# Switchable-magnetisation planar probe MFM sensor

Michael Verhage  Eindhoven University of Technology - M2N, Netherlands  Tunç
H. Çiftçi  Eindhoven University of Technology - FNA, Netherlands  Michiel Reul
Eindhoven University of Technology - M2N, Netherlands  Tamar Cromwijk
Eindhoven University of Technology - FNA, Netherlands  Thijs J.N. van Stralen
Eindhoven University of Technology - FNA, Netherlands  Bert Koopmans
Eindhoven University of Technology - FNA, Netherlands  Oleg Kurnosikov
University of Lorraine, Institut Jean Lamour, France  Kees Flipse  Eindhoven
University of Technology - M2N, Netherlands<EMAIL_ADDRESS>
###### Abstract

We present an alternative switching-magnetization magnetic force microscopy
(SM-MFM) method using planar tip-on-chip probes. Unlike traditional needle-
like tips, the planar probe approach integrates a microdevice near the tip
apex with dedicated functionality. Its $1\text{\,}\mathrm{mm}$ $\times$
$1\text{\,}\mathrm{mm}$ planar surface paves the way for freedom in ultra
thin-film engineering and micro-/nano-tailoring for application-oriented tip
functionalization. Here, we form a microscale current pathway near the tip end
to control tip magnetisation. The chip like probe or planar probe, was applied
to study the complex magnetic behaviour of epitaxial transition metal oxide
perovskite LaMnO3, which was previously shown to behave as complex material
with domains associated with superpara-, antiferro- and ferromagnetism. To
this end we successfully imaged an inhomogeneous distribution of weak
ferromagnetic islands with a resolution better than $10\text{\,}\mathrm{nm}$.

For Table of Contents Only

Key words: AFM, MFM, tip design, weak magnetic, LMO3, metal oxide.

##  0.1 Introduction

Magnetic force microscopy (MFM) is a widespread method in fundamental surface
studies and nanoscale technological applications with a high lateral
resolution of up to tens of nanometers and $\text{\,}\mathrm{pN}$ force
sensitivity1, 2. The working principle of MFM relies on the force interaction
between the tip’s magnetic stray field and a samples’ spatially varying
magnetic textures. By nanoscale utilization of this magnetic force
interaction, MFM covers a wide operational range from characterization to
manipulation of magnetic objects 3, 4, 5.

Despite its extensive use, a general MFM hits its capability limits mainly in
lateral resolution of imaging materials with weak or time-varying
magnetization. For instance, low coercive and weak ferromagnetic (FM) or
superparamagnetic (SP) structures generally require an external magnetic field
to saturate 6, and without this the magnetic force to the tip is weak or may
be undetectable by the bandwidth of the MFM. Hence, nonmagnetic interactions
such as those of electrostatic origin can mask the magnetic signal7, 8, 9. To
obtain the pure magnetic signal of nanoscale weak FM or SP textures, such as
isolated islands, an MFM variant called switching magnetization force
microscopy (SM-FM) 10, 11 or controlled magnetization-MFM (CM-MFM) 8 stands
out by extracting such signals out of the detected force 11, 12, 9. Beyond
traditional MFM, SM-FM measures a relative force change due to controlled
altering of the magnetic state of the tip or the sample (or both). Only the
magnetic field interaction is sensitive to the relative magnetic polarities
between the tip and sample and hence can thus be detected.

The need for a SM-FM imaging technique with a capability of imaging weak FM or
SP islands with a resolution beyond $10\text{\,}\mathrm{nm}$ can be found in
the study of epitaxial complex oxide perovskites such as LaMnO3 (LMO3). Wang
et al. 13 have shown that epitaxial LMO3 reveals an abrupt transition from an
antiferromagnetic (AF) state to a ferromagnetic (FM) depending on the
thickness of the LMO3 layer. The magnetic transition occurred at a film of
$5\text{\,}$ atomic unit cell (u.c.) thickness. Furthermore, Anahory et al.14
observed inhomogeneously distributed SP islands besides the FM domains, with
the former only detected following an applied in-plane magnetic field of
variable strength. Both groups used a scanning SQUID microscope (SSM), albeit
with different lateral resolution, to image the LMO3 sample’s stray field
distribution. However, the SSM imaging performed by Anahory et al. 14 could
not go beyond a resolution of $100\text{\,}\mathrm{nm}$, which left the SP
island size to be only indirectly inferred between $10\text{\,}\mathrm{nm}$
and $20\text{\,}\mathrm{nm}$.

To solve the problem of limited imaging resolution of traditional MFM, we
carefully designed a new type of SM-FM sensor. To this end, we design a
magnetic tip with a stray-field of several hundred mT strong enough to
saturate the magnetic textures. The tip is realised by forming an oriented
single domain state near the tip apex 15. Traditional needle-like MFM tips
generally only generate up to a few tens of mT of stray field 16, 2. With this
approach the LMO3 weak FM domains are simultaneously saturated and profiled
for imaging by the same tip. The tip’s stray field decays rapidly from the tip
and hence, by changing the height of the tip with respect to the sample
surface the weak magnetic textures can be actively saturated.

We demonstrate that our sensor is capable of imaging magnetic textures of LMO3
with a resolution beyond $10\text{\,}\mathrm{nm}$. For this, we present a new
approach combining planar chip-like probes17, 18, 19 with highly sensitive
tuning fork force sensors which we call the switching-magnetization planar
probe (SM-PP) and is illustrated in Figure 1a. This method aims to provide an
on-chip reorientable tip magnetization with no required external magnetic
field, to act as an switchable magnetic force sensor.

Figure 1: Planar probe with switchable tip magnetization (SM-PP). (a)
Illustration of the SM-PP sensor, with electrical contacts for force sensing
and sending current pulses $I_{p}$ to the tip apex. The tip is formed by a
tip-on-chip called the planar probe (PP). (b) SEM image of the PP with a sharp
tip apex formed by cleaving a Si wafer. Sending a current pulse generates an
Ørsted field ($\vec{H_{p}}$) within the metallic film to orient the tip
magnetization into a singular domain state. The current pathway is created by
the formation of a FIB milled bridge. (c) The metallic film with two main
layers: the current-carrying Pt layer and the ferromagnetic Co layer. The
polarity of $I_{p}$ determines the direction of the Ørsted field
($\vec{H_{p}}$) which alters (reverse) the direction of magnetization of the
Co film. (d) Multi-domain state can be poled into an oriented single domain by
a controlled current pulse. (e) Schematic side view of the SM-PP shows the
mass retuned tuning fork prong and a lateral view of the surrounding tip stray
field $\vec{B}$. The planar probe is placed under a
$45\text{\,}\mathrm{\SIUnitSymbolDegree}$ angle to the prong. (f) Kerr
microscopy image showing a poled magnetic tip domain after sending a single
$I_{p}$. The dark contrast at the bottom of the tip demonstrates the singular
domain with magnetization $\vec{M_{\text{tip}}}$. The white scale bar equals
$5\text{\,}\mathrm{\SIUnitSymbolMicro m}$.

##  0.2 Results and Discussion

The working principle of the SM-PP relies on switching from a multi-domain
state of the tip to a poled single domain via an internally generated Ørsted
field ($H_{p}$) within a planar chip-like probe, as illustrated in Figures 1a,
b and d. Initially, the magnetic layer on the tip is in a multi-domain state
with a closed flux loop, Figure 1d. The direction of this flux may be
irregular, and hence inappropriate for perturbing weak FM islands. The planar
probe design used in this study has a bi-metallic structure of thin-film
components: the current-carrying layer and the ferromagnetic layer, as
depicted in Figures 1b and c. By sending an electrical pulse ($I_{p}$) through
the current-carrying layer in a designated electrical pathway (called the
bridge) near the tip apex, we generate an Ørsted field of controlled magnitude
and well-defined direction which penetrates the ferromagnetic layer. This
action leads to a singular domain state of the tip apex, with a preferable
orientation.

