LETTERS PUBLISHED ONLINE: 15 DECEMBER 2014 | DOI: 10.1038/NNANO.2014.281
Control of quantum magnets by atomic exchange bias Shichao Yan1,2*, Deung-Jang Choi1,2, Jacob A. J. Burgess1,2, Steffen Rolf-Pissarczyk1,2 and Sebastian Loth1,2* Mixing of discretized states in quantum magnets has a radical impact on their properties. Managing this effect is key for spintronics in the quantum limit. Magnetic fields can modify state mixing and, for example, mitigate destabilizing effects in single-molecule magnets1,2. The exchange bias field3,4 has been proposed as a mechanism for localized control of individual nanomagnets5,6. Here, we demonstrate that exchange coupling with the magnetic tip of a scanning tunnelling microscope provides continuous tuning of spin state mixing in an individual nanomagnet. By directly measuring spin relaxation time with electronic pump–probe spectroscopy7, we find that the exchange interaction acts analogously to a local magnetic field that can be applied to a specific atom. It can be tuned in strength by up to several tesla and cancel external magnetic fields, thereby demonstrating the feasibility of complete control over individual quantum magnets with atomically localized exchange coupling. Miniaturizing spintronic devices to the point where magnetization of the elements of the device becomes quantized is a possible route to achieving quantum computation with magnetic elements2,8,9. Critical to such an approach is the ability to exert local control over the device via a short-range coupling mechanism. The exchange interaction arising from the overlap of electronic wavefunctions is localized to ångström distances. It is used statically in thin-film spintronic devices for pinning of ferromagnetic segments by an adjacent antiferromagnetic layer3,4, with pinning fields reaching the equivalent of several tesla10. Variable exchange interaction across a vacuum gap has been reported in atomic force microscopy (AFM) measurements on antiferromagnetic surfaces using magnetically coated tips11,12, where the distance between the tip and surface magnetic atoms determines the exchange coupling strength12–14. Here, we demonstrate that the exchange interaction with a magnetic tip can be used to control the quantum state mixing of individual few-atom nanomagnets. We used a low-temperature scanning tunnelling microscope (STM) to construct nanomagnets atom by atom, and manipulated their spin states by approaching a magnetic STM tip to selected constituent atoms. Using STMbased electronic pump–probe spectroscopy, we found that the exchange interaction modifies the transition matrix elements between the nanomagnet’s quantized spin states and dictates variations of the spin relaxation time. This approach provides direct, tunable and atomically specific exchange bias control of the quantum nature of a magnet. We focused on a nanomagnet consisting of a linear chain of three Fe atoms on a monatomically thin copper nitride (Cu2N) layer grown on Cu(100). The atoms were separated by 0.72 nm and exhibited a stable antiferromagnetic order in spin-polarized topographs under a magnetic field15 (Fig. 1b). A three-axis vector
magnet was used to align the magnetic field to the easy magnetic axis of the Fe atoms in the Fe trimer (the direction in which the Fe atom is neighboured by two nitrogen atoms, Fig. 1b). A paramagnetic tip, with its magnetic moment aligned to the magnetic field, was prepared by attaching three or four Fe atoms to the tip apex. Spin-polarized electronic pump–probe spectroscopy was used to measure the spin relaxation time of the excited spin states of the trimer (see Methods for details), which can be in excess of 1 μs (Fig. 1c). The collinear alignment of the easy axis, the magnetic field and the magnetic moment of the tip with an accuracy of ±3° maximized the pump–probe signal. When the magnetic field was aligned perpendicular to the easy axis of the Fe atoms, no pump– probe signal could be detected. With collinear alignment the pump–probe signal (at Δt > 0) alternated between negative and positive along the atoms of the trimer (Fig. 1c,d), consistent with antiferromagnetic order of the ground state. Our key finding is that the spin relaxation time T1 of the Fe trimer varies when the tip–sample distance, and consequently the exchange bias coupling between tip and nanomagnet, is changed (Fig. 1c,d). The dependence of T1 on tip–sample distance can be quantified (Fig. 2a). We found that T1 increases exponentially with decreasing tip–sample distance when the tip approaches the centre atom of the trimer. With the tip positioned over the side atoms, T1 decreases exponentially towards 0 and subsequently recovers for the closest approach. At a tunnel conductance below 10 mV, 25 pA (on a side atom), the influence of the tip becomes negligible. We chose this point as z = 0 (taking into account the difference in apparent topographic height between the trimer’s side and centre atoms of 20 pm). At the z = 0 position, T1 converges to the same value, 2.63 ± 0.1 µs, on all three atoms. This is the intrinsic spin lifetime of the unperturbed Fe trimer. The opposing evolution of T1 for side and centre atoms directly verifies that the interaction between tip and Fe trimer is of a magnetic origin. The short-range variation in its strength strongly implicates exchange as the origin of the tip interaction. Other magnetic interactions are possible but can be excluded. We verified that spin transfer torque arising from spin-polarized tunnelling current16 plays no role in tuning T1 by varying the amplitude of the pump and probe pulses while observing no variation in T1 (Fig. 2b). We also measured the spin excitation spectra of the Fe trimer with a non-magnetic tip for different tip–sample distances and found no variation in the magnetic anisotropy (Fig. 2c). This excludes changes in magnetic anisotropy induced by the proximity of the tip17 as the cause of variations in T1. Exchange coupling between tip and trimer is the only other magnetic interaction of sufficient strength to explain the observed variations in T1. To understand the influence of the tip–trimer exchange interaction on the spin relaxation process, we modelled the Fe trimer with an effective spin Hamiltonian incorporating quadratic magnetic
1
