1 / 16

Magnetism and Magnetic Materials DTU (10313) – 10 ECTS KU – 7.5 ECTS

Magnetism and Magnetic Materials DTU (10313) – 10 ECTS KU – 7.5 ECTS. Module 5 15/02/2011 Magnetic order. Mesoscale – nm- m m. Sub-atomic – pm-nm. Macro – m m-mm. Intended Learning Outcomes (ILO). (for today’s module). List the various forms of magnetic order in magnetic materials

hisano
Download Presentation

Magnetism and Magnetic Materials DTU (10313) – 10 ECTS KU – 7.5 ECTS

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Magnetism and Magnetic Materials DTU (10313) – 10 ECTS KU – 7.5 ECTS Module 5 15/02/2011 Magnetic order Mesoscale – nm-mm Sub-atomic – pm-nm Macro – mm-mm

  2. Intended Learning Outcomes (ILO) (for today’s module) List the various forms of magnetic order in magnetic materials Calculate the room-T magnetization of a given ferromagnet Relate exchange interactions with the ”molecular field” in Weiss models Explain the peak in magnetic susceptibility at the Neel temperature in antiferromagnets

  3. Flashback The spin Hamiltonian A new set of orbitals Superexchange Crystal field splitting The exchange integral

  4. Ferromagnetism In the Weiss model for ferromagnetism, exchange interactions are responsible for the huge “molecular field” that keeps moments aligned. We define an effective field acting upon each spin due to exchange interactions The Hamiltonian now looks just like the paramagnetic Hamiltonian, except there’s a field even with no applied field We relate the molecular field with the “order parameter”, i.e. the magnetization

  5. Review Brillouin paramagnetism J=1/2 J=3/2 J=5

  6. The spontaneous magnetization By solving numerically the two equations, we determine the spontaneous magnetization (in zero applied field) at a given temperature T>TC T=TC T<TC Re-estimate the effective molecular field Bmf=lMS if TC is 1000 K and J=S=1/2.

  7. The temperature dependence M(T) The case of Nickel (S=1/2) Near TC (mean-field critical exponent) Estimate the room-T M/Ms of Fe (J=S=3/2, Tc=1043 K) Low T (as required by thermodynamics)

  8. Ferromagnet and applied field T>TC T=TC T<TC Increasing B

  9. Origin of the molecular field When L is involved (e.g. 4f ions), only a part of S contributes to the spin Hamiltonian: de Gennes factor If we assume that exchange interactions are effective over z nearest-neighbours, we find: So that we reveal the proportionality between Tc and the exchange constant J L+2S=J+S L S (gJ-1)J This is valid when L is quenched (3d ions) and, therefore, J=S

  10. Antiferromagnetism Neglect those for now (but they are important for a realistic theory) Staggered magnetization (order parameter)

  11. The magnetic susceptibilities Paramagnet Ferromagnet Antiferromagnet

  12. AFM with a strong magnetic field

  13. Types of antiferromagnetic order Simple cubic BCC

  14. Ferrimagnetism and helical order Ferrimagnets: important technologically for their non-metallic nature and flexible magnetic response

  15. Sneak peek B M M Shape effects and magnetic domains

  16. Wrapping up • Ferromagnetism • Spontaneous magnetization • Ferromagnetic-to-Paramagnetic transition at Tc • Antiferromagnetism • Susceptibilities and Curie-Weiss laws • Ferrimagnetism • Helical order Next lecture: Friday February 18, 8:15, KU room 411D Micromagnetics I (MB)

More Related