# An Investigation into the Kinetics and Mechanism of Phase Transitions in
Optical Phase Change Ternary Alloy $Ge_{2}Sb_{2}Te_{5}$

Aditya Muralidharan

###### Abstract

Ternary alloys of Ge-Sb-Te (GST) have been extensively studied due to their
unique ability display a reversible change in their phase upon stimulation by
optical pulses i.e amorphous (a-GST) to crystalline (c-GST) and vice-versa.
The two phases exhibit remarkably different electrical and optical properties
like conductivity, reflectivity, refractive index and optical loss, this
coupled with their high phase switching speeds, low power phase switching,
large switching cycles, large measurable optical and electrical contrast, and
phase stability makes GST alloys stand out from other phase change materials
(PCM). GST alloys have already found extensive use in optical disks and
electronic memories due to their non-volatility and zero static power
consumption, but the precise mechanism of the phase change is not clearly
understood. The phase change mechanism has usually been attributed to the
optical pulse, usually a high power short pulse laser, heating up the c-GST
alloy to above its melting temperature ($T_{m}$) after which, if it is cooled
rapidly enough to below the glass transition temperature ($T_{g}$), the atoms
are fixed in place due to the drastic reduction in their mobility, resulting
in a phase which exhibits structure similar to a frozen liquid and lacks long
range order i.e amorphous. If alternatively the a-GST is heated above $T_{g}$
with a intermediate power laser pulse for a significant amount of time to
induce nucleation, then this favours the shift back to the energetically
favourable crystalline phase. With the growing interest in next generation
data storage technology for photonic and neuromorphic computing, the research
into understanding and improving the properties of GST alloys has also been
rekindled. In this term paper we hope to investigate and gain a deeper
understanding and appreciation of the kinetics and underlying atomistic
mechanism of this phase transition from c-GST to a-GST and vice-versa which is
only now becoming clearer.

## Introduction

The properties of materials, especially those used in the electronics industry
like silicon or $SiO_{2}$ are thought of as static, usually fixed at the time
of device fabrication.12 This behaviour is usually desirable to ensure the
stability and reliability of the device under variable operating conditions.
But with the emergence of new paradigms like photonic and neuromorphic
computing, it has become imperative to look for more dynamic material systems
which go beyond this passive behaviour and can respond more robustly to
optical stimulation, to achieve the ultimate goal of dynamically tunable and
reconfigurable optical and electronic systems.345

Phase change materials (PCM) represent a class of solids which undergo a
crystallographic phase transformation due to a change in their temperature
compared to the ambient, usually caused by electrical or optical stimulation.
67 This transition in their phase is also usually accompanied by a stark
contrast in the electrical and optical properties of the two phases which is
exploited for data storage applications.89 They can be see as stimuli
responsive materials that modulate their electrical and optical behaviour in
response to the external stimuli, usually a electrical potential or a laser
pulse.1011 One of the two phases is characterized as having low reflectivity
and refractive index, low dielectric constant and high resistivity i.e. they
behave like semiconductors, while the other phase shows a high reflectivity
and refractive index, high dielectric constant and low resistivity i.e. they
show metallic behaviour.1213

Ternary alloys of Ge-Sb-Te (GST) as shown in Figure 1(b) have long shown
promise for such phase change behaviour due to the existence of a metastable
crystalline phase in the rock-salt structure (FCC) which amorphizes upon
stimulation by a high-power short-width laser pulse. 141516 This transition
though is reversible, as upon stimulation of the a-GST by a intermediate-power
long-width laser pulse the a-GST recrystallizes into its metastable
crystalline form.17181920 The crystalline to amorphous transition of GST
requires the c-GST to be heated above its melting temperature $T_{m}$ and
rapidly quenched in order to fix the atoms in place before they have a chance
to migrate back to their equilibrium position, thus the resulting a-GST
structure is analogous to a ”frozen liquid” with its atoms frozen in place.
1221

