# Low power continuous-wave all-optical magnetic switching in ferromagnetic
nanoarrays

Kilian D. Stenning  Blackett Laboratory, Imperial College London, London SW7
2AZ, United Kingdom  These authors contributed equally  Corresponding author
e-mail<EMAIL_ADDRESS>Xiaofei Xiao  Blackett Laboratory,
Imperial College London, London SW7 2AZ, United Kingdom  These authors
contributed equally  Holly H. Holder  Blackett Laboratory, Imperial College
London, London SW7 2AZ, United Kingdom  Jack C. Gartside  Blackett Laboratory,
Imperial College London, London SW7 2AZ, United Kingdom  Alex Vanstone
Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom
London Centre for Nanotechnology, University College London, London WC1H 0AH,
United Kingdom  Oscar W. Kennedy  Blackett Laboratory, Imperial College
London, London SW7 2AZ, United Kingdom  London Centre for Nanotechnology,
University College London, London WC1H 0AH, United Kingdom  Rupert F. Oulton
Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom
Will R. Branford  Blackett Laboratory, Imperial College London, London SW7
2AZ, United Kingdom

###### Abstract

All-optical magnetic switching[1, 2, 3] represents a next-generation class of
local magnetisation control, with wide-ranging technological implications.
75$\%$ of all data is stored magnetically and the predominant current
recording technology uses power-consuming magnetic fields with plasmonic
focusing of laser heating for Heat Assisted Magnetic Recording (HAMR)[4, 5].
Existing (field-free) all-optical switching schemes are unsuitable for device
integration, typically requiring power-hungry femtosecond-pulsed lasers and
complex magnetic materials. Here, we demonstrate deterministic, all-optical
magnetic switching using a low-power, linearly-polarised continuous-wave laser
in nanostructures with sub-diffraction limit dimensions composed of simple
earth abundant ferromagnetic alloys (Ni81Fe19, Ni50Fe50) and dielectrics. An
interference effect dramatically enhances absorption in the nanomagnets,
enabling high fidelity writing at powers as low as 2.74 mW. Isolated and
densely-packed nanomagnets are switched across a range of dimensions, laser
wavelengths and powers. All artificial spin ice[6, 7, 8] vertex configurations
are written with high fidelity, including energetically and entropically
unfavourable ‘monopole-like’ states inaccessible by thermalisation methods. No
switching is observed in equivalent structures with pure Co magnets,
suggesting multi-species interactions within the nanomagnet play a role. The
results presented here usher in low-cost, low-power optically-controlled
devices with impact across data storage, neuromorphic computation and
reconfigurable magnonics.

## Main

All-optical magnetic switching (AOMS) has been demonstrated in several
schemes, all with distinct caveats precluding technological implementation.
Helicity-dependent switching with single or multiple femtosecond laser pulses
has been observed in ferrimagnetic, ferromagnetic and granular magnetic media
where the resulting state is determined by the helicity of light[1, 9, 10, 11,
12, 13]. Helicity-independent switching (HIS) has been demonstrated with a
single femtosecond pulse, yet is largely limited to rare-earth
ferrimagnets[14, 15, 16, 9, 17, 18]. HIS in ferromagnets is typically observed
when coupled to ferrimagnetic layers [19, 20, 21], bar a demonstration of HIS
in Pt/Co/Pt multilayers when focusing the laser spot down to single-domain
sizes[22]. These demonstrations have shown the promise of AOMS, but the
requirement of huge femtosecond-pulsed MW lasers and exotic magnetic materials
renders them unsuitable for device integration and up-scaling for application.
Additionally, the majority of studies concern continuous thin films or well-
spaced single nanostructures[18], restricting write-density.

Artificial spin systems comprising networks of strongly-interacting
nanomagnets serve as promising hosts for future information-processing
technologies including nanomagnetic logic[23, 24], neuromorphic
computation[25, 26, 27, 28, 29, 30] and reconfigurable magnonics[8, 31, 32,
33, 34, 35, 36]. Information can be stored in the magnetisation of a single
nanomagnet or the magnetic configuration of the entire network (microstate)
where collective microstate-dependent dynamics[8, 37, 34] may be harnessed to
process information[28, 29, 30, 27]. To date, local nanomagnet switching in
dense nanoarrays relies on slow scanning-probe techniques[38, 39, 40, 35, 41]
or diffraction-limited heat-assisted reversal relying on global fields in
conjunction with laser illumination[4]. Realising rapid low-power single-
element magnetic switching is pivotal for the development of functional ASI-
based computation and storage devices.

Here, we demonstrate deterministic all-optical magnetic switching in both
isolated nanomagnets and dense square artificial spin ice (ASI)[6, 7, 8]
arrays using simple NiFe alloys and low-power ($\sim$2.74 mW), linearly-
polarised continuous-wave (CW) lasers. No external magnetic fields were
applied. The substrates (here Si/SiO2 or Au/SiO2) on which the nanomagnets are
situated have an anti-reflection function, which enhances optical absorption
within the nanomagnets up to 65$\%$ of the total incident light across a broad
frequency range, a 16.25$\times$ increase compared to Si substrates. Sub-
diffraction ‘writing’ and ‘erasing’ of information is achieved in single
nanomagnets. Furthermore, all square ASI vertex configurations ranging from
low-energy ground state to high-energy monopole-like states are written.
Switching is not observed in Co nanostructures suggesting multi-species
interactions plays a role in the reversal mechanism. Our results usher in a
new paradigm of low-power magnetisation control with vast implications in
data-storage and nanomagnetic computation applications.

