Effect of temperature on remnant magnetization
Heating a sample above its Curie temperature is a way of demagnetizing it Thermal demagnetization
Non-linear responses
Non-linear responses
Generally, the response of M to H is non-linear Only at small values of H or high temperatures is response sometimes linear
Non-linear responses
M tends to saturate at high fields and low temperatures
The Microscopic Picture of Magnetic Materials
We will now revisit the experimentally observed magnetic behaviours and try to understand them from a microscopic point of view
Paramagnetic gas
Imagine a classical gas of molecules each with a magnetic dipole moment In zero field the gas would have zero magnetization
Paramagnetic gas
Applying a magnetic field would tend to orient the dipole moments Gas attains a magnetization
Paramagnetic gas
Very high fields would saturate magnetization Heating the gas would tend to disorder the moments and hence decrease magnetization
Ferromagnetism
Materials that retain a magnetization in zero field Quantum mechanical exchange interactions favour parallel alignment of moments Examples: iron, cobalt
Ferromagnetism
Thermal energy can be used to overcome exchange interactions Curie temp is a measure of exchange interaction strength Note: exchange interactions much stronger than dipoledipole interactions
Magnetic domains
Ferromagnetic materials tend to form magnetic domains Each domain is magnetized in a different direction Domain structure minimizes energy due to stray fields
Magnetic domains
Applying a field changes domain structure Domains with magnetization in direction of field grow Other domains shrink
Magnetic domains
Applying very strong fields can saturate magnetization by creating single domain
Magnetic domains
Removing the field does not necessarily return domain structure to original state Hence results in magnetic hysteresis
Break up of magnetization into domains due to energy minimization
Single domain Large magnetostatic energy Uniformly magnetized specimen Overall energy of the system Four domains 1/4 Two domains 1/2
Closure domains zero
180o domain wall
e = A (d / dx)2 + K sin2
Exchange J/m Anisotropy J/m3
Exchange energy
large
small
Change in domains during magnetization process
Partial magnetization E = - 0M.H Domain wall movement Irreversible rotation of domain magnetization Coherent rotation of moments from the easy axes lying close to the field direction Single-domain sample Spontaneous magnetization
Magnetic domain walls
Wall thickness, t, is typically about 100 nm
Antiferromagnetism
In some materials, exchange interactions favour antiparallel alignment of atomic magnetic moments Materials are magnetically ordered but have zero remnant magnetization and very low Many metal oxides are antiferromagnetic
Antiferromagnetism
Thermal energy can be used to overcome exchange interactions Magnetic order is broken down at the Nel temperature
Ferrimagnetism
Antiferromagnetic exchange interactions Different sized moments on each sublattice Results in net magnetization Example: magnetite, maghemite
Single domain particles
Particles (nano) smaller than t (100 nm) have no domains
Multidomain
t< 100 nm Single domain
Surface area increases and volume remains the same
Single cube
Eight smaller cubes 1000 tiny cubes
Length of one side Total surface area(H x W x Number of sides x Number of cubes) Total volume (L x W x H x Number of cubes) Surface area to volume ratio Surface area volume
20 m 2400 m2 8000 m3 0.3
10 m
2 m
4800 m2 24,000 m2 8000 m3 0.6 8000 m3 3.0
Magnetic nanoparticles behavior
Assembly of magnetic clusters (each comprised of many ferromagentically aligned elemental moments of magnitude () acting independently Superparamagnetic material
Superparamagnetism
Unblocked particles that respond to a field are known as superparamagnetic
Superparamagnetism
in nanoparticles No remanent magnetism upon field removal Applications: Magnetization (emu) Magnetic Inks 300 K Magnetic separation Vacuum sealing Magnetic marking Magnetic refrigeration Applied field, H (T) MRI
Superparamagnetism
Response of superparamagnets to applied field described by Langevin model Qualitatively similar to paramagnets At room temperature superparamagnetic materials have a much greater magnetic susceptibility per atom than paramagnetic materials
Room temp
Superparamagnetism
Superparamagnets are often ideal for applications where a high magnetic susceptibility is required zero magnetic remanence is required
Room temp
Size effect
Ferromagnet Paramagnet Superparamagnet
Magnetic interactions
Magnetic dipolar interaction
Two magnetic dipoles 1 and 2 separated by a distance r have an energy equal to E = 0/4r3[1 . 2 - 3/r2(1 . r)(2 . r)] : if = 1 B & r = 1 ~ 10-23 J (1 ~ K)
Exchange interaction
Direct exchange Indirect exchange (Superexchange, double exchange and anisotropic exchange)
Direct exchange
Magnetic moments interact via an exchange interaction
H = - J Si . Sj Heisenberg Hamiltonian J = Positive Ferromagnetic = Negative Antiferromagnetic In rare-earths, the 4f electrons are strongly localized and lie very close to the nucleus Even in transition metals, such as Fe, Co and Ni where the 3d orbitals extend further from the nucleus, it is difficult to explain the observed magnetic properties
Indirect exchange: Superexchange
An indirect exchange interaction between nonneighbouring magnetic ions which is mediated by a non-magnetic ion placed in between the magnetic ions
Double exchange
LaMn3+O3 d4
Antiferromagnetic
La1-xSrxMn3+O3
X=0.2
Ferromagnetic
Magnetic anisotropy
Are the magnetic properties same in all directions? No It depends on the crystallographic direction in which the magnetic dipoles are aligned
Crystal anisotropy (Spin Orbit Coupling) Shape anisotropy Stress anisotropy Externally induced anisotropy Exchange anisotropy
E = KVsin2 (simplest form)
K the effective uniaxial anisotropy energy per unit volume V particle volume angle between moments and easy axis
Magnetocrystalline anisotropy in magnetite
Magnetocrystalline anisotropy of cobalt
K = 4.1 x 105 J/m3
Magnetization of small particles
Easy direction
Hard direction
Ferrofluid
Audio speaker Domain detection Optical pick-up Biomedical applications
Drug Delivery
GMR can be considered one of the first real applications of the promising field of nanotechnology.
Nobel Prize Committee, October 2007 What's Giant in Giant Magnetoresistance? Although the term "giant" in giant magnetoresistance (GMR) seems incongruous for a nanotechnology device, it refers to a large change in resistance (typically 10 to 20%) when the devices are subjected to a magnetic field, compared with a maximum sensitivity of a few percent for other types of magnetic sensors.
Nanotechnology Structure GMR structures are ferromagnetic alloys sandwiched around an ultrathin nonmagnetic conducting middle layer:
A) is a conductive, nonmagnetic interlayer. Magnetic moment in alloy (B) layers face opposite directions due to antiferromagnetic coupling. Resistance to current (C) is high. The nonmagnetic conducting layer is often copper. Copper is normally an excellent conductor, but when it is only a few atoms thick, electron scattering causes coppers resistance to increase significantly. This resistance changes depending on the relative orientation of electron spins surrounding the conducting layer Applying an external magnetic field (D) overcomes antiferromagnetic coupling, aligning magnetic moments in alloy (B) layers:
Such exposure changes the device resistance so the structure can be used to sense an external field. Practical devices are often made of multiple layers of alternating magnetic and nonmagnetic layers to improve sensitivity.
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