Research ArticleQuantum Mechanics

Nonlocally sensing the magnetic states of nanoscale antiferromagnets with an atomic spin sensor

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Science Advances  26 May 2017:
Vol. 3, no. 5, e1603137
DOI: 10.1126/sciadv.1603137
  • Fig. 1 Sensing scheme with an atomic spin sensor.

    (A) Schematic of the experimental setup. The Fe trimer spin sensor (orange) and a nano-antiferromagnet (green) are assembled from individual Fe atoms on a Cu2N/Cu(100) surface (Cu, yellow circles; N, blue circles) and interact weakly with each other. The spin-polarized probe tip of an STM (gray) is polarized by an external magnetic field (purple arrow). A series of pump and probe voltage pulses are sent to the tip and stroboscopically measure the spin relaxation time of the spin sensor. Coordinate system: z (easy magnetic axis of Fe atoms in the Fe trimer), x (hard magnetic axis). (B) Top: Spin-polarized STM topographs of the Fe trimer spin sensor and the Fe nano-antiferromagnet that switches between two Néel states (labeled “0” and “1”). The distance between the Fe trimer and nano-antiferromagnet is 3.0 nm. Image size, 6.6 × 6.6 nm2; color, from low (black) to high (white); tunnel junction set point, 5 mV and 50 pA. Bottom: Pump-probe spectra of Fe trimer for the nano-antiferromagnet in Néel state “0” (red dots) or “1” (blue dots). Tip position is marked by a cross in the top panel. Pulse amplitude and duration: pump pulse, 8 mV and 80 ns; probe pulse, 3 mV and 100 ns. Solid lines are exponential decay fits to the experimental data showing that the spin relaxation time of Fe trimer differs by ΔT1 between the two curves. (C) Sketch of the avoided level crossing of the Fe trimer’s low-energy spin states, |φ〉 and |ρ〉, that enables spin sensing. Changes in the magnetic field modify the energy splitting of the spin states and the transition rate between them (blue and red arrows), thus modifying T1 by ΔT1. Any other magnetic perturbation that modifies the spin states also results in a ΔT1. (D) Time traces of the pump-probe signal measured on Fe trimer showing two-state switching of the nearby nano-antiferromagnet. The signal amplitude diminishes with increasing delay time between the pump and probe pulses [chosen delay times are indicated by vertical lines in (B)]. Magnetic bias field, 0.25 T; temperature, 0.5 K.

  • Fig. 2 Distance dependence of nonlocal spin sensing.

    (A) Spin-polarized STM topographs of different separations, d, between Fe trimer and nano-antiferromagnet. Tunnel junction set point, 5 mV and 20 pA. (B) Pump-probe measurements on the Fe trimer for each arrangement shown in (A), as the nano-antiferromagnet is in Néel state “0” (red dots) or “1” (blue dots). The pump-probe signal is normalized to 1 at zero delay time for clarity. Solid lines are exponential fits. Pulse amplitude and duration: pump pulse, 8 mV and 80 ns; probe pulse, 3 mV and 100 ns. Magnetic bias field during measurement, 0.25, 0.5, 0.75, and 0.75 T (left to right). (C) Magnetic interaction energy between Fe trimer and nano-antiferromagnet for the arrangements shown in (A) as a function of sensor-antiferromagnet separation (blue points). The blue line is an exponential fit to the measured interaction energies. The black line is the calculated magnetic dipolar interaction between the Fe trimer and nano-antiferromagnet.

  • Fig. 3 Sensing local magnetic interaction with a quantum spin sensor.

    (A) Level diagram of the Fe trimer (orange atoms) showing the two low-energy spin states |φ〉 and |ρ〉. In the absence of magnetic fields and other perturbations, the two spin states are very close in energy, and spin relaxation time, T1, is minimal. By applying an external magnetic bias field parallel to the z axis, B0 (blue arrow), the energy splitting increases to Eρφ given by the Zeeman energy. Magnetic interaction, JnAF, with a nearby nano-antiferromagnet (blue atoms) adds a perturbation to the spin states that modifies T1 by ±ΔT1/2 and Eρφ by ±ΔE/2 depending on the Néel state of the nano-antiferromagnet. (B) Variation of spin relaxation time, ΔT1, with magnetic perturbation, ΔE, plotted for magnetic bias fields 1 T (solid lines) and 0.5 T (dotted lines). Calculated perturbations are longitudinal magnetic field parallel to the z axis, B|| (orange); transverse magnetic fields, B⊥x (green) and B⊥y (pink); and magnetic interaction with a nearby nano-antiferromagnet, JnAF (blue). The curves ΔT1 (B||) and ΔT1 (JnAF) are almost identical. Experimental data were obtained by perturbing the sensor using an external magnetic field, B||, and considering a bias field of B0 = 1 T (orange squares) and 0.5 T (open squares). Plot shows Fe trimer at a 1.5-nm distance from nano-antiferromagnet. (C) Difference in spin relaxation time of the Fe trimer, ΔT1, for the different Néel states of the nano-antiferromagnet plotted as a function of the longitudinal magnetic field for trimer–nano-antiferromagnet separation of 1.1, 1.5, 2.2, and 3.0 nm. Experimental data (dots and squares) and calculated behavior (solid lines) are shown.

  • Fig. 4 Calculated long-range magnetic interaction.