22 The reverse transition on the other hand only heats the a-GST to above its
glass transition temperature $T_{g}$ which is maintained long enough to induce
nucleation and crystallization, thus allowing it to transition back to
c-GST.2324 We can also infer from the phase diagram that different
compositions of the ternary alloy are possible as we travel across the line
from $GeTe$ to $Sb_{2}Te_{3}$ such as $GeSb_{2}Te_{4}$ and
$Ge_{2}Sb_{2}Te_{5}$.1225 We also observe that the transition time between
phases ($t$) and the stability of the amorphous phase along with $T_{m}$ and
$T_{g}$ decrease as we move in the same direction.252627 $Ge_{2}Sb_{2}Te_{5}$
$(GST-225)$ is of particular interest in this regard, as of all the alloys on
the ternary phase diagram shown in Figure 1(b), it shows the optimum position
for both fast phase transition (t $<$ 20ns) and phase stability, while having
a workable $T_{m}\sim 650^{o}C$ and $T_{g}\sim 100^{o}C-150^{o}C$. 2528 The
amorphous phase of $Ge_{2}Sb_{2}Te_{5}$ also has a degradation lifetime
$t_{d}\sim 10$ years making it suitable for use in next generation non-
volatile memory. 29303132

(a)

(b)

Figure 1: (a) The process of amorphization and recrystallization in a phase
change material using a optical pulse. The material is amorphized by the
action of a high-power short-duration laser pulse that rapidly heats the
material to above $T_{m}$ and quenches it below $T_{g}$. The material is then
recrystallized using a intermediate-power longer-duration laser pulse that
keeps it at a temperature above $T_{g}$. A low power laser pulse can be used
to measure the reflectivity of the two phases without altering them thus
allowing us to read the stored information.12 (b) Ternary phase diagram for
the Ge-Sb-Te system.31

In this term paper we investigate the kinetics and mechanism of such phase
transitions in $GST-225$. We will first look at the stability of the two
phases of $GST-225$ involved in the transition, namely the crystalline rock-
salt phase $(c-GST)$ and the amorphous phase $(a-GST)$, we will also briefly
touch upon the hexagonal phase $(h-GST)$.Then we will move on to study how
various factors such as laser power, pulse width, quench time & cooling rate
affect both the $(c\rightarrow a)$ and ($a\rightarrow c$) transitions and the
macroscopic kinetics and mechanism of phase change namely nucleation and rim
to centre growth. We will also investigate the atomistic mechanism of the
phase change and look at bond distortions in the structure which when coupled
with atomic migrations and carrier collisions facilitate phase change in
$GST-225$ upon stimulation.

(a)

(b)

Figure 2: (a) hexagonal-GST (b) rock-salt cubic-GST.14

## $Ge_{2}Sb_{2}Te_{5}$

$Ge_{2}Sb_{2}Te_{5}$ $(GST-225)$ is a ternary alloy in the Ge-Sb-Te system
which contains Germanium, Antimony and Tellurium in a stoichiometric ratio of
$2:2:5$, being roughly in the middle of the $GeTe-Sb_{2}Te_{3}$ line in the
ternary phase diagram. 25 $GST-225$ is an excellent PCM that is of immense
interest due to its splendid set of properties, namely high thermal
stability,fast crystallization speed non-volatility and reliability. 2527

(a)

(b)

(c)

(d)

Figure 3: (a) real part of the refractive index $(n)$ (b) imaginary part of
the refractive index $(k)$ (c) absorption coefficient for $GST-225$6(ds)
Urbach-Martiensenn tail in the absorption coefficient of $GST-225$29