Max Planck Institute for the Structure and Dynamics of Matter, 22761 Hamburg, Germany. 2 Max Planck Institute for Solid State Research, 70569 Stuttgart, Germany. *e-mail: [email protected]; [email protected]
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Figure 1 | Spin relaxation time variations of an Fe trimer. a, Schematic of the tip–sample distance-dependent exchange interaction between a magnetic STM tip and an Fe trimer. The black arrows indicate the spin orientations of the atoms in the Fe trimer, while the grey and blue arrows indicate the spin orientation of the magnetic tip at large and small tip–sample distances. The image shows the three-dimensional rendering of a constant-current topograph. The orange arrow indicates the direction of the external magnetic field. b, Top: Constant-current topograph of an Fe trimer on Cu2N/Cu(100) recorded with a spinpolarized tip. Image size, 3.3 × 2.2 nm2. Tunnel junction setpoint, 3 mV, 50 pA. Bottom: Positions of Fe atoms in a trimer on the Cu2N lattice. c, Pump–probe spectra recorded on a side atom of the Fe trimer shown in b. Slow decay of the pump–probe signal as a function of delay time (Δt) is observed for a large tip–sample distance (pink curve, setpoint 10 mV, 1.25 nA) and fast decay for small tip–sample distance (blue curve, 10 mV, 2.5 nA). Inset: Two pump–probe cycles. Pulse amplitudes: pump pulse, Vpump = 35 mV; probe pulse, Vprobe = 5 mV. d, Pump–probe spectra recorded on the centre atom of the Fe trimer in b. Small tip–sample distance (blue curve, 10 mV, 4 nA) features slower decay than a large tip–sample distance (pink curve, 10 mV, 1 nA). Pulse amplitudes: Vpump = 40 mV, Vprobe = 5 mV. Topograph and spectra were measured with an external magnetic field of Bext = 2 T at 0.5 K. Spectra in c and d are normalized by the pump–probe signal at Δt = 0 for clarity.
anisotropy, Zeeman energy and Heisenberg coupling between the three atoms18,19. The anisotropy and coupling parameters were fit such that the model Hamiltonian reproduced the conventional inelastic tunnelling spectra (Supplementary Fig. 1)20,21. Figure 3a shows the spin state energies computed for an isolated trimer with a varying magnetic field. Only two states are at low energy. All other spin states are separated by an energy gap of ∼7.5 meV due to the strong easy-axis anisotropy (>2 meV) and significant antiferromagnetic interaction (1.15 meV). The pump–probe spectra detect spin relaxation between the two low-energy spin states. Decay of the high-energy spin states remains too fast for us to observe. In the absence of external perturbations, the two low-lying spin states of the Fe trimer feature an avoided level crossing, and are the symmetric and antisymmetric superposition states of |+2 –2 +2〉 and |–2 +2 –2〉, where ±2 denotes the expectation value mi , of each atom’s spin along the easy magnetic axis (Fig. 3a inset, Fig. 3b). The mixing of the states at the avoided level crossing is induced by the finite transverse magnetic anisotropy of Fe atoms on the Cu2N surface. Application of a magnetic field moves the trimer away from the avoided level crossing and splits the two lowlying states in energy. They de-mix, becoming mostly |+2 –2 +2〉 and |–2 +2 –2〉, respectively (Fig. 3b, 3c(1)). Electron scattering is the dominant spin relaxation channel for magnetic atoms on the 2
Cu2N/Cu(100) surface22–24. This scattering obeys the selection rule Δmi = {±1, 0} (where Δmi is the change in mi during scattering), and consequently cannot cause a transition between |+2 –2 +2〉 and |–2 +2 –2〉. Therefore, the observed spin relaxation is a direct measure of the degree of state mixing: T1 is short near the avoided level crossing and increases as the trimer’s states de-mix, away from the avoided level crossing. We found that the antiferromagnetic exchange interaction with the magnetic tip modifies the energy splitting between the two low-energy spin states and thereby affects T1 directly. The sign of the change depends on the relative alignment of the tip magnetic moment and atom spin in the trimer. In the anti-aligned case, the energy splitting will increase, and T1 with it. This is observed when the tip approaches the trimer’s centre atom (Fig. 3b, 3c(3)). In contrast, the tip spin and the spins of the trimer’s side atoms are aligned. Approaching the tip counteracts the Zeeman splitting, and T1 decreases (Fig. 3b, 3c(2)). To gain quantitative insight into the exchange bias control of T1 , we modelled the coupling between the magnetic tip and atoms in the Fe trimer as a Heisenberg exchange interaction25, Jts , with exponential dependence on tip–sample distance, Jts = J0 (exp(–γz) − 1). J0 is the coupling coefficient setting the coupling strength, γ is the decay constant, and z is the tip–sample distance
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Figure 2 | Exchange interaction control of the spin relaxation time. a, Variation of the Fe trimer’s spin relaxation time, T1 , as a function of tip position z. Symbols are experimental data recorded on the side atoms (squares and triangles) and centre atom (circles). Inset: The precise locations where data were recorded. Solid lines are the calculated dependence of T1 including exchange coupling with the magnetic tip. More negative values of z indicate smaller tip–sample distance. Tip–sample distance z = 0 was chosen as the tunnel junction setpoint (10 mV, 25 pA) on a side atom. The top axis indicates the exchange interaction energy at each position of the tip as deduced from equation (1) and the spin Hamiltonian model (Supplementary Section 5). b, T1 measured on a side atom of another Fe trimer as a function of pump and probe pulse amplitude (setpoint: 10 mV, 1 nA). Blue circles show the dependence on Vpump with Vprobe = 5 mV, and green squares the dependence on Vprobe with Vpump = −30 mV. Dashed vertical lines indicate the threshold voltage Vthr for spin excitations, as determined in c. The horizontal dashed line is a guide to the eye for T1 = 3.24 µs. c, Differential conductance as a function of voltage, dI/dV(V), recorded on a side atom of the Fe trimer with a non-magnetic tip. The steps in the differential conductance at ±Vthr (dashed lines) are caused by a spin excitation and show no variation in position with different tunnel junction setpoints. Measurement uncertainties in a and b are comparable to the symbol size. Bext = 2 T for all measurements.
