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Measurement of Fast Electron Spin Relaxation Times with Atomic Resolution

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Science  24 Sep 2010:
Vol. 329, Issue 5999, pp. 1628-1630
DOI: 10.1126/science.1191688

Abstract

Single spins in solid-state systems are often considered prime candidates for the storage of quantum information, and their interaction with the environment the main limiting factor for the realization of such schemes. The lifetime of an excited spin state is a sensitive measure of this interaction, but extending the spatial resolution of spin relaxation measurements to the atomic scale has been a challenge. We show how a scanning tunneling microscope can measure electron spin relaxation times of individual atoms adsorbed on a surface using an all-electronic pump-probe measurement scheme. The spin relaxation times of individual Fe-Cu dimers were found to vary between 50 and 250 nanoseconds. Our method can in principle be generalized to monitor the temporal evolution of other dynamical systems.

When a magnetic atom is placed in a solid or onto a surface, it can exchange energy and angular momentum with the local environment, giving a finite lifetime to its excited spin states. For non-itinerant (localized) electron systems, these interactions occur on the atomic length scale and on a time scale generally in the pico- to microsecond range. Magnetic resonance techniques are widely used to measure spin relaxation times (1), but achieving high spatial resolution of individual spins rather than ensembles has remained a challenge (24). Spin-polarized scanning tunneling microscopy (STM), by contrast, can probe static magnetic properties on the atomic scale, such as complex magnetic order (5), g-values (6), anisotropy (7, 8) and exchange energies (9, 10). However, the bandwidth of conventional STM current amplifiers (11) is insufficient to directly access typical spin relaxation times. Efforts to enhance the STM’s temporal resolution through faster current amplifiers (12) or pulsed laser techniques (13, 14) have so far lacked atomic spatial resolution.

Here we show that the combination of an all-electronic pump-probe scheme with a spin-sensitive contrast mechanism (15, 16) allows the STM to measure electron spin relaxation times of individual atoms with nanosecond time resolution. In this pump-probe scheme (Fig. 1), we apply a strong voltage pulse (the pump pulse) across the tunnel junction to create spin excitations of the surface atom and a weaker voltage pulse (the probe pulse) to interrogate the state of the atom’s spin at a time Δt after the pump pulse (17). Integrating the probe-pulse current over many pump-probe cycles and slowly varying Δt allows us to map out the average dynamical evolution of the atom’s spin.

Fig. 1

Spin-sensitive pump-probe measurement scheme. The conductance of the STM tunnel junction varies according to the alignment of the sample spin with the tip spin. A series of fast voltage pulses with voltage Vpump for the pump pulse and Vprobe for the probe pulse is sent to the tip. Measurement of the time-averaged probe-pulse current as a function of the delay time between the pulses, Δt, reveals the dynamical evolution of the sample spin.

Atomic-scale structures having long spin relaxation times may have applications in information storage or quantum information processing (18). It was shown that large easy-axis magnetic anisotropy can lead to long spin relaxation times (19) that are sufficient for coherent spin manipulation (20). Fe atoms placed on a Cu2N overlayer on a Cu(100) surface have shown considerable magneto-crystalline anisotropy (8). Cu2N binds the Fe atoms in a polar-covalent network that enables large anisotropy and decouples the adatoms from the Cu conduction electrons (10, 21, 22), allowing Fe to retain its free atom spin of S = 2 (8). Here we increased the easy-axis anisotropy of an Fe atom by placing it adjacent to a Cu adatom (Fig. 2A). We probed the dimer using spin-excitation spectroscopy (Fig. 2B) and found the first excitation at a threshold voltage of Vthr = 16.7 mV, a factor of 4 higher than for the individual Fe atom. This indicates an unusually large easy-axis anisotropy, and indeed we find spin relaxation times that exceed 200 ns.