### Deterministic reversal of isolated nanomagnets

Figure 1 a) shows a schematic of nanomagnets exposed with a linearly-polarised
CW laser. We first consider reversing isolated Ni81Fe19 (permalloy, Py)
nanomagnets separated by 1 µm such that dipolar interactions are negligible.
The nanomagnets are patterned on top of an Au (250 nm) / SiO2 (290 nm)
substrate. Figure 1 b) shows a ‘before’ magnetic force microscopy (MFM) image
of field-saturated nanomagnets with lengths $L$ = 0.28-1.08 µm. Each bar
exhibits a positive (light) and negative (dark) magnetic charge indicating
magnetisation direction, shown by adjacent arrows. Figure 1 c) shows the same
bars after exposure to a $\lambda$ = 633 nm linearly-polarised (parallel to
nanomagnet long-axis) CW laser with 580 nm spot size and 3.5 mW power, swept
across the nanomagnets perpendicular to their long axis. Magnetic switching is
observed in the three left-most bars (L $\leq$ 0.28-0.38 µm), indicated by
light-blue arrows. Figures 1 d-f) demonstrate write/erase functionality in
three L = 0.28 µm bars. Bars are initially globally-saturated (Figure 1 d)),
then exposed to a $\lambda$ = 633 nm, 3.75 mW power linearly-polarised CW
laser such that all bars switch (‘write’, Figure 1 e)). All bars then switch
back following a second exposure (‘erase’, Figure 1 f)). Note that powers
stated are measured before focussing and $\leq$ 90$\%$ of the power reaches
the sample (see methods for details).

Figure 1: a) Schematic of linearly-polarised CW laser exposure of isolated
nanomagnets (left) and densely-packed Py nanomagnets in a square ASI (right)
patterned on an Si or Au substrates with an SiO2 coating. MFM images of
isolated nanomagnets patterned on an Au (250 nm) / SiO2 (290 nm) substrate b)
in the saturated state and c) after linearly-polarised CW laser exposure with
3.5 mW power. Bars with length (L) $\leq$ 380 nm switch. MFM images of d)
three nanomagnets with L = 280 nm in an initial saturated state. e) Subsequent
switching after linearly-polarised CW exposure with 3.75 mW. f) Switching
after a second 3.75 mW exposure demonstrating the ability to rewrite / erase
previously written states. In each case laser polarisation is parallel to
long-axis of nanomagnets and the laser scans perpendicular to the bar long
axis. Figure 2:  Experimental (Exp) and simulated (Sim) reflection spectra and
calculated absorption of a 2 mm$\times$2 mm nanomagnet array (90∘ / 45∘
incident polarisation) fabricated on a) Si / SiO2 (300 nm) and b) Au (250 nm)
/ SiO2 (290 nm) substrates (S). This system significantly reduces reflections
and thereby enhances absorption in the nanomagnets. In a) sample dimensions
are $t_{1}$ = 15 nm, $t_{2}$ = 20 nm, $t_{3}$ = 15 nm, $H$ = 300 nm. Each Py
nanomagnet is enclosed in two Al2O3 coatings to protect against oxidation. In
b) sample dimensions are $d$ = 250 nm, $H$ = 290 nm, $t$ = 20 nm. Here, a 4nm
Al2O3 cap is used. Schematic illustrates nanomagnet array dimensions,
structure and unit cell with $L$ = 226 nm, $W$ = 78 nm and $P$ = 356 nm.
Absorption in the horizontal (A) and vertical (B) Py bars are shown for laser
polarisation angles of 45∘ and 90∘ relative to the horizontal, highlighting
the contrast and subset selectivity afforded. Up to 65$\%$ and 38$\%$
absorption is achieved in the Au/SiO2 and Si/SiO2 respectively. (c,d)
Simulated optical absorption in the Py layer of nanomagnet array for varying
unit cell period (c) and SiO2 thickness (d). Here equivalent dimensions to
panel a) are used.

### Enhancing nanomagnet light-absorption

The all-optical switching mechanism requires strong polarisation-dependent
absorption of light in the nanomagnets. The size and shape of the nanomagnets
thus have dual roles controlling both magnetic behaviour and the polarisation-
dependent optical absorption. There are three light-absorption mechanisms: the
plasmonic antenna resonance; a plasmonic grating effect due to the in-plane
nanoarray periodicity; and the interference effect of reflection from the
substrate-silica interface. We find the latter mechanism dominates. Here,
partial reflections from the substrate-silica and silica-nanomagnet-air
interfaces interfere destructively when the SiO2 is approximately an integer
multiple of a quarter wavelength in optical depth. The cancellation of
reflection and the minimisation of transmission combine to maximise the
absorption. This is to our advantage since this mechanism allows design
freedom over the nanomagnet dimensions and array geometry, as well as greater
tolerance to nanofabrication imperfections.

Figure 2 a) compares experimental (‘Exp’) and simulated (‘Sim’) Fourier
Transform Infrared (FTIR) reflection spectra for the Si/SiO2 substrates with
and without nanomagnet arrays. Here, Py nanomagnets are enclosed by two Al2O3
layers (15 nm) to protect against oxidation. Excellent experimental-simulation
correspondence is observed. SEM images are provided in supplementary note 1.
The addition of the Py nanomagnet layer introduces absorption and reflection
that modifies the partial reflections from the substrate-silica and silica-air
interfaces. Strong absorption in the nanomagnets corresponds to the condition
where these partial reflections destructively interfere, as shown by the
reflectivity minimum near 600 nm in Figure 2 a). Remarkably for $\sim$ 28%
fill factor of the Py ASI system, the total reflection from the device can be
< 1%, leading to a calculated absorption of $38$%, as shown in Figure 2 a).
Furthermore, the high nanomagnet aspect-ratio provides an optical polarisation
response; light is absorbed dominantly in antennas whose long axis is aligned
to the optical polarisation. Figure 2 a) shows that at a wavelength of 633 nm,
the absorption ratio for polarisation along long and short axes is a factor
$>4$. This enables selective optical switching via incident polarisation
control. Figure 2 b) shows the reflection and absorption for nanomagnetic
arrays fabricated on an Au (250 nm) / SiO2 (290 nm) substrate. Here, each
nanomagnet is coated with a 4nm protective Al2O3 layer. Transmission into the
substrate is inhibited by the gold under-layer, which enhances the absorption
to 65%. This is a 16.25 $\times$ and 3.6 $\times$ enhancement in absorption
compared to Si and SiO2 substrates respectively (see supplementary note 2).