(Supplementary Section 2). The calculated variation of T1 with tip–sample distance fits quantitatively to the experimental result (Fig. 2a). Under moderate tunnelling conditions of 6 nA and 10 mV, the interaction reaches a strength of 0.8 meV, far exceeding the possible strength of the dipolar magnetic interaction for this tip–sample distance range. For the tip used to make this set of measurements, we obtained a characteristic decay length for the tip-induced exchange interaction of 60 ±2 pm, matching the decay length of the Fe–Fe direct exchange interaction12,14. However, the decay length varies by up to 50% for different magnetic tips, indicating that the effective exchange interaction across the vacuum gap is sensitive to the atomic configuration of the tip apex. The magnitude of the tip-induced exchange interaction can be expressed as a local magnetic field, Bloc , acting on one atom with amplitude proportional to the exchange coupling strength (Supplementary Section 5): (1) Bloc = B0 exp −γz − 1
where γ is the decay constant of the local magnetic field Bloc , and B0 is the coefficient setting the absolute strength of Bloc. This local magnetic field is analogous to the exchange bias field imposed onto ferromagnetic layers by coupling to antiferromagnetic thin films in spintronic devices3,4. Fitting the tip–sample distance dependence of T1 with the exchange coupling model yields a linear variation of T1 away from the avoided level crossing when |Bext + Bloc| > 0.2 T, where Bext is the strength of the external magnetic field (Supplementary Fig. 4). The rate of change is |dT1/dBloc| = 1.31 ± 0.04 µs T−1 on the centre atom of the trimer, and 1.28 ± 0.04 µs T−1 on the side atoms. In comparison, T1 changes linearly for an external magnetic field in excess of 0.2 T. The measured T1 as a function of Bext on the side and centre atoms differs only by a constant offset that is induced by the local magnetic field, and the rate of change is |dT1/dBext| = 1.32 ± 0.08 µs T−1 (Fig. 3d). The good agreement in the rate of change between the local and external magnetic field dependence of T1 is a consequence of the near-identical response of the trimer’s two low-lying spin states to local and external magnetic fields (Supplementary Sections 4 and 6).
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Figure 3 | Model for the local exchange bias field of the magnetic tip. a, Calculated energy levels of an Fe trimer as a function of external magnetic field Bext (for details see Supplementary Section 1). Inset: Zoom-in to the avoided level crossing of the trimer’s two low-lying spin states. b, Schematic of the avoided level crossing identified in a. Solid lines show evolution of the two states, |φ+〉 and |φ−〉, in an external magnetic field. The colour indicates the amount of mixing between |+2 −2 +2〉 (red) and |−2 +2 −2〉 (blue). Green arrows indicate different scenarios with varied spin relaxation (thicker arrows depict faster spin relaxation): (1) intrinsic relaxation in the external magnetic field, (2) faster relaxation when the local magnetic field Bloc counteracts Bext , and (3) slower relaxation when Bloc adds to Bext. c, Sketches of scenarios (1) to (3), which lead to variations in T1 , depicting the relative orientation of Bext (orange arrow), the spins of the trimer’s Fe atoms (red arrows) and the magnetic tip (blue arrow). Jts is the exchange coupling strength between the magnetic tip and the target Fe atom in the trimer. J1 is the coupling strength between the trimer’s Fe atoms. d, T1 as a function of external magnetic field. Symbols are experimental data for a fixed tunnel junction setpoint (10 mV, 300 pA) measured on a side atom (blue squares) and the centre atom (green squares). Solid lines are calculated T1 accounting for exchange interaction with the tip with strength 0.13 T on a side atom (blue line) and 0.23 T on the centre atom (green line). The intrinsic relaxation time (pink line) is calculated without tip interaction and agrees with the measured intrinsic lifetime T1(z = 0) (open circle) deduced in Fig. 2a. e, Local exchange bias field of the tip, Bloc , as a function of tip position z. Bloc is derived by relating T1(z) (Fig. 2a) with T1(Bext) (d) using Bloc(z) = |T1(z) − T1(0)| · (dT1 /dBext)−1. Symbols are experimental data measured on a side atom (blue) and the centre atom (green). The solid line is a fit using equation (1) (see main text). Error bars are comparable to the symbol size.
This unique property of the Fe trimer permits the establishment of an absolute energy scale for the exchange interaction of the magnetic tip with individual atoms on the surface (Fig. 3e). Surprisingly, the strength of this effective local magnetic field can exceed several tesla, even for moderate tunnelling conditions (for example, 3.2 T at 6 nA and 10 mV). The ability to counteract strong external magnetic fields with the tip interaction opens the possibility for deliberate control of quantum spins. Figure 4a shows that T1 drops smoothly to zero as the local magnetic field applied to the side atom reaches a value equal to the external magnetic field, |Bloc| = Bext. This point marks an avoided level crossing for the trimer’s spin states similar to that at Bext = 0. 4
As the trimer is tuned through the critical point of the avoided level crossing, the two low-energy spin states are expected to change character (Fig. 4a). This can be observed by pump–probe spectroscopy. For |Bloc| < Bext (z > –204 pm), the excited state carries most weight in |−2 +2 −2〉 (Fig. 4a) and the pump–probe signal measured on the side atom is negative at Δt > 0 (Fig. 4b). For |Bloc| > Bext (z < –204 pm), the excited state becomes mostly |+2 –2 +2〉 and the pump–probe signal becomes positive, indicating the reversal of ground and excited states. Directly at the critical point of the avoided level crossing (z = –204 pm), the excited spin state is expected to be an equal superposition of |+2 –2 +2〉 and |–2 +2 –2〉, despite the presence of an external magnetic field. The spin
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Figure 4 | Spin state control using the tip-induced exchange bias field. a, Top: Calculated variation of the composition of the excited spin state showing the probability distribution of |+2 −2 +2〉 and |–2 +2 −2〉. Bottom: T1 as a function of local exchange bias field Bloc , applied to a side atom at fixed external magnetic field Bext = 1 T. b, Pump–probe spectra recorded consecutively for decreasing tip–sample distance from z = −176 pm to z = −239 pm. The avoided level crossing is found at z = −204 pm when the pump–probe signal, ΔI, vanishes for Δt > 0. The pump–probe signal at Δt > 0 is negative for z > −204 pm, indicating a ground-state spin configuration of the trimer in which the side atoms’ spins are aligned with Bext (lower right sketch). For z < −204 pm the pump–probe signal becomes positive, indicating a reversal of the Fe trimer’s ground state and anti-alignment of the side atoms’ spins with Bext (upper right sketch). The sketches depict the relative orientation of the external magnetic field (orange arrow) and the spin orientations of the magnetic tip and Fe atoms in the trimer (red and blue arrows). Jts is the exchange coupling strength between the magnetic tip and the target Fe atom in the trimer. J1 is the coupling strength between the trimer’s Fe atoms. Bext = 1 T and the temperature is 0.5 K for measurements in b, and Vpump = 40 mV and Vprobe = 5 mV.
