1. rock magnetism

2. Rock magnetism Remanent magnetism Anisotropy & domains
High-field analyses
Magnetic stability

3. Remanent magnetism

4. At atomic level: electronic shells
Electron shells around the nucleus: negatively charged particles
Niels Bohr, early 1900s

5. At atomic level: electronic shells
Three rules:
Pauli’s exclusion principle: electrons may not be ‘equal’ in spins. Single electron in an orbital: magnetic moment 1 Mb (Bohr magnetron)
Orbitals are filled following the least energy principle
Electrons are added to the system so that the spins are as parallel as possible (Hund’s rule)

6. Electronic shells Fe: 4 mb Fe2+: 4 mb Fe3+: 5 mb Bohr magneton (mb):
9.27 × Am2
Look at the d-shell: a lot of unpaired electrons
Fe: 4 mb
Fe2+: 4 mb
Fe3+: 5 mb

7. Diamagnetism
The orbit of the electron has an angular momentum vector L which creates a magnetic moment. In the presence of a magnetic field H, the moment experiences a torque which causes a change in angular momentum ΔL. The precession of the electronic orbit about H creates an induced magnetic moment Δm in a sense opposite to the applied field H.
Weak, present in all materials.
Frog in 16 T field in Nijmegen

8. Paramagnetism
unpaired electrons without exchange interaction. VERY STRONG

9. Ferromagnetism
REMANENT. At least as function of time, and temperature.
Role of oxygen as ‘catalist’ for magnetic coupling -> bridging neighboring cations.

10. Ferromagnetism in magnetite

11. Ferromagnetic spin alignment
Fe, Ni, Co
wüstite
hematite
hematite, goethite
ferro: exchange energy is minimized when all the spins are parallel, as occurs in pure iron.
antiferro: When spins are perfectly antiparallel, there is no net magnetic moment, as occurs in ilmenite.
spin-canting: gives rise to a weak net moment, as occurs in hematite
defect moment: The uncompensated spins result in a so-called defect moment.
Ferrimagnetism, spins are also aligned antiparallel, but the magnitudes of the moments in each direction are unequal, resulting in a net moment
(titano)magnetite, greigite, pyrrhotite

12. Shape anisotropy Preferred axis or ‘easy axis’ of magnetization
Long axis preferred:
Minimal surface poles
Minimal field leakage
Minimal demagnetizing field
Preferred axis or ‘easy axis’ of magnetization

13. Energy contributions
Exchange energy: magnetic spin moments as much parallel as possible
Magnetostatic energy: energy of the particle because of its magnetization/magnetic moment
Anisotropy energy: energy barrier to switch among local energy minima
Torque: because of angle between particle’s preferred magnetization and the applied field
Magnetostriction: energy because of material deformation as a consequence of the action of the applied field
exchange: source of spontanous magnetization, based on Pauli’s exclusion principle (electrons with same config cannot borrow each other’s orbit and are forced in a certain direction.
magnetotstatic: ‘paramagnetism’ because of magnetic particles
anisotropy: many forms -> crystalline, stress
Torque -> unimportant
Magnetostriction: stress/deformation induced magnetism (dynamite blows)

14. Magnetocrystalline anisotropy
For equant single-domain particles or particles with low saturation magnetizations, the crystal structure dominates the magnetic energy. In such cases, the so-called easy directions of magnetization are crystallographic directions along which magnetocrystalline energy is at a minimum. The energy surface represents the magnetocrystalline anisotropy energy density, ϵa for magnetite at room temperature. The highest energy bulges are in directions perpendicular to the cubic faces ([001, 010, 100]). The lowest energy dimples are along the body diagonals ([111]).

15. Magnetostriction
Exchange energy depends strongly on the details of the physical interaction between orbitals in neighboring atoms with respect to one another, hence changing the positions of these atoms will affect that interaction. Put another way, straining a crystal will alter its magnetic behavior. Similarly, changes in the magnetization can change the shape of the crystal by altering the shapes of the orbitals. This is the phenomenon of magnetostriction.