Figures 2 c,d) further explore nanomagnet optical absorption by varying the
nanoarray unit-cell period (c) and silica thickness (d). In Figure 2 c) we fix
the nanomagnet geometry and silica thickness, but vary array periodicity. This
leads to a diffraction order near a wavelength of 633 nm for a periodicity =
500 nm, which decreases the absorption and should be avoided. Other
periodicities and isolated nanomagnets perform well. Figure 2 d) considers a
fixed nanomagnet geometry and varying silica thickness, again exhibiting
diffraction orders. Here, silica thickness is 300 nm, giving a resonance near
the 633 nm wavelength of a He-Ne laser. The final absorption mechanism
concerning the localised plasmonic antenna resonance of each individual
nanomagnet is explored in calculations in supplementary note 3. The
nanomagnets have no clear plasmonic resonance that can provide strong
absorption in the Py. Thus, for periodicity < 500 nm, the substrate
interference phenomenon is the dominant absorption mechanism.

Figure 3: Single nanomagnet switching in a dense array. a) Vertex types in
square ASI. b) SEM image of a square ASI array. c) MFM images of an equivalent
array after global-field initialisation. d) MFM image showing a grid of
reversals after $\lambda$ = 663 nm laser exposure with a 580 nm focal spot at
5 mW for $\sim$ 0.25 s. Zoomed-in MFM images and schematics of colour-coded
regions of panel d) showing nanomagnet reversal after laser exposure with e,f)
$\hat{x}$ polarisation, g,h) $\hat{y}$ polarisation, i-l) $\hat{x}$ then
$\hat{y}$ polarisation. Panel g) is from a different region of the array. The
single polarisation exposure in e-h) result in a pair of Type 3 vertices. When
exposing both polarisations, both i,j) Type 1 (GS) and k,l) high-energy T4
(MP) vertices can be prepared depending on which nanomagnets are exposed. In
e-l) the scale bar corresponds to 500 nm. Only written vertices are coloured.

### Deterministic reversal in ASI networks

Having demonstrated switching in isolated nanomagnets, we now expose strongly-
interacting, sub-diffraction limited nanomagnets arranged in a dense square
ASI, patterned on a Si / SiO2 (300 nm) substrate. This substrate was selected
to demonstrate the efficacy of the switching technique on commercially
available, sub-optimal substrates (no additional absorption-enhancing Au
layer). Strong interactions between neighbouring nanomagnets leads to four
vertex types with differing energies[6] (Figure 3a), providing a challenging
testing ground for local magnetic control as high-energy dipolar interactions
will oppose reversal. Figure 3 a) shows all possible vertex configurations in
square ASI in order of increasing energy labelled as Types 1-4 (vertex
energies detailed further in supplementary note 4). Figure 3 b) shows an SEM
image of the ASI array. Nanomagnet dimensions are $L=226$ nm, $W=78$ nm and
$P=356$ nm.

First, we consider exposing ASI to discrete spot illuminations of a $\lambda$
= 633 nm, 5 mW CW laser for $\sim$ 0.25 s. The laser position is static
throughout illumination. Laser focal spot size is 580 nm. Prior to exposure,
the ASI is initialised via global-field saturation (-$x$,+$y$) to define an
array of type 2 vertices (Figure 3 c)). Figure 3 d) shows the array microstate
after grid like spot exposures with a variety of laser polarisations. Laser
polarisation governs the resultant written vertex state, with colour-coded
regions of Figure 3 d) shown zoomed-in in Figure 3 e-l). Higher powers and
longer illuminations lead to sample damage (not shown). The zoomed regions
show successful writing of ASI vertex types 1 (i,j), 3 (e,f) and 4 (k,l) (g,h
are from a different region of the array). Note that the MFM images are
supplemented with magnetic charge schematics and the corresponding laser
polarisations required to prepare each state, indicated above each MFM image.
When illuminating the array at a single spot (Figure 3 e-h)), a single
nanomagnet with long-axis parallel to the laser polarisation switches. This
selectivity arises from the polarisation-dependent absorption shown in Figure
2 b). This forms a high-energy state comprising a pair of type 3 vertices. Two
subsequent $\hat{x}$ then $\hat{y}$-polarised exposures results in two
nanomagnets switching (one from each $x,y$ subset). Here both low energy Type
1 (Figure 3 i,j)) and high-energy Type 4 (Figure 3 k,l)) vertices may be
written. The position of the incident laser determines whether a Type 1 or
Type 4 is written. The ability to write type 4 vertices strongly suggests that
switching occurs in a deterministic manner rather than via nanomagnet
thermalisation and relaxation, which would strongly-favour the system’s ground
state.

This Gaussian distribution of power across the beam gives a FWHM of $\sim$ 340
nm which lies between the nanoisland length and periodicity of the array.
Combining this with selectivity enabled by the polarisation-dependent
absorption results in a single nanomagnet switching during each exposure. The
demonstration of writing low and high-energy states with single-nanomagnet
precision illustrates the applicability of this method to next-generation
storage and memcomputing applications.

Figure 4: MFM images of switching chains after exposure to $\lambda$ = 633 nm
scanning laser with a) polarisation $\parallel$ scan direction writing a chain
of type 2 vertices b) polarisation $\perp$ scan direction writing a chain of
type 3 vertices and c) polarisation at 45∘ to the scan direction where both
subsets of bars are exposed to the same incident power and both subsets are
written. d) and e) show MFM images and schematics of switching via $\lambda$ =
785 nm after saturating the array in opposite directions. Type 2 chains are
written in both cases, ruling out the effect of stray field which would assist
switching in one case and oppose switching in the other. f) MFM images and
schematics after exposure to a $\lambda$ = 785 nm laser with polarisation
$\parallel$ scan direction. f) shows similar writing characteristics to the
shorter wavelength but at $\sim$6$\times$ power increase due to the lower
absorption at this wavelength.

We now explore switching when scanning the laser spot across the array during
exposure. Here, the beam traverses the entire 30 µm array at 20 µm/s, exposing
each nanomagnet for $\sim$ 18 ms. The relative angle between the polarisation
and the scan direction is either 0∘, 45∘ or 90∘. Figure 4) shows MFM images
and corresponding magnetisation schematics of line-scanned writing exposures
at laser wavelengths of 633 nm (Figure 4 a-c)) and 785 nm (Figure 4 d-f)). At
633 nm wavelength, switching occurs at laser powers as low as 2.74 mW, while
785 nm wavelength switching has an optimum power of 17.7 mW; higher than
expected from Figure 2 a) due to wavelength dependent optical losses in the
experimental setup (see Methods). For ASI fabricated on Au/SiO2 substrates, we
observe switching across a wide range of nanomagnet dimensions (up to 1 µm bar
length) at similar laser powers (supplementary note 5).