polarization of the trimer should then vanish. Indeed, no pump–probe signal is detected (purple spectrum, Fig. 4b). The exchange interaction has been proposed as a possible way of controlling atomic spins5,6. This Letter demonstrates that this approach can be extended to fully control quantum spins by tuning spin state mixing. The exchange control shown here solely relies on distance-dependent exchange interaction with a magnetic tip; consequently, it can be extended to other quantum systems exposed on a surface. It is worth noting that spin state reversal through state mixing does not require the input of energy to overcome the magnetic anisotropy barrier and may enable new low-energy spintronic device schemes. Furthermore, we show that pump–probe methods can be used in STM to study physical phenomena in the absence of tunnelling current or electric field effects, enabling sensitive experiments for a broad range of atom–atom or molecule–molecule interactions26.
Methods
Experimental parameters. Experiments were conducted with a Unisoku ultrahighvacuum low-temperature STM. All measurements were carried out at 0.5 K and with the external magnetic field aligned to the easy magnetic axis of Fe with ±3° accuracy using a three-dimensional vector magnet. PtIr tips were sputtered with argon and flashed by electron-beam bombardment for several seconds before use. The Cu(100) crystal was cleaned by several Ar-sputtering and annealing cycles at 850 K. The monatomic Cu2N layer was prepared by sputtering with N2 at 1 kV and annealing to 600 K. The sample was precooled to 4 K, and Fe atoms were deposited by positioning the cold sample in a low flux of Fe vapour from a Knudsen cell. We confirmed that the sample temperature did not exceed 100 K during Fe dosing by replacing the sample with a temperature sensor. Constant-current topographs were filtered with WSxM to remove the background noise27. For inelastic tunnelling spectra, the differential conductance (dI/dV ) was measured using lock-in detection of the tunnelling current by adding 72 µVrms modulation at 730.5 Hz to the sample bias voltage. Pump–probe technique. An all-electronic pump–probe method was used to measure the spin relaxation time on each atom of the Fe trimer. A sequence of alternating pump and probe voltage pulses was sent to the sample using a pulse pattern generator and semi-rigid coaxial wires. The tunnel current resulting from the probe pulses was measured by lock-in detection of the amplitude-modulated probe pulses at 690.6 Hz. In the measurements, the widths of the pulses were 50 ns for the pump pulse and 200 ns for the probe pulse. The pump pulses excited the Fe trimer by inelastic scattering of tunnelling electrons and were fixed at an amplitude of 35 mV or 40 mV (and varied in Fig. 2b). The probe pulses detected the spin state of the trimer by spin-polarized tunnelling. The probe amplitude was maintained at 5 mV, below the threshold for spin excitations (and varied in Fig. 2b).
Between pump and probe pulses, no voltage was applied to avoid disturbing the free evolution of the trimer’s spin. The average dynamical evolution of the Fe trimer was measured by slowly varying the time delay between pump and probe, Δt. The spin relaxation time T1 was determined by fitting an exponential decay function to the delay-time-dependent tunnel current, I(Δt). Magnetic tips were prepared by attaching three or four Fe atoms to the tip apex and yielded a spin polarization of η ≈ 0.1–0.3 (for Bext = 2 T). To optimize the pump–probe signal, the magnetic moment of the tip was aligned to the easy axis of the Fe atoms by a three-axis vector magnet with an accuracy of ±3° in all spatial directions. Spin Hamiltonian. All calculations were based on the spin Hamiltonian for an Fe trimer on the Cu2N surface exchange-coupled to a rigid magnetic moment at the STM tip (for details see Supplementary Sections 1 and 3). Free parameters of the spin Hamiltonian are the Landé g-factor, the uniaxial magneto-crystalline anisotropy D, transverse magnetic anisotropy E and Heisenberg exchange interaction J. Parameters g = 2.1 and E = 0.31 meV were fixed to the values for individual Fe atoms on Cu2N/Cu(100) (ref. 18). J = 1.15 ± 0.1 meV and D = [−2.1 meV, −3.6 meV, −2.1 meV] ± 0.1 meV were determined by fitting dI/dV spectra recorded on each atom of the Fe trimer with calculated spin excitation spectra. Note that the value of D for Fe atoms in the trimer differs from the value for individual atoms19.
