1 Single Nanomagnet Behaviour: Surface and Finite-Size Effects
9
• At zero temperature, an applied static magnetic field h reduces the energy barrier
as follows E = σ (1 − h)
2 . When h reaches a critical value h c (here 1), the
energy barrier is entirely suppressed and the magnetic moment of the system
switches to the new available minimum. This hysteretic switching mechanism is
well described by the so-called Stoner-Wohlfarth model [4, 8].
• At finite temperature, and even at zero magnetic field, the switching probability
of the magnetic moment becomes nonzero owing to thermal fluctuations. Such a
stochastic mechanism is well described by the so-called Néel-Brown model [5, 7,
9, 11]. Alongside the well-known work of Néel, Brown, and also that of Aharoni
(1969), there is a fundamental approach developed by Langer (1967–69) for multivariate systems [12–15]. The only limitation of Langer’s approach is that it applies
to situations where the extrema of the energy potential are well defined in the sense
that they are not flat. Indeed, this approach is based on the quadratic expansion of
the energy potential at the various extrema (minima, maxima and saddle points). In
practice, this turns out to be applicable to intermediate-to-high damping regimes.
For practical applications, such as information storage, one seeks to increase the
storage density by using rather small magnetic elements. However, reducing the
volume of these elements leads to rather low energy barriers and thereby to large
switching rates, especially at room temperature. This drastically deteriorates the
temporal stability of the information stored in the media. One way out consists in
considering magnetic materials with large anisotropy constants K (as in CoPt), but
then the critical field h c required to suppress the energy barrier, which corresponds
to writing a new information, becomes too large and inaccessible to nano-scaled
devices. This is what we could call the superparamagnetic tri-lemma. Consequently,
the nanomagnetism community sought for other alternatives while keeping in mind
the two main objectives for practical applications, namely large storage densities
and long temporal stability at room temperature. Two of such alternatives have been
suggested: (i) add a time-dependent field on top of the static magnetic field [16–21],
thus assisting the switching process without having to entirely suppress the energy
barrier, and (ii) apply a laser beam to the system so as to locally reduce the anisotropy
contribution. This is what it is called heat-assisted magnetization reversal (HAMR)
mechanism.
1.2.2 Many-Spin Approach
In NMs of a diameter of the order of 10 nm (e.g. of cobalt), a great number of atoms
is located on the outer shell. Now, we know that the latter undergoes lattice reconstructions and atomic rearrangements which in turn lead to a crystal-field symmetry
breaking inducing strong local inhomogeneities. The consequence of this is nonuniform atomic spin configurations. For instance, as the surface anisotropy increases
in intensity, the switching mechanism becomes less coherent and rather operates
cluster-wise, leading to steps in the hysteresis loop and the limit-of-metastability
9
• At zero temperature, an applied static magnetic field h reduces the energy barrier
as follows E = σ (1 − h)
2 . When h reaches a critical value h c (here 1), the
energy barrier is entirely suppressed and the magnetic moment of the system
switches to the new available minimum. This hysteretic switching mechanism is
well described by the so-called Stoner-Wohlfarth model [4, 8].
• At finite temperature, and even at zero magnetic field, the switching probability
of the magnetic moment becomes nonzero owing to thermal fluctuations. Such a
stochastic mechanism is well described by the so-called Néel-Brown model [5, 7,
9, 11]. Alongside the well-known work of Néel, Brown, and also that of Aharoni
(1969), there is a fundamental approach developed by Langer (1967–69) for multivariate systems [12–15]. The only limitation of Langer’s approach is that it applies
to situations where the extrema of the energy potential are well defined in the sense
that they are not flat. Indeed, this approach is based on the quadratic expansion of
the energy potential at the various extrema (minima, maxima and saddle points). In
practice, this turns out to be applicable to intermediate-to-high damping regimes.
For practical applications, such as information storage, one seeks to increase the
storage density by using rather small magnetic elements. However, reducing the
volume of these elements leads to rather low energy barriers and thereby to large
switching rates, especially at room temperature. This drastically deteriorates the
temporal stability of the information stored in the media. One way out consists in
considering magnetic materials with large anisotropy constants K (as in CoPt), but
then the critical field h c required to suppress the energy barrier, which corresponds
to writing a new information, becomes too large and inaccessible to nano-scaled
devices. This is what we could call the superparamagnetic tri-lemma. Consequently,
the nanomagnetism community sought for other alternatives while keeping in mind
the two main objectives for practical applications, namely large storage densities
and long temporal stability at room temperature. Two of such alternatives have been
suggested: (i) add a time-dependent field on top of the static magnetic field [16–21],
thus assisting the switching process without having to entirely suppress the energy
barrier, and (ii) apply a laser beam to the system so as to locally reduce the anisotropy
contribution. This is what it is called heat-assisted magnetization reversal (HAMR)
mechanism.
1.2.2 Many-Spin Approach
In NMs of a diameter of the order of 10 nm (e.g. of cobalt), a great number of atoms
is located on the outer shell. Now, we know that the latter undergoes lattice reconstructions and atomic rearrangements which in turn lead to a crystal-field symmetry
breaking inducing strong local inhomogeneities. The consequence of this is nonuniform atomic spin configurations. For instance, as the surface anisotropy increases
in intensity, the switching mechanism becomes less coherent and rather operates
cluster-wise, leading to steps in the hysteresis loop and the limit-of-metastability