Magnetization Noise in Magnetoelectronic Nanostructures

Abstract

By scattering theory we show that spin current noise in normal electric conductors in contact with nanoscale ferromagnets increases the magnetization noise by means of a fluctuating spin-transfer torque. Johnson-Nyquist noise in the spin current is related to the increased Gilbert damping due to spin pumping, in accordance with the fluctuation-dissipation theorem. Spin current shot noise in the presence of an applied bias is the dominant contribution to the magnetization noise at low temperatures.PACS numbers: 72.25. Mk, 74.40.+k, 75.75.+a Time-dependent fluctuations of observables ("noise") are a nuisance for the engineer but also a fascinating subject of study for the physicist. The thermal current fluctuations in electric circuits as well as the Poissonian current fluctuations due to the discrete electron charge emitted by hot cathodes are classical textbook subjects. The fluctuations of the order parameter in ferromagnets, such as Barkhausen noise due to moving domain walls, have been studied by the magnetism community for almost a century. Recently, it has been discovered that electronic noise is dramatically modified in nanostructures. Theoretical predictions on the suppression of charge shot noise in quantum devices have been confirmed experimentally [1]. Spin current fluctuations, i.e., spin shot noise, is as yet a purely theoretical concept [2]. In nanoscale magnetism, thermal noise plays an important role by activating magnetization reversal of ferromagnetic clusters [3]. Charge shot noise in ferromagnetic spin valve devices has been discussed as well [4,5]. Interesting new questions have been raised by recent experimental studies on the dynamics of nano-scale spin valves [6,7,8] in which electric transport is affected by the magnetization direction of the ferromagnetic elements. Central to these studies is the spin-transfer torque exerted by a spin-polarized current on the magnetization causing it to precess or even reverse direction [9,10,11]. Covington et al. [8] interpreted the observed dependence of noise spectra in nano-pillar spin valves on bias current direction in terms of this spin torque, but a full consensus has not yet been reached [12].In a normal metal the average current of net spin angular momentum (spin current) vanishes but its fluctuations are finite. In this Letter we demonstrate that equilibrium and non-equilibrium spin current noise in normal metals is directly observable in hybrid ferromagnetnormal metal structures: The noise exerts a fluctuating spin-transfer torque on the magnetization vector causing an observable magnetization noise. The theory of noise in magnetoelectronic devices requires a consistent treatment of fluctuations in the currents as well as the magnetization. We demonstrate that thermal spin current fluctuations are instrumental for the spin pumping-enhanced Gilbert damping in magnetic multilayers [13] and that spin shot noise should be observable at low temperatures. The better understanding of noise in ferromagnetic spin valves should aid the development...

Spin torque dynamics with noise in magnetic nanosystems

“…By analogy with the charge shot noise the quantization of the angular momentum transfer leads to spin shot noise, which manifests itself in a random Langevin force entering the equations of motion for the free magnetic layer. It was shown by Foros et al 16 in the context of normal metal / ferromagnet / normal metal (NFN) structures that the spin shot noise is the dominant contribution to magnetization noise at low temperatures. In the realistic experiments on spin torque and spin switching the nonequilibrium noise starts to dominate at temperatures below several Kelvins.…”

“…Since then, temperature effects on the LLG equation have been considered, both with [12][13][14][15][16] and without the spin torque term 17,18 . The emphasis of these approaches has been on the influence of noise on switching rates, often by performing explicit numerical calculations 12,13,17,18 .…”

Quantum Spin Torque

“…The contribution of quantum fluctuations to spin transfer in antiferromagnets [43] must be larger than in ferromagnets, due to higher magnon frequencies. Quantum fluctuations may contribute to other phenomena involving interaction between magnetization and conduction electrons, including spin pumping [44], spin-orbit [45][46][47], optically driven [48][49][50], and spin-caloritronic effects [51][52][53][54][55].…”

Charge pumping and the colored thermal voltage noise in spin valves

“…Similarly, the ferromagnet loses energy and angular momentum by spin pumping. The magnetic damping increment ␣Ј must be accompanied by a fluctuating transverse spin current ͑torque͒ I s fl from the contacts, 29 which can be represented by another random magnetic field hЈ : I s fl =−M tot m ϫ hЈ with autocorrelator 29…”

“…23,24 In magnetic structures such as spin valves, thermal fluctuations of the magnetization direction have to be considered. 25 Some consequences of thermal fluctuation in spin valves, such as noise-facilitated magnetization switching [26][27][28] and resistance fluctuations, 29,30 have been studied before. In the so-called thermal ferromagnetic resonance, frequencies are studied by means of resistance fluctuations without applied magnetic fields.…”