Received 29 July 2014; accepted 31 October 2014; published online 15 December 2014
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24. Oberg, J. C. et al. Control of single-spin magnetic anisotropy by exchange coupling. Nature Nanotech. 9, 64–68 (2014). 25. Otte, A F. et al. Spin excitations of a Kondo-screened atom coupled to a second magnetic atom. Phys. Rev. Lett. 103, 107203 (2009). 26. Weymouth, A. J., Hofmann, T. & Giessibl, F. J. Quantifying molecular stiffness and interaction with lateral force microscopy. Science 343, 1120–1122 (2014). 27. Horcas, I. et al. WSXM: a software for scanning probe microscopy and a tool for nanotechnology. Rev. Sci. Instrum. 78, 013705 (2007).
Acknowledgements The authors thank S. Heinze, C. Hübner and D. Pfannkuche for discussions, and E. Weckert and H. Dosch (Deutsches Elektronen-Synchrotron) for providing laboratory space. D.J.C. and J.A.J.B. acknowledge postdoctoral fellowships from the Alexander von Humboldt Foundation. J.A.J.B. acknowledges support from the Natural Sciences and Engineering Research Council of Canada.
Author contributions S.Y. and S.L. conceived the experiment. S.Y. carried out the experiments and performed the analysis and calculations. All authors participated in the experimental work and contributed to writing the manuscript.
Additional information Supplementary information is available in the online version of the paper. Reprints and permissions information is available online at www.nature.com/reprints. Correspondence and requests for materials should be addressed to S.Y. and S.L.
Competing financial interests
The authors declare no competing financial interests.
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Control of quantum magnets by atomic exchange bias Shichao Yan1,2*, Deung-Jang Choi1,2, Jacob A. J. Burgess1,2, Steffen Rolf-Pissarczyk1,2 and Sebastian Loth1,2* Mixing of discretized states in quantum magnets has a radical impact on their properties. Managing this effect is key for spintronics in the quantum limit. Magnetic fields can modify state mixing and, for example, mitigate destabilizing effects in single-molecule magnets1,2. The exchange bias field3,4 has been proposed as a mechanism for localized control of individual nanomagnets5,6. Here, we demonstrate that exchange coupling with the magnetic tip of a scanning tunnelling microscope provides continuous tuning of spin state mixing in an individual nanomagnet. By directly measuring spin relaxation time with electronic pump–probe spectroscopy7, we find that the exchange interaction acts analogously to a local magnetic field that can be applied to a specific atom. It can be tuned in strength by up to several tesla and cancel external magnetic fields, thereby demonstrating the feasibility of complete control over individual quantum magnets with atomically localized exchange coupling. Miniaturizing spintronic devices to the point where magnetization of the elements of the device becomes quantized is a possible route to achieving quantum computation with magnetic elements2,8,9. Critical to such an approach is the ability to exert local control over the device via a short-range coupling mechanism. The exchange interaction arising from the overlap of electronic wavefunctions is localized to ångström distances. It is used statically in thin-film spintronic devices for pinning of ferromagnetic segments by an adjacent antiferromagnetic layer3,4, with pinning fields reaching the equivalent of several tesla10. Variable exchange interaction across a vacuum gap has been reported in atomic force microscopy (AFM) measurements on antiferromagnetic surfaces using magnetically coated tips11,12, where the distance between the tip and surface magnetic atoms determines the exchange coupling strength12–14. Here, we demonstrate that the exchange interaction with a magnetic tip can be used to control the quantum state mixing of individual few-atom nanomagnets. We used a low-temperature scanning tunnelling microscope (STM) to construct nanomagnets atom by atom, and manipulated their spin states by approaching a magnetic STM tip to selected constituent atoms. Using STMbased electronic pump–probe spectroscopy, we found that the exchange interaction modifies the transition matrix elements between the nanomagnet’s quantized spin states and dictates variations of the spin relaxation time. This approach provides direct, tunable and atomically specific exchange bias control of the quantum nature of a magnet. We focused on a nanomagnet consisting of a linear chain of three Fe atoms on a monatomically thin copper nitride (Cu2N) layer grown on Cu(100). The atoms were separated by 0.72 nm and exhibited a stable antiferromagnetic order in spin-polarized topographs under a magnetic field15 (Fig. 1b). A three-axis vector
magnet was used to align the magnetic field to the easy magnetic axis of the Fe atoms in the Fe trimer (the direction in which the Fe atom is neighboured by two nitrogen atoms, Fig. 1b). A paramagnetic tip, with its magnetic moment aligned to the magnetic field, was prepared by attaching three or four Fe atoms to the tip apex. Spin-polarized electronic pump–probe spectroscopy was used to measure the spin relaxation time of the excited spin states of the trimer (see Methods for details), which can be in excess of 1 μs (Fig. 1c). The collinear alignment of the easy axis, the magnetic field and the magnetic moment of the tip with an accuracy of ±3° maximized the pump–probe signal. When the magnetic field was aligned perpendicular to the easy axis of the Fe atoms, no pump– probe signal could be detected. With collinear alignment the pump–probe signal (at Δt > 0) alternated between negative and positive along the atoms of the trimer (Fig. 1c,d), consistent with antiferromagnetic order of the ground state. Our key finding is that the spin relaxation time T1 of the Fe trimer varies when the tip–sample distance, and consequently the exchange bias coupling between tip and nanomagnet, is changed (Fig. 1c,d). The dependence of T1 on tip–sample distance can be quantified (Fig. 2a). We found that T1 increases exponentially with decreasing tip–sample distance when the tip approaches the centre atom of the trimer. With the tip positioned over the side atoms, T1 decreases exponentially towards 0 and subsequently recovers for the closest approach. At a