Fig. 2

Measurement of spin relaxation time. (A) STM topograph of an Fe-Cu dimer and a Cu adatom (yellow: high; blue: low). (B) Spin excitation spectra dI/dV versus voltage, of an Fe-Cu dimer and a Cu adatom measured with a non–spin-polarized tip at magnetic field B = 7 T. Steps in dI/dV indicate spin excitation energies. (C) Pump-probe measurements, ΔN versus Δt, at B = 7 T. Region I: probe pulse precedes the pump pulse; region II: pump and probe pulses overlap (fig. S1) (17); region III: probe pulse follows the pump pulse and senses the postexcitation dynamics of the system. Insets depict the relative orientation of tip and sample spins. For the Fe-Cu dimer (top panel) ΔN decays exponentially in region III, with a spin relaxation time of T1 = 87 ± 1 ns obtained from an exponential fit (magenta). Control experiments on the same Fe-Cu dimer but without spin sensitivity in the tip (middle panel) and on a Cu atom with spin-sensitivity in the tip (bottom panel).

Spin excitations of the surface atom are driven by inelastic scattering of the tunneling electrons (6). In this process, the pump voltage must exceed the threshold voltage, Vthr, required to drive the atom’s spin from the ground state to an excited state. In general, the magnetic orientation of an excited spin state will be different from that of the ground state. We can sense the orientation of the surface atom’s spin by magneto-resistive tunneling with a spin-polarized tip (Fig. 1) (17). The tunnel current that flows during the probe pulse then depends on the projection of the surface atom’s spin along the spin-polarization axis of the tip.

A pump-probe measurement of an Fe-Cu dimer at 0.6 K temperature and 7 T magnetic field is shown in Fig. 2C. In our experiments, we record the probe-pulse current, which can be expressed as the number of electrons per probe pulse, N. We plot ΔN = Nt) − N(−600 ns), the change in N with respect to its value when the probe pulse precedes the pump pulse, a condition in which the spin is in its ground state during the probe pulse. The behavior of ΔN for positive delay times reveals the dynamical evolution of the Fe-Cu dimer after the end of the pump pulse. Between pump and probe pulse, no voltage was applied that could disturb the free evolution of the surface atom's spin. We observe ΔN to be negative and to exponentially decay to zero as Δt is increased. ΔN is expected to be negative: In the ground state, the surface spin is aligned nearly parallel to the spin-polarization axis of the tip. Any spin excitation reduces the projection of the surface spin along the polarization axis of the tip and hence reduces the conductance of the tunnel junction. The exponential decay of ΔN is characteristic for a system with a single rate-limiting relaxation mechanism. Fitting an exponential to the time dependence of ΔN yields a relaxation time of T1 = 87 ± 1 ns.

To demonstrate that the observed exponential decay is indeed due to spin relaxation, we performed two control experiments. First, we repeated the measurement on the same Fe-Cu dimer but with a non–spin-polarized tip (Fig. 2C). We switched between spin-polarized and non–spin-polarized STM tips by means of the reversible transfer of a Mn atom from the surface to the apex of the tip (15). Without spin polarization of the tip, the conductance of the tunnel junction is insensitive to the orientation of the dimer spin, and we correspondingly observe ΔN to be zero. Second, we repeated the measurement with a spin-polarized tip but on a Cu adatom, which has no features in its spin excitation spectrum (Fig. 2B), consistent with having no net spin. As expected, we observe ΔN to be zero in this case (Fig. 2C).

We tested whether the pump-probe measurement was itself affecting the spin relaxation time and found that T1 does not change under variation of the amplitude and widths of the pump and probe pulses and the tip-sample separation (Fig. 3B and fig. S2). However, the magnitude of the pump-probe signal, ΔN, depends strongly on the pump voltage, with a distinct onset at Vthr, below which the pump pulse does not lead to a detectable spin relaxation signal (Fig. 3A). This observation agrees with the spin excitation spectrum, where the first spin excitation is observed at the same threshold voltage (Fig. 2B). The polarity of the pump pulse is not crucial, but negative voltages help in exciting the Fe-Cu dimer’s spin by spin-momentum transfer from the spin-polarized tip (15).

Fig. 3

Threshold dependence of spin excitation at B = 7 T. (A) Pump-probe signal ΔN versus pump voltage Vpump, for Δt = 50 ns, exhibiting the same threshold voltage observed in the spin excitation spectrum (Fig. 2B). The solid line is a fit to the data with a two-state model (29). (B) Spin relaxation time, T1, is independent of the pump voltage. (C) Energy-level diagram of the spin states of the Fe-Cu dimer as a function of the magnetic quantum number, m. The measured relaxation time, T1, corresponds to the |m = −2〉 → |+2〉 transition.