The planar probe is formed by cleaving a silicon wafer into a small
$1\text{\,}{\mathrm{mm}}^{2}$ square piece with a
$90\text{\,}\mathrm{\SIUnitSymbolDegree}$ tip apex 20, 17. Near the tip apex,
i.e. the cleaved corner, naturally increases the flux density, increasing the
tip stray field compared to a needle-like MFM tip. This magnetic field
strength and distribution is discussed later on. The single domain state of
the tip can be used to probe weak FM domains. To this end, we used a
$30\text{\,}\mathrm{nm}$ Pt film for the current-carrying layer and a
$15\text{\,}\mathrm{nm}$ Co film for the ferromagnetic layer, placed on top of
the planar probe. Detailed fabrication procedures of the film and planar probe
are given in Supplementary S1.

Contrary to the traditional passive needle-like MFM tips, we can orient the
SM-PP multi-domains into a singular domain by only a single current pulse as
often as needed to combat transient tip demagnetisation, a known issue in MFM.
The resulting tip domain after sending a current pulse is illustrated in
Figure 1d. As a result, we can obtain consistently oriented tip domains,
resulting in a predictable stray field in the tip vicinity, as indicated by
$\vec{B}$ in Figure 1e. Figure 1e illustrates the side view of the SM-PP with
the tip stray field distribution predominately out-of-plane from the sample’s
perspective. In Supplementary S4 we discuss in-depth the tip stray field
distribution derived from a numerical study. Finally, Figure 1f shows a Kerr
microscopy image of the SM-PP, after having sent a current pulse of sufficient
amplitude. A poled tip domain is formed as observed with the dark contrast
near the apex, highlighted within the dashed circle.

We attached this functionalized planar probe to a mass retuned 20 quartz
tuning fork (QTF) force sensor with integrated electrical access to the probe
for the current pulse $I_{p}$, as schematically illustrated in Figure 1a.
QTF’s have been successfully used before for MFM 21 and are easily integrated
in an UHV scanning probe microscope. The retuned tuning fork approach
significantly improved the load capacity of the QTF sensor. As widespread AFM
and MFM applications have previously experienced, once the mass exceeds
several tens of $\text{\,}\mathrm{\SIUnitSymbolMicro g}$ 22, which is far
below the mass of a chip-like probe, the oscillation’s Q-factor value drops to
only several hundred from the original 40 thousand. This reduction in Q-factor
results in a large loss in force sensing capabilities 23, 20. For degraded
Q-factor sensors, we would be unable to use the planar probe for imaging
magnetic fields of LMO3. To this end, the retuned tuning fork approach
compensates for the mass unbalancing from planar probe attachment and recovers
sensitivity. As a result we are able to restore the Q-factor to over
$2\text{\times}{10}^{4}\text{\,}$ at room temperature in ultra-high vacuum
(UHV) 18, 20. In Supplementary S3 we discuss further the need for a high $Q$.

As a consequence, the Q-factor drops to only a few hundred 18, leading to
degraded force sensing capabilities. The same effect can arise from the
additional wires connecting the current control signal for pulsing, which is
the reason why dedicated electrical contacts to the tip are now integrated on
the tuning fork itself 24. We solve the mass-imbalance by mass retuning 23 the
QTF as described in our previous work 20 and utilising readily available
electrodes on the tuning fork.

For extracting the magnetic signal of weak FM islands, the SM-PP needs to
change to a fully oriented $M_{\text{tip}}$ near the tip apex, starting from a
multi-domain state. We turned to finite element modeling (FEM), with COMSOL™,
to simulate the generated Ørsted field within the bridge to assess the
required $I_{p}$ magnitude for tip magnetisation control. Furthermore, we can
investigate the thermal response of the tip by Joule heating.

Figure 2: Numerical and experimental validation of the magnetic switch of the
SM-PP tip. (a) Numerical calculations of $\vec{H_{\text{p}}}(\vec{r})$
magnetic field components ($B_{x}$,$B_{y}$) and $B_{z}$) from a
$150\text{\,}\mathrm{mA}$ pulse. The bridge is
$5\text{\,}\mathrm{\SIUnitSymbolMicro m}$ wide. (b) Numerical switching
behaviour of the SM-PP, covering bridge width $d$ varying from
$50\text{\,}\mathrm{nm}$ to $7\text{\,}\mathrm{\SIUnitSymbolMicro m}$,
presented in the phase diagram. The colors indicate a switch between two
oppositely poled single domain state (green), domain fluctuations (orange) or
no switch (red). (c), (f) Simulated single domain formation of the tip for
inverting $I_{p}$ polarity. (d)-(h) Kerr microscopy results show domain
orientation switching after inverting $I_{p}$ polarity. The vertical component
of the altered magnetization (indicated in blue and yellow) is visible in the
location near the tip end in d and g. The horizontal component is mostly aside
the tip end e, h.

Figure 2 presents the numerical and experimental validation of the magnetic
switch of SM-PP tip. The simulations cover various bridge widths $d$ in the
range from $50\text{\,}\mathrm{nm}$ to $7\text{\,}\mathrm{\SIUnitSymbolMicro
m}$ and different $I_{p}$ values from $10\text{\,}\mathrm{mA}$ to
$200\text{\,}\mathrm{mA}$. The pulse duration is $500\text{\,}\mathrm{ns}$.
See Supplementary S4 for details on the simulations. First, Figure 2a shows
the calculated spatial field components of $\vec{H_{\text{p}}}(\vec{r})$ of a
$5\text{\,}\mathrm{\SIUnitSymbolMicro m}$ bridge under application of $I_{p}=$
$150\text{\,}\mathrm{mA}$. The in-plane field components $B_{x}$ and $B_{y}$
of $\vec{H_{\text{p}}}(\vec{r})$ follow the bridge structure. This indicates
that both symmetric sides of the tip have opposing magnetic direction, as is
evident from the current flow pathway. Near the tip apex, $B_{x}$ and $B_{y}$
are relatively small since the current density is lowest (between the white
lines of Figure 2a). A strong out-of-plane component $B_{z}$ (Figure 2a) is
only observed at the boundary of the tip and bridge, but is of little
importance with respect to the in-plane magnetisation of the Co film. At just
$1\text{\,}\mathrm{\SIUnitSymbolMicro m}$ away from the tip apex, above the
upper white line, the in-plane magnetic field is larger than
$10\text{\,}\mathrm{mT}$ which implies the nucleation of oriented in-plane Co
domains. In Supplementary S1 the magnetisation response of the Co film is
given.

Following, $\vec{H_{\text{p}}}(\vec{r})$ is used as an input parameter within
Mumax3 to calculate the magnetisation response (switch vs. no switch) of the
Co film at the tip apex, as a function of the bridge width $d$ and
$I_{\text{p}}$. In Figure 2b the color scale represents three different states
of the tip magnetization after applying $I_{p}$. Green means the tip end
domain shows a 180° reversal, so a full switch. Yellow represents an observed
modification or a limited rotation by less than 180° in the tip domain. Red
implies that the magnetization remained identical to the pre-pulse
orientation. The results show a few tens of mA increase in critical current
level for the bridge gap width values from $50\text{\,}\mathrm{nm}$ until
$1\text{\,}\mathrm{\SIUnitSymbolMicro m}$, as given in Figure 2a. For the
bridge gap widths greater than $1\text{\,}\mathrm{\SIUnitSymbolMicro m}$, the
critical current shows a larger increase.