tunnel conductance below 10 mV, 25 pA (on a side atom), the influence of the tip becomes negligible. We chose this point as z = 0 (taking into account the difference in apparent topographic height between the trimer’s side and centre atoms of 20 pm). At the z = 0 position, T1 converges to the same value, 2.63 ± 0.1 µs, on all three atoms. This is the intrinsic spin lifetime of the unperturbed Fe trimer. The opposing evolution of T1 for side and centre atoms directly verifies that the interaction between tip and Fe trimer is of a magnetic origin. The short-range variation in its strength strongly implicates exchange as the origin of the tip interaction. Other magnetic interactions are possible but can be excluded. We verified that spin transfer torque arising from spin-polarized tunnelling current16 plays no role in tuning T1 by varying the amplitude of the pump and probe pulses while observing no variation in T1 (Fig. 2b). We also measured the spin excitation spectra of the Fe trimer with a non-magnetic tip for different tip–sample distances and found no variation in the magnetic anisotropy (Fig. 2c). This excludes changes in magnetic anisotropy induced by the proximity of the tip17 as the cause of variations in T1. Exchange coupling between tip and trimer is the only other magnetic interaction of sufficient strength to explain the observed variations in T1. To understand the influence of the tip–trimer exchange interaction on the spin relaxation process, we modelled the Fe trimer with an effective spin Hamiltonian incorporating quadratic magnetic
1
Max Planck Institute for the Structure and Dynamics of Matter, 22761 Hamburg, Germany. 2 Max Planck Institute for Solid State Research, 70569 Stuttgart, Germany. *e-mail: [email protected]; [email protected]
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Figure 1 | Spin relaxation time variations of an Fe trimer. a, Schematic of the tip–sample distance-dependent exchange interaction between a magnetic STM tip and an Fe trimer. The black arrows indicate the spin orientations of the atoms in the Fe trimer, while the grey and blue arrows indicate the spin orientation of the magnetic tip at large and small tip–sample distances. The image shows the three-dimensional rendering of a constant-current topograph. The orange arrow indicates the direction of the external magnetic field. b, Top: Constant-current topograph of an Fe trimer on Cu2N/Cu(100) recorded with a spinpolarized tip. Image size, 3.3 × 2.2 nm2. Tunnel junction setpoint, 3 mV, 50 pA. Bottom: Positions of Fe atoms in a trimer on the Cu2N lattice. c, Pump–probe spectra recorded on a side atom of the Fe trimer shown in b. Slow decay of the pump–probe signal as a function of delay time (Δt) is observed for a large tip–sample distance (pink curve, setpoint 10 mV, 1.25 nA) and fast decay for small tip–sample distance (blue curve, 10 mV, 2.5 nA). Inset: Two pump–probe cycles. Pulse amplitudes: pump pulse, Vpump = 35 mV; probe pulse, Vprobe = 5 mV. d, Pump–probe spectra recorded on the centre atom of the Fe trimer in b. Small tip–sample distance (blue curve, 10 mV, 4 nA) features slower decay than a large tip–sample distance (pink curve, 10 mV, 1 nA). Pulse amplitudes: Vpump = 40 mV, Vprobe = 5 mV. Topograph and spectra were measured with an external magnetic field of Bext = 2 T at 0.5 K. Spectra in c and d are normalized by the pump–probe signal at Δt = 0 for clarity.
anisotropy, Zeeman energy and Heisenberg coupling between the three atoms18,19. The anisotropy and coupling parameters were fit such that the model Hamiltonian reproduced the conventional inelastic tunnelling spectra (Supplementary Fig. 1)20,21. Figure 3a shows the spin state energies computed for an isolated trimer with a varying magnetic field. Only two states are at low energy. All other spin states are separated by an energy gap of ∼7.5 meV due to the strong easy-axis anisotropy (>2 meV) and significant antiferromagnetic interaction (1.15 meV). The pump–probe spectra detect spin relaxation between the two low-energy spin states. Decay of the high-energy spin states remains too fast for us to observe. In the absence of external perturbations, the two low-lying spin states of the Fe trimer feature an avoided level crossing, and are the symmetric and antisymmetric superposition states of |+2 –2 +2〉 and |–2 +2 –2〉, where ±2 denotes the expectation value mi , of each atom’s spin along the easy magnetic axis (Fig. 3a inset, Fig. 3b). The mixing of the states at the avoided level crossing is induced by the finite transverse magnetic anisotropy of Fe atoms on the Cu2N surface. Application of a magnetic field moves the trimer away from the avoided level crossing and splits the two lowlying states in energy. They de-mix, becoming mostly |+2 –2 +2〉 and |–2 +2 –2〉, respectively (Fig. 3b, 3c(1)). Electron scattering is the dominant spin relaxation channel for magnetic atoms on the 2
Cu2N/Cu(100) surface22–24. This scattering obeys the selection rule Δmi = {±1, 0} (where Δmi is the change in mi during scattering), and consequently cannot cause a transition between |+2 –2 +2〉 and |–2 +2 –2〉. Therefore, the observed spin relaxation is a direct measure of the degree of state mixing: T1 is short near the avoided level crossing and increases as the trimer’s states de-mix, away from the avoided level crossing. We found that the antiferromagnetic exchange interaction with the magnetic tip modifies the energy splitting between the two low-energy spin states and thereby affects T1 directly. The sign of the change depends on the relative alignment of the tip magnetic moment and atom spin in the trimer. In the anti-aligned case, the energy splitting will increase, and T1 with it. This is observed when the tip approaches the trimer’s centre atom (Fig. 3b, 3c(3)). In contrast, the tip spin and the spins of the trimer’s side atoms are aligned. Approaching the tip counteracts the Zeeman splitting, and T1 decreases (Fig. 3b, 3c(2)). To gain quantitative insight into the exchange bias control of T1 , we modelled the coupling between the magnetic tip and atoms in the Fe trimer as a Heisenberg exchange interaction25, Jts , with exponential dependence on tip–sample distance, Jts = J0 (exp(–γz) − 1). J0 is the coupling coefficient setting the coupling strength, γ is the decay constant, and z is the tip–sample distance
