The state of very small ferromagnetic particles in which the barrier to reversal, KV, is small compared with the thermal energy, so the magnetization reverses thermally and the coercivity is almost zero.
Japanese name: 超常磁性
Superparamagnetism appears in 2 practice questions across 1 topic, including Magnetic materials.
Field: Magnetic materials
In small single-domain particles, the magnetization of the whole particle behaves as one large magnetic moment and can switch between the two directions along the easy axis by crossing an energy barrier KV. If the barrier is not sufficiently large compared with the thermal energy kT, the magnetization reverses frequently by thermal activation and appears to be 0 on average. This is superparamagnetism, and ferromagnetic order is preserved inside the particle. The moment of a single magnetite particle 10 nm in diameter is about 27000 times the Bohr magneton, so the susceptibility is far larger than that of paramagnetic atoms. The super in the name comes from this large moment.
The mean time before the magnetization reverses (the Néel relaxation time) is τ = τ₀ exp(KV/kT), where τ₀ is of the order of 10⁻⁹ s. Whether a particle appears superparamagnetic depends on how τ compares with the time taken by the measurement. In DC magnetization measurements (about 100 s) the boundary is KV ≈ 25kT, and the temperature that satisfies this is called the blocking temperature T_B. T_B is proportional to volume, so for the same material, doubling the particle volume also doubles T_B. In Mössbauer spectroscopy, whose measurement time is much shorter, the same particles show a higher T_B, so it is important to state the method of measurement.
The magnetization curve of an assembly of superparamagnetic particles has no hysteresis and approaches saturation in the form of a Langevin function, which resembles paramagnetism. But because each moment is large, it approaches saturation at fairly modest fields even at room temperature. Below the blocking temperature, reversal of the magnetization is frozen and coercivity appears. Experimentally, the ZFC curve, measured after cooling without a field, is compared with the FC curve, measured after cooling in a field, and blocking is examined from the temperature at which the two begin to separate. A distribution of particle sizes spreads T_B, so analysis is combined with the size distribution.
The property of retaining no magnetization once the field is switched off is useful in medicine and biology. Superparamagnetic iron oxide nanoparticles are used as MRI contrast agents, in hyperthermia, where they are heated by an AC field, and in separating cells and molecules by collecting them with magnets; an advantage is that once the field is off the particles do not readily cluster magnetically. In hard disks, on the other hand, the limit at which shrinking the bits makes the grains superparamagnetic and the data disappear (the superparamagnetic limit) is a problem. Keeping data for 10 years with τ₀ = 10⁻⁹ s requires KV/kT of about 40 or more by a simple estimate, and heat-assisted recording, which temporarily makes high-anisotropy FePt easier to write by heating, was developed.
Answer: C. About 26 nm
The boundary volume is V = 25kT/K = 25 × 1.38×10⁻²³ × 300/(1.1×10⁴) ≈ 9.4×10⁻²⁴ m³. From the volume of a sphere V = πd³/6, d = (6V/π)^(1/3) ≈ 2.6×10⁻⁸ m, so particles with diameters of about 26 nm or less become superparamagnetic. About 13 nm is the radius, given as if it were the diameter, and about 9 nm drops the factor of 25 and uses KV = kT. The factor of 25 comes from ln(100 s/10⁻⁹ s) ≈ 25, taking the attempt time for reversal as about 10⁻⁹ s. The diameter is inversely proportional to the cube root of K, so materials with larger anisotropy can keep their magnetization stable even in smaller particles.
Paramagnetism is a state in which the small moments of individual atoms point in random directions; superparamagnetism is a state in which the large moment of each whole ferromagnetic particle is randomized by heat. Because the moments are thousands to tens of thousands of times larger, superparamagnetic particles magnetize strongly even in weak fields. They also differ in that coercivity appears on cooling.
It depends on the material's anisotropy constant, the temperature and the measurement time. Taking KV ≈ 25kT as a guide, at room temperature the limit is a diameter of roughly 20 to 30 nm or less for iron oxides with small anisotropy, and a few nanometers or less for ordered FePt with large anisotropy. The larger the anisotropy, the smaller the particle that can keep a stable magnetization.
Yes. They magnetize strongly when an external field is applied, so particles in a liquid can be collected with a magnet. When the field is removed, the magnetization returns almost to 0 and the particles disperse again. This property is used in magnetic fluids and magnetic separation.
From the volume of a sphere V = πd³/6, d = (6V/π)^(1/3) ≈ 2.6×10⁻⁸ m, so particles with diameters of about 26 nm or less become superparamagnetic.
Take the energy barrier for thermal reversal of the magneti…Making them smaller still makes the energy barrier to reversal, KV, small compared with the thermal energy, so the magnetization reverses spontaneously by thermal activation (superparamagnetism) and the coercivity approaches zero.
As particles of a ferromagnet are made smaller, from a few …Coercivity Magnetic domain Domain wall Eddy-current loss Ferrimagnetism Magnetocrystalline anisotropy Maximum energy product Saturation magnetization