Although the nanometer scale of the bridge can be achieved with various
techniques and types of lithography, in our experiments we used focused ion
beam (FIB) milling. This resulted in bridges on the micrometer scale and as
the simulations results shows, we require a current magnitude in the order of
${10}^{2}\text{\,}\mathrm{mA}$. Supplementary S1 discusses the FIB fabrication
in further detail. When we simulate a current pulse with
$130\text{\,}\mathrm{mA}$ amplitude and $500\text{\,}\mathrm{ns}$ duration for
a bridge of $5\text{\,}\mathrm{\SIUnitSymbolMicro m}$, the tip magnetization
changes fully accordingly to the pulse polarity, as shown in Figures 2c and f.
The notion of tip switch at values below $130\text{\,}\mathrm{mA}$ is
important, especially for micrometer scale bridges, because it significantly
limits the Joule heating, as we discuss later.

Based on the simulation results, a Kerr microscopy experiment was performed to
validate the magnetic switch. The Kerr microscopy experimental details are
given in Supplementary S2. Gray/black tones in Figure 2d, e, g, and h
represent Co domains preserving initial orientations before the pulse, upon
applying a current pulse. False colored areas represent the Co domains’
response to $I_{p}$. Figures 2c and f indicate the orientation in the vertical
direction expressed by the blue-to-yellow color scale. Figures 2d and g show
the domain orientation in the horizontal direction, given by the pink-to-green
color scale. The domain is mainly confined to the bridge region, as only here
the current density is sufficient for inducing Co domain reversal. Along the
length of the FIB bridge, the domains are inverted (pink and green), which
follows closely those of the numerical simulations of Figures 2c and f,
validating the realisation of the SM-PP.

Figure 3: Numerical study of the thermal response. (a) On the right, the
calculated current density across the bridge for a current pulse of
$150\text{\,}\mathrm{mA}$. The current density increases up to
$6\text{\times}{10}^{11}\text{\,}\mathrm{A}\text{\,}{\mathrm{m}}^{-2}$ at the
smallest section of the bridge. On the left, the corresponding temperature
profile. (b) The current pulse $I_{p}$ has to form of an asymmetric double
sigmoidal function plotted as the black curve. With a FWHM of
$160\text{\,}\mathrm{ns}$ and a peak value of $150\text{\,}\mathrm{mA}$. The
transient temperature response, red curve, show a rapid decay of the
temperature, highlighting the efficient thermal dissipation of the bridge and
ensuring mechanical stability.

After applying $I_{p}$, the temperature increase should be excessive i.e.
above $100\text{\,}\mathrm{K}$, because it would hamper operation in UHV and
degrade the tip’s metallic layers. Examples and solution by metallic layer
composition with respect to preventing degradation of tips are discussed in
Supplementary S1. Hence, we modelled the (transient) temperature response of
the tip for $I_{p}=$ $150\text{\,}\mathrm{mA}$ for an upper limit of thermal
increase. Figure 3a compares the simulated spatial current density across the
bridge for a $I_{p}$ of $160\text{\,}\mathrm{ns}$, with the thermal profile.
As expected, the current density is highest near the shortest width of the
metallic film and is in the order of
${10}^{11}\text{\,}\mathrm{A}\text{\,}{\mathrm{m}}^{-2}$. Yet, the maximum
temperature increase is observed to be only $50\text{\,}\mathrm{K}$, which
means operation in UHV is possible and would minimize Joule heating damage to
the metallic films. We experimentally pulsed several tips for tens of times
and no degradation was observed. The transient heating response was also
simulated, with the results given in Figure 3b. Here, a
$160\text{\,}\mathrm{ns}$ asymmetric double sigmoidal pulse, see Supplementary
S4 for pulse details, is simulated. The temperature decreases quickly within a
microsecond due to efficient thermal dissipation of the Si substrate. We
studied the effects of substrate capping material, i.e. Si coated with SiO2 or
MgO, on this thermal dissipation and the results are also discussed in
Supplementary S4.

To conclude the first part of this work; the design, fabrication and
optimisation of SM-PP provides us a SM-PP sensor with high Q-factor. Combined
with the current-controlled tip magnetization it enables the possibility to
study the magnetic surface textures of LMO3 13, 14. For the second part of
this work we turn to applying the SM-PP sensor to saturate and image the weak
FM islands, aswell the AF domains the former are embedded into, of epitaxial
LMO3.

The magnetic texture of a 6 u.c. LMO3 on STO3 sample was imaged with our MFM
operating both below ($T=$ $100\text{\,}\mathrm{K}$) and above ($T=$
$300\text{\,}\mathrm{K}$) of LMO3’s $T_{c}=$ $115\text{\,}\mathrm{K}$ 13. The
first aim was to identify the AF and weak-FM texture distribution across the
surface. Secondly, the SM-PP is able to magnetize magnetic islands by the
tip’s oriented stray field exceeding $300\text{\,}\mathrm{mT}$, see
Supplementary S4, and hence the size of the magnetic islands can be observed
with a lateral scale between $10\text{\,}$ and $20\text{\,}\mathrm{nm}$ 14.
The same SM-PP sensor was used for all imaging, with Frequency Modulation (FM)
feedback. The scanning parameters are kept constant throughout all the
measurements, see Supplementary S6 for methods and experimental details.

Figure 4: MFM images obtained with the SM-PP sensor on 6 u.c. LMO3/STO. (a)
Topographic images of LMO3. (b) Multi-domain tip state MFM measurement at
$100\text{\,}\mathrm{K}$ showing no magnetic contrast. (c) The SM-PP tip is
magnetised into a single domain. MFM imaging reveals spatially inhomogenous
magnetic contrast at $100\text{\,}\mathrm{K}$. (d) Typical force-distance
(F-z) spectroscopy and damping (voltage) signal taken at red areas of c. F-z
spectroscopy shows a sudden kink in the attractive regime as highlighted with
the blue arrow. The orange arrow indicated short range vdW forces. The damping
signal (red line) is simultaneously taken, showing a sudden change in
dissipation as indicated with the red arrow, (e) F-z spectroscopy and damping
signal taken at a blue spot of c, showing significant reduction in sudden
dissipation and force changes at the blue and red arrow, compared to d. (f, g)
Magnetic features observed with a poled tip. The tip’s stray field induces
local magnetic domain perturbation (streaks) as indicated with the black
circles and arrows. The forward and backward scan are compared. In all images
the black scale bar is equal to $30\text{\,}\mathrm{nm}$.

First, we scanned at a temperature of $100\text{\,}\mathrm{K}$ and imaged a
plateau of the LMO3/STO3 stepped surface. The 90$\times$90
$\text{\,}{\mathrm{nm}}^{2}$ topography images are given in Figure 4a and
demonstrates a LMO film RMS roughness $S_{q}$ of $32\text{\,}\mathrm{pm}$.
Although the surface of LMO3 can show up to 1 u.c. roughness variations, in-
homogeneously distributed across the stepped surface, which is a known surface
feature for manganites 25. The lateral resolution in topography is limited by
the relatively large amplitude of $10\text{\,}\mathrm{nm}$ used for detecting
the long range magnetic force. Ideally, one would use a small amplitude for
high resolution topography and a large amplitude for lift mode magnetic
imaging 21. We leave this for future work, as currently this approach of
consecutively switching of the amplitude introduced large drift in our setup.

