Magnetic Properties
of nanostructures
Scott Allen
Physics Department
University of Guelph
Outline
Types of magnetism
Ferromagnetism
terminology
Domains
nano impact on magnetism
references for further investigation
Types of Magnetism
constituent atoms have magnetic dipole moments
paramagnetism
moments are unaligned, but in the presence of an external
magnetic field they do attempt to align
ferromagnetism
all atoms contribute positively to a spontaneous net
alignment in the absence of an external magnetic field
ferrimagnetism
net alignment in the absence of an external magnetic field,
with some moments opposing, found in ionic compounds
such as oxides (antiferromagnetism – special case is which
there is full antialignment)
Ferromagnetism
exchange field (BE)
strong internal interaction tending to line up the moments
in a parallel manner (paramagnetism to ferromagnetism)
Curie temperature
above this temperature the spontaneous magnetization is
lost due to thermal fluctuation
separates disordered paramagnetic phase from the ordered
ferromagnetic phase
saturation magnetization
maximum induced magnetic moment that can be obtained
in an external magnetic field
Ferromagnetism
hysteresis
ferromagnets can have a memory of an applied field after it
has been removed
http://hyperphysics.phy-astr.gsu.edu/hbase/solids/magperm.html#c1
Ferromagnetism
in some cases a material in bulk will have a remanence of
nearly zero
but if the exchange interaction between the magnetic
moments is so high, why wouldn’t the material always be
magnetically saturated?
Domains
http://hyperphysics.phy-astr.gsu.edu/hbase/solids/ferro.html#c4
bulk materials are divided into domains
each domain is spontaneously magnetized to saturation,
but from domain to domain the direction of magnetization
can be different  thus leading to net magnetizations well
below saturation
domain formation
surface charges form creating
demagnetizing field
magnetostatic energy
decreases through creation of
second domain
http://www.irm.umn.edu/hg2m/hg2m_d/hg2m_d.html
Domain walls
interfaces between domains having differing directions of
magnetization
exchange energy acts to keep spins parallel
a thinner wall requires more energy to create and maintain
as the change in spin direction must be more abrupt
anisotropy energy tends to keep spins aligned along
certain crystallographic planes
a thinner wall is more
energetically favorable
competition exists between
anisotropy and exchange energy
( domain walls have a finite width
~ 100 nm)
http://www.irm.umn.edu/hg2m/hg2m_d/hg2m_d.html
nano impact
nanoscale particles are so small that it is not
energetically favorable to have more than one
domain  single domain regime (10 - 100 nm)
in this regime the direction of magnetization can
only change through rotation (not domain growth
or formation)
this rotation is energetically difficult and leads to
high coercivities and remanence
as the particle size decreases within the single
domain regime the “superparamagnetic limit” is
reached
coercivity and remanence are zero
nano impact
http://www.irm.umn.edu/hg2m/hg2m_d/hg2m_d.html
super paramagnetism – a single domain particle
that is magnetically saturated along a particular
direction will overcome the anisotropy energy and
reverse its direction if  the particle is sufficiently
small and the temperature is high enough (thermal
energy is enough)
P. Moriarty, Rep. Prog. Phys. 64 (2001) 297
nano impact
http://www.irm.umn.edu/hg2m/hg2m_d/hg2m_d.html
with no applied field, and T > 0K, the
superparamagnetic particles net moment will
average to zero
in an applied field, there will be a net alignment of
the magnetic moments
similar to paramagnetism, except it’s the
alignment of domains (many atoms) as opposed
to single atoms
nano impact  taking it further
this brief discussion of superparamagnetism was
considering ideal bulk-like behaviour
due to the high surface to volume ratio in
nanoparticles, one finds that surface effects start
to play a dominant role
a good starting point for a more in depth look is:
R.H. Kodama, J. Magn. Magn. Mater. 200 (1999) 359.
references
magnetism
C. Kittel, “Introduction to Solid State Physics”, Wiley, (1986).
intrinsic nanoparticle properties
R.H. Kodama, J. Magn. Magn. Mater. 200 (1999) 359.
R.H. Kodama, Phys. Rev. B. 59 (1999) 6321.
S.A. Majetich, J.H. Scott, E.M. Kirkpatrick, K. Chowdary, K. Gallagher, M.E.
McHenry, Nanostruct. Mater. 9 (1997) 291.
S.A. Majetich, Y. Jin, Science 284 (1999) 470.
C.P. Bean, J. Appl. Phys. 26 (1955) 1381.
interactions between nanoparticles
M.F. Hansen, S.Morup, J. Magn. Magn. Mater. 184 (1998) 262.
I.M.L. Billas, A. Chatelain, W.A. de Heer, Science 265 (1994) 1682.