Research ArticlePHYSICS

Longitudinal and transverse electron paramagnetic resonance in a scanning tunneling microscope

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Science Advances  30 Sep 2020:
Vol. 6, no. 40, eabc5511
DOI: 10.1126/sciadv.abc5511
  • Fig. 1 Principle of EPR-STM and representative EPR spectra.

    (A) Schematic of the STM junction showing single magnetic adatoms on a double-layer MgO on Ag(100) driven by an rf antenna using a spin-polarized tip. The tip is at a standoff distance s from point contact with the surface. The tip magnetization makes an angle α with respect to the out-of-plane external magnetic field Bext. The schematic includes a three-dimensional rendering of a constant-current STM image (10 nm by 10 nm) of Fe and TiH adatoms, on which all EPR measurements are performed (subscripts O and B label apical and bridge binding sites relative to the oxygen lattice, respectively). Set point current, 50 pA; dc bias, 30 mV. (B) Representative EPR spectra measured by sweeping Bext on TiHB and Fe adatoms shown in (A) (left Fe adatom) while applying an rf voltage to the antenna. The solid lines are fits to the data (see main text). A nonresonant background is subtracted from both spectra; for clarity, the Fe spectrum is offset by −1 pA. Settings: Idc = 70 pA, Vdc = 160 mV, Vrf = 256 mV, and ωrf/2π: 8 GHz for TiB and 36 GHz for Fe.

  • Fig. 2 EPR dataset on Fe and TiH.

    EPR spectra of Fe at ωrf/2π = 36 GHz (A and C) and TiH at 8 GHz (B and D) recorded with the same microtip for varying the standoff distance s and rf voltage amplitude Vrf. For better visibility, the Fe spectra are inverted. (A) and (B) show data for a constant rf voltage amplitude of Vrf = 161 mV. The spectra are vertically offset for better visibility. In (C) and (D), the spectra are offset along the Bext axis for distinct values of Vrf. Rows from left to right correspond to Vrf = 64, 81, 102, 128, 161, 203, and 256 mV.

  • Fig. 3 Amplitude and width of the EPR spectra and experimental Rabi rates.

    A fit of all 119 EPR spectra using Eq. 1 (see main text, section S3, and fig. S4) allows for calculating the spectral line widths (A and B) and amplitudes (C and D) for varying rf voltage amplitude Vrf, dc voltage Vdc and set point current Idc. In (C), most symbols for a given Idc overlap. Experimental Rabi rate Ω versus standoff distance s for Fe (E) and TiH (F) at different Vrf values. The errors in (E) to (F) of ±2% are smaller than the size of the symbols.

  • Fig. 4 Energy levels and EPR matrix elements of Fe/MgO/Ag(100).

    (A) Calculated lowest energy levels of Fe obtained from the multiplet theory for an out-of-plane magnetic field ranging from 0 to 7 T. (B) Calculated components of the matrix elements of the orbital and spin momentum operator L̂ and Ŝ, respectively, for an external magnetic field along z. Note that apart from the operators Sz and Lz, all other matrix elements are <10−14. (C) Schematic of the transition matrix elements between the EPR-active states ∣0⟩ and ∣1⟩ represented in the orbital momentum basis ml. Wave function contributions below 1% are omitted.

  • Fig. 5 Characterization of the tip magnetic field.

    Measured resonance field Bext0 versus standoff distance s for Fe (A) and TiH (B). Solid lines are fits based on Eq. 2. (C) Cross-sectional view of the effective tip magnetic field Beff experienced by the Fe atom at different locations with respect to the STM tip deduced from Eq. 2 assuming an isotropic exchange interaction. The cross section is a cut along the tip-atom plane with dimensions of 0.8 nm by 0.6 nm. (D) Gradient of the effective magnetic field dBeff/ds along x and z versus standoff distance s for Fe (left) and TiH (right) with the corresponding dipolar (Bdip) and exchange (Bxc) contributions. The gradients along y vanish.

  • Fig. 6 Adatom displacement induced by the electric field in the STM junction and calculated Rabi rate.

    (A and B) Detail of the atomic arrangement used for the DFT calculations of Fe (A) and TiH (B) and calculated displacement versus static out-of-plane electric field. Color code: Mg (black), O (light-blue), Ti (red), H (yellow), and Fe (purple). (C) Schematic of linear and nonlinear displacements ∆z due to the applied electric field ∆E. (D) Calculated linear and nonlinear displacement for Fe at the radio frequency ∆zωrf versus dc electric field Edc for Vrf = 10 mV. (E) Calculated displacement ∆z for Fe versus rf electric field Erf for Vdc = 10 mV at the fundamental frequency ωrf and the second harmonic frequency 2ωrf of the driving rf field. Standoff distance is 300 pm for (D) and (E). (F and G) Calculated Rabi rate ΩPEC versus standoff distance s for Fe (F) and TiH (G) deduced from Eq. 3.

Supplementary Materials

  • Supplementary Materials

    Longitudinal and transverse electron paramagnetic resonance in a scanning tunneling microscope

    Tom S. Seifert, Stepan Kovarik, Dominik M. Juraschek, Nicola A. Spaldin, Pietro Gambardella, Sebastian Stepanow

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    • Sections S1 to S6
    • Figs. S1 to S9
    • Table S1
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