Néel effect

Theory

If a coil of ${\displaystyle N}$ turns with a surface ${\displaystyle S}$ through which passes a current of excitation ${\displaystyle I_{\text{exc}}}$ is immersed in a magnetic field ${\displaystyle H_{ext}}$ 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, ${\displaystyle e}$, is given by the formula:

${\displaystyle e=-d\varphi /dt=-SdB/dt}$

where ${\displaystyle B}$ is the magnetic induction given by the equation:

${\displaystyle B={\mu }_0{\mu }_r(H+M)}$

In the absence of magnetic material,

${\displaystyle M=0}$

and

${\displaystyle B={\mu }_0{\mu }_r(H_{ext}+H_{\text{exc}})}$.

Differentiating this expression, the frequency of the voltage is the same as the excitation current ${\displaystyle i_{\text{exc}}}$ or the magnetic field ${\displaystyle H_{ext}}$.

In the presence of superparamagnetic material, neglecting the higher terms of the Taylor expansion, we obtain for B:

${\displaystyle B={\mu }_0{\mu }_r((1+{\chi }_0)(H_{ext}+H_{\text{exc}})+N_e(H_{ext}+H_{\text{exc}}{)}^3)}$

A new derivation of the first term of the equation ${\displaystyle {\mu }_0{\mu }_r(1+{\chi }_0)(H_{ext}+H_{\text{exc}})}$ provides frequency voltage components of the stream of excitement ${\displaystyle i_{\text{exc}}}$ or the magnetic field ${\displaystyle H_{ext}}$.

The development of the second term ${\displaystyle (H_{ext}+H_{\text{exc}}{)}^3=H_{ext}^3+3H_{ext}^2{H}_{\text{exc}}+3H_{ext}{H}_{\text{exc}}^2+H_{\text{exc}}^3}$ multiplies the frequency components in which intermodular frequencies start components and generate their linear combinations. The non-linearity of the superparamagnetic material acts as a frequency mixer.

Calling ${\displaystyle H(l)}$ the total magnetic field within the coil at the abscissa, integrating the above induction coil along the abscissa between 0 and ${\displaystyle L_p}$ and differentiating with respect to ${\displaystyle t}$ obtains:

${\displaystyle u(t)=L\frac{dI(t)}{dt}+F_{Rog}\frac{d}{dt}\left[{\int }_0^{H}Lp(l)dl\right]+F_{\text{Neel}}\left[{\int }_0^{H}Lp(l)dl\right]I(t)\frac{dI(t)}{dt}}$

with ${\displaystyle I_{\text{exc}}(t)=I_{\text{exc}}\cos (w_{\text{exc}}t)}$

The conventional terms of self-inductance and Rogowski effect are found in both the original frequencies. The third term is due to the Néel effect; it reports the intermodulation between the excitation current and the external field.

When the excitation current is sinusoidal, the effect is Néel characterized by the appearance of a second harmonic carrying the information flow field:

${\displaystyle u(t)=L{I}_{\text{exc}}{w}_{\text{exc}}\cos (w_{\text{exc}}t)+F_{Rog}\frac{d}{dt}\left[{\int }_0^{Lp}{H}_{ext}(l)dl\right]+F_{\text{Neel}}\left[{\int }_0^{Lp}{H}_{ext}(l)dl\right]\frac{I_{\text{exc}}^2}{2}{w}_{\text{exc}}\sin (2w_{\text{exc}}t)}$

Applications

An important application of the Néel effect is as a current sensor, measuring the magnetic field radiated by a conductor with a current; this is the principle of Néel effect current sensors. The Néel effect allows the accurate measurement of currents with very low-frequency-type sensors in a current transformer without contact.

The transducer of a Néel-effect current sensor consists of a coil with a core of superparamagnetic nanoparticles. The coil is traversed by a current excitation:

${\displaystyle i_{\text{exc}}(t)}$.

In the presence of an external magnetic field to be measured:

${\displaystyle H_{ext}(t)}$

the transducer transposes (with the Néel effect) the information to be measured, H (f) around a carrier frequency, the harmonic of order 2 excitation current 2:

${\displaystyle f_{\text{exc}}}$

which is simpler. The electromotive force generated by the coil is proportional to the magnetic field to measure:

${\displaystyle H_{ext}(t)}$

and to the square of the excitation current:

${\displaystyle fem(t)=F_{\text{Neel}}{i}_{\text{exc}}^2(t)H(t)}$

To improve the measurement's performance (such as linearity and sensitivity to temperature and vibration), the sensor includes a second permanent winding-reaction against it to cancel the second harmonic. The relationship of the current reaction against the primary current is proportional to the number of turns against reaction:

${\displaystyle I_{cr}=I_p/N_{cr}}$.