### Crystalline $Ge_{2}Sb_{2}Te_{5}$

Such a impressive set of properties is partly due to the structural
arrangement of atoms in $GST-225$ which crystallizes in two phases, the
metastable cubic rock-salt phase $(c-GST)$ and more energetically favourable
hexagonal phase $(h-GST)$ as seen in Figure 2. 1425 As deposited films of
$a-GST$ using magnetron sputtering are observed to transition to $(c-GST)$ at
$\sim 150^{o}C$ and again to $(h-GST)$ at $\sim 260^{o}C$ indicating that the
actual order of phase transitions is
$(a-GST)\rightarrow(c-GST)\rightarrow(h-GST)$. 33 The reason that the
metastable $c-GST$ phase is preferred for most applications is twofold. First,
the activation energy of the $(a-GST)\rightarrow(c-GST)$ is of the order of
$\sim 2-3eV$ and an effective activation energy of $\sim 0.29-0.33eV$, which
is considerably lower than the activation energy and effective activation
energy for the $(a-GST)\rightarrow(h-GST)$ transition.2434 Second, the $c-GST$
is a metastable phase between $a-GST$ and $h-GST$ thus is easier to reverse
back to the amorphous phase from $c-GST$ than the more energetically
favourable $h-GST$. 3435 It can also be seen from Figure 3 that the change in
the optical properties such as the real and imaginary part of the refractive
index $(n)$ and $(k)$ as well as the absorption coefficient $(\alpha)$ is more
striking between the $a-GST$ and $c-GST$, and less between $c-GST$ and
$h-GST$. 63637 This optical contrast is primarily due to atomic migration of
the $Ge/Sb$ atoms during phase transition and the associated change in the
band structure which creates differences in the band gaps $(E_{g})$ of the
$c-GST(E_{g}\sim 0.56eV$ with a indirect component of $E_{g}\sim 0.1eV)$,
$h-GST(E_{g}\sim 0.2eV)$ and the $(a-GSTE_{g}\sim 0.68eV)$. 3238 Notice, how
$a-GST$ also shows a significant Urbach-Martiensenn tail in its absorption
coefficient compared to $c-GST$ and $a-GST$, this is primarily due to the lack
of long range order, presence of carriers near the band edge and dangling
bonds caused by localized vacancies as shown in Figure 3(d). 293940

(a)

(b)

(c)

Figure 4: (a) Band-gap of Hexagonal $GST$ (b) Band-gap of Cubic $GST$ (c)
absorption coefficient for $GST-225$ 14 (c) Simplified band gap diagrams for
$a-GST$ and $c-GST$.41

#### Hexagonal $Ge_{2}Sb_{2}Te_{5}$

Hexagonal $GST$ $(h-GST)$ is the most energetically stable phase of $GST-225$,
with its atoms arranged in a hexagonal close packed structure with nine atoms
arranged in a stacked layered structure in each unit cell with one of the
possible orders being $(Te-Ge-Te-Sb-Te-Te-Sb-Te-Ge)$ as shown in Figure 2(a)
.1441 The lattice parameters for the hexagonal unit cell have been
experimentally determined to be $a=4.22$ Å and $c=17.18$ Å, leading to a
larger $Te-Te$ bond length of $\sim 3.7$Å compared to the $Ge-Te$ and $Sb-Te$
bond length of $\sim 3$Å.1442 Additionally Density Functional Theory $(DFT)$
has been used in studies to calculate the band structures of both $h-GST$ and
$c-GST$ in order to explain their electrical and optical properties as shown
in Figure 4. 3843 These studies calculate the band gap of $h-GST$ to be $\sim
0.2eV$, thus predicting its behaviour as a semi-metal, which has been
experimentally verified. 3841 They have also proven instrumental in explaining
the contrast in the optical properties between the phases, such as the
refractive index contrast $(\Delta n)$ and the contrast in the spectral
transmittance between the different phases $((a-GST)$ $T\sim 92$%$)$,
$((c-GST)$ $T\sim 46$%$)$ and $((h-GST)$ $T\sim 2$%$)$ at $\lambda\sim 2740nm$
and the Near-IR region in general.41 These can be explained by the change in
the shape of the valence band as well as the density of states after the phase
transition.384445 $DFT$ studies have also helped us explain the low thermal
conductivity in $h-GST$ $(\kappa=1.76W/m.K)$ as well as the large electronic
component to thermal conductivity $(\kappa_{e}\sim 0.46W/m.K)$ when compared
to $a-GST$ by calculating the electronic band structures, phonon dispersion
curves and density of states as shown in Figure 5. 42464748 The $h-GST$ phase
is also known to have lower vacancy densities, $Ge-Te$ bond distortion and a
higher resistance towards disorder when compared to the $c-GST$ phase which
partly contributes to its stability, but also makes the transformation to
$a-GST$ more difficult. 15363738 This is due to the fact that the vacancies in
the $h-GST$ have to arrange themselves into highly ordered layers $(super-
lattice$ $layers)$ when sufficient energy is provided to the stable $hcp$
structure to show a metal to insulator transformation $(IMT)$.3644 This is due
to a weak Van der Walls force between the low-coordinated $Te$ atomic layers
between the highly ordered vacancy layers which results in the formation of a
Van der Walls gap, generally thought of as responsible for the metallic
conduction and behaviour of the $h-GST$ as a degenerate p-type
semiconductor.49 It has also been hypothesized that disorder induced
$(Anderson)$ localizations play a pivotal role in the IMT process, making the
the electrical and optical properties of the phase strongly dependent on the
degree of disorder within the material.4349 Thus the central role that
vacancies and bond distortions play in theses $Ge/Sb$ atomic migrations that
cause the $(h-GST\rightarrow a-GST)$ and $(c-GST\rightarrow a-GST)$ phase
changes is studied in following sections.

