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Electron paramagnetic resonance of individual atoms on a surface

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Science  23 Oct 2015:
Vol. 350, Issue 6259, pp. 417-420
DOI: 10.1126/science.aac8703

EPR, one atom at a time

Electron paramagnetic resonance (EPR) usually detects atoms with unpaired electrons as ensemble averages. Baumann et al. used a spin-polarized scanning tunneling microscope tip to measure EPR spectra of single iron atoms adsorbed on a magnesium oxide surface at cryogenic temperatures. The measurement depends on the atomic orbital symmetry; no signal was observed for cobalt atoms under the same conditions

Science, this issue p. 417

Abstract

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.

In a spin resonance experiment, radio-frequency (RF) radiation excites transitions between low-energy electron or nuclear spin states. Electron paramagnetic resonance (EPR), also known as electron spin resonance (ESR), reveals, for example, the electronic environment of paramagnetic defects in solids (1) and distances between spin labels in biological macromolecules (2). Conventionally, magnetic resonance depends on absorption and emission of electromagnetic radiation and generally requires a large ensemble of nearly identical spins. However, in certain systems, magnetic resonance can be detected on individual spin centers, notably by optical readout (3) or by force microscopy (4). Couplings between itinerant and localized spins have been exploited to electrically detect magnetic resonance in small ensembles (5), in individual spins in quantum dots (6), in individual P atoms in Si (7, 8), and in individual magnetic molecules in an electromigration device (9).

A promising avenue to improve the spatial resolution of spin measurements is the use of scanning tunneling microscopy (STM). STM can drive inelastic excitations in spin systems (spin excitation spectroscopy), revealing the energy spacing between levels of a quantum spin (10, 11). In addition, spin-polarized STM can measure the spin orientation in magnetic nanostructures via a change in the tunnel current caused by atomic-scale tunneling magnetoresistance (1214). Although spectroscopy in STM offers atomic-scale spatial resolution, it suffers from temperature-limited energy resolution. Previous attempts to combine ESR and STM have focused on the detection of increased noise in the tunnel current I at the spin precession frequency (1517), and a number of theoretical mechanisms for non–spin-polarized contrast have been proposed (18). However, the experiments operated at room temperature, and the presence of a frequency-dependent current signal has been sporadic (18). A recent STM experiment applied an RF electric field to a magnetic molecule (19) and attributed an RF-frequency–dependent dI/dV signal to spin resonance, where V is the tunneling voltage.

A schematic of our experimental setup (Fig. 1A) shows that Fe atoms are separated from the Ag substrate via a one-monolayer MgO film. Iron atoms adsorb on the oxygen binding site of MgO and have four Mg atoms as second-nearest neighbors, in a C4v symmetry (Fig. 1C). This bonding structure results in a strong easy-axis magnetic anisotropy perpendicular to the surface (z direction), i.e., along the Fe-O bond. Figure 1B and fig. S1 (20) show STM topographic images of the Fe atoms studied. The energy landscape of the lowest five states of the Fe atom (Fig. 1D) consists of low-energy states Embedded Imageand Embedded Image that are degenerate states except for the Zeeman splitting, separated by an anisotropy barrier formed by the additional spin states.

Fig. 1 Experimental setup for EPR of Fe on MgO.

(A) Schematic model: a spin-polarized STM tip is brought close to an Fe atom on a thin MgO film. A magnetic field is applied to produce a large in-plane field BX and a small proportional out-of-plane field BZ. Spin resonance of the Fe atom is driven by a gigahertz frequency electric field Embedded Image. (B) Constant-current STM image of Fe (yellow) and Co (green) atoms on a single atomic layer of MgO. EPR curves shown in subsequent figures were measured on the indicated Fe atom. Imaging conditions: 10 pA at 0.1 V, T = 1.2 K, B = 5.375 T. (C) Geometry of Fe atom (yellow) binding on top of O (red) on an MgO layer. (D) Diagram of the five lowest energy levels of the Fe atom. The BZ field splits the lowest two energy levels, Embedded Imageand Embedded Image, by an amount hf0 ≈ 0.1 meV, where h is Planck’s constant.

