Fig. 3: Simulation of the LZSM interference by considering the spin-transfer torque effects using the generalized Bloch equations.
From: Electrically tunable quantum interference of atomic spins on surfaces
a Schematic of the spin-transfer torque on the Ti atom under the influence of spin-polarized tunnel current at different bias polarities, showing \(\Delta {{\rm{\sigma }}}=+ 1\) (red arrow), \(\Delta {{\rm{\sigma }}}=-1\) (blue arrow), and \(\Delta {{\rm{\sigma }}}=0\) (dashed arrows) electron tunneling between the spin-dependent (⇑ or ⇓) densities of states (DOS) of Ag and STM tip. The bias is given with respect to the sample. b Time evolution of energy levels of the Ti spin driven by bias voltage modulation for \({V}_{{\mbox{DC}}}\) < 0. The polarity of \({V}_{{{\rm{bias}}}}\) is indicated by + (red regions) and – (blue regions) signs. c Simulated ESR signals as a function of detuning \({\omega }_{{{\rm{RF}}}}-{\omega }_{0}\) and modulation frequency \(f\) for a fixed modulation amplitude \(\delta V\) of 140 mV. Simulations parameters: \({\omega }_{0}\) = 15.5 GHz, ∆↑↓ = 40 MHz, \({\delta }_{{{\rm{bias}}}}\left(t\right)=273\sin (2{{\rm{\pi }}}ft)\) MHz, \({V}_{{\mbox{DC}}}=-50\) mV, \(\eta\) = \(3.5\times {10}^{-5}\), \(\alpha\) = 0.5, \({\left\langle {S}_{z}\right\rangle }_{0}\) = −0.18, \(\left\langle {S}_{{{\rm{tip}}}}^{z}\right\rangle\) = 1, \(\left\langle {S}_{{{\rm{tip}}}}^{{xy}}\right\rangle\) = 0.5, \({\left\langle {S}_{{{\rm{z}}}}^{{{\rm{p}}}}\right\rangle }_{0 ,{{\rm{STT}}}}=-0.2\), \({\left\langle {S}_{{{\rm{z}}}}^{{{\rm{n}}}}\right\rangle }_{0 ,{{\rm{STT}}}}=0.3\), \(k=0.01\), \({V}_{{\mbox{RF}}}\) = 20 mV, \({T}_{1}^{{\mathrm{int}}}=161\,{{\rm{ns}}} ,\,{T}_{2}^{{\mathrm{int}}}=\,322\,{{\rm{ns}}}\). See Supplementary Note 2 for the meaning of each parameter. d Simulated ESR signals at \(f=\) 2, 30, 60 and 230 MHz, respectively.