(a)

(b)

(c)

(d)

(e)

(f)

Figure 5: Comparison of DFT and Experimental Data $(dotted$ $lines)$ (a) $n,k$
and $\alpha$ (b) Real and imaginary parts of dielectric $\epsilon_{re}$ and
$\epsilon_{im}$ (c) Transmittance $T$ and Reflectance $R$14 (d) phonon
dispersion relation (e) phonon density of states46 (f) Ultra-fast DSC
measurements of $GST$ nano-particles.17

(a)

(b)

(c)

(d)

(e)

Figure 6: (a) Fourier Transform EAXFS measurement for $c-GST$. The bond length
$L_{b}$ is measured by studying the position of the peaks. It can be observed
that the peaks for $Ge/Sb$ both show a double maxima at the distances
corresponding to their bond length., indicating that the $Ge-Te$ and $Ge-Sb$
have a longer $(\sim 3.20$Å$)$ and shorter $(\sim 2.84$Å$)$ bond. The other
bond lengths, namely $(Te-Te)$ $FCC$ $(\sim 4.26$Å$)$ bond and $(Te-Te)$
lattice parameter bond $(\sim 6.02$Å$)$ are extracted similarly. (b) Unit cell
of the distorted Rock-salt cubic-$GST$ structure and the amorphous-$GST$. (c)
layer stacking in $c-GST$ (d) $a-GST$ (e) Frontal view of a unit cell with a
vacancy in the octahedral site.32

#### Face Centered Cubic $Ge_{2}Sb_{2}Te_{5}$

$GST-225$ also crystallizes in a rock-salt type structure with the $Te$ atoms
occupying the Face Centred Cubic $(FCC)$ lattice while the $Ge$ and $Sb$ atoms
and vacancies occupy the octahedral voids in the body centre as shown in
Figure 6(e). 2532 It can also be seen that the equilibrium position for the
atom at the body centre of the $c-GST$ unit cell is deviated towards one of
the quadrants, this is confirmed by both XRD and EAXFS measurements of the
lattice parameter $(a\sim 6.02$Å$)$ and the bond lengths of the $Ge-Te$ and
$Sb-Te$ bonds as seen in Figure 6(a) & 8(a). 32 It should also be mentioned
that even though the isotropic displacement of the $Ge$ and $Sb$ atoms
$<u^{2}>$ are large $\sim 0.04$ Å2, the mean square relative displacement
obtained by EAXFS of the $Ge-Te$ and the $Sb-Te$ is small $\sim 0.02$Å2.32
This definitively implies that the structure is not an ideal but a distorted
rock-salt arrangement where the direction of the distortion is not perfectly
random but is heavily influenced by the surrounding $Te$ atoms. 3244 The
reason for this distortion is thought to be due to the differences in the
covalent radii of the $Ge/Sb$ atoms, mainly $Ge$, which is deviated from the
perfect $FCC$ centre resulting in a system with shorter $(L_{b}\sim 2.84$Å$)$
and longer $(L_{b}\sim 3.20$Å$)$ $Ge-Te$ bonds, and $Te-Te$ bonds$(L_{b}\sim
4.26$Å$)$ in the same unit cell, thus forming an overall buckled system.
324448 The shorter bonds are more rigid than the longer bonds thus bringing
the $Ge$ atom closer to one of the corners, and three of the $FCC$ $Te$ atoms,
effectively resulting in a Peierls distortion in the local structure as seen
in Figure 6(b) .153243