After obtaining the local topography, we switched to MFM. The MFM signal was
first acquired with a multi-domain, closed flux tip, where negligible (out-of-
plane oriented) stray field should interact with the sample magnetic domains.
Indeed, Figure 4b shows that no MFM signal could be measured below the noise
level of $1.5\text{\,}\mathrm{mHz}$. The lack of topography cross-talk in the
lift mode image also demonstrates that the lateral variation of the
electrostatic force is neglible.

Following, the tip was pulsed by a $160\text{\,}\mathrm{mA}$ current pulse for
$205\text{\,}\mathrm{ns}$, which aligned the tip domain in the downward
position, as indicated schematically in Figure 4c and confirmed with Kerr
microscopy prior. For safety, the tip was retracted by
$0.5\text{\,}\mathrm{\SIUnitSymbolMicro m}$ from the surface during the pulse,
which can give rise to lateral drift of around $10\text{\,}\mathrm{nm}$ in our
SPM at these temperatures. With the magnetically oriented tip, we continue MFM
imaging at $100\text{\,}\mathrm{K}$ and observed a complex landscape of
magnetic textures across the scanned area, as given in Figure 4c. The smallest
magnetic objects are highlighted with red circles in Figure 4c, which also
correspond to the strongest attractive magnetic forces. These features have on
average a diameter of $10\text{\,}\mathrm{nm}$. We attribute these area’s as
stray field induced magnetised domains. Observing the nominal size, it is very
likely that these corresponds to the weak FM textures 14, even at
$100\text{\,}\mathrm{K}$.

Performing force-distance (F-z) spectroscopy on the red islands of Figure 4d
showed complex behaviour and provides more evidence for weak FM properties.
The tip was retracted up to $20\text{\,}\mathrm{nm}$ above the surface, and
then lowered until a notable repulsive fore was observed. The frequency shift
$df$ was measured during spectroscopy. Evidence of the tip stray field induced
magnetic alignment is given in Figure 4d. We observe four distinct regimes;
firstly we note a long-range attractive forces between
$20\text{\,}\mathrm{nm}$ and $8\text{\,}\mathrm{nm}$. This can be assigned to
long range electrostatic forces. At around $7.5\text{\,}\mathrm{nm}$, a sudden
negative change in frequency (force) is observed as indicated with a blue
arrow. We attribute this to the significant increase of the magnetic field the
sample experiences as the SM-PP tip approaches the weak FM domain and hence
saturating it. At $3.4\text{\,}\mathrm{nm}$, indicated with an orange arrow,
the attractive van der Waals force region is noted. At very small tip-sample
distances the frequency shift becomes positive evidence of repulsive forces.
We also measured the damping, a sign of energy loss via local magnetization
change of the weak FM islands 7. In Figure 4d, the red curve shows a sudden
rise in the damping as indicated with the red arrow. Likely, at this distance
the weak FM islands are magnetized periodically as the tip oscillates up and
down. As a comparison, Figure 4e shows the same F-z spectroscopy experiment
performed on the blue areas of Figure 4c. Less perturbing of the attractive
force is noted, and no measurable dissipation change is observed as
highlighted with the colored arrows. We conjecture that those blue colored
areas are the antiferromagnetic domains.

Generally, the weak FM features (coloured red) are embedded in magnetic
labyrinth-like domains colored yellow/green in Figure 4c. These domains are
continuous and spread across the surface. Furthermore, they have smaller
attractive force than the weak FM areas. Due to the tip’s large stray field
induced magnetization of LMO3, no repulsive area’s could be observed. Areas
depicted in blue are observed in two distinct regimes. First, we note
distributed areas highlighted with the dashed white line. Secondly, blue
circular like objects are noted as highlighted with the blue circle. These
objects show very little attractive frequency shift. Hence, excluding
electrostatic forces as these are constant across the surface, these domains
form an antiferromagnetic texture, corroborating the SSM observations of Wang
et al. 13 and Anahory et al. 14.

Furthermore, we note that the tip stray field can induce local magnetic
perturbations in the real-space imaging. By comparing the forward and the
backward scan, Figures 4f-g, the areas highlighted in the black circle show
clear distinction between the two images. We conjecture that the field from
the tip perturbed the local weak FM domains. This would also be in agreement
with the observation of streak-lines as indicated with the arrows.

In conclusion, the results lay strong indications of the imaging capabilities
of the magnetically controllable SM-PP tips for weak FM islands with a
resolution higher than $10\text{\,}\mathrm{nm}$. Firstly, we achieved a
repeatable control over the magnetization at the SM-PP tip with a consistently
distributed domain state at the tip apex. Following, we demonstrated imaging
of a complex magnetic texture of the rare-earth metal oxide perovskite LMO3
with nanometric identification of weak FM islands. For further investigation
of LMO3 the SM-PP can be employed for ultra-high resolution imaging of the
local u.c. variation in film thickness and the possible correlation with weak
FM islands. Furthermore, the integration of the SM-PP in a LHe cryostat would
increase the Q-factor by another order of magnitude, significantly improving
the signal-to-noise ratio. Finally, future application the SM-PP can be
combined with scanning tunneling microscopy functionality because of the tip
metallic layers and electrode accessibility of the tuning fork. This way we
can combine ultra-high lateral resolution imaging of conductive metal-oxide-
perovskites and measure the long range MFM forces without the need to switch
to different setups. This possibility opens up a approach to disentangle the
atomic scale structure and long range magnetic ordering relations of
transition metal oxides for application in spintronic and catalytic devices.
Considering its enhanced sensitivity, the widened scope of tip-on-chip design
can convert the MFM/AFM from a surface analysis tool with passive probes to a
more sophisticated device with active more complex probes for
characterization, e.g. nitrogen-vacancy centers diamond tips as quantum
sensors for detecting ultra-small magnetic fields 26, 27 or currents 28.

##  0.3 Materials and Methods

###  0.3.1 Planar probe fabrication

The metallic layers was sputtered on a thin
$150\text{\,}\mathrm{\SIUnitSymbolMicro m}$ thin Si $<100>$ wafer (intrinsic,
UniversityWafer). The wafer was cleaved by a diamond scriber in
$1\text{\,}{\mathrm{mm}}^{2}$ pieces and inspected by an optical microscope.
Following, the tip apex radius was inspected and selected for a radius below
$50\text{\,}\mathrm{nm}$ by a ZEISS-Sigma SEM. A FEI Nova600i SEM-FIB was used
to fabricate the bridge structure by Ga-ion etching. A sequential beam current
of $0.05\text{\,}$, $0.46\text{\,}$ and $2.8\text{\,}\mathrm{nA}$ was used.
Near the bridge the smallest current prevents damage and increases the etching
resolution. The acceleration voltage was $30\text{\,}\mathrm{kV}$. The planar
probe was placed onto the QTF (AB38T) prong with UV-curable resin with minimal
volume (less than $100\text{\,}\mathrm{\SIUnitSymbolMicro L}$) employed by the
use of a syringe needle. Silver paste was used to connect the electrical leads
of the planar probe to those of the QTF. EPO-TEK 4410 was used to connect the
wires from the QTF to a custom PEEK sensor holder. Detailed fabrication
procedure is further outlined in Supplementary S1.

###  0.3.2 Kerr Microscopy

A Zeiss Axio Imager.D2m Kerr microscope was used with a $50\times$
magnification lens, assembled by Evico Magnetics with a polariser/analyser
pair and manual slit diaphragm. The setup was combined with a set of water
cooled Helmholtz coils for magnetic moment alignment by in-plane magnetic
fields with respect to the Co film orientation. Kerrlab software was used for
data acquisition.

