Fig. 5: Tuning the LZSM interference of coupled spins.
From: Electrically tunable quantum interference of atomic spins on surfaces
a Schematic showing two Ti spins with a coupling J (green curve). The tip-Ti coupling is indicated by the red curve. b Energy-level diagram of two spins as a function of the energy detuning \({\delta }_{{{\rm{bias}}}}\) due to \({V}_{{{\rm{bias}}}}\). \(\left|{{\rm{S}}}\right\rangle\) and \(\left|{{{\rm{T}}}}_{0}\right\rangle\) exhibit an anticrossing (red dashed line). c ESR spectra of a Ti spin dimer (J = 0.4 GHz) as a function of \({\omega }_{{{\rm{RF}}}}\) and \({V}_{{{\rm{bias}}}}\) (setpoint: \({V}_{{{\rm{sp}}}}\) = 50 mV, \({I}_{{{\rm{sp}}}}\) = 150 pA; \({B}_{{{\rm{ext}}}}\) = 0.65 T). d Energy-level diagram of two spins as a function of detuning \({\omega }_{{{\rm{RF}}}}-{\omega }_{0}\). Avoided crossings are labeled as \({\Delta }_{{{\rm{S}}} ,-}\), \({\Delta }_{+,-}\) and \({\Delta }_{+,{{\rm{S}}}}\). e–g ESR spectra measured using a sinusoidal frequency modulation of \({V}_{{{\rm{RF}}}}\), as a function of detuning \({\omega }_{{{\rm{RF}}}}-{\omega }_{0}\) and frequency modulation amplitude \({\delta }_{{{\rm{RF}}}}\) at a fixed modulation frequency \(f\) of 20, 20, 30 MHz, respectively (\({V}_{{{\rm{bias}}}}\) = 50 mV, \({V}_{{{\rm{RF}}}}\) = 17, 20, 20 mV; \({B}_{{{\rm{ext}}}}\) = 0.60 T; setpoint: \({V}_{{{\rm{sp}}}}\) = 50 mV, \({I}_{{{\rm{sp}}}}\) = 30, 30, 50 pA). The coupling J/interatomic distances are 0.2 GHz/11.9 Å (e), 0.4 GHz/11.0 Å (f) and 0.8 GHz/10.2 Å (g). In f, white arrows indicate when the avoided crossings are reached for the static detuning indicated by the vertical dashed line. Insets show the STM images. h Energy-level diagram of two spins as a function of the energy detuning \({\delta }_{{{\rm{bias}}}}\) due to \({V}_{{{\rm{bias}}}}\) near avoided crossings \({\Delta }_{{{\rm{S}}} ,-}\) (left) and \({\Delta }_{+,-}\) (right). i–k ESR spectra measured under a square-wave amplitude-modulated \({V}_{{{\rm{bias}}}}\), as a function of detuning \({\omega }_{{{\rm{RF}}}}-{\omega }_{0}\) and modulation amplitude \(\delta V\) at a fixed \(f\) of 100 MHz (VDC = 50 mV, \({V}_{{{\rm{RF}}}}\) = 15 mV; \({B}_{{{\rm{ext}}}}\) = 0.59, 0.64, 0.66 T; setpoint: \({V}_{{{\rm{sp}}}}\) = 50 mV, \({I}_{{{\rm{sp}}}}\) = 60, 52, 70 pA). The white dashed lines indicate the boundaries between the two branches of LZSM patterns.
