There are several directions along which the magnetization takes place easily. These are called directions of easy magnetization [1, 2]. For instance, (100), (010), and (001) are the directions of easy magnetization for iron. This means that the internal magnetization is stable when pointing parallel to one of these directions.
Consider an assembly of single axial, single domain particles, each with anisotropy energy,
E = KV sin2q ---------- (1)
Where K is the anisotropy constant, q the angle between Ms and the easy axis and V is the particle volume [3]. If the volume of each particle is V, then the energy barrier DE that must be overcome before a particle can reverse its magnetization is KV. Now in any material, fluctuations of thermal energy are continually occurring on a microscopic scale. In 1949 Neel pointed out that, if single domain particle become small enough, KV would become so small that energy fluctuations could overcome the anisotropy forces and spontaneously reverse the magnetization of a particle from one easy direction to the other, even in the absence of an applied field. Each particle has a magnetic moment,
m = MsV ---------- (2)
If a field is applied, the field will tend to align the moments of the particles, whereas the thermal energy will tend to misalign them. This is just like the behavior of normal paramagnetic, with one notable exception that the magnetic moment per atom or ion is very high in this case. As a result, Bean has coined the very apt term superparamagnetism for describing the magnetic behavior of such particles.
In the superparamagnetic state, the magnetic direction is not fixed along any of the easy axes. It fluctuates among the easy axes of magnetization when there is no external magnetic field. The superparamagnetic relaxation time ‘t’ is the average time that it takes the particle magnetization to jump from one direction to another. The relaxation time ‘t’ depends on the size of the particle and the temperature, which is approximated by Neel as
t = t0 exp (KV/kBT) ---------- (3)
Here K is the anisotropy constant of the particle, V the particle volume, kB the Boltzmann constant and T the temperature [4]. t0 is a constant and is usually taken as t0 @ 10-10 s.
Under the application of a magnetic field H, the equation (1.5) becomes,
E = KV sin2q + HMsV cosq ---------- (4)
Solving for saturation magnetization (Ms) from the above equation,
Ms= [2K/Hc][1-(25kT/KV) 1/2] ---------- (5)
For particles of constant size there will be a temperature TB, called the blocking temperature, below which the magnetization will be stable [3]. For single axial particles,
TB = KV/25k ---------- (6)
References:
1.Physics of magnetism, Soshin Chikazumi, John Wiley and sons, Inc., New York.
2.Introduction to magnetism and magnetic materials, David Jiles, Chapman and hall,London.
3.Introduction to magnetic materials, B.D.Cullity, Addison Wesley publishing Company. 4.QiChen,Adam.J.Rondinone,Bryan.C.Chakoumakos,Z.John.Zhang1999J.Magn.Magn.Mater 194 1
Consider an assembly of single axial, single domain particles, each with anisotropy energy,
E = KV sin2q ---------- (1)
Where K is the anisotropy constant, q the angle between Ms and the easy axis and V is the particle volume [3]. If the volume of each particle is V, then the energy barrier DE that must be overcome before a particle can reverse its magnetization is KV. Now in any material, fluctuations of thermal energy are continually occurring on a microscopic scale. In 1949 Neel pointed out that, if single domain particle become small enough, KV would become so small that energy fluctuations could overcome the anisotropy forces and spontaneously reverse the magnetization of a particle from one easy direction to the other, even in the absence of an applied field. Each particle has a magnetic moment,
m = MsV ---------- (2)
If a field is applied, the field will tend to align the moments of the particles, whereas the thermal energy will tend to misalign them. This is just like the behavior of normal paramagnetic, with one notable exception that the magnetic moment per atom or ion is very high in this case. As a result, Bean has coined the very apt term superparamagnetism for describing the magnetic behavior of such particles.
In the superparamagnetic state, the magnetic direction is not fixed along any of the easy axes. It fluctuates among the easy axes of magnetization when there is no external magnetic field. The superparamagnetic relaxation time ‘t’ is the average time that it takes the particle magnetization to jump from one direction to another. The relaxation time ‘t’ depends on the size of the particle and the temperature, which is approximated by Neel as
t = t0 exp (KV/kBT) ---------- (3)
Here K is the anisotropy constant of the particle, V the particle volume, kB the Boltzmann constant and T the temperature [4]. t0 is a constant and is usually taken as t0 @ 10-10 s.
Under the application of a magnetic field H, the equation (1.5) becomes,
E = KV sin2q + HMsV cosq ---------- (4)
Solving for saturation magnetization (Ms) from the above equation,
Ms= [2K/Hc][1-(25kT/KV) 1/2] ---------- (5)
For particles of constant size there will be a temperature TB, called the blocking temperature, below which the magnetization will be stable [3]. For single axial particles,
TB = KV/25k ---------- (6)
References:
1.Physics of magnetism, Soshin Chikazumi, John Wiley and sons, Inc., New York.
2.Introduction to magnetism and magnetic materials, David Jiles, Chapman and hall,London.
3.Introduction to magnetic materials, B.D.Cullity, Addison Wesley publishing Company. 4.QiChen,Adam.J.Rondinone,Bryan.C.Chakoumakos,Z.John.Zhang1999J.Magn.Magn.Mater 194 1
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