###  0.3.3 Numerical calculations

MuMax3 was employed to simulate the domain structure of a
$16\text{\,}\mathrm{nm}$ Co film. Exchange length of $5\text{\,}\mathrm{nm}$
and grid unit cell of 4x4 $\text{\,}{\mathrm{nm}}^{2}$ were used. For study of
the thermal and magnetic properties of the SM-PP COMSOL Multiphysics was used
with the AC/DC module and Heat Transfer module. Further numerical details are
outlined in Supplementary S4.

###  0.3.4 Imaging in UHV

A Scienta Omicron VT-SPM setup was modified to carry two additional electrical
contacts for pulsing the planar probe tip. The contacts are constructed from 2
gold coated pogo pins placed on a custom PEEK holder onto the scanning tube.
An square wave generator (Agilent 33120A) was connected to a custom MOSFET
circuit to reduce the pulse down to several hundred ns. Coax cables where used
to connect the function generator to the VT-SPM. Detailed imaging methods are
outlined in Supplementary S5.

The authors thank W. Dijkstra for assistance in both the modification of the
UHV-SPM and fabrication of the custom pulse generator. Special thanks to H.
Hilgenkamp of Twente University of Technology, Netherlands, for providing the
6 u.c. LaMnO3 thin film on SrTiO3 sample. O. Kurnosikov acknowledge support
from ANR-15-IDEX-04-LUE CAP-MAT ans by the “FEDER-FSE Lorraine et Massif
Vosges 2014–2020. Financial support from the Eindhoven University of
Technology is acknowledged.

##  0.4 Supplementary S1: Fabrication and characterisation of the SM-PP

Figure 5: Fabrication procedure of the switching-magnetisation planar probe.
(a) A $150\text{\,}\mathrm{\SIUnitSymbolMicro m}$ thin intrinsic (110) silicon
wafer is diced into smaller pieces, (b). (c) The pieces of wafer are sputtered
with a $150\text{\,}\mathrm{nm}$ MgO layer for electrical insulation needed to
reduce the doping effect of Ga-ion implantation by FIB milling. Following, the
metallic layers are sequentially deposited by plasma sputtering deposition, as
schematically drawn. (d) After film deposition, the wafer pieces are cleaved
into small rectangular planar probes with
$90\text{\,}\mathrm{\SIUnitSymbolDegree}$ angles forming the SPM tip. (e)
Finally, the probe is functionalised with a bridge fabricated by FIB milling.
(f) SEM images of a FIB fabricated bridge structure. (g) The magnetisation
curve of the thin Co film on a planar probe as measured with Kerr microscopy.

The fabrication procedure of the SM-PP is schematically given in Figure 5. The
use of a thin $150\text{\,}\mathrm{\SIUnitSymbolMicro m}$ Si wafer (intrinsic,
from UniversityWafer) makes it possible to facilitate easy mechanical cleaving
without having to apply large mechanical force and simultaneously reduce the
planar probe’s mass. First the wafer is diced into
$20\text{\,}$x$20\text{\,}{\mathrm{mm}}^{2}$ pieces, as shown in Figure 5b.
Single crystal silicon (100) is known to cleave in atomically smooth planes
29. By cleaving in two perpendicular directions a nanometer scale tip apex can
be achieved. The cleaving results in square pieces up to
$1\text{\,}$x$1\text{\,}{\mathrm{mm}}^{2}$, with the tip apex’ are evaluated
for their radius (sharpness) with SEM, see Figure 5e for a large scale image.
For integration into a sensor, tips with a radius below
$50\text{\,}\mathrm{nm}$ were chosen for further fabrication steps, tips with
larger radii where discarded. Because of the square nature of the cleaved
planar probes, each piece offers up to $4\text{\,}$ adequate tip apices. This
makes the availability of many excellent tips with a small radius very likely,
fabricated in a short amount of time.

With FIB milling, significant Ga-ion implantation occurred into the Si wafer
which shortened the milled trench and voiding the bridge functionality. Hence,
we resorted to growing an insulator spacer layer of SiO2 or MgO between the
metallic stack and the wafer. The integration of a microscale current pathway
requires to reduce thermal-induced damage by excessive Joule heating. To
enhance thermal management near the tip apex a high thermal conductivity MgO
spacer layer is sputtered on top of the silicon wafer. MgO has a sufficient
thermal conductivity of about
$40\text{\,}\mathrm{W}\text{\,}{\mathrm{m}}^{-1}\text{\,}{\mathrm{K}}^{-1}$
30. Furthermore, MgO simultaneously facilitates electrical insulation to
reduce electrical leakage currents. In Supplementary S4 we discuss the thermal
dissipation behaviour between Si/MgO and Si/SiO2 substrates after sending a
current pulse through the bridge.

Next, the metallic multilayer was deposited. The planar probe metallic layer
consists of the following structure, see Figure 5c. First, a
$4\text{\,}\mathrm{nm}$ tantalum (Ta) seed layer is grown to induce good
mechanical adhesion of the subsequent metal layers with the MgO/Si substrate.
The Ta seed layer also smooths the surface roughness of the MgO layer to to
some extent, which still results in a final RMS roughness of
$6\text{\,}\mathrm{nm}$. Such a reduced roughness can actually be beneficial
as it can be expected that near the cleaved tip apex small nanometer scale
bumps form the nano-tip and reduce the van der Waals forces compared to a
fully triangular structure, as it scales with the tip volume. The measured
roughness of SiO2 and MgO layered films are given in Figure 6.

Subsequently, a $30\text{\,}\mathrm{nm}$ current-carrying Pt layer is grown.
This relatively thick Pt layer has the lowest film electrical resistance of
the metallic stack; the majority of the current will flow through this layer.
The ferromagnetic film is made from $15\text{\,}\mathrm{nm}$ Co. Finally, the
stacking is capped with $3\text{\,}\mathrm{nm}$ of Ta and
$3\text{\,}\mathrm{nm}$ of Pt to induce high mechanical rigidity of the tip
apex and prevent native oxidation.

Figure 6: Surface roughness of planar probe tips measured with AFM. (a) A
topographic AFM image of SiO2 layered planar probe covered with the multi-
layer metallic stack. The roughness is found to be around
$400\text{\,}\mathrm{pm}$. (b) A planar probe surface but with a
$100\text{\,}\mathrm{nm}$ MgO layer instead of SiO2. The surface roughness is
larger compared to (a) and around $6\text{\,}\mathrm{nm}$. The black arrows
point to the FIB milled trenches.