A spin-polarized (SP) STM tip was fabricated by transferring one Fe atom from the surface to the nonmagnetic tip apex (20). The SP tip was positioned over the Fe atom under study, and a gigahertz frequency voltage VRF was applied between tip and sample, in addition to the DC bias voltage VDC. The RF voltage created a time-dependent electric field between tip and sample (Fig. 1A, blue). This RF electric field drove the resonant transition between states Embedded Imageand Embedded Image. During EPR measurements, we swept the RF frequency and varied the source power to compensate for the frequency-dependent transmission of the wiring, and thereby obtained a constant-amplitude VRF at the tunnel junction (figs. S2 and S3). The DC voltage was used to measure the tunneling magnetoresistance of the tunnel junction with the SP tip, which resulted in a tunnel current that depended on the relative population of states Embedded Imageand Embedded Image (14).

We applied a large static magnetic field, Embedded Image, mostly in the plane of the sample but tilted out by ~2°, which created a strong in-plane magnetic field, BX, and a small out-of-plane field, BZ. The out-of-plane BZ established an energy splitting between states Embedded Imageand Embedded Image, and the in-plane magnetic field BX modified the spin components of these two quantum states to strengthen the spin resonance transition between them (see below). We set BZ so that the frequency f0 of the RF electric field needed to excite the transition between states Embedded Imageand Embedded Image fell at ~25 GHz (~100 μeV). Given the known magnetic moment 5.2 μB (Bohr magneton) of Fe on MgO (21), this energy spacing was obtained for BZ ≈ 0.18 T. At the STM operating temperature of 0.6 K and at low tunnel currents, the spin system was mostly (>75%) in state Embedded Image, except when resonantly excited.

To obtain EPR spectra, we swept the frequency f of the RF electric field and monitored the time-average tunnel current. Figure 2A shows a constant tunnel-current signal over the entire frequency sweep, except for a single EPR peak. The peak position changed linearly with the magnetic field (Fig. 2D). On resonance, the tunnel current increased from the set-point current of 1.0 pA to 1.1 pA. The full-width at half-maximum (FWHM) of the resonance signal was 21 ± 2 MHz, which is limited here by the strong driving RF field and tip-sample vibrations (20). When a non–spin-polarized tip was used, the EPR signal was absent (fig. S11), so the contrast observed represented spin-polarized detection. We excited spin resonance in the Fe on the MgO surface, not on the Fe atom on the tip apex, which served only as spin-polarized detector, owing to its subpicosecond excited-state lifetimes (22).

Fig. 2 EPR spectra of individual Fe atoms.

(A) EPR peaks in the tunnel current as a function of frequency of RF electric field at five different values of B. Tip height setpoint 1 pA at 5 mV, T = 0.6 K, VRF = 5 mV. Plots show the change in tunnel current, ΔI, between RF on and RF off, obtained by chopping VRF at 95 Hz. The spin-polarized tip is positioned at the topographic peak of Fe atom indicated in Fig. 1B (and identified as “FeB” in Fig. 2D). For clarity, traces are offset vertically in proportion to the magnetic field. (B and C) Enlargement of a small frequency window at two B fields as labeled, using the same conditions as in (A). Averaging time was 50 min per data set. (D) EPR peak positions of five different Fe atoms as a function of BZ and B. The B = 0 intercepts of the linear fits (lines) for each atom fall at −0.8 ± 0.9 GHz. We use the mean value of the measured slopes and compare it to the known magnetic moment 5.2 μB of Fe on MgO (21) to infer BZ relative to B (20). STM images of all five atoms are shown in fig. S1.

