ESR-STM of a single precessing spin: Detection of exchange-based spin noise A. V. Balatsky, 1 Yishay Manassen, 2 and Ran Salem 2 1 Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 2 Department of Physics and the Ilse Katz Center for Nanometer Scale Science and Technology, Ben Gurion University, Beer Sheva, 84105, Israel Received 10 April 2002; revised manuscript received 1 August 2002; published 27 November 2002 Electron Spin resonance scanning tunneling microscopy ESR-STM is an emerging technique which is capable of detecting the precession of a single spin. We discuss the mechanism of ESR-STM based on a direct exchange coupling between the tunneling electrons and the local precessing spin S. We claim that since the number of tunneling electrons in a single precessing period is small ( 20), one may expect a net temporary polarization within this period that will couple via exchange interaction to the localized spin. This coupling will randomly modulate the tunneling barrier and create a dispersion in the tunneling current which is a product of a Larmor frequency component due to the precession of the single spin and the dispersion of the spin of the tunneling electrons. This noise component is spread over the whole frequency range for random white noise spin polarization of electrons. In the opposite case where the power spectrum of the spins of the tunneling electrons has a peak at zero frequency an elevated noise in the current at  L will appear. We discuss the possible source of this spin polarization. We find that for relevant values of parameters the signal-to-noise ratio in the spectral characteristic is 2– 4 and is comparable to the reported signal to noise ratio. 1,2 The magnitude of the current fluctuation is a relatively weak increaing function of the dc current and magnetic field. The linewidth produced by the back action effect of tunneling electrons on the precessing spin is also discussed. DOI: 10.1103/PhysRevB.66.195416 PACS numbers: 76.30.-v, 07.79.Cz, 75.75.+a There is a growing realization that the technique of elec- tron spin resonance scanning tunneling microscopy ESR- STM is capable of detecting the precession of a single sur- face spin by modulating the tunneling current at the Larmor frequency. This technique was successful in measuring Lar- mor frequency modulations in defects in semiconductor surfaces 1 and in paramagnetic molecules. 2 The increasing in- terest in this technique is due to the possibility to detect and manipulate a single spin. 3 The alternative technique that allows one to detect single spin is the optically detected magnetic resonance ODMR spectroscopy in a single molecule. 5 In comparison, ESR- STM has the unique ability to correlate spectroscopic infor- mation with spatial information, detected at the atomic level. It also allows one to manipulate the position of the spin centers at the atomic level. 4 There have been several proposals for the mechanism of detection. One is a polarization of the mobile carriers through spin-orbit coupling and modulation of the LDOS as a result of the precession. 6 Another one is the interference between two resonant tunneling components through the magnetic-field-split Zeeman levels. 7 Both of these mecha- nisms rely on a spin-orbit coupling to couple a local spin S to the conduction electrons and have assumed no spin polariza- tion of tunneling electrons. Recently, however, Durkan and Welland 2 observed a strong signal in a system with a sub- stantially smaller spin-orbit coupling than what was assumed in the calculations. 6,7 Motivated by these experiments we addressed a question: what is the role of the direct exchange interaction between the localized spin and the tunneling elec- trons. The exchange interaction has a tremendous influence on the physics of conducting substances when magnetic im- purities are present 8 and it is natural to ask here: Does ex- change interaction play a role in ESR-STM also? We find that a direct Heisenberg exchange interaction be- tween the localized spin and conduction electrons is capable of producing a modulation of the tunneling current. The qualitative difference compared with the previous models is that we consider temporal fluctuations of the spin polariza- tion of the electrons that are tunneling between the tip and surface. The spin-orbit interaction is irrelevant for this con- sideration. We argue in this paper that although the spin po- larization of the tunneling electrons is zero in the long time limit, it is not zero on the scale of the period of the preces- sion, typically 1/ L 2 ns. On this time scale there are very few electrons that pass nearby the localized spin. There ex- ists a temporary spin polarization of the tunneling electrons which may interact through an exchange interaction with the localized spin center. It is important to point out that the ESR-STM technique performs a noise spectroscopy. We do not drive the single spin with an external coherent rf field, and we are basically detecting an incoherent phenomenon we avoid here the question of the meaning of this concept on a single-particle level. There have been several demonstrations in the past of detecting magnetic resonance with noise spectroscopy. 9 We argue that it is possible to get a noise-related signal from an exchange interaction between the tunneling electrons and the localized surface spin center. The overlap of the electron wave function in the tip and surface, separated by a distance d, is exponentially small and is given by a spin-dependent tunneling matrix element  ˆ = 0 exp -  -J S t   ˆ  0  , 1 where we consider the spin S( t ) in the magnetic field B || z , precessing with the Larmor frequency  L =g  B B ,  ˆ is un- PHYSICAL REVIEW B 66, 195416 2002 0163-1829/2002/6619/1954165/$20.00 ©2002 The American Physical Society 66 195416-1