Optical spin-wave detection beyond the diﬀraction limit Juriaan Lucassen1aMark J.G. Peeters1aCasper F. Schippers1Rembert A. Duine1 2 Henk J.M. Swagten1Bert Koopmans1and Reinoud Lavrijsen1

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Optical spin-wave detection beyond the diﬀraction limit

Juriaan Lucassen,1, a) Mark J.G. Peeters,1, a) Casper F. Schippers,1Rembert A. Duine,1, 2

Henk J.M. Swagten,1Bert Koopmans,1and Reinoud Lavrijsen1

1)Department of Applied Physics, Eindhoven University of Technology,

5600 MB Eindhoven, the Netherlands

2)Institute for Theoretical Physics, Utrecht University, Leuvenlaan 4,

3584 CE Utrecht, the Netherlands

(Dated: 24 October 2022)

Spin waves are proposed as information carriers for next-generation computing de-

vices because of their low power consumption. Moreover, their wave-like nature

allows for novel computing paradigms. Conventional methods to detect spin waves

are based either on electrical induction, limiting the downscaling and eﬃciency com-

plicating eventual implementation, or on light scattering, where the minimum de-

tectable spin-wave wavelength is set by the wavelength of the laser. In this Article

we demonstrate magneto-optical detection of spin waves beyond the diﬀraction limit

using a metallic grating that selectively absorbs laser light. Speciﬁcally, we demon-

strate the detection of propagating spin waves with a wavelength of 700 nm using a

diﬀraction-limited laser spot with a size of 10 µm in 20 nm thick Py strips. Addi-

tionally, we show that this grating is selective to the wavelength of the spin wave,

providing wavevector-selective spin-wave detection. This should open up new avenues

towards the integration of the burgeoning ﬁelds of photonics and magnonics, and aid

in the optical detection of spin waves in the short-wavelength exchange regime for

fundamental research.

a)These two authors contributed equally. Electronic mail: m.j.g.peeters@tue.nl or r.lavrijsen@tue.nl

arXiv:2210.12016v1 [cond-mat.mes-hall] 21 Oct 2022

Within magnetism, spin waves are ubiquitous in their presence and applications. Spin

waves are fundamental excitations in the magnetization of a material and their behaviour

is governed by fundamental magnetic interactions, such as the anisotropy or exchange in-

teraction. Based on this dependence, spin waves are often used to probe these fundamental

magnetic interactions.1–4 In recent years it has been suggested that spin waves can also be

used for novel computing methods. Spin-wave propagation occurs without charge trans-

port which allows for computation without Ohmic losses.5,6 Moreover, spin waves also make

excellent candidates for interference based logic devices and non-linear wave computing.5,6

For applications, short-wavelength (<100 nm) spin waves are preferred to reduce the

device footprint and increase the group velocity.7The conventional method of exciting and

detecting spin waves is based on micron sized microwave antennas through Oersted ﬁelds and

magnetic induction.5Scaling these antennas down such that short wavelength spin waves

can be excited and detected (<100 nm), however, is extremely challenging because of the

impedance mismatch.

On the excitation side, several alternatives have been proposed to excite short wave-

length spin waves,8such as spin-transfer torque based methods,9grating-like couplers,10,11

and using the resonance of antiferromagnetically coupled vortex states.12 However, when it

comes to the detection of short-wavelength spin waves progress there are considerably less

alternatives. The aforementioned grating couplers can also be used to detect the spin waves.