When using (native) SiO2 as a spacer layer between the intrinsic silicon
substrate and the metallic stack of the planar probe, the low thermal
conductivity of SiO2 of only
$1\text{\,}\mathrm{W}\text{\,}{\mathrm{m}}^{-1}\text{\,}{\mathrm{K}}^{-1}$,
limits the thermal durability of the device. This low thermal conductivity was
found to be insufficient to prevent damage from Joule heating to the bridge
when using pulses above $80\text{\,}\mathrm{mA}$. Limiting the current below
$80\text{\,}\mathrm{mA}$ proved insufficient for full domain reversal for many
devices with bridges in the micrometer widths. Figures 7a, b and c show SEM
images of FIB fabricated tips with either a single straight trench or the
crossed configuration. The tips have a nominal bridge width, measured from the
end of the trench to the tip end, of (a)
$12\text{\,}\mathrm{\SIUnitSymbolMicro m}$, (b)
$10\text{\,}\mathrm{\SIUnitSymbolMicro m}$ and (c)
$8\text{\,}\mathrm{\SIUnitSymbolMicro m}$. Figures 7e, f and g show optical
microscope images of observed tip damage, highlighted with orange circles,
after sequential $80\text{\,}\mathrm{mA}$ pulsing. In these images, the
metallic films have clearly degraded by excessive Joule heating. The Joule
heating is most intense where the bridge width is smallest i.e. near the tip
end, corresponding to the highest current density. Figures 7d and 7h show AFM
topographic images of the FIB trench end, after 2 pulses. Clearly, the
metallic film shows first signs of degradation or ”peel-back”, before full
layer destruction occurs. With the inclusion of MgO, which is directly
sputtered on top of the silicon wafer, we observed no Joule heating induced
damage. MgO has a much high thermal conductivity of
$40\text{\,}\mathrm{W}\text{\,}{\mathrm{m}}^{-1}\text{\,}{\mathrm{K}}^{-1}$
30. MgO devices pulsed over 25 times showed no degradation or change of the
bridge resistance, even for pulses up to $250\text{\,}\mathrm{mA}$.

Figure 7: SEM and AFM images of Joule heating-induced bridge damage with a
SiO2 layer. (a) - (c) SEM image of pristine tips with FIB fabricated bridges.
(e) - (g) Same tips after consecutive current pulsing of
$80\text{\,}\mathrm{mA}$ showing film degradation. (d) and (h) AFM topography
shows signs of film degradation and ”peal-back” from excessive heating.

##  0.5 Supplementary S2: Kerr microscopy

A Zeiss Axio Imager.D2m Kerr microscope was used with a $50\times$
magnification lens, assembled by Evico Magnetics with a polariser/analyser
pair and manual slit diaphragm. The setup was combined with a set of water
cooled Helmholtz coils for magnetic moment alignment by in-plane magnetic
fields with respect to the Co film orientation. Kerrlab software was used for
data acquisition. The slit diaphragm makes it possible to filter light and
select a magnetisation direction to visualise (horizontal or vertical) moment
sensitivity. A custom-made sample holder was fabricated with integrated
electrical wiring. The holder offered 3-degree’s of positioning freedom needed
for positioning of the SM-PP below the Kerr lens. A custom pulsing circuit was
used to pulse a $50\text{\,}\mathrm{mA}$ to $300\text{\,}\mathrm{mA}$ current
for $150\text{\,}\mathrm{ns}$ to $500\text{\,}\mathrm{ns}$. By ramping up the
current in consecutive pulses, the domain switching threshold was found.

Figure 8: Kerr microscopy. (a) Setup to measure the tip magnetisation of a SM-
PP device. The SM-PP is placed on a movable holder, to align the tip with the
lens of the microscope. (b) and (c) show SEM images of FIB fabricated tips
either with a straight trench, or with a crossed configuration. The black
arrows highlight the pulsed tip Co domain, with a more stable domain with a
crossed structure. The orange arrows point to the bridge section of smallest
diameters. These regions have the highest current density under pulsing.

It was found that fabricating a single straight FIB trench does not always
result in a stable magnetic domain reversal, with an example given in
Supplementary Figure 8b. For these straight trench devices, a stable domain
was observed only after several consecutive current pulses. Even then, the
domain does not extend across the complete bridge region, as indicated with
the black arrows. With a single trench structure, only two nucleation sites
are formed, near the very tip apex where the current density is highest
(orange arrows). Although our numerical model suggests that it is possible to
fully switch the domain with a single pulse, we attribute some devices needing
more pulses to the fact that the FIB bridge was not always placed perfectly
placed along the mirror-symmetrical axis of the probe. Hence, the current
distribution is not equal along the bridge which could hamper full domain
reversal near the tip apex. In our numerical models we have always assumed
fully symmetrical structures.

To remedy this problem a perpendicular and smaller trench was FIB milled near
the original trench, close to the tip apex, see Figure 8c. This design adds an
extra nucleation site, indicated with orange arrows, in close proximity to the
bridge end. It was observed that this enables formation of a very stable
domain that can be reliably reversed with a single pulse in all fabricated
tips (number of tips exceeding 15). Figure 8c show gray-scale Kerr Microscope
images focused on the crossed bridge design. Kerr sensitivity was selected
which corresponds to the domain pointing in-plane. Thus, the double crossed
trench solution overcomes the non-perfect mirror-symmetric alignment of the
FIB trench and induces multiple nucleation sites across the bridge.

##  0.6 Supplementary S3: Note on the QTF function

The large mass of the planar probe would decrease the Q-factor $Q$ below a few
hundred, with $Q$ strongly influencing the sensitivity of the force sensor 24.
Hence, mass retuning of the QTF is performed by offsetting the mass of the
planar probe carrying prong to equate that of the added mass of the oversized
tip. This effectively restores $Q$ to its pristine value 20. The need to
enhance $Q$ is vital by satisfying two requirements for the SM-PP to function.
First, the frequency noise in frequency-modulation (FM) AFM scales inversely
with $Q$ 24. Hence, a higher $Q$ results in larger signal-to-noise ratio
needed to measure the smaller forces associated with magnetic stray field
gradient sensing 24.

Second, due to the mentioned separation of the electrode layout, the actual
force-to-voltage conversion signal by the piezo-electric effect of the quartz
tuning fork, is measured in the upper prong of the QTF. This prong essentially
measures the tip-sample force indirectly and works most efficiently if the two
oscillating prongs operate in the anti-phase mode with little dissipation in
the connecting node 20. A low $Q$ would lead to insufficient coupling between
the two oscillating prongs and hence impede operation of the force sensing.
This is fundamentally different from the qPlus sensor, were only one prong
oscillates and hence the force sensing is limited to this prong 24.

Using the retuned tuning fork approach, we explore the possibility of using a
high spring constant $k$
($\sim${10}^{4}\text{\,}\mathrm{N}\text{\,}{\mathrm{m}}^{-1}$$) force sensors,
which is remarkably higher than those of the qPlus
($1500\text{\,}\mathrm{N}\text{\,}{\mathrm{m}}^{-1}$). With a high $k$, the
minimal detectable force gradient $dF_{\text{m}}/dz$ is reduced together with
the detectable frequency shift down to several tens of mHz, according to the
equation $\omega/\delta\omega=1/(2k)\cdot dF/dz$ 24. Hence, the tip needs to
scan only a few nanometers above the sample surface to measure the magnetic
stray field gradients, above the noise level of approximately
$1.5\text{\,}\mathrm{mHz}$. This small $dF_{\text{m}}/dz$ simultaneously
prevents the signals from areas beyond the dimensions of the tip to be picked
up and hence the resolution can be increased significantly, needed for imaging
nanometer scale SP islands of LMO3. Our SM-PP realises a $Q$ above
$20\,000\text{\,}$ at room temperature, in ultra-high vacuum (UHV), which
results in a noise floor of $1.5\text{\,}\mathrm{mHz}$. For MFM imaging of
nanometer sized SP textures, the high $k$ and large $Q$ are beneficial, as
forces coming from area’s not directly beneath the tip are not picked up by
the SM-PP because the $df/dz$ decreases rapidly below the noise floor.