To understand the mechanism of coherent transition, we describe the spin and orbital nature of the magnetic states Embedded Imageand Embedded Image. Fe on MgO was recently measured with spin excitation spectroscopy and x-ray absorption spectroscopy to determine its low-energy quantum states (21). When bound to MgO, the free-atom’s spin and a large portion of its orbital angular momentum are preserved (21). By using the approximation that the Fe atom is in the d6 configuration and in the lowest Hund’s rule term (orbital moment L = 2 and spin S = 2), the quantum states determined previously (21) are well approximated by the ligand-field Hamiltonian

Embedded Image (1)

Here D = −433 meV gives the axial (out-of-plane) anisotropy; F0 = 2.19 meV is the tetragonal (fourfold rotational) ligand field that describes the splitting between in-plane orbitals (dxy and dx2−y2) that results from the four nearest Mg atoms; λ = −12.6 meV gives the spin-orbit coupling; and the last term determines the Zeeman energy. Operators Lz, L, and L+ refer to the orbital moment’s z-axis and ladder operators. The use of this Hamiltonian, rather than an effective-spin Hamiltonian (1, 11, 14), gives richer insight into the effects of electric fields (20).

We propose that the large RF electric field Embedded Image, applied mostly along z, moves the Fe atom with respect to the MgO lattice. This structural change modifies the ligand field parameters, which results in a time-dependent Hamiltonian H1 that can drive coherent transitions between states Embedded Imageand Embedded Image

Embedded Image(2)

In the absence of an in-plane magnetic field, the largest terms of the eigenstates of H0, expressed in the basis of z-axis orbital and spin quantum numbers Embedded Image, are

Embedded Image (3)Embedded Image (4)

These two states overlap in their orbital components under application of H1 (both contain ML = ±2), but are effectively polarized in their spin component. The absence of overlap in the spin component leads to a nearly vanishing coherent transition rate Embedded Image. In accordance, we did not observe any EPR signals on Fe at BX ≈ 0. When BX >> 0, the states Embedded Imageand Embedded Image contain other Embedded Image components [see (20)] making the spin component less polarized, thus increasing the coherent transition rate.

We did not observe a spin resonance signal for Co atoms on the MgO surface, even though Co’s magnetic moment is similar to that of Fe (21, 23) (fig. S11). The orbital symmetry of Fe matches the fourfold symmetry of the binding site and leads to resonant transitions, whereas the same binding site symmetry does not lead to resonant transitions in Co because its lowest-energy states are dominantly composed of ML = ±3 components. These are not mixed by the fourfold symmetric effect of Embedded Image, so no resonant transitions between states Embedded Imageand Embedded Imageunder application of the time-dependent H1 are expected.

To estimate the magnitude of the driving RF electric field available in our STM geometry, we used a simple plate capacitor model. The distance from the tip to the surface of the Ag substrate is ~0.8 nm, and applying VRF = 5 mV results in an electric field of ~6 × 106 V/m. The effects of similar strengths of electric fields were studied in bulk EPR to modulate parameters of a spin Hamiltonian (24, 25), nitrogen vacancy centers in diamond for the purpose of electric-field sensing (26), and P in Si to electrically control quantum gates (27).

In a traditional EPR experiment, an ensemble average over a large number of spins is required to obtain sufficient signal. Variations in the local environments of individual spins in the ensemble inhomogeneously broaden the EPR peak. We compared the EPR signal of five different Fe atoms in our experiment (Fig. 2D), whose resonance energies at a given magnetic field differ from each other by up to 3 GHz (~10 μeV). However, all resonances move in proportion to the magnetic field. The subtly different local environments lead either to different magnetic moments or to variable tilting of the easy axis relative to the magnetic field. STM images of the local environment of each Fe atom (fig. S1) show no detectable imperfections within ~1 nm of each Fe atom. This comparison demonstrates the importance of single-atom measurement, as the linewidth in the equivalent ensemble measurement would be broadened to ~1 GHz.

To investigate the influence of the tip on the measured EPR spectra, we measured the same set of atoms for a different Fe-terminated tip. The EPR frequency shifted by a constant ~800 MHz for all (except one) atom on the surface (fig. S8). Thus, differences in resonance frequency remain independent of the tip, and energy differences can be interpreted with high accuracy even though the absolute frequencies are somewhat tip dependent. A plausible origin of the observed shift is a local magnetic field created by the spin-polarized tip.

