Spin resonance amplitude and frequency of a single atom on a surface in a vector magnetic field

Abstract

We used electron spin resonance (ESR) combined with scanning tunneling microscopy (STM) to measure hydrogenated Ti (spin-1/2) atoms at low-symmetry binding sites on MgO in vector magnetic fields. We found strongly anisotropic g-values in all three spatial directions. Interestingly, the amplitude and lineshape of the ESR signals are also strongly dependent on the angle of the field. We conclude that the Ti spin is aligned along the magnetic field, while the tip spin follows its strong magnetic anisotropy. Our results show the interplay between the tip and surface spins in determining the ESR signals and highlight the precision of ESR-STM to identify the single atom's spin states.Electron spin resonance (ESR) offers high energy resolution for the measurement of spins, which is not limited by temperature. However, it usually requires a very large number of identical spins to achieve sufficient signal [1] and, thus, provides averaged information on an ensemble of spins. Scanning tunneling microscopy (STM), on the other hand, offers access to individual spins and to the surrounding environment at the atomic scale, albeit with an energy resolution that is limited by the temperature of tip and sample [2].Recently, it was shown that these advantages could be combined in ESR-STM, which achieves an energy resolution of around 10 nano-electronvolt with atomic-scale spatial resolution on individual spins [3,4].The most common type of spin centers in ensemble ESR has the spin of S = 1/2 and measuring the dependence of the Zeeman energy on both the magnitude and the direction of magnetic fields lies at the core of ESR. A well-studied spin-1/2 system in ESR-STM is a Ti atom on a thin MgO film supported on Ag(100) [5][6][7], where Ti atoms are found at two different binding sites and are presumably hydrogenated [5,7,8]. Among the intensive reports of ESR-STM on Ti atoms, there was a discrepancy in the reported g-values [6,7,9,10]. Unlike ensemble ESR, ESR-STM rarely has the capability to change the direction of magnetic fields, which makes it difficult to unravel the origin of anisotropic g-values. It was recently found that such Ti at the oxygen binding site has a very highly anisotropic g-factor with the in-plane component being 2.7 times larger than the out-of-plane one [10]. Due to the 4-fold symmetry of the O binding site, the two in-plane components of the g-factor have to be identical. Initial measurements also hinted at an anisotropic g-factor on the lower symmetry (2-fold) bridge binding site on the same substrate [7,9]. Three different transition metal atoms have been studied using ESR-STM [3,5,11] and several mechanisms have been proposed to explain the coherent driving and the detection of spins in ESR-STM.Proposed driving mechanisms include the physical motion of the ESR-active spin in the presence of an inhomogeneous magnetic field created by the tip, also referred to as piezoelectric coupling (PEC) [6,12], as well as a modulation of the tunneling barrier by the applied AC voltage [13]. Recently, strongly persuasiv...

Harnessing the Quantum Behavior of Spins on Surfaces

“…Another practical benefit of an adjustable field angle is that it can be used to maximize the ESR signal of a given spin-polarized tip. This is because the ESR signal intensity can vary strongly with the field angle due to changes in the driving strength and the detection sensitivity [77].…”

“…Note * : it remains unclear at the moment whether the 80-meV IETS step of oxygen-site Ti is related to a higher-lying orbital state or a vibrational mode. Note * * : the magnetic moment of bridge-site Ti is 0.96 µ B along the other in-plane direction [77]. Note * * * : Higher-order anistropy terms mix the Fe spin states, allowing the ESR transition of Fe on MgO to occur [29].…”

“…The tip's magnetic moment is largely classical because of its proximity to the metallic tip body and hence fast decoherence. While magnetic tips with only one Fe atom on the apex were found to be paramagnetic [71], ESR tips commonly used (with three to ten Fe atoms) often have large enough anisotropy to keep the tip spin fixed along a certain direction (typically at a 15-60 • angle to the external field applied during the preparation of the spin-polarized tip [77]). Similar to two coupled surface spins as discussed in section 2.7, the tip spin S tip and the surface spin S are also coupled via dipolar and exchange interactions as…”

“…Other sensors such as spin-1/2 Ti and FePc have also been utilized. Ti sensors have been used to determine the Ti-Ti interactions at different binding sites [66,36] and the magnetization direction of a magnetic tip [77]. FePc molecules have been used to determine FePc-FePc and FePc-Ti couplings [34].…”

All-electric electron spin resonance studied by means of Floquet quantum master equations

“…Interestingly, this matches the experimental observations of Refs. [10,56], where I peak is found to be proportional to the square of the Rabi frequency, 2 , under the constraint that T 1 T 2 1, with T 1 and T 2 the involved life and coherence times, respectively. Equation ( 36) makes clear the key role of the electrode polarization.…”