##  0.7 Supplementary S4: Numerical calculations of thermal and magnetic
properties

###  0.7.1 Influence of current pulse characteristics on Joule heating

Figure 9: Temperature response of the SM-PP for different pulse
characteristics and spacer layer materials. (a) Increase in temperature for
different current densities. Even for very high currents exceeding
${10}^{12}\text{\,}\mathrm{A}\text{\,}{\mathrm{m}}^{-2}$, the temperature does
barely exceed $400\text{\,}\mathrm{K}$. (b) The temperature magnitude strongly
depends on the pulse length between $300\text{\,}$ and
$900\text{\,}\mathrm{ns}$. (c) Operation in UHV at $77\text{\,}\mathrm{K}$
should be possible since only a marginal increase in temperature is observed
for a pulse sufficient to change the magnetisation of the SM-PP. (d, e)
Simulation of the temperature response of MgO vs. SiO2 spacer layers. The
pulse shape is varied between an asymmetric double sigmoid (d) and a square
pulse (e), highlighting the need to keep the maximum current as short as
possible to reduce thermal heating.

The (transient) temperature response of the SM-PP bridge was numerically
studied with COMSOL ™. First we address the current pulse shape.

In our SPM setup, capacitance of the cables that are connected to the SM-PP
affect the pulse shape, resulting in a more asymmetric shape deviating from a
square current pulse input. We simulate this curve in COMSOL using the
asymmetric double sigmoidal function, which has the following functional form:

$I\left(t\right)=A_{1}/\left(1+\exp\left(-\left(t-t_{c}+w_{1}/2\right)/w_{2}\right)\right)\left[1-1/\left(1+\exp\left(-\left(t-t_{c}-w_{1}/2\right)/w_{3}\right)\right)\right]$
(1)

Here, $w_{1}$ defines the width of the pulse, $w_{2}$ and $w_{3}$ together
define the asymmetry of the pulse, $t_{c}$ is the centre of the pulse and $A$
is proportional to the amplitude of the current pulse $I_{0}$. We fit Eq 1 to
the real pulse of which we obtain the full-width-at-half-maximum (FWHM), and
pulse amplitude $I_{0}$.

Heat transport in ultrahigh vacuum (UHV) conditions is modelled via
COMSOL™heat conduction. Thermal dissipation occurs via conduction within the
planar probe and via radiative emission. The environment is set at room
temperature, as is the case for the Scienta Omicron VT-SPM lacking a cryostat.
Only the sample is cooled. The radiative thermal dissipation is set by the
surface emissivity $\varepsilon$. We used the values for the following
materials that were used in the functionalised planar probe:
$\varepsilon_{\text{Si}}=0.6$, $\varepsilon_{\text{Pt}}=0.04$,
$\varepsilon_{{\rm SiO}_{2}}=0.8$ and $\varepsilon_{\text{MgO}}=0.5$. The
other metals, Ta and Co, are neglected.

First, we consider the maximum current through the bridge without overheating
it. To this end, we varied the current density $J$ in the planar probe, which
is related to the total current $I_{p}$ via $J=\frac{I_{p}}{d_{Pt}d}$, where
$d_{Pt}$ is the thickness of the main platinum layer and $d$ is the width of
the bridge gap ($5\text{\,}\mathrm{\SIUnitSymbolMicro m}$), respectively. The
situation we consider is the asymmetric pulse from Equation 1 with a current
peak of $150\text{\,}\mathrm{mA}$, which amounts to a current density of
$6\text{\times}{10}^{11}\text{\,}\mathrm{A}\text{\,}{\mathrm{m}}^{-2}$. We
vary the current density from
${10}^{11}\text{\,}\mathrm{A}\text{\,}{\mathrm{m}}^{-2}$ to
${10}^{12}\text{\,}\mathrm{A}\text{\,}{\mathrm{m}}^{-2}$, in steps of
$0.5\text{\times}{10}^{11}\text{\,}\mathrm{A}\text{\,}{\mathrm{m}}^{-2}$. The
results are shown in Figure 9a, in which the temperature barely increases by
$20\text{\,}\mathrm{K}$ for the smallest current densities, and increases by
approximately $115\text{\,}\mathrm{K}$ in case of the highest current density.

To characterize the temperature increase with respect to the current pulse
length, we simulate three current pulses with a different pulse duration:
$300\text{\,}$, $600\text{\,}$ and $900\text{\,}\mathrm{ns}$ FWHM. The pulses
are indicated in Figure 9b in dark solid lines. The resulting temperature
evolution at the probe’s tip end is shown in Figure 9b in dotted red lines.
Indeed, the temperature increases with the duration of the pulse. The
temperature increases by about $45\text{\,}\mathrm{K}$ in case of a short
$160\text{\,}\mathrm{ns}$ pulse, up to an increase of over
$100\text{\,}\mathrm{K}$ for the $900\text{\,}\mathrm{ns}$ pulse. This large
difference illustrates that the current pulse duration has a major impact on
the temperature increase, so the current pulses need to be as short as
possible in order to prevent overheating the probe.

We also investigated the thermal aspects of the planar probe when it is cooled
down to liquid nitrogen temperature ($77\text{\,}\mathrm{K}$). The values of
the surface emissivity are set to the same values as at
$293\text{\,}\mathrm{K}$. The temperature evolution of the probe’s tip at
$77\text{\,}\mathrm{K}$ is shown in Figure 9c. Evidently, the temperature of
the probe increases by only $35\text{\,}\mathrm{K}$, which would make
operation in a cryostat possible.

Finally, we discuss the thermal characteristics of a SiO2 layer. As
Supplementary S1 discussed, the inclusion of SiO2 as a spacer layer to reduce
electrical shorting by FIB milling, turned out to negatively impact the
thermal dissipation, eventually leading to bridge damage after several pulses
above $80\text{\,}\mathrm{mA}$. Numerical calculations of MgO and SiO2 are
shown in Figure 9d. These plots show a temperature increase when SiO2 is used,
to a maximum above $400\text{\,}\mathrm{K}$. These values were calculated with
a pulse of equation 1, with a FWHM of $160\text{\,}\mathrm{ns}$. In the case
of a $230\text{\,}\mathrm{nm}$ MgO layer, the temperature increase is less
than $40\text{\,}\mathrm{K}$, supporting the experimentally observed stability
of MgO as a spacer layer. For comparison, we have also used a block pulse of
$160\text{\,}\mathrm{ns}$ with a magnitude of $150\text{\,}\mathrm{mA}$ with
the thermal response shown in Figure 9e, with much higher temperature peaks
observed, exceeding over $500\text{\,}\mathrm{K}$. Hence, the peak value needs
to be minimized to only a few ns to prevent damage to the tip, and a block
pulse is not sufficient.

###  0.7.2 MuMax3 calculation of tip domain orientation

MuMax3 31 was used in which a $16\text{\,}\mathrm{nm}$ Co film was simulated,
with an exchange length of $5\text{\,}\mathrm{nm}$ and grid unit cell of 4x4
$\text{\,}{\mathrm{nm}}^{2}$. The following values are taken to simulate the
cobalt; saturation magnetisation $M_{sat}$ =
$1.4\text{\,}\mathrm{MA}\text{\,}{\mathrm{m}}^{-1}$, exchange constant
$A_{ex}$ = $16\text{\,}\mathrm{pJ}\text{\,}{\mathrm{m}}^{-1}$ and the $1^{st}$
order uniaxial anisotropy constant $Ku_{1}$ of
$0.72\text{\,}\mathrm{MJ}\text{\,}{\mathrm{m}}^{-3}$.