Parallel polarisation and line-scan direction (Figure 4 a,d-f)) gives rise to
long chains of switches where adjacent nanomagnet reversals share a common
vertex. Lines written in this configuration comprise a chain of type 2
vertices (yellow circles) with a single type 3 vertex at either end (blue and
orange circles). Other than creating the type 3 vertex pair, system energy is
not increased as the written type 2 vertices are equal in energy to the
initial saturated type 2 background state. Up to 22 consecutive reversals are
observed in this configuration. Perpendicular polarisation and scan direction
(Figure 4 b)) results in a type 3 vertex pair at every point on the line-scan
(as observed in the static exposures Figure 3 c-f)), continually increasing
system energy. Up to 7 consecutive reversals are observed in this
configuration, demonstrating strong reversal control over highly
energetically-unfavourable states. If the laser polarisation is oriented 45∘
to the scan direction (Figure 4 c)), both $x,y$-subsets receive equal power
and both can switch, resulting in a chain of type 1 vertices (green circles).
Here, $\sim$2$\times$ power is required as expected.

No magnetic fields are applied and Hall probe measurements reveal stray fields
of less than 1 Oe at the sample. Figure 4 d,e) show MFM images and vertex type
schematics after saturating the same array in opposite initial directions and
exposing to a scanning beam ($\lambda$ = 785 nm) with polarisation parallel to
the scan direction. Any unintended stray field in the experimental setup that
assists reversal in one direction will oppose reversal in the other.
Crucially, switching is observed in both cases - ruling out any role of
external fields on the switching mechanism.

Our results demonstrate deterministic and rewriteable AOMS in isolated and
densely-packed nanomagnets. Our methodology requires no external field and
operates using simple CW-lasers operating at low-power (2.74 - 6 mW) and low
power-densities (1.04 - 2.27 MW/cm2 for 580 nm spot). The absorption profiles
allow for read/write functionality by tuning the incident wavelength (e.g.
write at 633 nm, read at 900 nm).

### Reversal mechanism

Here, we discuss potential mechanisms of this deterministic reversal,
beginning with a process of deduction. The deterministic switching into any
allowed magnetic state with the same sample mounting as illustrated in Figure
4 d,e) excludes field-driven heat-assisted switching (as in Pancaldi et al[4])
from unintentional stray fields in our system. We are not using circularly
polarised light which precludes helicity-dependent processes. Our findings are
also not consistent with thermalisation effects from stochastic switching via
heating nanomagnets beyond the Curie temperature Tc or superparamagnetic
limit. The written high-energy, low entropy monopole defect states are never
favoured by thermalisation[40]. The observed switching fidelity in Figure 4 f)
of 22 consecutive switches has a corresponding thermalisation probability of
0.522 = $2.3\times 10\textsuperscript{-7}$. We anticipate that the low-power
illumination would not heat the lattice temperature above 380 K[4].
Magnetometry measurements of a 2 $\times$ 2 mm ASI array with equivalent
dimensions reveals only a $\sim$10$\%$ drop in the magnetisation is observed
between 120 - 380 K implying that we are not heating close to Tc for these
nanomagnet samples (supplementary note 6).

Existing AOMS theories depend strongly on the materials employed and the
optical pulsed excitation method. Optical pulse-duration varies between
studies and increasing the duration does not significantly enhance switching
fidelity, precluding the necessity for CW exposure. Multi-pulse AOMS in
ferromagnets occurs through an initial demagnetisation regime leaving a multi-
domain state, followed by subsequent domain growth. The later stage requires
circularly polarised light which facilitates preferential growth of one domain
orientation via the Inverse Faraday Effect (IFE)[10], dichroism effects or
thermally-induced domain wall motion. Here, IFE is ruled out due to the
linearly-polarised exposure.

Single-shot AOMS has primarily been observed in ferrimagnets with the
requirement of two antiferromagnetically coupled sublattices with different
relaxation timescales[15, 14]. These conditions are not met in ferromagnetic
materials. However, there has been recent theoretical and experimental
evidence of optically induced spin transfer (OISTR) in ferromagnetic
alloys[42, 43] whereby incoming photons may excite electrons between spin
minority bands of a heterogeneous material provided that the band structure
satisfies necessary requirements. Specifically, there should be an available
transition between two spin minority bands at the incident photon energy and
no available transitions in the spin majority bands. These studies do not
observe switching, yet single-pulse helicity-independent switching is observed
in Co/Pt multilayers[22] which possess the necessary band structure[44]. The
effect is strong in Ni50Fe50[42], more so than Py, but not present in Co.

To test our working hypothesis, that AOMS is occurring by a plasmonically
enhanced OISTR mechanism, we fabricated a set of Ni50Fe50 (20 nm thickness)
and Co (8 nm thickness) nanomagnetic arrays patterned on a Au/SiO2 substrate
(supplementary note 7), with the prediction that the switching fidelity would
be as good or better in Ni50Fe50 and significantly worse in pure Co. Both
predictions were confirmed in the subsequent experiments. For Ni50Fe50,
isolated nanomagnet switches were observed at 3 mW ($\sim$ 14$\%$ reduction in
power) across a broader range of nanomagnet dimensions compared to Ni81Fe19.
Conversely, no switches were observed in Co nanostructures up to incident
powers of 30 mW. These results give an indication, but not confirmation, of
the switching mechanism. If an ultrafast process such as OISTR is indeed the
mechanism then an interesting question is posed - why is a single
deterministic reversal observed even after CW exposure times measured in
seconds, rather than multiple stochastic reversals mediated by a continuous
OISTR process? The well-established three-temperature model explanation is
that the process occurs within a short timeframe after the exposure stimulus
following which the system relaxes to an equilibrium, preventing further
reversals during that exposure.

In summary, we have demonstrated selective and deterministic all-optical
magnetic switching of individual and densely-packed ferromagnetic
nanostructures using a linearly-polarised, low-power CW laser. We achieve sub-
diffraction limit, single nanomagnet switching of diverse ASI microstates
including thermally unfavourable high-energy configurations. The materials
employed are cheap and earth-abundant, and we expect switching functionality
to be retained across a broad range of substrate and ferromagnetic materials
making the technique scaleable and highly integratable with existing
technologies. The low-power consumption and cheap cost of the non-specialised
CW laser have profound implications across a host of device technologies
including data storage and non-conventional computing functionalities,
particularly neuromorphic and memcomputing hardware.

