Biomedical Engineering Reference
In-Depth Information
quantum mechanical property, which cannot be described by classical
mechanics. It is represented by the spin quantum number, which can take
the values 1/2 or
1/2 in the case of an electron. These two eigenstates are
usually referred to as spin-down and spin-up.
The foundation of spin tunneling lies in the high magnetic anisotropy, S
z
,
of the system and the resulting double-well potential, which can be
perturbed with both longitudinal, H
z
, and transverse, H
x
, magnetic fields to
induce degenerate states that can be manipulated as qubits.
The application of an external longitudinal magnetic component to the
system results in a perturbation of the double potential, while the presence
of an external transverse field is responsible for the spin tunneling effect. By
assuming low temperatures (
1 K) to minimize spin-phonon interactions,
the single-spin Hamiltonian for molecules like Mn
12
and Fe
8
becomes:
H
~
¼
H
a
þ
H
Z
þ
H
0
½
2
:
8
H
a
¼
AS
z
BS
z
½
2
:
9
H
Z
¼
g
m
B
A
z
S
z
½
2
:
10
H
0
¼
g
m
B
A
x
S
x
½
2
:
11
where equations 2.9, 2.10 and 2.11 are the anisotropic, Zeeman (longitudinal
external field) and transverse field components of the Hamiltonian,
respectively. It is sufficient to attribute the presence of spin tunneling to
the non-commutability of the H
*
term with the remaining S
z
elements of the
Hamiltonian. Hence, each eigenstate M
is not stationary and will tunnel
through the anisotropic barrier when the state is degenerate with
ji
.Itis
important to note that even in a zero transverse field environment, Mn
12
has
been shown to still exhibit spin tunneling due to violations of transverse-
anisotropic selection rules, indicating the inherent presence of a transverse
component. One fascinating aspect of this phenomenon is its appearance in
magnetic hysteresis (see Fig. 2.7).
j
M
i
2.6.2 The Kondo effect and controlled spin entanglement in
coupled double-quantum-dots (DQDs)
Manipulation of the electron spin degree of freedom for future device
applications is of increasing importance in the field of quantum mechanics.
In particular, spintronics is an area of research that seeks to develop future-
generation spin-based devices. On a more fundamental level, the spin degree
of freedom plays a major role in diverse, strongly correlated systems, such as
