Nanomagnetism
Nanomagnetism is a very broad field where one can find exciting physics ranging from the correlations induced in the Kondo effect, to the dynamics of spin excitation and de-excitation
on the atomic scale, passing by exotic state such as Majorana bound states in superconductors.
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,
T1. The other obvious lifetime is the pure dephasing time, or the
time when the relative phase between the two spin states is constant,
T2*. 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, f0 such that the excitation energy is E=h f0 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.
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