### Author contributions

KDS, XX, JCG, RO and WRB conceived the work.
KDS drafted the manuscript other than the working principle, with
contributions from all authors in editing and revision stages. XX and RO
drafted the working principle section.
KDS, JCG, AV, OK and HH fabricated the ASI.
XX and HH performed the laser illumination protocols.
KDS, HH and JCG performed MFM measurements.
XX performed FTIR measurements, simulations and absorption calculations.
KDS, AV and JCG performed magnetometry measurements.
KDS performed simulations of vertex energies.
KDS created CGI images.

### Acknowledgements

This work was supported by the Leverhulme Trust (RPG-2017-257) to WRB.
AV was supported by the EPSRC Centre for Doctoral Training in Advanced
Characterisation of Materials (Grant No. EP/L015277/1).
Simulations were performed on the Imperial College London Research Computing
Service[45].
The authors would like to thank Professor Lesley F. Cohen of Imperial College
London for enlightening discussion and comments and David Mack for excellent
laboratory management.

### Data availability statement

The datasets generated during and/or analysed during the current study are
available from the corresponding author on reasonable request.

### Simulation details

The linear optical response of the nano-structures was determined using the
finite difference time domain (FDTD) technique (Lumerical FDTD). In these
simulations, incident waves with different polarisations were applied to both
individual structures and the periodic array. The simulations were simplified
by including three layers of bar structures with rounded ends and a semi-
infinite substrate. For single structure simulations, the absorption and
extinction cross-sections were calculated by an analysis group of monitors
located inside and outside of a total-field scattered-field source,
respectively. A perfectly matched layer was applied in all directions to
absorb incident light with minimal reflections. For array simulations,
periodic boundary conditions were used in the plane of the substrate. In these
simulations, the linear polarised waves of varying wavelength were incident
from the air side. For the reflection calculation in Figure 2a, we normalised
to the reflection spectrum of a gold mirror. In the simulations, the complex
refractive indexes of gold, silica, silicon, and aluminium oxide were taken
from Palik models reported in ref[46]. The refractive index of gold was taken
from Johnson and Christy experimental data[47], and the refractive index of Py
was taken from ref[48].

### Experimental methods

Samples were fabricated via electron-beam lithography liftoff method on a
Raith eLine system with a bilayer 495K / 950K PMMA resist. Si substrates with
a 300 nm SiO2 layer were purchased commercially. The Au substrates were
deposited on an Si/SiO2 substrate with the following thicknesses (nm)
Cr(2)/Au(250)/Cr(2)/SiO2(290). Cr is used to aid Au adhesion. Al2O3, Ni81Fe19,
Ni50Fe50 and Co were thermally evaporated at a base pressure of $2\times
10\textsuperscript{-6}$ mbar. For samples fabricated on Si / SiO2, a 15 nm
Al2O3 layer is deposited on either side of the nanomagnet to protect against
oxidation. For samples fabricated on Au / SiO2 substrates, a 4 nm Al2O3
coating on the top layer is used to protect oxidation. The presence and
thickness of Al2O3 does not significantly affect light absorption.

Magnetic force micrographs were produced on a Dimension 3100 using
commercially available low-moment and normal-moment MFM tips.

### Illumination experiments

Laser illumination by continuous wave lasers with different wavelengths (633
nm and 785 nm) were focused to a diffraction limited spot on the sample
through a confocal Raman microscope (alpha300 RSA+, WITec). The light was
linearly polarized and focused by a 100$\times$ (NA = 0.9, Zeiss) microscope
objective. The focal spot was scanned to illuminate the locations of interest.
To achieve the fastest line scanning speed, the instrument was simply scanned
between two pre-defined points. For slower scans, 50 points were defined along
each scan line and the detector integration time was used to control the dwell
time. It should be noted that the integration time is usually used to control
spectra collection, but here this parameter controls the illumination time.
The power of the beam was measured by a power meter (PM100D, Thorlabs)
attached to the objective turret and all powers stated are measured before
focussing. The power transmitted through the objective is $\leq$ 90 $\%$, and
may be lower due to optical losses in the set up. Measurements suggest that
$\sim$ 65 % and $\sim$ 45 % of the power may be reaching the sample at
wavelengths of 633 nm and 785 nm respectively.

### Fourier transform infrared measurements

Fourier transform infrared (FTIR) spectroscopy was used to characterise the
linear optical response of the nanomagnetic particle arrays. The spectra were
collected with a Bruker Hyperion 2000 FTIR microscope installed with a
15$\times$, NA = 0.4 metallic reflective objective. The reflection spectra
were obtained by normalising the reflection curve from areas containing arrays
and the neighbouring bare substrate against a reference spectrum taken from a
gold mirror. Spectra were obtained in the ranges $500$–$1200$ nm using a
silicon detector.

