1. Magnetic Properties Scott Allen Physics Department University of Guelph of nanostructures

2. Outline Domains Ferromagnetism Types of magnetism nano impact on magnetism terminology references for further investigation

3. 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)

4. Ferromagnetism exchange field (B E ) 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 saturation magnetization maximum induced magnetic moment that can be obtained in an external magnetic field separates disordered paramagnetic phase from the ordered ferromagnetic phase

5. 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

6. 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?

7. Domains 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 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

8. 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

9. 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

10. 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

11. 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

12. 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:

13. 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).