The Fluctuation-Dissipation Theorem (FDT) describes the close relationship between the fluctuation and dissipation, i.e. the fluctuation and dissipation are caused by the exact same physical process. For example, in Brownian motion, the random force that gives rises to the random walk also causes the viscous force for the motion.
The thermal noise in normal conductors is called the Johnson-Nyquist noise. [1,2] By FDT, the spectrum of Johnson-Nyquist noise S(ω) = 4kBTR(ω), with Boltzmann constant kB, temperature T, and frequency dependent resistance R. This thermal noise arises from the random walks of electrons in the conductor.
In magnetic structures, like a spin valve (see above), in addition to the random walks of electrons, there is also random walks of magnetization m, i.e. the fluctuations of the magnetization direction, which also manifest themselves as thermal noise. This thermal noise current consists of two contributions, 1) the spin pumping current noise flowing from FM toward NM induced by the random dynamics of the magnetization due to thermal fluctuation, 2) the fluctuating spin current flowing from NM toward FM due to the thermal activation of electron distribution in NM. The sum of these two contributions gives the total current noise in the structure and thus the voltage noise. [3]
The spectrum of the noise depends on the relative orientation of the two magnetizations in the spin valve. Assuming m fluctuates around z-axis, then the voltage noise measured across the spin valve is different for m0 in x or z direction. The spectrum is plotted on the left figure, where we see when m0 is parallel to x the spectrum consists of a white noise background (similar to the Johnson-Nyquist noise), and an absorption dip at the resonance frequency of the free layer m. The width and the depth of the dip are proportional to the total magnetic damping and the spin-pumping enhanced damping respectively. Therefore by studying the thermal noise spectrum of a magnetic structure, one my get information about the magnetic film properties and structure properties. [3]
- Reference:
[1]. Johnson, J.B. Thermal Agitation of Electricity in Conductors. Phys. Rev. 32, 97 (1928).
[2]. Nyquist, H. Thermal Agitation of Electric Charge in Conductors. Phys. Rev. 32, 110 (1928).
[3]. Xiao, J., Bauer, G.E.W., Maekawa, S. & Brataas, A. Charge pumping and the colored thermal voltage noise in spin valves. Phys. Rev. B 79, 174415-9 (2009).