## References

  * [1] Stanciu, C. D. _et al._ All-optical magnetic recording with circularly polarized light.  _Physical review letters_ 99, 047601 (2007).
  * [2] Kirilyuk, A., Kimel, A. V. & Rasing, T.  Ultrafast optical manipulation of magnetic order.  _Reviews of Modern Physics_ 82, 2731 (2010).
  * [3] Kimel, A. V. & Li, M.  Writing magnetic memory with ultrashort light pulses.  _Nature Reviews Materials_ 4, 189–200 (2019).
  * [4] Pancaldi, M., Leo, N. & Vavassori, P.  Selective and fast plasmon-assisted photo-heating of nanomagnets.  _Nanoscale_ 11, 7656–7666 (2019).
  * [5] Kryder, M. H. _et al._ Heat assisted magnetic recording.  _Proceedings of the IEEE_ 96, 1810–1835 (2008).
  * [6] Wang, . R. _et al._ Artificial ‘spin ice’in a geometrically frustrated lattice of nanoscale ferromagnetic islands.  _Nature_ 439, 303–306 (2006).
  * [7] Skjærvø, S. H., Marrows, C. H., Stamps, R. L. & Heyderman, L. J.  Advances in artificial spin ice.  _Nature Reviews Physics_ 2, 13–28 (2020).
  * [8] Lendinez, S. & Jungfleisch, M.  Magnetization dynamics in artificial spin ice.  _Journal of Physics: Condensed Matter_ 32, 013001 (2019).
  * [9] El Hadri, M. S. _et al._ Two types of all-optical magnetization switching mechanisms using femtosecond laser pulses.  _Physical review B_ 94, 064412 (2016).
  * [10] Medapalli, R. _et al._ Multiscale dynamics of helicity-dependent all-optical magnetization reversal in ferromagnetic co/pt multilayers.  _Physical review B_ 96, 224421 (2017).
  * [11] Ellis, M. O., Fullerton, E. E. & Chantrell, R. W.  All-optical switching in granular ferromagnets caused by magnetic circular dichroism.  _Scientific reports_ 6, 1–9 (2016).
  * [12] Lambert, C.-H. _et al._ All-optical control of ferromagnetic thin films and nanostructures.  _Science_ 345, 1337–1340 (2014).
  * [13] Kichin, G. _et al._ From multiple-to single-pulse all-optical helicity-dependent switching in ferromagnetic co/pt multilayers.  _Physical Review Applied_ 12, 024019 (2019).
  * [14] Ostler, T. _et al._ Ultrafast heating as a sufficient stimulus for magnetization reversal in a ferrimagnet.  _Nature communications_ 3, 1–6 (2012).
  * [15] Stanciu, C. _et al._ Subpicosecond magnetization reversal across ferrimagnetic compensation points.  _Physical review letters_ 99, 217204 (2007).
  * [16] Radu, I. _et al._ Transient ferromagnetic-like state mediating ultrafast reversal of antiferromagnetically coupled spins.  _Nature_ 472, 205–208 (2011).
  * [17] El Hadri, M. S., Hehn, M., Malinowski, G. & Mangin, S.  Materials and devices for all-optical helicity-dependent switching.  _Journal of Physics D: Applied Physics_ 50, 133002 (2017).
  * [18] Le Guyader, L. _et al._ Demonstration of laser induced magnetization reversal in gdfeco nanostructures.  _Applied Physics Letters_ 101, 022410 (2012).
  * [19] Gorchon, J. _et al._ Single shot ultrafast all optical magnetization switching of ferromagnetic co/pt multilayers.  _Applied physics letters_ 111, 042401 (2017).
  * [20] Iihama, S. _et al._ Single-shot multi-level all-optical magnetization switching mediated by spin transport.  _Advanced Materials_ 30, 1804004 (2018).
  * [21] Igarashi, J. _et al._ Engineering single-shot all-optical switching of ferromagnetic materials.  _Nano Letters_ 20, 8654–8660 (2020).
  * [22] Vomir, M., Albrecht, M. & Bigot, J.-Y.  Single shot all optical switching of intrinsic micron size magnetic domains of a pt/co/pt ferromagnetic stack.  _Applied Physics Letters_ 111, 242404 (2017).
  * [23] Camsari, K. Y., Faria, R., Sutton, B. M. & Datta, S.  Stochastic p-bits for invertible logic.  _Physical Review X_ 7, 031014 (2017).
  * [24] Caravelli, F. & Nisoli, C.  Logical gates embedding in artificial spin ice.  _New Journal of Physics_ 22, 103052 (2020).
  * [25] Tanaka, G. _et al._ Recent advances in physical reservoir computing: A review.  _Neural Networks_ 115, 100–123 (2019).
  * [26] Marković, D., Mizrahi, A., Querlioz, D. & Grollier, J.  Physics for neuromorphic computing.  _Nature Reviews Physics_ 2, 499–510 (2020).
  * [27] Gartside, J. C. _et al._ Reconfigurable training, reservoir computing and spin-wave fingerprinting in an artificial spin-vortex ice.  _arXiv preprint arXiv:2107.08941_ (2021).
  * [28] Jensen, J. H., Folven, E. & Tufte, G.  Computation in artificial spin ice.  In _Artificial Life Conference Proceedings_ , 15–22 (MIT Press, 2018).
  * [29] Jensen, J. H. & Tufte, G.  Reservoir computing in artificial spin ice.  In _Artificial Life Conference Proceedings_ , 376–383 (MIT Press, 2020).
  * [30] Hon, K. _et al._ Numerical simulation of artificial spin ice for reservoir computing.  _Applied Physics Express_ 14, 033001 (2021).
  * [31] Chumak, A., Serga, A. & Hillebrands, B.  Magnonic crystals for data processing.  _Journal of Physics D: Applied Physics_ 50, 244001 (2017).
  * [32] Barman, A., Mondal, S., Sahoo, S. & De, A.  Magnetization dynamics of nanoscale magnetic materials: A perspective.  _Journal of Applied Physics_ 128, 170901 (2020).
  * [33] Kaffash, M. T., Lendinez, S. & Jungfleisch, M. B.  Nanomagnonics with artificial spin ice.  _Physics Letters A_ 402, 127364 (2021).
  * [34] Gartside, J. C. _et al._ Reconfigurable magnonic mode-hybridisation and spectral control in a bicomponent artificial spin ice.  _Nature Communications_ 12, 1–9 (2021).
  * [35] Stenning, K. D. _et al._ Magnonic bending, phase shifting and interferometry in a 2d reconfigurable nanodisk crystal.  _ACS nano_ (2020).
  * [36] Gartside, J. C. _et al._ Current-controlled nanomagnetic writing for reconfigurable magnonic crystals.  _Communications Physics_ 3, 1–8 (2020).
  * [37] Vanstone, A. _et al._ Spectral-fingerprinting: Microstate readout via remanence ferromagnetic resonance in artificial spin systems.  _arXiv preprint arXiv:2106.04406_ (2021).
  * [38] Wang, Y.-L. _et al._ Rewritable artificial magnetic charge ice.  _Science_ 352, 962–966 (2016).
  * [39] Gartside, J., Burn, D., Cohen, L. & Branford, W.  A novel method for the injection and manipulation of magnetic charge states in nanostructures.  _Scientific reports_ 6, 32864 (2016).
  * [40] Gartside, J. C. _et al._ Realization of ground state in artificial kagome spin ice via topological defect-driven magnetic writing.  _Nature nanotechnology_ 13, 53 (2018).
  * [41] Albisetti, E. _et al._ Nanopatterning reconfigurable magnetic landscapes via thermally assisted scanning probe lithography.  _Nature nanotechnology_ 11, 545–551 (2016).
  * [42] Hofherr, M. _et al._ Ultrafast optically induced spin transfer in ferromagnetic alloys.  _Science advances_ 6, eaay8717 (2020).
  * [43] Dewhurst, J. K., Elliott, P., Shallcross, S., Gross, E. K. & Sharma, S.  Laser-induced intersite spin transfer.  _Nano letters_ 18, 1842–1848 (2018).
  * [44] Uba, S. _et al._ Optical and magneto-optical properties of co/pt multilayers.  _Physical Review B_ 53, 6526 (1996).
  * [45] Imperial college research computing service.  DOI: 10.14469/hpc/2232.
  * [46] Edward, D. P. & Palik, I.  Handbook of optical constants of solids (1985).
  * [47] Johnson, P. B. & Christy, R.-W.  Optical constants of the noble metals.  _Physical review B_ 6, 4370 (1972).
  * [48] Tikuišis, K. K. _et al._ Optical and magneto-optical properties of permalloy thin films in 0.7–6.4 ev photon energy range.  _Materials & Design_ 114, 31–39 (2017).
  * [49] Kuz’min, M.  Shape of temperature dependence of spontaneous magnetization of ferromagnets: quantitative analysis.  _Physical review letters_ 94, 107204 (2005).