Spin-pumping13 and spin-caloritronics14 based techniques do allow for short wavelength de-

tection, but they are not wavelength selective. When using a spectroscopic light-scattering

approach, such as Brillouin light scattering, the minimum detectable spin-wave wavelength

is determined by the laser wavelength, other optical detection techniques suﬀer from the

diﬀraction limit and x-ray based techniques have the required resolution but require large

scale facilities.12,15,16 In this Article we therefore demonstrate a grating-based magneto-

optical (MO) method to circumvent the diﬀraction limit when using optical detection of

spin waves. It is very much related to the ﬁeld of near-ﬁeld optics (see Ref. 17 and refer-

ences therein), but simpler to implement than the techniques commonly used to reach super

resolution for MO measurements.18

In Fig. 1a we illustrate the method that we demonstrate in this Article. A metallic grating

is placed on top of a magnetic strip with a spin wave. The incident laser light is partially re-

ﬂected by this grating. However, the light that is transmitted—and is subsequently reﬂected

(a) (b)

5 μm

Polarization

Laser

Grating

Spin wave

in out

FIG. 1. (a) Proposed detection scheme. A laser impinges on a magnetic strip (grey) that contains

a spin wave. As this strip is covered with a grating (gold), this modiﬁes the reﬂection of the

incident laser light. The polarization of the incoming laser light that reﬂects of the magnetic strip

(left and right) changes due the magneto-optical Kerr eﬀect in the presence of a spin wave, whilst

the polarization of the part that reﬂects of the grating (middle) remains unaﬀected, indicated by

the rotation of the polarization in the Cartesian coordinate system. (b) SEM micrograph of the

fabricated device with km= 5 µm−1. We drive a microwave current jthrough the antenna (middle)

to generate spin waves with two diﬀerent wavevectors km,sin the magnetic strip placed underneath.

These waves propagate outwards and to measure these spin waves a laser spot (red) is placed on

top of the grating (periodicity km) following the principle sketched in (a).

oﬀ the magnetic strip—carries information on the direction of the magnetization through a

rotation of its polarization as a result of the magneto-optical Kerr eﬀect (MOKE). Any spin

wave whose periodicity matches that of the grating can be detected because the grating acts

as a Fourier ﬁlter for the magnetization components in the strip. This also allows us to do

studies as a function of position by moving the laser spot. By adjusting the relative phase

between the probing laser pulses and the excitation current we can achieve phase sensitivity

as well. Moreover, this technique will work even when the grating periodicity is smaller

than the diﬀraction limit, although complex scattering eﬀects might need to be taken into

account. In the remainder of this Article, we start by demonstrating spin-wave excitation

through conventional meandered microwave antennas.19 We then move on to actual optical

propagating spin wave transmission measurements using the metallic grating. In the last

part we focus on an understanding of the measured spectra using a simple analytical model.

We fabricate devices such as the one shown in Fig. 1b. Here we show a meandering spin-

wave antenna located between two gratings. This device allows us to excite spin waves with

speciﬁc wavevectors belonging to the main periodicities of the spin-wave antenna (kmand a

small secondary periodicity ks= 0.36×km),19 and measure the spin waves by focusing a laser

on the grating. The magnetic strip underneath the grating consists of 20 nm of Py. Spin

waves are measured in the Damon-Eshbach geometry, with the magnetic ﬁeld and wave vec-

tor perpendicular and in the plane. The electrical characteristics of the spin-wave excitation

were measured using a vector network analyzer following a procedure described elsewhere.20

The optical detection of spin waves was performed using a pulsed laser (80 MHz, pulse

length 150 fs at a wavelength of 780 nm) with a diﬀraction limited spot size of ∼10 µm

measuring the Kerr rotation in combination with continuous wave excitation of the spin

waves such that measured magneto-optical (MO) signal is proportional to the spin-wave

amplitude at the given phase (the details on the experimental setup and sample fabrica-

tion can be found in supplementary note I). Diﬀerent devices were measured with diﬀering

combinations of gratings and spin-wave antennas resonant to spin waves with wavevectors

k= 5.0,7.0,9.0µm−1, which have wavelengths smaller than our laser spot size and which

have long enough attenuation lengths to measure propagating spin waves away from the

antenna.

