Measuring a population of spin waves from the electrical noise of an inductively coupled antenna

T. Devolder, S.-M. Ngom, A. Mouhoub, J. Létang, J.-V. Kim, P. Crozat, J.-P. Adam, A. Solignac, and C. Chappert

Phys. Rev. B 105, 214404 – Published 3 June 2022

Abstract

We study how a population of spin waves can be characterized from the analysis of the electrical microwave noise delivered by an inductive antenna placed in its vicinity. The measurements are conducted on a synthetic antiferromagnetic thin stripe covered by a micron-sized antenna that feeds a spectrum analyzer after amplification. The antenna noise contains two contributions. The population of incoherent spin waves generates a fluctuating field that is sensed by the antenna: this is the “magnon noise.” The antenna noise also contains the contribution of the electronic fluctuations: the Johnson-Nyquist noise. The latter depends on all impedances within the measurement circuit, which includes the antenna self-inductance. As a result, the electronic noise contains information about the magnetic susceptibility of the stripe, though it does not inform on the absolute amplitude of the magnetic fluctuations. For micrometer-sized systems at thermal equilibrium, the electronic noise dominates and the pure magnon noise cannot be determined. If in contrast the spin wave bath is not at thermal equilibrium with the measurement circuit, and if the spin wave population can be changed then one could measure a mode-resolved effective magnon temperature provided specific precautions are implemented.

Received 4 April 2022
Accepted 24 May 2022

DOI:https://doi.org/10.1103/PhysRevB.105.214404

Physics Subject Headings (PhySH)

Spin waves

Synthetic antiferromagnetic multilayers

Brillouin scattering & spectroscopy Noise measurements

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

T. Devolder ^1,*, S.-M. Ngom¹, A. Mouhoub¹, J. Létang¹, J.-V. Kim ¹, P. Crozat¹, J.-P. Adam¹, A. Solignac², and C. Chappert ¹

¹Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies, 91120, Palaiseau, France
²SPEC, CEA, CNRS, Université Paris-Saclay, 91191 Gif-sur-Yvette, France

^*thibaut.devolder@u-psud.fr

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Vol. 105, Iss. 21 — 1 June 2022

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Images

Figure 1
Properties of synthetic antiferromagnet (SAF) films. (a) Sketch of the stack. (b) Sketch of the device and main notations. (c) Field derivative of the imaginary part of the permeability of the film measured by VNA-FMR prior to patterning using an external stripline of width 0.05 mm and an rf power of 0 dBm. The optical and acoustical spin wave resonances at zero wave vector have frequencies corresponding to the red/blue frontiers. (d) Spin wave thermal spectra measured by BLS microscopy at the middle of a 5 $μ m$ wide SAF stripe, on a film with thinner (hence more transparent) Ta cap. The red vertical bars illustrate the frequency range in which thermal spin waves are detected. (Inset) Hysteresis loops along the easy and hard axes.
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Figure 2
Noise sources within the sample: (a) variance of the Johnson-Nyquist e.m.f due to the Brownian motion of the electrons within the measurement conductive and dissipative path and (b) inductive e.m.f. arising from the fluctuations within the spin wave bath underneath the antenna.
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Figure 3
Experimental set-ups for the measurement of the spectral density of the electrical power delivered by the antenna. (a) The first ”conventional” configuration (red color) allows the electrical signal to flow back (red arrows) and forth (blue arrows) between the antenna and the amplifier which both partially reflect at the planes $Π_{1}$ and $Π_{2}$ , thereby forming a cavity hosting standing microwaves. (b) The second ”modified” configuration (green color) includes an isolator that prevents the back flow (hatched green arrow) of electromagnetic energy from the amplifier towards the antenna. The standing waves are largely mitigated in the operating range of the isolator.
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Figure 4
Procedure, results and modeling for the first experimental configuration. (a) Reflection coefficient of the antenna for two different applied fields and zoom thereof (inset). (b) Spectral density of the noise power at 100 mT. (c): Excess noise with respect to the $H_{ref} = 0$ reference. The black vertical lines in (a-c) are at a frequency $f_{ac}$ corresponding to the uniform acoustical mode at 100 mT. The curly brace with the “wavy” label in (b) is meant for comparison with Fig. 5. (d) Field dependence of the experimental excess noise. The horizontal feature near 1 GHz is an artefact caused by ambient wireless devices. (e) Expected excess Johnson-Nyquist noise of the antenna calculated from Eq. (2) and the measured field dependence of the antenna impedance. (d) and (e) were decremented with the $H_{ref} = 0$ reference data.
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Figure 5
Results for the second experimental configuration. (a) Spectral density of the noise power. The passing band of the isolator appears as the grey zone. (b) Excess noise with respect to the $H_{ref} = 0$ reference. The black vertical line recall the frequency $f_{ac}$ of the acoustical mode at $k = 0$ . The curly braces in (a) illustrate the part of the spectrum in which the presence of the isolator strongly attenuates the ripple, in contrast with Fig. 3. (c) Field dependence of the excess noise, with scales comparable to these of Fig. 4.
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Figure 6
Principle of the derivation of the power spectral density of the inductive e.m.f. generated by a population of incoherent spin waves (i.e., the magnon noise). (a) Inductive geometry: the antenna collects the flux of the magnetic field lines (green) intercepting the surface $S$ above the magnetic film (blue) of cross section $S_{0}$ , in the presence of a spin wave (green arrows) of wave vector ${\vec{k}}_{y}$ perpendicular to the antenna. (b) Sketch of the density of states of the spin waves propagating perpendicularly to the antenna at 50 mT for the acoustic branch. The grey part is when the linear Taylor expansion of the dispersion relation breaks down. (c) Corresponding positive and negative wave vectors. (d) Corresponding antenna efficiency functions $h {(k)}^{2}$ .
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