### Supplementary Information

### Supplementary note 1 - SEM images of nanomagnetic arrays used for FTIR
measurements

Supporting Figure S1 shows scanning electron micrographs (SEM) of nanomagnetic
arrays patterned on top of a) Si / SiO2 (300 nm) and b) Au (250 nm) / SiO2
(290 nm) substrates which were used for FTIR measurements. Nanomagnetic array
dimensions are consistent across both samples and are found to be a) $L$ = 226
nm, $W$ = 78 nm and $P$ = 356 nm and b) $L$ = 223 nm, $W$ = 85 nm and $P$ =
353 nm. The patches observed in Supporting Figure S1 a) are attributed to
residual PMMA. This does not significantly influence absorption in the
nanomagnets as demonstrated by the switching fidelity observed throughout this
work.

Supporting Figure S1. SEM images of the nanomagnetic arrays patterned on top
of a) Si / SiO2 (300 nm) and b) Au (250 nm) / SiO2 (290 nm) substrates.
Dimensions are found to be a) $L$ = 226 nm, $W$ = 78 nm and $P$ = 356 nm and
b) $L$ = 223 nm, $W$ = 85 nm and $P$ = 353 nm.

### Supplementary note 2 - Simulation absorption for Si and SiO2 substrates

Supporting Figure S2 shows the simulation absorption for nanomagnets in a
square ASI geometry patterned on semi-infinite a) Si substrate and b) SiO2
substrates. Nanomagnet dimensions of $L$ = 226 nm, $W$ = 78 nm and $P$ = 356
nm are used. The absorption at 633 nm is found to be 4$\%$ and 18$\%$ for Si
and SiO2 respectively. This is 16.25 and 3.61 $\times$ less absorption than
the optimum Au (250 nm) / SiO2 (290 nm) substrate in Figure 2.

Supporting Figure S2. Simulated absorption for nanomagnets patterned on semi-
infinite a) Si substrate and b) SiO2 substrate. Absorption at 633 nm is found
to be 4$\%$ and 18$\%$ respectively. Nanomagnet dimensions of $L$ = 226 nm,
$W$ = 78 nm, $t$ = 20 nm and $P$ = 356 nm are used.

### Supplementary note 3 - Further information on the optical absorption
mechanism

Here we explore the localised surface plasmon (LSP) response of the permalloy
(Py) nanomagnetic particles and argue that this is not the dominant absorption
mechanism. Supporting Figure S3 shows the simulated absorption (panels a and
c) and scattering (panels b and d) cross sections for a single nanomagnet on a
silica substrate (panels a and b) and silicon substrate with a 300 nm silica
layer (panels c and d). At the nanomagnet lengths and incident wavelengths
explored in this work, low cross sections are observed. Furthermore, including
the silicon substrate only has a weak influence on the LSP response.

In Figure 2 c) diffraction orders were observed, which decrease the absorption
in the Py layer of the nanomagnet array. Supporting Figure S4 a) shows an
equivalent simulation to Figure 2 c) overlayed with a red and blue dashed
lines indicating the grating diffraction orders described by
$\lambda=n_{\mathrm{SiO2}}P$ and $\lambda=n_{\mathrm{SiO2}}P/\sqrt{2}$, where
$P$ and $n_{\mathrm{SiO2}}$ are the period and the refractive index of the
silica substrate, respectively. Supporting Figure S4 b) shows the calculated
absorption for a Py ASI array with a period $P=600$ nm for a silica substrate
(blue line) and silicon substrate with 300 nm silica layer (red line). The
diffraction orders are blue-shifted for the silicon substrate with a silica
layer which is attributed to interference within the silica layer.

Supporting Figure S3. Simulated LSP response of the nanomagnetic particles. (a
and c) show the absorption cross sections and (b and d) show the scattering
cross sections of a single nanomagnet particle. (a and b) are for a silica
substrate and (c and d) are for silicon substrate with a silica layer (300
nm), respectively. The Silicon substrate has a very weak influence on the LSP
response, which is quite weak in this wavelength range, with low cross
sections. Supporting Figure S4. The emergence of diffraction orders for large
period values and their origin. a) Simulated optical absorption in the Py
layers in the nanomagnet array for varying unit cell period. The vertical
dashed line indicates the period of 356 nm used in experiments. The horizontal
dashed lines indicate the wavelengths of 633 nm and 785 nm. The red and blue
dashed lines indicate the grating diffraction orders, described by
$\lambda=n_{\mathrm{SiO2}}P$ and $\lambda=n_{\mathrm{SiO2}}P/\sqrt{2}$, where
$P$ and $n_{\mathrm{SiO2}}$ are the period and the refractive index of the
silica substrate, respectively. b) Calculated absorption in Py for a
nanomagnet array with $P$ = 600 nm for a silica substrate (blue line) and a
silicon substrate with a silica layer (300 nm) (red line). The diffraction
orders for the silica substrate match those shown in (a). The diffraction
orders for the silicon substrate are clearly blue shifted, which we attribute
to interference in the silica layer.