A resonantly driven magnetic moment is typically described with three parameters: (i) the energy relaxation time T1; (ii) the quantum phase coherence time T2; and (iii) the strength of the driving field, or equivalently, the rate at which the driving field coherently rotates the quantum system (Rabi rate Ω).

The energy relaxation time T1 describes the time to relax from the excited state Embedded Image to the ground state Embedded Image. More precisely, it is the time to relax to steady-state population, which typically is thermally distributed. We used an electrical pump-probe technique (28) and observed an exponentially decaying tunnel current yielding T1 = 88 ± 20 μs (Fig. 3A) at the tip height and voltage used in the EPR measurements of Fig. 2. A lower bound of the coherence time T2 (20) can be obtained from the resonance peak width of Δf = 3.6 ± 0.4 MHz (Fig. 3B), which gives T2 exceeding 1/πΔf ≈ 100 ns.

Fig. 3 Determining spin resonance parameters.

(A) Electrical pump-probe measurements to determine T1. Tunnel current shows magnetic state of the Fe atom (indicated in Fig. 1B) as a function of delay time after exciting it with a pulse of VDC = 75 mV lasting 16 μs. Signal decays with time constant T1 = 180 μs (blue curve) when VDC = 0 during the delay time. When VDC = 5 mV to match EPR conditions of Fig. 2, T1 is reduced to 88 μs (green curve), and the signal amplitude is reduced, owing to direct transitions induced by the tunneling electrons. Tip apex and tip position are the same as in the spectra in Fig. 2; T = 0.6 K, B = 5.7 T. (B) EPR peak at conditions that reduce broadening: small drive amplitude VRF = 1 mV, and tip positioned at minimum in f0 (20), setpoint I = 0.56 pA, VDC = 5 mV. Fit of Lorentzian line shape (solid line) gives width Δf = 3.6 MHz and T2 = 88 ns. (C) EPR signal at five drive amplitudes VRF. Same conditions as in (B). The low-amplitude spectra are symmetric. The origin of the asymmetry in the saturated spectra is not known. (D and E) Peak width (FWHM) and height for the spectra in (C). Points show width and height of a Lorentzian fit for each VRF in (C). Curves show simultaneous fit to all points in (C) (20). Fit uses T1 = 139 μs [obtained by interpolating (A) for 0.56 pA] to yield phase coherence time T2 = 210 ± 50 ns and Rabi flop time π/Ω = 1.2 ± 0.1 μs at VRF = 8 mV.

The Rabi rate Ω and a more accurate value of T2 can be determined from the EPR signal as a function of RF drive amplitude (Fig. 3C). Simultaneous fits to all five spectra of Fig. 3C yielded a coherence time T2 = 210 ± 50 ns, and a driving strength of Ω = 2.6 ± 0.3 rad/μs for a driving voltage VRF = 8 mV (20). This gives a Rabi flop time, the time needed to reverse the magnetic state coherently, of π/Ω = 1.2 ± 0.1 μs. Despite the flop time exceeding T2 by a factor of ~6, the EPR peaks reached saturation. As is known from traditional EPR, this saturation occurs because of the long T1 time, which allows the spin to perform a random walk consisting of many successive periods of coherent evolution before T1 elapses (1). We did not observe any Rabi oscillations in pulsed EPR experiments; instead, we observed a simple exponential change in polarization because of the small ratio of T2 to Rabi flop time. We cannot increase VRF much further to improve this ratio without exceeding the spin excitation at 14 meV. Thus, we expect that fully coherent reversal of the spin will require further increases in T2—for example, by increasing the MgO thickness.

Supplementary Materials

www.sciencemag.org/content/350/6259/417/suppl/DC1

Supplementary Text

Figs. S1 to S13

Table S1

References (29, 30)

References and Notes

  1. Supplementary materials are available on Science Online.
  2. Acknowledgments: We thank B. Melior for expert technical assistance and B. A. Jones, S. Gangopadhyay, and R. M. Macfarlane for fruitful discussions. We gratefully acknowledge financial support from the Office of Naval Research. W.P. thanks the Natural Sciences and Engineering Research Council of Canada for fellowship support.
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