# Introduction on noise in magnetic systems

The electronic noise in magnetic systems comes from various origins and ca n be separated as function of their frequency dependence. This has been well described in a chapter written by Bertrand Raquet in a Spin electronics book published by MagOX [1].

## White thermal noise

The thermal noise is due to spontaneous fluctuations induced by the thermal excitations. This noise, owing the fluctuation-dissipation theorem (2nd thermodynamic law consequence) is related to the resistance of the system investigated by the Nyquist [2] formula.

A Fourier transform analysis gives a power spectral density :

(1)

This noise has no magnetic origin and cannot be suppressed or modified but it is independent of the sensitivity of the sensor and depends only on the total resistance of the sensor.
At high frequencies, quantum corrections should be taken into account.

## Low frequency noise

In addition to the white noise, a 1/f frequency dependent noise appears in all magnetic or non magnetic systems. This noise is due to fluctuations of energy around equilibrium. It can be seen as a weighted sum of two level fluctuators. In magnetic systems, magnetic domain fluctuations (in size or orientation) can create such a 1/f noise.

This noise is very important for applications like neuro-imaging but also for applications of magnetic sensors like, compass, position control; current sensors etc…

Its main characteristic is to be created by resistance fluctuations and then it varies in the case of GMR sensors as fast as the sensing current (i.e the sensitivity). It cannot be avoided in a easy way.

There is a general formula given by  Hooge in 1969 [3].

(2)

The parameter is called Hooge constant and it is used as comparison reference for 1/f noise.

This parameter is about 10-210-3 for standard good metallic systems but it can be much higher in case of magnetic fluctuations.

Presence of magnetic fluctuators like domain walls is a strong source of magnetic 1/f noise. A lot of examples are shown in the literature(references given below). In the project magnoise, we have demonstrated that the absence of magnetic domains induces noise in sensors which is comparable to non magnetic metallic systems.

The 1/f noise is inversely proportional to the volume of the sample. For that reason, it is often necessary to measure the noise in thin films with reduced lateral sizes.

## Random telegraph noise or RTN

If the size decreases, there are only a few number of fluctuators and the noise has a behaviour of a random telegraph noise (RTN) with strong jumps between 2 or several levels.
RTN is very interesting for the determination of the fluctuating object . This can be achieved by investigating the average time in the low state as function of temperature

## High frequency noise

In magnetic system, high frequency noise can by created by 2 different mechanisms.

The first one is related to high frequency magnetic fluctuations which can be directly linked to spin waves. This noise appears for frequencies higher than 200 MHz. The second one is due to the fact that electrons are discrete. This noise called shot noise gives a rather flat noise. It is very small for metallic systems except in the special case of TMR junctions where small constrictions can strongly enhance this effect.

[1] Spin electronics, M. Ziese and M. Thornton (eds), Sringer

[2] H. Nyquist, Phys. Rev. 32, 110 (1928)

[3] F.N. Hooge Physica B 83, 14 (1969)