### Supplementary note 4 - Micromagnetic simulations of vertex energies

Supporting Figure S5. Simulated microstate energies of a 5 $\times$ 5 vertex
grid obtained from MuMax3. Nanomagnetic dimensions are $L$ = 226 nm, $W$ = 78
nm and $P$ = 356 nm, $t$ = 20 nm. Microstates and total energies of a) the
saturated type 2 state. b) A single spin flip on a saturatd background. A
double flip leaving a central c) type 1 vertex and d) type 4 vertex each with
two type 3 vertices. e) Microstate and energy of a single type 2 vertex with
periodic boundary conditions. f) Table of vertex energies expressed as
relative to the T2 state ($\Delta$ET2) and absolute values (E).

Micromagnetic simulations were used to obtain an estimate of each vertex
energies for the nanomagnetic arrays explored in this work. Supporting Figure
S5 shows four microstates in a) a saturated type 2 state, b) a single switch
on a saturated background leaving 2 type 3 monopoles. c,d) A further spin flip
giving c) 2 x type 3 and 1 x type 1 and d) 2 x type 3 and 1 x type 4. From
this the relative energies of each state are calculated. e) shows the
microstate and energy of a single type 2 vertex with periodic boundary
conditions. f) Shows the relative (compared to the type 2 state) and absolute
energies for each vertex type. The temperature is set to 0 K making the
energies a likely overestimate. Nanomagnetic dimensions are $L$ = 226 nm, $W$
= 78 nm and $P$ = 356 nm, $t$ = 20 nm.

### Supplementary note 5 - Scanning beam switching on Au/SiO2 substrates

Supporting Figure S6. MFM images of switching of nanomagnets patterned on an
Au/SiO2 substrate. Bar lengths up to 1.02 µm are reversed. Here the scan
direction and polarisation are parallel. A higher power is required for longer
nanomagnets

Supporting Figure S6 shows MFM images of a range of ASI arrays with increasing
nanomagnet lengths patterned onto a Au / SiO2 substrate. Here, the scan
direction and polarisation are parallel. All nanomagnet lengths up to 1.02 µm
can be reversed, demonstrating the efficacy of the technique when combined
with a substrate which inhibits transmission.

### Supplementary note 6 - Magnetometry of nanomagnetic arrays

Supporting Figure S7. Showing a) Magnetisation as a function of temperature
between 120 K and 380 K for a 2 mm x 2 mm ASI array and a 6.5 mm x 5.5 mm thin
film deposited at the same time. Both datasets are fitted to M(T) =
M(0)(1-(T/Tc)$\alpha$)$\beta$ where Tc is the Curie temperature, M(0) and M(T)
are the magnetisation at 0 K and T K respectively and $\alpha$ and $\beta$ are
empirical constants where $\alpha$ASI = 2, $\alpha$film = 2.18 , $\beta$ASI =
0.476, $\beta$film = 0.476. Tc is estimated to be 770 K and 832 K for ASI and
the reference film respectively. Fits to conventional bloch law yield
unrealistic high Tc b) Coercive field field of the ASI array as a function of
temperature. Error bars indicate the start and end of switching. The coercive
field (Hc) reduces by 10.7 mT from 120 - 370 K. Magnetic field is applied at
45∘ to both subsets of bars.

Supplementary Figure S7 a) shows the temperature dependence of magnetisation
of a 2 mm x 2 mm square ASI array (Py) and Py thin film. The sample is the
same one used for the FTIR measurements in Figure 2. A $\sim$10$\%$ reduction
in magnetisation occurs between 120 - 380 K. Also shown in extrapolated fits
to the equation M(T) = M(0)(1-(T/Tc)α)β) [49]. Tc is found to be 770 K and 832
K for ASI and the thin film respectively. Fits to conventional bloch law M(T)
= M(0)(1-T/Tc)3/2 yield unrealistically high values of Tc. Nevertheless, it is
unlikely that the temperatures reached during CW exposure reach Tc.
Supplementary Figure S4 b) shows the coercive field of the nanomagnets as a
function of temperature from 120 - 370 K. Error bars indicate the start and
end of switching arising from the distribution of coercive fields across the
sample. Magnetic field is applied at 45∘ to both subsets of bars. The coercive
field reduces by 10.7 mT in this range indicating a high Tc of the samples.

### Supplementary note 7 - Ni50Fe50 and Co nanomagnetic array exposure

Supporting Figure S8 shows writing of a,b) Ni50Fe50 (20 nm thickness) and c)
attempted writing of a Co (8 nm thickness) nanostructures patterned on an
Au/SiO2 substrate. Co dimensions are L = 320 nm, W = 110 nm, P = 385 nm.
Ni50Fe50 possesses the necessary band structure for OISTR to take effect
whereas Co does not. Ni50Fe50 nanowires with length $\leq$ 490 nm are switched
at 3 mW power. This is a lower power and broader dimension set than observed
in Py. Conversely, no switches are observed in Co for powers up to 8 mW
displayed and 30 mW (not shown). This is consistent across a broad range of
nanomagnet dimensions. These results indicate that the multi-species nature of
NiFe alloys which allow for the necessary band structure plays a role in the
observed switching. Lower contrast in Supporting Figure S8 b is due to the
necessity of using a low-moment MFM tip for this thickness of Co.

Supporting Figure S8. mFM images of Ni50Fe50 in a) a saturated state and b)
after exposure to a $\lambda$ = 633 nm laser with 3 mW power. Polarisation is
parallel to the bar long axis. Bars with length $\leq$ 0.49 µm switch. c)
Shows MFM image of a Co array with nanomagnet dimensions of L = 320 nm, W =
110 nm, P = 385 nm after exposure to a $\lambda$ = 633 nm laser with powers
ranging from 1-8 mW. No switches are observed. Here we use a low moment MFM
tip for imaging to avoid MFM-tip writing[40].