The pump-probe measurements corroborate the finding of large easy-axis magnetic anisotropy for the Fe-Cu dimers. Such anisotropy gives rise to a spin state distribution with two low-lying states, |+2〉 and |−2〉, that are separated by an energy barrier (Fig. 3C). In a magnetic field along the easy axis, |+2〉 is the ground state and |−2〉 a long-lived excited state. Excitation of the Fe-Cu dimer over the barrier starts with a transition from |+2〉 to |+1〉 and requires at least eVthr energy (Fig. 3C, red arrow), which results in the threshold behavior found in the pump-probe measurement (Fig. 3A). Once excited to the |+1〉 state, successive excitations and de-excitations (Fig. 3C, light red arrows) are immediately possible as none require energy exceeding eVthr. Upon termination of the pump pulse, the spin can be in any of the states but relaxes to either |+2〉 or |−2〉 on a time scale that is as yet too rapid for us to observe (15). The time-dependent signal recorded in the pump-probe measurement for t > 0 (Fig. 2C, region III) then corresponds to the relaxation from the long-lived |−2〉 state (Fig. 3C, green arrow). At 0.6 K the thermal energy is insufficient to relax over the energy barrier, and indeed no thermally activated relaxation is observed for temperatures between 0.6 and 10 K (fig. S3). Hence, the relaxation out of |−2〉 is likely due to magnetic tunneling (23, 24), as we discuss next.

Figure 4A shows that ΔN decays as a single exponential for all values of magnetic field, but the relaxation time varies strongly with magnetic field. T1 first grows with magnetic field, but declines rapidly above ~6 T (Fig. 4B). A similar nonmonotonous field dependence of T1 was recently observed for quantum tunneling of magnetization in molecular magnets (19). Finite transverse anisotropy makes magnetic tunneling possible for Fe-Cu dimers by mixing the |−2〉 and |+2〉 states. As the magnetic field is increased from zero, the Zeeman energy increasingly splits these states, which reduces the tunneling matrix element between them and thereby increases T1 (23). The reduction in T1 above 6 T indicates a nonzero angle between the magnetic field and the easy magnetic axis of the Fe-Cu dimer. A transverse component of the magnetic field increases mixing of the spin states and shortens T1 (25).

Fig. 4

Field and site dependence of the spin relaxation time. (A) Pump-probe measurements for different magnetic fields on an Fe-Cu dimer; solid lines are exponential fits. (B) T1 as a function of magnetic field for the two Fe-Cu dimers shown in the accompanying 5-nm by 5-nm STM topographs.

One of the Fe-Cu dimers in Fig. 4B always exhibits a larger T1 than the other. We speculate that this variation is due to differences in the nearby surface features as seen in the accompanying topographs. This observation emphasizes the capability of the all-electronic pump-probe technique presented here to resolve local variations in the spin relaxation time with atomic precision.

The pump-probe scheme we have described can be used to monitor the temporal evolution of any excitation provided (i) the excitation can be driven by tunneling electrons; (ii) the conductance of the tunnel junction exhibits a postexcitation time dependence; and (iii) the system evolves on an accessible time scale. Excitations fulfilling these requirements include long-lived vibrational excitations, conformational changes of molecules (26) such as in molecular motors (27), or fast localized heating (28). We emphasize that this pump-probe scheme can in principle be used to monitor the dynamical evolution of the excited state, not just its relaxation; with sufficient temporal resolution it should be possible to monitor the vibration of an atom or molecule and even the precession of a spin.

Supporting Online Material

www.sciencemag.org/cgi/content/full/329/5999/1628/DC1

Materials and Methods

Figs. S1 to S3

References

Movie S1

References and Notes

  1. Materials and methods are available as supporting material on Science Online.
  2. We thank B. Melior for technical assistance. S.L., C.P.L., and A.J.H. acknowledge financial support from the Office of Naval Research, S.L. from the Alexander von Humboldt Foundation, and M.E. from European Science Foundation project FunSMARTs II.
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