We study nanomagnetism from the point of view of atomic spins. Their dynamics and correlations entail the processes we just described. But quantum coherence and entanglement naturally appear when atomic spins interact with each other. Recently, a new development of the STM has produced the exciting possibility of fully characterizing the properties of atomic spins one by one. This is the study of Electron Spin Resonance using the STM.

Manassen and collaborators and Komeda and Manassen used GHz excitation frequencies to study single magnetic moments in Si. More recently, other experiments also using STM showed data that molecular spins could also be addressed in a GHz pulsed STM. New highly-reproducible data with quantitative measurements and explanation recently came available in the low-temperature set-up of IBM (USA) and QNS (Republic of Korea). They showed compelling evidence that Rabi oscillations were established between to Zeeman-split spin states of an Fe atom on an MgO surface when a GHz modulation signal was injected on the electron current. Evidence was given that time-dependent electrons can drive the magnetic oscillations.

Let us assume that we have two clear spin states that can be connected via an oscillating driving term (the electric field between tip and sample in the STM setup). Then there are three possibilities: each state is populated (two states) and a cross term between the two states. This cross term measures how coherent the two spin states are. When this term goes to zero, the two states are totally disconnected they are incoherent. Incoherence means that their respective phases change in time randomly. If the phase is constant (or almost constant) in time between the two states, they will interfere.

The lifetime of each state, the coherence time and the Rabi frequency and the resonance frequency. Here, we have one excited states then there is only one lifetime, T

_{1}. The other obvious lifetime is the pure dephasing time, or the time when the relative phase between the two spin states is constant, T

_{2}

^{*}. Please be aware that in NV centers a different notation is followed. The third time is the one corresponding to the period of the Rabi oscillations. The Rabi oscillation frequency corresponds to population oscillations when quantum tunneling between two states controls the population dynamics. This frequency gives the strength of the coupling between the external driving force and the reaction of the system to that external field. The fourth time is given by the resonance frequency or the energy of the excited spin state, f

_{0}such that the excitation energy is E=h f

_{0}where h is Planck's constant.

The experiments are performed with spin-polarized currents, such that the STM is sensitive to the spin state. The change in current is proven to follow the classical Bloch equations for magnetic moments, and the lineshape with oscillation frequency f, found in the experiments, is reproduced.