Magnetic Properties

Scott Allen

Physics Department

University of Guelph

of nanostructures

Outline

Domains

Ferromagnetism

Types of magnetism

nano impact on magnetism

terminology

references for further investigation

Types of Magnetism

paramagnetism

ferromagnetism

constituent atoms have magnetic dipole moments

moments are unaligned, but in the presence of an external magnetic field they do attempt to align

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 temperatureabove this temperature the spontaneous magnetization is lost due to thermal fluctuation

saturation magnetizationmaximum induced magnetic moment that can be obtained in an external magnetic field

separates disordered paramagnetic phase from the ordered ferromagnetic phase

Ferromagnetism

hysteresisferromagnets 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

bulk materials are divided into domainseach 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

http://hyperphysics.phy-astr.gsu.edu/hbase/solids/ferro.html#c4

domain formation

http://www.irm.umn.edu/hg2m/hg2m_d/hg2m_d.html

surface charges form creating demagnetizing field

magnetostatic energy decreases through creation of second domain

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

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)

http://www.irm.umn.edu/hg2m/hg2m_d/hg2m_d.html

P. Moriarty, Rep. Prog. Phys. 64 (2001) 297

nano impact

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

http://www.irm.umn.edu/hg2m/hg2m_d/hg2m_d.html

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

R.H. Kodama, J. Magn. Magn. Mater. 200 (1999) 359.

a good starting point for a more in depth look is:

references

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.

intrinsic nanoparticle properties

C.P. Bean, J. Appl. Phys. 26 (1955) 1381.

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.

magnetism

C. Kittel, “Introduction to Solid State Physics”, Wiley, (1986).