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(Supplementary Section 2). The calculated variation of T1 with tip–sample distance fits quantitatively to the experimental result (Fig. 2a). Under moderate tunnelling conditions of 6 nA and 10 mV, the interaction reaches a strength of 0.8 meV, far exceeding the possible strength of the dipolar magnetic interaction for this tip–sample distance range. For the tip used to make this set of measurements, we obtained a characteristic decay length for the tip-induced exchange interaction of 60 ±2 pm, matching the decay length of the Fe–Fe direct exchange interaction12,14. However, the decay length varies by up to 50% for different magnetic tips, indicating that the effective exchange interaction across the vacuum gap is sensitive to the atomic configuration of the tip apex. The magnitude of the tip-induced exchange interaction can be expressed as a local magnetic field, Bloc , acting on one atom with amplitude proportional to the exchange coupling strength (Supplementary Section 5): (1) Bloc = B0 exp −γz − 1
where γ is the decay constant of the local magnetic field Bloc , and B0 is the coefficient setting the absolute strength of Bloc. This local magnetic field is analogous to the exchange bias field imposed onto ferromagnetic layers by coupling to antiferromagnetic thin films in spintronic devices3,4. Fitting the tip–sample distance dependence of T1 with the exchange coupling model yields a linear variation of T1 away from the avoided level crossing when |Bext + Bloc| > 0.2 T, where Bext is the strength of the external magnetic field (Supplementary Fig. 4). The rate of change is |dT1/dBloc| = 1.31 ± 0.04 µs T−1 on the centre atom of the trimer, and 1.28 ± 0.04 µs T−1 on the side atoms. In comparison, T1 changes linearly for an external magnetic field in excess of 0.2 T. The measured T1 as a function of Bext on the side and centre atoms differs only by a constant offset that is induced by the local magnetic field, and the rate of change is |dT1/dBext| = 1.32 ± 0.08 µs T−1 (Fig. 3d). The good agreement in the rate of change between the local and external magnetic field dependence of T1 is a consequence of the near-identical response of the trimer’s two low-lying spin states to local and external magnetic fields (Supplementary Sections 4 and 6).
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This unique property of the Fe trimer permits the establishment of an absolute energy scale for the exchange interaction of the magnetic tip with individual atoms on the surface (Fig. 3e). Surprisingly, the strength of this effective local magnetic field can exceed several tesla, even for moderate tunnelling conditions (for example, 3.2 T at 6 nA and 10 mV). The ability to counteract strong external magnetic fields with the tip interaction opens the possibility for deliberate control of quantum spins. Figure 4a shows that T1 drops smoothly to zero as the local magnetic field applied to the side atom reaches a value equal to the external magnetic field, |Bloc| = Bext. This point marks an avoided level crossing for the trimer’s spin states similar to that at Bext = 0. 4
As the trimer is tuned through the critical point of the avoided level crossing, the two low-energy spin states are expected to change character (Fig. 4a). This can be observed by pump–probe spectroscopy. For |Bloc| < Bext (z > –204 pm), the excited state carries most weight in |−2 +2 −2〉 (Fig. 4a) and the pump–probe signal measured on the side atom is negative at Δt > 0 (Fig. 4b). For |Bloc| > Bext (z < –204 pm), the excited state becomes mostly |+2 –2 +2〉 and the pump–probe signal becomes positive, indicating the reversal of ground and excited states. Directly at the critical point of the avoided level crossing (z = –204 pm), the excited spin state is expected to be an equal superposition of |+2 –2 +2〉 and |–2 +2 –2〉, despite the presence of an external magnetic field. The spin
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Figure 4 | Spin state control using the tip-induced exchange bias field. a, Top: Calculated variation of the composition of the excited spin state showing the probability distribution of |+2 −2 +2〉 and |–2 +2 −2〉. Bottom: T1 as a function of local exchange bias field Bloc , applied to a side atom at fixed external magnetic field Bext = 1 T. b, Pump–probe spectra recorded consecutively for decreasing tip–sample distance from z = −176 pm to z = −239 pm. The avoided level crossing is found at z = −204 pm when the pump–probe signal, ΔI, vanishes for Δt > 0. The pump–probe signal at Δt > 0 is negative for z > −204 pm, indicating a ground-state spin configuration of the trimer in which the side atoms’ spins are aligned with Bext (lower right sketch). For z < −204 pm the pump–probe signal becomes positive, indicating a reversal of the Fe trimer’s ground state and anti-alignment of the side atoms’ spins with Bext (upper right sketch). The sketches depict the relative orientation of the external magnetic field (orange arrow) and the spin orientations of the magnetic tip and Fe atoms in the trimer (red and blue arrows). Jts is the exchange coupling strength between the magnetic tip and the target Fe atom in the trimer. J1 is the coupling strength between the trimer’s Fe atoms. Bext = 1 T and the temperature is 0.5 K for measurements in b, and Vpump = 40 mV and Vprobe = 5 mV.
polarization of the trimer should then vanish. Indeed, no pump–probe signal is detected (purple spectrum, Fig. 4b). The exchange interaction has been proposed as a possible way of controlling atomic spins5,6. This Letter demonstrates that this approach can be extended to fully control quantum spins by tuning spin state mixing. The exchange control shown here solely relies on distance-dependent exchange interaction with a magnetic tip; consequently, it can be extended to other quantum systems exposed on a surface. It is worth noting that spin state reversal through state mixing does not require the input of energy to overcome the magnetic anisotropy barrier and may enable new low-energy spintronic device schemes. Furthermore, we show that pump–probe methods can be used in STM to study physical phenomena in the absence of tunnelling current or electric field effects, enabling sensitive experiments for a broad range of atom–atom or molecule–molecule interactions26.