16. Magnetic domains Vortex, concept of walls
‘self-energy’ vs ‘wall-energy’

17. Magnetic domains
Walls and cancelling out its internal moment

18. Magnetic domains Single domain (SD) Pseudo-single-domain (PSD)
domain configs, closure domains
Single domain (SD)
Pseudo-single-domain (PSD)
Multidomain (MD)

19. Magnetic domains
in 3D…

20. Domain walls
It’s all about energy… Width of the wall vs self-energy

21. Bloch wall
Bloch walls = panel b
Neel = in plane of wall

22. Néel wall
Bloch walls = panel b
Neel = in plane of wall

23. Domain observations: Bitter patterns
Bitter patterns from an oriented polished section of magnetite. [Figure from Özdemir et al., 1995].
Typical angles for magnetite: 71, 109, and 180 degrees.

24. Imaging domains as function of T
a) AF demagnetized state, b), c) thermal cycle, magnetocrystalline dominated patterns (at higher temperature wavy magnetostriction-dominated pattern). d), e) on cooling different pattern develops, it resembles but does not duplicate original structure f) after another thermal cycle.

25. Domain observations: MOKE
Domains revealed by longitudinal magneto-optical Kerr effect. [Image from Heider and Hoffmann, 1992.]

26. Domain observations: MFM
Etna 1971 flow
a) AF demagnetized state, b), c) thermal cycle, magnetocrystalline dominated patterns (at higher temperature wavy magnetostriction-dominated pattern). d), e) on cooling different pattern develops, it resembles but does not duplicate original structure f) after another thermal cycle.
14.6 mm
14.6 mm
Standard polish

27. Sample processing… Etna 1971 flow 14.6 mm 14.6 mm Syton polish
a) AF demagnetized state, b), c) thermal cycle, magnetocrystalline dominated patterns (at higher temperature wavy magnetostriction-dominated pattern). d), e) on cooling different pattern develops, it resembles but does not duplicate original structure f) after another thermal cycle.
14.6 mm
14.6 mm
Syton polish

28. Domain observations: Electron holography
Harrison et al., 2002 PNAS

29. SD vs. MD vs. shape

30. High-field rock-magnetic analyses

31. Our lab: 2 T ‘Micromag’

32. Our lab: 2.2 T ‘VSM’ Cupboard with stuff VSM Argon bottle N2 tap
Magnets
Touch screen
Controller rack

33. High Magnetic Field Lab., Nijmegen: 32 T
Own 50 kV power switching station
40 MW consumption at peak field

34. High Magnetic Field Lab., Toulouse: 60 T
Laboratoire National des Champs Magnétiques Intenses
~60 ms upramp
~300 ms downramp
Max. field ~60 Tesla: 14 MJ at 19 kV, equiv. of 200 MW

35. Hysteresis loop

36. Hysteresis loop

37. Hysteresis loop

38. Hysteresis loop

39. Hysteresis loop

40. Single vs. multidomain grains
H = Hmax
Single domain
Multidomain

41. Single vs. multidomain grains
H = 0
Single domain
Multidomain

42. Hysteresis loop Fig. 8.11 diamagnetic paramagnetic super- uniaxial
single domain
magn. crystal.
pseudo-single
domain
mt. + ht
SD+SP mt.

43. IRM & Back-field curves
Mr (Mrs) = isothermal remanent saturation magnetization
Bs = saturation field
Bcr = remanent coercive force

44. Back-field curves & hys loopsMs Mr
Bcr Bc

45. Classic hysteresis parameters
Mr/Ms = squareness, remanence ratio
Bcr/Bc = Hcr/Hc = coercivity ratio
Plotted against each other : Day plot

46. Day plots MD SD PSD SP: offset to the right Mr/Ms Bcr/Bc
Dunlop, 2002, JGR

47. Domain structure & grain size
From small to large grain size:
Superparamagnetic (SP)
Single domain (SD)
(Flower state) / (Vortex state)
Pseudo-single-domain (PSD)
Multidomain (MD)

48. Next: finish computer assignment
van Unnik 402 (GIS-room)