###  0.7.3 Note on the magnetic stray field computation

To study the magnetic properties of the SM-PP, specifically its tip magnetic
field component distribution $B_{x}$, $B_{y}$ and $B_{z}$ and the field
magnitude, a 3D COMSOL™FEM model was made. The SM-PP is modelled as a
$15\text{\,}\mathrm{nm}$ ferromagnetic Co layer with a magnetization of
$M=$1400\text{\,}\mathrm{kA}\text{\,}{\mathrm{m}}^{-1}$$. In the main text we
showed the stray field of the SM-PP in the in-plane direction of the tip as it
extends outwards, when placed a certain height $z$ above a flat sample. In the
calculations, the SM-PP and sample are placed in an air medium. Figure 10
presents the modeled stray field results.

Figures 10a and b show the field distribution at two different cross-sections:
in the $xy$-plane, and parallel to the probe surface, respectively. Important
to note is that the probe length is much larger than the tip-sample distance
$z$. However, for computational reasons the probe was made smaller (”cut-
off”), which gives rise to an additional curvature of the field near the upper
side of the probe. Near the tip, where the calculations were performed, the
effect of this curvature has been taken into account during the final
calculations. Figure 10c presents the calculated $B_{x}$, $B_{y}$ and $B_{z}$
between the tip sample distance $z$.

Figure 10: COMSOL-calculated magnetic field distribution around the tip. (a),
(b) Arrow plot of the magnetic field distribution. Color bar gives the
absolute strength in $\mathrm{mT}$. (c) Magnetic field components $B_{x}$,
$B_{y}$ and $B_{z}$ as a function of tip-sample distance $z$.  Figure 11:
Distribution of the SM-PP tip stray field on a sample surface in the xy plane.
(a)-(c) Numerically calculated stray field components across the sample
surface placed at z = 0 nm and the tip apex positioned at
$1\text{\,}\mathrm{nm}$. (d),(e) Numerical calculated stray field and spatial
distribution at different heights of the tip (z)

We calculated the spatial distribution of the tip’s stray field $\vec{B}$
across the sample surface. Figure 11 shows the lateral distribution of
$B_{x}$, $B_{y}$ and $B_{z}$ at a tip-sample distance of
$1\text{\,}\mathrm{nm}$. We expect this to be the closest tip-sample distance
during oscillation. At the lowest point of the amplitude extension with
respect to the sample surface, the stray field perturbation should be
strongest. The $B_{x}$ and $B_{y}$ components in Figure 11a and 11b show sign
inversion close to the (0,0) point, where the tip apex is positioned. This is
to be expected from the symmetry of the planar probe. The magnitude of
$\vec{B}$ can become quite large up to $100\text{\,}\mathrm{mT}$. However, at
(0,0) the field is minimal for $B_{y}$. But for $B_{x}$ a sizable field up to
$80\text{\,}\mathrm{mT}$ is observed directly below the tip. For a fabricated
planar probe, the tip is never fully symmetric, nor is the bridge shape and
it’s position on the tip apex. The in-plane values are hence expected to be
larger below the tip during experiments. The out-of-plane component $B_{z}$ is
strongest at (0,0) and given in Figure 11c. The magnitude can reach up to over
$300\text{\,}\mathrm{mT}$. For measuring LMO3, having both an in-plane and
out-of-plane field is beneficial, as the SM-PP in-plane field magnetises the
SP islands, while $B_{z}$ is used to read out the stray signal. This is
similar to the SSM experiments of Anahory et al. 14 and supports our work on
observing the complex SP islands.

We also examined the dependency of the magnetic field magnitude $|B|$ and
distribution on $z$, between $5\text{\,}\mathrm{nm}$ and
$20\text{\,}\mathrm{nm}$. The spatial distribution of $|B|$ is given in Figure
11d and 11e, respectively. Evidently, $|B|$ increases by almost a factor of
$3$ as $z$ decreases down to $5\text{\,}\mathrm{nm}$. Hence, this may explain
why we observe a sudden change (kink) in F-z spectroscopy, in Figure 4 in the
main text, as the SP islands are magnetized and a sudden change in the
magnitude of the attractive force occurs.

Figure 12: Distribution of the SM-PP tip stray field on a sample surface in
the xy plane, depending on the off-axis orientation of the in-plane
magnetisation of the Co layer.

Finally, we examined the effect of the direction of the Co magnetisation along
the planar probe symmetry axis, on the tip stray field magnitude and
distribution. Figure 12 shows the calculated $|B|$ at a fixed
$z=$0.5\text{\,}\mathrm{nm}$$. Here, the relative Co magnetisation direction
on both sides of the symmetry axis are depicted in blue and red with the angle
between the two directions indicated as $\theta$. Two main conclusions can be
derived from these results: the magnitude of magnetic field strength is
relatively independent on $\theta$. And secondly, the shape of the magnetic
field distribution on the surface changes only slightly. In conclusion,
changing the symmetry of Co magnetisation along the planar probe vertical
symmetry axis does not alter the final $|B|$ distribution a lot. Hence it is
reasonable to assume $|B|$ is mainly tip-sample distance $z$, dependent.

##  0.8 Supplementary S5: Methods SM-PP MFM experiment

###  0.8.1 LMO3 sample in UHV

The 6 u.c. LMO3/STO3 sample was exposed to ambient air prior to measurement,
hence we expect a thin layer of contaminates present of the LMO3 surface
before being loaded into UHV. Gently heating to
$100\text{\,}\mathrm{\SIUnitSymbolDegree}$ in UHV removed the water
adsorbents. Higher temperatures were not used to prevent oxygen diffusion
which likely alters the stochiometry and magnetic behaviour 32, 33. However,
we cannot attest if small stochiometric changes have occurred (and also over
time) or between sample growths. This variable offers future investigation
possibilities between the stochiometry relationship and the magnetic textures.

###  0.8.2 FM-MFM imaging and data visualisation

To measure the long-range MFM signal, the tip was retracted by
$5\text{\,}\mathrm{nm}$ and followed the previously obtained topography, the
so-called lift mode 1. For measuring the long range magnetic gradient force
$dF_{m}/dz$ , the oscillation amplitude $A$ was set to
$10\text{\,}\mathrm{nm}$.

A Scienta Omicron VT-SPM was used with a custom tip holder and low temperature
sample holder for enhanced thermal conduction. Imaging was performed by
locking the amplitude and tracking the frequency shift with a phase lock loop
(PLL). Care was taken to keep all the scanning parameters constant, with
optimized feedback settings for the phase, amplitude and frequency. The PLL
bandwidth was set to $384\text{\,}\mathrm{Hz}$. After a topography line-scan
was obtained, the tip was lifted by the predefined lift height. Both forward
and backward scans where compared to identify repeatability and exclude
artifacts. We imaged with a speed of
$39\text{\,}\mathrm{nm}\text{\,}{\mathrm{s}}^{-1}$ at a resolution of 256x256
pixels. Gwyddion software was used for the AFM and MFM data plotting and
analysis. We used plane projection to level the image, and line-alignment in
the vertical direction. Due to thermal drift induced by the thermal gradient
between the cold sample and the room temperature SM-PP (as dictated by the VT-
SPM design), a small eigenmode frequency shift of $50\text{\,}\mathrm{mHz}$
was observed during the prolonged imaging, hence we renormalized the frequency
MFM shift accordingly to the first few line-scans. No influence on the MFM
lateral dimensions was noted by this effect. Finally, both the sample and tip
are grounded. Future work will translate the SM-PP to a cryostat to reduce
thermal gradients which would also significantly increase the $Q$ further.

##  0.9 Supplementary S6: Variable temperature MFM

Figure 13: MFM images at variable temperature. (a), (b). MFM images taken with
a multi-state and single-state domain at $100\text{\,}\mathrm{K}$,
respectively. (c), (d) Multi-domain and single domaing MFM imaging at
$300\text{\,}\mathrm{K}$, respectively.

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