    (A) Magnetic interaction energy between a Fe nano-antiferromagnet (blue atoms in inset) and a Fe chain sensor (orange atoms in inset) calculated by DFT using a broken symmetry approach (see Materials and Methods for details). Energies are calculated analogous to Fig. 3A. Within the DFT calculation, the Fe trimer sensor was approximated by an infinite one-dimensional chain of Fe atoms and the nano-antiferromagnet by either an infinite ladder (purple squares) or another one-dimensional chain (blue dots). In the latter approximation, a significantly smaller supercell could be used. This enables calculations for large distances but overestimates interaction energies because of the absence of the second antiferromagnetically aligned chain in the nano-antiferromagnet (see fig. S6 for supercell geometries). (B) Density of states of the Cu2N surface projected on the Cu atoms (orange) and N atoms (blue). Energies are given with respect to the Fermi energy. States between −4.5 and −1.5 eV are localized on Cu and have d-orbital character. States between −6 and −4.5 eV and between −1.5 and +0.5 eV are p-d hybrids between Cu and N of σ and π character. In particular, the antibonding σ bands give a sharp peak at −1 eV, and the π bands extend across the Fermi level. (C) Top: Spin density distribution for two Fe atom chains at a 1.1-nm distance. Isosurfaces show 10−3 e/Å majority spin (red) and minority spin (blue) densities that extend well beyond the Fe atoms into the Cu-N network. Bottom: Side view of the DFT supercell on the same scale as the top panel, showing Fe atoms (red spheres), Cu atoms (orange spheres), and N atoms (blue spheres).

  • Fig. 5 Sensing a nano-antiferromagnet located on different Cu2N patches.

    (A) Constant-current STM topographs of Fe trimer spin sensor and nano-antiferromagnet located on different Cu2N patches. Image size, 7.7 × 7.7 nm2; tunnel junction set point, 5 mV and 10 pA. (B) Time trace of the pump-probe signal measured on Fe trimer resulting from Néel state switching of the nano-antiferromagnet shown in (A). The position of the STM tip during pump-probe measurement is shown as the blue cross. The measurement was taken with a 0.25-T external magnetic bias field. Pulse amplitude and duration: pump pulse, 10 mV and 50 ns; probe pulse, 3 mV and 100 ns. Time delay between pump and probe pulse is fixed at 150 ns.

  • Fig. 6 Simultaneously sensing the spin states of two Fe nano-antiferromagnets.

    (A) STM constant current topographs showing two antiferromagnets constructed near a Fe trimer. The four magnetic configurations are labeled as (0, 1), (0, 1), (1, 0), and (1, 1), where the first (second) number indicates the magnetic state of the 10-atom nano-antiferromagnet (12-atom nano-antiferromagnet). Image size, 7.5 × 7.5 nm2; tunnel junction set point, 5 mV and 20 pA. (B) Pump-probe spectra of Fe trimer (dots) recorded at the position marked in (A) for the four configurations in (A). ΔT1 is 210 ± 30 ns for a switch of the 12-atom nano-antiferromagnet and 60 ± 10 ns for switching of the 10-atom nano-antiferromagnet, indicating that the 12-atom nano-antiferromagnet interacts more strongly with the Fe trimer. Pulse amplitude and duration: pump pulse, 9 mV and 50 ns; probe pulse, 3 mV and 100 ns. (C) Time trace of the pump-probe signal measured on the Fe trimer [position marked by a cross in (A)]. The delay time between pump and probe pulses is 180 ns. Magnetic bias field, 1.5 T; tunnel junction set point, 5 mV and 500 pA. (D) Histogram of the state distribution shown in (C) but measured for 4000 s (see fig. S5 for the full time trace), with corresponding state occupation probabilities for the four configurations [(0, 0), (1, 0), (0, 1), and (1, 1)]. The observed occupation probability may differ from the mean occupation probability because of the finite observation time. The stated error gives the standard derivation (±1σ) of the mean probability and was determined by resampling subsets of the measured time trace.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/3/5/e1603137/DC1

    section S1. Correspondence between nano-antiferromagnet Néel states and Fe trimer lifetime T1

    section S2. Response of T1 to different magnetic perturbations

    section S3. Deducing magnetic interaction between nano-antiferromagnet and Fe trimer spin sensor (Eq. 1)

    section S4. Tuning the signal-to-noise ratio by external magnetic field and interaction with magnetic tip

    section S5. DFT calculations for the magnetic interaction

    fig. S1. Spin-state diagram of the trimer.

    fig. S2. Pump pulses induced switching of antiferromagnetic nanostructures.

    fig. S3. Calibrating Fe trimer with external magnetic field.

    fig. S4. Improving the signal-to-noise ratio by external magnetic field or local magnetic field exerted by the magnetic STM tip.

    fig. S5. Time trace of the pump-probe signal for 4000 s about the four-state switching in Fig. 6.

    fig. S6. Supercells used for the DFT calculations.

    fig. S7. Calculated magnetic interaction energy for different spin chain and supercell geometries.

    References (42–44)

  • Supplementary Materials

    This PDF file includes:

    • section S1. Correspondence between nano-antiferromagnet Néel states and Fe trimer lifetime T1
    • section S2. Response of T1 to different magnetic perturbations
    • section S3. Deducing magnetic interaction between nano-antiferromagnet and Fe trimer spin sensor (Eq. 1)
    • section S4. Tuning the signal to noise by external magnetic field and interaction with magnetic tip
    • section S5. DFT calculations for the magnetic interaction
    • fig. S1. Spin-state diagram of the trimer.
    • fig. S2. Pump pulses induced switching of antiferromagnetic nanostructures.
    • fig. S3. Calibrating Fe trimer with external magnetic field.
    • fig. S4. Improving the signal-to-noise ratio by external magnetic field or local magnetic field exerted by the magnetic STM tip.
    • fig. S5. Time trace of the pump-probe signal for 4000 s about the four-state switching in Fig. 6.
    • fig. S6. Supercells used for the DFT calculations.
    • fig. S7. Calculated magnetic interaction energy for different spin chain and supercell geometries.
    • References (42–44)

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