interaction, resulting in Ax = Ay ≈ +10 MHz. As a result, Δf is smaller for TiO than for TiB. The strength of the hyperfine interaction and the importance of quadrupole interaction revealed the profound change in the chemical environment of the Ti atom upon moving it from a bridge site to an oxygen site: Modeling the hyperfine interaction and taking the DFT ground state into account, we find that the bonding with oxygen reduces the electron spin density at the Ti nucleus for TiO [~−1 instead of ~−2.8 atomic units for TiB (22)]. Moreover, the radial spread of the spin-polarized orbital Embedded Image can be deduced from the hyperfine splitting and the electric quadrupole contribution, which lies at ~(0.5 Å)−3 for both binding sites (22).

Hyperfine spectra can also reveal changes in the magnetic environment, as we demonstrate here using assembled structures of Ti atoms. Figure 4A shows a 47TiB atom with a nuclear spin Embedded Image that was moved to a position ~7 Å from a 48TiO atom (I = 0). Because of the exchange interaction between the electronic spins, an electronic singlet-triplet system was formed [right panel of Fig. 4B and section 3 in (22)] (19, 20). The Zeeman term split the triplet states (T, T0, and T+), whereas the energies of both the singlet S0 and the triplet state T0 remained independent of magnetic field.

Fig. 4 Tuning the hyperfine splitting of a coupled two-atom nanostructure.

(A) Topography of a dimer of Ti atoms created by atom manipulation (separation 7.2 Å). J denotes the exchange coupling strength between them. The bridge-site atom has a nuclear magnetic moment (47TiB, Embedded Image); the oxygen-site atom is nuclear spin–free (48TiO, I = 0). (B) Energy levels of the single 47TiB atom (left) and the dimer (right). For the dimer, the electronic spins form a singlet-triplet system because of exchange coupling (coupling strength J/h = 29.1 ± 0.2 GHz). (C) ESR spectrum of the transitions between T0 and T taken on 47TiB in the dimer reveals a decrease in hyperfine splitting Δf (middle, Iset = 10 pA, VDC = 40 mV, VRF = 20 mV, and f0 = 22.89 GHz) compared with that of the isolated case (top, same data as in Fig. 2A). In the case of the singlet-triplet transition, S0T0, no hyperfine splitting was observed (bottom, Iset = 5 pA, VDC = 40 mV, VRF = 20 mV, and f0 = 29.72 GHz).

Analogously, the hyperfine interaction did not split either S0 or T0, and for the T+ and T states, the splitting remained the same as for the single atom (Fig. 4B). Thus, the hyperfine splitting for the TT0 transition, which involved one of the magnetic field–independent states (T0), decreased to only 27.2 ± 0.4 MHz, roughly half the value of the isolated Ti case (Fig. 4C). Accordingly, the hyperfine splitting of the singlet-triplet transition (S0T0) in Fig. 4C was essentially zero (less than our ~10 MHz linewidth). These transitions allowed us to probe the polarization of the coupled-atom states and to quantify the degree of state mixing to 87% in the singlet state [section 3 in (22)]. Here A remained constant, and instead, the electronic spin magnetization was changed (20). This Ti dimer structure showed that the collective properties that emerged in a correlated multispin structure yielded characteristics sharply different than those of the constituents.

Supplementary Materials

www.sciencemag.org/content/362/6412/336/suppl/DC1

Materials and Methods

Supplementary Text

Figs. S1 to S4

Table S1

References (2832)

  • * On leave from Departamento de Física Aplicada, Universidad de Alicante, San Vicente del Raspeig 03690, Spain.

References and Notes

  1. Materials and methods are available as supplementary materials.
Acknowledgments: We thank B. Melior for expert technical assistance and W. Paul, F. Natterer, and S. Fatayer for further discussions. Funding: We gratefully acknowledge financial support from the Office of Naval Research. P.W., Y.B., T.C., and A.J.H. acknowledge support from the Institute for Basic Science under grant IBS-R027-D1. A.F. acknowledges funding from CONICET (PIP11220150100327) and FONCyT (PICT-2012- 2866). J.L.L. is grateful for financial support from the ETH Fellowship program. J.F.-R. thanks the Fundação para a Ciência e a Tecnologia, under project no. PTDC/FIS-NAN/4662/2014 (016656). A.A. thanks the Engineering and Physical Sciences Research Council, under project no. EP/L011972/1. P.W. acknowledges support from the Alexander von Humboldt Foundation. Author contributions: A.J.H. and C.P.L. supervised the project. P.W., Y.B., K.Y., and T.C. carried out the STM measurements. P.W. performed the analysis and wrote the manuscript with help from all authors. A.F., J.L.L., and J.F.-R. performed the DFT calculations. All authors discussed the results and edited the manuscript. Competing interests: None declared. Data and materials availability: All data needed to evaluate the conclusions in the paper are present in the paper and/or the supplementary materials. Additional data related to this paper may be requested from the authors.
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