In an ideal $FCC$ cubic structure every atom needs to form 6 bonds due to
inherent octahedral symmetry, this implies each atom must contribute $6e^{-}$
to bonding. The $Ge$ atoms and $Sb$ atoms having only $4e^{-}$ and $5e^{-}$ in
their valence shell respectively are thus in need of excess electrons, which
are provided by $Te$ atoms adjacent to octahedral vacancies.32 This strongly
suggests that the presence of vacancies is an intrinsically important part of
the structure. Experiments in which the concentrations of $Ge/Sb$ atoms were
increased showed that the excess $Ge/Sb$ did not occupy the octahedral
vacancies but accumulates at the grain boundary.3132363743 It is proposed that
this is due to the need for vacancies to maintain the long range order in the
crystal structure and thus maintain crystal stability.323637 It is also
proposed that vacancies are usually formed at the sites that would have been
occupied by the $Ge$ atoms, which has been experimentally verified and
reported.3644 Studies have reported formation of upto $10\%$ $-$ $25\%$ of the
vacancies in $Ge$ occupied sites upon the thermal crystallization of as-
deposited $GeTe$ films. The ideal crystal structure of $c-GST$ is shown in
Figure 6(c), where only the shorter $Ge-Te$ and $Ge-Sb$ bonds are shown for
simplicity.213243

The real crystal structure of $GST-225$ deviates from the ideal in two
respects, namely that $Ge/Sb$ atoms may swap places resulting in randomness
and that each additional unit cell may rotate $90^{o}$ arbitrarily.3250 This
results in the $Te$ atoms forming a $FCC$ sub-lattice and $Ge/Sb$ atoms and
vacancies in the other $FCC$ sub-lattice. An important point to note is that
even though the $Ge/Sb$ vacancies are distributed randomly in the long range,
in the short range they form well defined rigid blocks.1732 It is known that
$FCC$ $(-A-B-C-A-B-C-)$ and $HCP$ $(-A-B-A-B-)$ are both close packed
structures with minor differences in the way that atomic layers arrange
themselves, thus the ideal structure depicted by Figure 6(c) seen as a ordered
chain of 9 atomic layers $(-Sb-Te-Ge-Te-Te-Ge-Te-Sb-Te-)$ can be thought of as
a prelude to the energetically favourable hexagonal arrangement.141751 This
can be observed in the differential scanning calorimetry measurements in
Figure 5(f) where an extra exothermic peak is seen between those corresponding
to the crystallization of the $a-GST$ and the transformation into $h-GST$.17
The band structure of $c-GST$ calculated using $DFT$ also indicates that it
should behave like a semiconductor with a band gap of $\sim 0.56eV$,
consistent with experimental measurements.1438

(a)

(b)

(c)

Figure 7: (a) Raman spectra for the $a-GST$ and $c-GST$ phases. (b) Measured
and (c) simulated XANES spectra for $a-GST$ and $c-GST$.32

### Amorphous $Ge_{2}Sb_{2}Te_{5}$

We now turn to the amorphous phase of $GST-225$ in which the $Ge-Te$ $(\sim
2.61$Å$)$ and $Sb-Te$ $(\sim 2.85$Å$)$ bonds are shorter and stronger. 3218
Such behaviour is unusual for such solids as the bond lengths tend to get
longer upon amorphization due to the anharmonicity of the inter-atomic
potential.3252 It has been hypothesized that rupturing of longer $Ge-Te$ bonds
in $c-GST$ resulting in a system with shorter bond lengths is responsible for
the effect.3252 This may well be the case, as the existence of long and short
$Ge-Te$ and $Sb-Te$ bonds is experimentally verified in the distorted
structure of the $c-GST$ .32 The local order present in the $a-GST$ structure
is also investigated with the help of Raman scattering where the Raman modes
measured for $a-GST$ were more rigid than the crystalline state as seen in
Figure 7(a), which supports the theory of bond rupture .3245 It is also
observed that the volume of $a-GST$ decreases upon crystallization which is
due to the weakening of the intermolecular interactions caused by the same
ruptured bonds.32 XANES measurements and simulations for the $a-GST$ structure
also indicate that the $Ge$ atom was allowed to acquire its favoured
tetrahedral arrangement, only possible with the rupture of the longer bonds as
discussed in section $4.1$.324547

