1 Single Nanomagnet Behaviour: Surface and Finite-Size Effects
21
thickness r independent of D and with reduced magnetization with respect to the
core. With these assumptions, the size dependence of M can be expressed as
M(D) = M Core − M
r S
V
= M Core − M
6r
D
,
(1.14)
where S and V are the surface and volume of the NM, and M = M Core − M Surface .
1.3.2 Effects of Shape and Surface Anisotropy
Recent advances in the synthesis methods and characterization techniques in the field
of nanomagnetism have allowed us to have control on the production of NM with
specific shapes and morphologies. It has been demonstrated that magnetic nanoparticles can be synthesized with precise control over their sizes, shapes, compositions,
and structures [76–79]. In particular, the control of their shape can be used to tailor
functional properties for specific biomedical and technological applications [80, 81].
In what follows, we will first present examples that illustrate how shape is related
to distinct magnetic properties of NM and then will continue presenting three phenomena that illustrate how the existence of surface anisotropy and interfaces affect
the magnetic properties of NM.
1.3.2.1 Effects of Shape in the Reversal of Oxide NPs
As a first example, let us consider two maghemite NM with spherical and cubic shape
and similar radius and length of 20 nm, as the ones used in an experimental study
of the heating properties relevant to hyperthermia applications [82]. Analyzing the
hysteresis loops simulated by atomistic MC (see Fig. 1.13), we see that their shape
and area undergo a substantial change just for the fact of changing their shape, since
they have the same (real) values of the core and surface anisotropies. In particular,
notice that the loop area of the cubic NM is larger than that of the spherical one. It has
been checked that this is accomplished independently of the NM size, thus pointing
to a genuine shape effect associated with changes occuring at the surface of the NM.
Note that the difference in areas stems from qualitative loop shape differences around
the coercive and closure field points that can be traced back to the different reversal
processes of the surface spins as clearly observed on in the right panel of Fig. 1.13.
Since the loop area is directly related to the specific absorption rate, these simulation
results give a convincing explanation of experiments that show a systematic superior
magnetic heating efficiency of cube-shaped NM as compared to spherical ones of
similar sizes [82–87].
In our next example, we compare the phenomenology of spherical and ellipsoidal
NM [88, 89]. Notice that, in contrast with the previous sections, the values of the
21
thickness r independent of D and with reduced magnetization with respect to the
core. With these assumptions, the size dependence of M can be expressed as
M(D) = M Core − M
r S
V
= M Core − M
6r
D
,
(1.14)
where S and V are the surface and volume of the NM, and M = M Core − M Surface .
1.3.2 Effects of Shape and Surface Anisotropy
Recent advances in the synthesis methods and characterization techniques in the field
of nanomagnetism have allowed us to have control on the production of NM with
specific shapes and morphologies. It has been demonstrated that magnetic nanoparticles can be synthesized with precise control over their sizes, shapes, compositions,
and structures [76–79]. In particular, the control of their shape can be used to tailor
functional properties for specific biomedical and technological applications [80, 81].
In what follows, we will first present examples that illustrate how shape is related
to distinct magnetic properties of NM and then will continue presenting three phenomena that illustrate how the existence of surface anisotropy and interfaces affect
the magnetic properties of NM.
1.3.2.1 Effects of Shape in the Reversal of Oxide NPs
As a first example, let us consider two maghemite NM with spherical and cubic shape
and similar radius and length of 20 nm, as the ones used in an experimental study
of the heating properties relevant to hyperthermia applications [82]. Analyzing the
hysteresis loops simulated by atomistic MC (see Fig. 1.13), we see that their shape
and area undergo a substantial change just for the fact of changing their shape, since
they have the same (real) values of the core and surface anisotropies. In particular,
notice that the loop area of the cubic NM is larger than that of the spherical one. It has
been checked that this is accomplished independently of the NM size, thus pointing
to a genuine shape effect associated with changes occuring at the surface of the NM.
Note that the difference in areas stems from qualitative loop shape differences around
the coercive and closure field points that can be traced back to the different reversal
processes of the surface spins as clearly observed on in the right panel of Fig. 1.13.
Since the loop area is directly related to the specific absorption rate, these simulation
results give a convincing explanation of experiments that show a systematic superior
magnetic heating efficiency of cube-shaped NM as compared to spherical ones of
similar sizes [82–87].
In our next example, we compare the phenomenology of spherical and ellipsoidal
NM [88, 89]. Notice that, in contrast with the previous sections, the values of the