In superparamagnetism (a form of magnetism), the Néel effect appears when a superparamagnetic material in a conducting coil is subject to varying frequencies of magnetic fields. The non-linearity of the superparamagnetic material acts as a frequency mixer, with voltage measured at the coil terminals. It consists of several frequency components, at the initial frequency and at the frequencies of certain linear combinations. The frequency shift of the field to be measured allows for detection of a direct current field with a standard coil.
History In 1949 French physicist Louis Néel (1904-2000) discovered that when they are finely divided, ferromagnetic nanoparticles lose their hysteresis below a certain size; this phenomenon is known as superparamagnetism. The magnetization of these materials is subject to the applied field, which is highly non-linear. This curve is well described by the Langevin function, but for weak fields it can be simply written as:
M ( H ) = χ 0 H + N e H 3 + ε ( H 3 ) {\displaystyle M(H)=\chi _{0}H+N_{e}H^{3}+\varepsilon (H^{3})} , where χ 0 {\displaystyle \chi _{0}} is the susceptibility at zero field and N e {\displaystyle N_{e}} is known as the Néel coefficient. The Néel coefficient reflects the non-linearity of superparamagnetic materials in low fields.
Theory
If a coil of N {\displaystyle N} turns with a surface S {\displaystyle S} through which passes a current of excitation I exc {\displaystyle I_{\text{exc}}} is immersed in a magnetic field H e x t {\displaystyle H_{ext}} collinear with the axis of the coil, a superparamagnetic material is deposited inside the coil. The electromotive force to the terminals of a winding of the coil, e {\displaystyle e} , is given by the formula:
e = − d ϕ / d t = − S d B / d t {\displaystyle e=-d\phi /dt=-SdB/dt}
where B {\displaystyle B} is the magnetic induction given by the equation:
B = μ 0 μ r ( H + M ) {\displaystyle B=\mu _{0}\mu _{r}(H+M)}
In the absence of magnetic material,
M = 0 {\displaystyle M=0}
and
B = μ 0 μ r ( H e x t + H exc ) {\displaystyle B=\mu _{0}\mu _{r}(H_{ext}+H_{\text{exc}})} . Differentiating this expression, the frequency of the voltage is the same as the excitation current i exc {\displaystyle i_{\text{exc}}} or the magnetic field H e x t {\displaystyle H_{ext}} . In the presence of superparamagnetic material, neglecting the higher terms of the Taylor expansion, we obtain for B:
B = μ 0 μ r ( ( 1 + χ 0 ) ( H e x t + H exc ) + N e ( H e x t + H exc ) 3 ) {\displaystyle B=\mu _{0}\mu _{r}((1+\chi _{0})(H_{ext}+H_{\text{exc}})+N_{e}(H_{ext}+H_{\text{exc}})^{3})}
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