1. Montek Singh COMP790-084 Sep 6, 2011

2.  Basics of magnetism  Nanomagnets and their coupling  Next class: ◦ Challenges and Benefits ◦ Open questions

3. Magnetic domains  Magnetic domains  regions within magnetic material with uniform magnetization…  … separated by “domain walls”  magnetic moments all exactly aligned  responsible for magnetic behavior of “ferromagnetic” materials: iron, nickel, etc.  What causes them?  magneto-static energy is minimized  Other energy terms:  magnetoelastic anisotropy  magnetocrystalline anisotropy  Zeeman energy

4.  Magnetic domains ◦ more domains reduces magnetostatic energy ◦ but increases wall energy  Single Domain (SD) ◦ 10 to 100nm is a good size

5.  Magnetization ◦ … under externally applied magnetic field (H) ◦ domains change shape and magnetic moments re-orient  walls shift or disappear ◦ even physical shape of material can change somewhat!  called magnetostriction  useful in actuators and sensors ◦ in strong enough field, all domains aligned  minimizes Zeeman energy

6.  Shape-induced magnetic anisotropy ◦ long grains tend to have magnetic moments along the longer dimension ◦ magnetized grain produces internal magnetic field that counters external field  internal field is anisotropic  Magnetization axis can be determined by fabricated shape ◦ gives us two states! ◦ comes in handy for magnetic storage!

8.  Two types of coupling ◦ ferromagnetically ordered coupling  collinear along the long axes  states line up ◦ antiferromagnetically ordered coupling  side-by-side, in parallel  favors antiparallel: up-down-up-down…