Methods
Experimental parameters. Experiments were conducted with a Unisoku ultrahighvacuum low-temperature STM. All measurements were carried out at 0.5 K and with the external magnetic field aligned to the easy magnetic axis of Fe with ±3° accuracy using a three-dimensional vector magnet. PtIr tips were sputtered with argon and flashed by electron-beam bombardment for several seconds before use. The Cu(100) crystal was cleaned by several Ar-sputtering and annealing cycles at 850 K. The monatomic Cu2N layer was prepared by sputtering with N2 at 1 kV and annealing to 600 K. The sample was precooled to 4 K, and Fe atoms were deposited by positioning the cold sample in a low flux of Fe vapour from a Knudsen cell. We confirmed that the sample temperature did not exceed 100 K during Fe dosing by replacing the sample with a temperature sensor. Constant-current topographs were filtered with WSxM to remove the background noise27. For inelastic tunnelling spectra, the differential conductance (dI/dV ) was measured using lock-in detection of the tunnelling current by adding 72 µVrms modulation at 730.5 Hz to the sample bias voltage. Pump–probe technique. An all-electronic pump–probe method was used to measure the spin relaxation time on each atom of the Fe trimer. A sequence of alternating pump and probe voltage pulses was sent to the sample using a pulse pattern generator and semi-rigid coaxial wires. The tunnel current resulting from the probe pulses was measured by lock-in detection of the amplitude-modulated probe pulses at 690.6 Hz. In the measurements, the widths of the pulses were 50 ns for the pump pulse and 200 ns for the probe pulse. The pump pulses excited the Fe trimer by inelastic scattering of tunnelling electrons and were fixed at an amplitude of 35 mV or 40 mV (and varied in Fig. 2b). The probe pulses detected the spin state of the trimer by spin-polarized tunnelling. The probe amplitude was maintained at 5 mV, below the threshold for spin excitations (and varied in Fig. 2b).
Between pump and probe pulses, no voltage was applied to avoid disturbing the free evolution of the trimer’s spin. The average dynamical evolution of the Fe trimer was measured by slowly varying the time delay between pump and probe, Δt. The spin relaxation time T1 was determined by fitting an exponential decay function to the delay-time-dependent tunnel current, I(Δt). Magnetic tips were prepared by attaching three or four Fe atoms to the tip apex and yielded a spin polarization of η ≈ 0.1–0.3 (for Bext = 2 T). To optimize the pump–probe signal, the magnetic moment of the tip was aligned to the easy axis of the Fe atoms by a three-axis vector magnet with an accuracy of ±3° in all spatial directions. Spin Hamiltonian. All calculations were based on the spin Hamiltonian for an Fe trimer on the Cu2N surface exchange-coupled to a rigid magnetic moment at the STM tip (for details see Supplementary Sections 1 and 3). Free parameters of the spin Hamiltonian are the Landé g-factor, the uniaxial magneto-crystalline anisotropy D, transverse magnetic anisotropy E and Heisenberg exchange interaction J. Parameters g = 2.1 and E = 0.31 meV were fixed to the values for individual Fe atoms on Cu2N/Cu(100) (ref. 18). J = 1.15 ± 0.1 meV and D = [−2.1 meV, −3.6 meV, −2.1 meV] ± 0.1 meV were determined by fitting dI/dV spectra recorded on each atom of the Fe trimer with calculated spin excitation spectra. Note that the value of D for Fe atoms in the trimer differs from the value for individual atoms19.
Received 29 July 2014; accepted 31 October 2014; published online 15 December 2014
References 1. Gatteschi, D. & Sessoli, R. Quantum tunneling of magnetization and related phenomena in molecular materials. Angew. Chem. Int. Ed. 42, 268–297 (2003). 2. Leuenberger, M. N. & Loss, D. Quantum computing in molecular magnets. Nature 410, 789–793 (2001). 3. Nogués, J. & Schuller, I. K. Exchange bias. J. Magn. Magn. Mater. 192, 203–232 (1999). 4. Wolf, S. A. et al. Spintronics: a spin-based electronics vision for the future. Science 294, 1488–1495 (2001). 5. Wieser, R. et al. A theoretical study of the dynamical switching of a single spin by exchange forces. New J. Phys. 15, 013011 (2013). 6. Tao, K. et al. Switching a single spin on metal surfaces by a STM tip: ab initio studies. Phys. Rev. Lett. 103, 057202 (2009). 7. Loth, S., Etzkorn, M., Lutz, C. P., Eigler, D. M. & Heinrich, A. J. Measurement of fast electron spin relaxation times with atomic resolution. Science 329, 1628–1630 (2010). 8. Ardavan, A. et al. Will spin-relaxation times in molecular magnets permit quantum information processing? Phys. Rev. Lett. 98, 057201 (2007). 9. Meier, F., Levy, J. & Loss, D. Quantum computing with spin cluster qubits. Phys. Rev. Lett. 90, 047901 (2003). 10. McEnroe, S. A. et al. Magnetic exchange bias of more than 1 tesla in a natural mineral intergrowth. Nature Nanotech. 2, 631–634 (2007).
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Acknowledgements The authors thank S. Heinze, C. Hübner and D. Pfannkuche for discussions, and E. Weckert and H. Dosch (Deutsches Elektronen-Synchrotron) for providing laboratory space. D.J.C. and J.A.J.B. acknowledge postdoctoral fellowships from the Alexander von Humboldt Foundation. J.A.J.B. acknowledges support from the Natural Sciences and Engineering Research Council of Canada.
Author contributions S.Y. and S.L. conceived the experiment. S.Y. carried out the experiments and performed the analysis and calculations. All authors participated in the experimental work and contributed to writing the manuscript.
Additional information Supplementary information is available in the online version of the paper. Reprints and permissions information is available online at www.nature.com/reprints. Correspondence and requests for materials should be addressed to S.Y. and S.L.
Competing financial interests
The authors declare no competing financial interests.
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