1 Single Nanomagnet Behaviour: Surface and Finite-Size Effects
33
Finally, in the [134], the authors investigated the effects of surface anisotropy (and
the ensuing spin misalignment) on the magnetization dynamics of ferromagnetic
nanocubes in the many-spin approach. It was shown that such inhomogeneous spin
configurations induce nutation in the dynamics of the particle’s magnetization. In
addition to the ordinary precessional motion with a frequency of 10 GHz, it was
found that the dynamics of the net magnetic moment exhibits two more resonance
peaks with frequencies that are higher than the FMR frequency. In particular, a much
higher frequency of 1 THz was attributed to the magnetization fluctuations at the
atomic level driven by exchange interactions.
1.4 Conclusion
In this chapter, we have studied the equilibrium, and to a lesser extent the dynamic,
properties of nano-scaled magnetic systems taking account of their “intrinsic” features, such as finite-size, boundary and surface effects. We deemed it necessary to first
emphasize the difference between these effects illustrated through simple models of a
nanomagnet. Then, we presented the various models and approximations employed
for describing nanomagnets depending on the range of their physical parameters
and their ratios. Next, we discussed the corresponding computing methods that have
been developed for these specific systems, such as the Monte Carlo simulations,
Landau-Lifshitz equation (with and without the Langevin field), and the spin-wave
theory.
We have covered some of our previous results for the thermal and hysteretic behavior of the magnetization. We first did so for model NM so as to build a qualitative
picture of the general behavior and a fair understanding of the underlying mechanisms. Then, we considered more realistic NM with maghemite as the underlying
structure as well as nanomagnets in core-shell configurations. For the model NM and
the more realistic iron oxide nanocubes, we have also succinctly reported on some
of our works that dealt with the effects of surface anisotropy on the relaxation rate
and the spectrum of spin-wave excitations.
The examples studied allow us to appreciate the wealth of novel features and
physical phenomena, and on the other hand the big challenges, brought about by
nano-scaled spin systems. Their reduced size has deep consequences on their internal magnetic state as well as their macroscopic behavior. Indeed, finite-size, boundary and surface effects induce nonuniform magnetic states (spin noncolinearities)
which lead to incoherent switching and novel hysteretic properties, reduced critical
temperature and complex magnetization processes. The reduced size also leads to
the interesting phenomenon of superparamagnetism which has redefined the relevant
temperature and time scales. The study of the dynamics of such systems is a daunting
task that requires the analysis of a multi-valley energy potential. Nevertheless, it has
been possible to build macroscopic and microscopic models for investigating these
phenomena and for shedding light on the underlying mechanisms. In addition, these
models have allowed us to make estimates of the various physical parameters and to
33
Finally, in the [134], the authors investigated the effects of surface anisotropy (and
the ensuing spin misalignment) on the magnetization dynamics of ferromagnetic
nanocubes in the many-spin approach. It was shown that such inhomogeneous spin
configurations induce nutation in the dynamics of the particle’s magnetization. In
addition to the ordinary precessional motion with a frequency of 10 GHz, it was
found that the dynamics of the net magnetic moment exhibits two more resonance
peaks with frequencies that are higher than the FMR frequency. In particular, a much
higher frequency of 1 THz was attributed to the magnetization fluctuations at the
atomic level driven by exchange interactions.
1.4 Conclusion
In this chapter, we have studied the equilibrium, and to a lesser extent the dynamic,
properties of nano-scaled magnetic systems taking account of their “intrinsic” features, such as finite-size, boundary and surface effects. We deemed it necessary to first
emphasize the difference between these effects illustrated through simple models of a
nanomagnet. Then, we presented the various models and approximations employed
for describing nanomagnets depending on the range of their physical parameters
and their ratios. Next, we discussed the corresponding computing methods that have
been developed for these specific systems, such as the Monte Carlo simulations,
Landau-Lifshitz equation (with and without the Langevin field), and the spin-wave
theory.
We have covered some of our previous results for the thermal and hysteretic behavior of the magnetization. We first did so for model NM so as to build a qualitative
picture of the general behavior and a fair understanding of the underlying mechanisms. Then, we considered more realistic NM with maghemite as the underlying
structure as well as nanomagnets in core-shell configurations. For the model NM and
the more realistic iron oxide nanocubes, we have also succinctly reported on some
of our works that dealt with the effects of surface anisotropy on the relaxation rate
and the spectrum of spin-wave excitations.
The examples studied allow us to appreciate the wealth of novel features and
physical phenomena, and on the other hand the big challenges, brought about by
nano-scaled spin systems. Their reduced size has deep consequences on their internal magnetic state as well as their macroscopic behavior. Indeed, finite-size, boundary and surface effects induce nonuniform magnetic states (spin noncolinearities)
which lead to incoherent switching and novel hysteretic properties, reduced critical
temperature and complex magnetization processes. The reduced size also leads to
the interesting phenomenon of superparamagnetism which has redefined the relevant
temperature and time scales. The study of the dynamics of such systems is a daunting
task that requires the analysis of a multi-valley energy potential. Nevertheless, it has
been possible to build macroscopic and microscopic models for investigating these
phenomena and for shedding light on the underlying mechanisms. In addition, these
models have allowed us to make estimates of the various physical parameters and to