Néel effect

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The Néel effect appears when a superparamagnetic material placed within a conducting coil is subjected to varying frequencies of magnetic fields. The non-linearity of the superparamagnetic material acts like a frequency mixer. The voltage measured at the coil terminals then comprises several frequential components, not only at initial frequencies, but also at some frequencies of certain linear combinations. Therefore, the frequency shift of the field to be measured allows for the detection of a DC field using a standard coil.

Magnetization of a superparamagnetic material
Picture 1: magnetizing a superparamagnetic material.


French physicist Louis Néel (1904-2000) discovered in 1949 that when finely divided, ferromagnetic nanoparticles lose their hysteresis below a certain size.[1][2] This phenomenon is called superparamagnetism. The magnetization of these materials is subject to the applied field − which is highly non-linear, as shown in the graph in Picture 1. This curve is well described by the Langevin function, but for weak fields it can be simply written as:


where \chi_0 is the susceptibility at zero field and  N_e is called the Néel coefficient. The Néel coefficient reflects the non-linearity of superparamagnetic materials at low fields.


Picture 2: Demonstration of the Néel effect.

Is a coil of N turns with a surface S through which a current excitation I_{exc} and immersed in a magnetic field 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, is given by the well known formula:

e=-d\phi /dt = - SdB/dt

where B is the magnetic induction itself given by the equation:

B=\mu_0 \mu_r (H + M)

In the absence of magnetic material M = 0 and B = \mu_0 \mu_r (H_{ext} + H_{exc}). Differentiating this expression, it is obvious that the frequency of the voltage is the same as the excitation current i_{exc} and / or magnetic field H_{ext}.

In the presence of superparamagnetic material Neglecting the higher terms of the Taylor expansion, we obtain for B: B=\mu_0\mu_r((1+\chi_0)(H_{ext} + H_{exc}) + N_e (H_{ext} + H_{exc})^3)

New derivation of the first term of the equation \mu_0 \mu_r (1 + \chi_0) (H_{ext} + H_{exc}) provides frequency voltage components of the stream of excitement i_{exc} and/or of the magnetic field H_{ext}. On the other hand, the development of the second term (H_{ext} + H_{exc})^3 = H_{ext}^3 + 3H_{ext}^2H_{exc} + 3H_{ext}H_{exc}^2 + H_{exc}^3 multiplies the different frequency components which intermodule frequencies starting components and generates their linear combinations.

'The non-linearity of the superparamagnetic material acts as a frequency mixer.'

Calling H(l) the total magnetic field within the coil located at the abscissa, by integrating the above induction coil along the abscissa between 0 and L_p, and differentiating with respect to t, we get:

 u(t) = L \frac{dI(t)}{dt} + F_{Rog} \frac{d}{dt} \left[\int_0^{H} Lp(l) dl \right] + F_{Neel} \left[\int_0^{H} Lp(l) dl \right] I(t) \frac{dI(t)}{dt}

We can find the conventional terms of self-inductance and Rogowski effect 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 harmonic 2, carrying the information flow field:

u(t)=LI_{ex}w_{ex}\cos(w_{ex}t) + F_{Rog}\frac{d}{dt}\left[\int_0^{Lp}H(l)dl\right]+F_{Neel}\left[\int_0^{Lp}H(l)dl\right]\frac{I_{ex}^2}{2}w_{ex}\sin(2w_{ex}t)

with I(t)=I_{ex}\sin(w_{ex}t)

Picture 3: spectral representation of the appearance of the emf due to the Néel effect around a high-frequency carrier.


The Néel effect current sensor[edit]

Picture 4: Design of current sensor Néel effect.

An important application of the Néel effect is the measure of magnetic field radiated by a conductor with a current.[3] This is the principle of Néel effect current sensors,[4] which have been developed and patented by the company Neelogy. The interest of Néel effect is particularly to allow accurate measurement of currents or very low frequency type sensor with a current transformer without contact.

The transducer of a Néel effect current sensor consists of a coil with the core is a filled composite of superparamagnetic nanoparticles. The coil is traversed by a current excitation i_{exc}(t). In presence of an external magnetic field to be measured H_{ext}(t) the transducer transposes by Néel effect the information to be measured, H (f), around a carrier frequency, the harmonic of order 2 excitation current 2f_{exc}, which is far easier. The electromotive force generated by the coil is proportional to the magnetic field to measure H_{ext}(t) and to the square of the excitation current:

fem(t)= F_{Neel} i_{exc}^2(t) H(t)

To improve the performance of the measurement (linearity, temperature sensitivity, sensitivity to vibration, etc.), the sensor also includes a second winding-reaction it against permanently to cancel the second harmonic. The relationship between the current reaction against-and the primary current is then purely proportional to the number of aliens against reaction (I_{cr} = I_p / N_{cr}).


  1. ^ Proceedings weekly meetings of the Academy of Sciences, 1949-1901 (T228) -1949/06, pp. 664-666.
  2. ^ Louis Néel, "Theory of ferromagnetic magnetic drag grained applications with the terracotta", in Annals of Geophysics V, fasc. 2, February 1949, pp. 99-136.
  3. ^ Magnetic field and current control method and magnetic core for these sensors / publicationDetails / library? CC = EN & NR = 2891917 "Patent FR 2891917."
  4. ^ method for measuring current by means of a flow sensor of magnetic fields of a specific shape, and the resulting system has from such a process, "Patent FR 2971852"]

See also[edit]