To demonstrate spin-wave excitation, we show the self-induction Lof a km= 9 µm−1

antenna in Fig. 2a. In this spectrum two resonances are observed at 60 mT and 100 mT,

which correspond to the excitation of the spin waves with wavelengths equal to the two

main periodicities of the antenna (km,s= 9.0,3.2µm−1).19,20 The real and imaginary part

of the spectrum are ﬁtted simultaneously with symmetric and anti-symmetric Lorentzian

line shapes to extract the resonance ﬁelds (solid lines), which are plotted in Fig. 1b as a

function of frequency f. These resonance ﬁelds are then ﬁtted with the dispersion relation

for these spin waves (using MS= 0.83 MA m−1and g= 2.11)21–24 which results in Meﬀ =

0.76 ±0.07 MA m−1and thickness t= 16 ±5 nm, in line with what we expect for Py.22

With the veriﬁcation of spin-wave excitation complete, we move on to the optical mea-

surement of the spin waves. A typical measurement for a device tuned to km= 9 µm−1

is displayed in Fig. 2c, which contains the spin-wave amplitude at two diﬀerent phases (0°

and 90°) with respect to the microwave excitation source.25 In this measurement there is a

(a)

(d)(c)

(b) (e)

FIG. 2. (a) Self induction Lfor a km= 9 µm−1antenna including a ﬁt with two (anti)symmetric

Lorentzians. We also indicate the resulting resonance ﬁelds of the ﬁts for both resonance modes

(solid vertical lines). (b) Fitted resonance ﬁelds Hres as a function of frequency ffor both resonances

[see (a)]. (c) Two phases (0◦and 90◦) of the magneto-optical (MO) signal as a function of magnetic

ﬁeld Hfor a km= 9 µm−1device measured at f= 10.24 GHz and with the laser spot positioned

12 µm away from the antenna. The solid vertical lines indicate the resonance ﬁelds belonging to the

main (km) and secondary peak of the spin-wave excitation (ks). (d) Both phases of the MO signal

as a function of magnetic ﬁeld Hfor three diﬀerent gratings optimized for diﬀerent wavevectors k,

where no grating corresponds to measurements without a grating present on top of the magnetic

strip. The spin-wave antenna generated km= 9 µm spin waves at 10.24 GHz, with the laser spot

positioned 12 µm away from the antenna. The vertical solid lines indicate the resonance ﬁeld of

the spin wave for which the corresponding grating is optimized (k= 0 µm−1without a grating).

Curves are oﬀset for clarity. (e) Several measurements at 1 speciﬁc phase for a km= 9 µm−1device

measured at f= 10.24 GHz at diﬀerent positions along the grating, indicated by the sketch on the

right. The measurements are spaced 5 µm apart and are vertically oﬀset for clarity.

resonance at ∼55 mT, the resonance ﬁeld of the km= 9 µm−1spin wave. Furthermore,

there is a small resonance at ∼100 mT which is the result of the large wavelength (ks)

spin waves that are also excited. A second feature in the spectrum is the amplitude diﬀer-

ence between the resonances at positive and negative ﬁelds, which is a well-known eﬀect of

spin-wave excitation using electrical antennas. It is the result of a diﬀerence in spin-wave

excitation eﬃciency because of the magnetic ﬁeld chirality that either matches or opposes

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Opticalspin-wavedetectionbeyondthediractionlimitJuriaanLucassen,1,a)MarkJ.G.Peeters,1,a)CasperF.Schippers,1RembertA.Duine,1,2HenkJ.M.Swagten,1BertKoopmans,1andReinoudLavrijsen11)DepartmentofAppliedPhysics,EindhovenUniversityofTechnology,5600MBEindhoven,theNetherlands2)InstituteforTheoreticalPhysics...

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Optical spin-wave detection beyond the diﬀraction limit Juriaan Lucassen1aMark J.G. Peeters1aCasper F. Schippers1Rembert A. Duine1 2 Henk J.M. Swagten1Bert Koopmans1and Reinoud Lavrijsen1.pdf

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Optical spin-wave detection beyond the diﬀraction limit Juriaan Lucassen1aMark J.G. Peeters1aCasper F. Schippers1Rembert A. Duine1 2 Henk J.M. Swagten1Bert Koopmans1and Reinoud Lavrijsen1

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