### Contrast in electrical & optical properties between c-GST & a-GST

The primary reason for immense interest in $GST$ phase change materials as
opposed to other classes of PCM’s is that they display a unusually high
contrast in electrical and optical properties, like real and imaginary
component of the refractive index $(\Delta n$ and $\Delta k)$, conductivity
$(\sigma)$, transmittance $(T)$, reflectance $(R)$, and absorptivity
$(\alpha)$, under and after stimulation, while also maintaining that change
long after the source of the stimulation has been removed.6123032 These
changes in electronic and optical properties are caused by a combination of
structural changes to the lattice after transformation and the band gap change
associated with it.3638 Quantum mechanical $DFT$ calculations using fermi’s
golden rule have also shown that the profound change in optical properties can
be explained by such structural alterations.363845

Vacancies in the material, especially $Ge$ vacancies in the body centre are
thought to play a major role in the materials ability to show such contrast on
phase transformation due to the intimate role that vacancies have in
facilitating IMT as discussed in the previous sections.21374349 Although the
exact mechanism behind the trend is not well understood, increasing the
stoichiometric concentration of $Ge$ in the lattice has shown to increase the
optical contrast considerably, increasing from $(\Delta n+i\Delta
k=-1.48+i1.35)$ for $Ge_{8}Sb_{2}Te_{11}$ to $(\Delta n+i\Delta k=-1.2+i1.05)$
for $Ge_{2}Sb_{2}Te_{5}$. The electron behaviour and the density of states in
the longer and shorter $Ge-Te$ bonds is also speculated to play a role in the
optical contrast displayed by these materials.323444

## Macroscopic Kinetics of Solidification and Phase transformation

$GST-225$ and other phase change alloys have been used in next generation
rewritable optical media for the last few years and are being considered for
use in high speed non-volatile memory. The primary method for inducing this
phase change, which is used for writing and rewriting bits onto a memory cell,
is a $SET$ and $RESET$ laser pulse of varying power and temporal width.1221
Therefore fast recrystallization speeds, high data transfer rate, good
scalability and non-volatility of the phase transformation are major factors
that make it imperative to understand and improve the kinetics of the phase
transformation for out-competing existing and emerging non-volatile
memories.121753

Phase transformation in $GST-225$ is fundamentally in response to temperature
change caused by a incident laser pulse, which in case of a $(c-GST\rightarrow
a-GST)$ transformation is high-power and short pulse width, causing the
temperature of the $c-GST$ to increase rapidly to above $T_{m}$ $(\sim
650^{o}C)$.125455 The rapid quenching of the heated $GST$ $(\sim 1^{o}C/ns)$
cause atoms to freeze in place as the temperature drops below $T_{g}$. The
$(c\rightarrow a)$ transformation usually does not fully amorphize the
crystalline phase leaves behind some sub-critical crystalline domains which
play an integral part in the $(a-GST\rightarrow c-GST)$ transformation.5657

Crystallization of $a-GST$ involves the use of a intermediate-power long-pulse
width which increases the temperature of the system to above $T_{g}$ $(\sim
150^{o}C)$, this allows the atoms enough wiggle room to arrange themselves in
a energetically favourable position, allowing the formation of nucleation
sites and subsequent crystallization of the domains.125859 The nucleation step
in this process is inherently slow and the time limiting step for the phase
change to occur.121760 The growth step on the other hand is significantly
faster thus it is favourable for better phase switching behaviour.
Crystallization of melt-quench $GST$ is different from as-deposited films,
which are dominated by a nucleation driven process while melt-quench favours a
growth dominated process.1231 The amorphization of $c-GST$ by melt-quenching
also leaves behind sub-critical crystalline domains in the amorphous matrix,
making it possible for the slow nucleation step $(t\sim 1\mu s)$ to be
bypassed by significantly faster growth dominated recrystallization $(t\sim
20-30ns)$.1231 The application of a preconditioning short laser pulse
$(t_{p}\sim 100ns)$ can help as-deposited films mimic the speed of melt-quench
films.31

(a)

(b)

(c)

(d)

(e)

(f)

Figure 8: (a) XRD spectra for $GST-225$ at different laser fluences. (b) Grain
size for $GST-225$ at different laser fluences. (c) Reflectivity contrast for
$GST-225$ at different laser fluences.50(d) Crystal growth velocity $(v_{g})$
for $GST-225$ at different laser fluences.61(e) XRD spectra for $GST-225$ at
different temperatures. (f) Crystallization fraction for $GST-225$ at
different temperatures.50

Laser power is another important factor influencing the kinetics of $GST$
films that has been extensively studied in literature.12315162 The evolution
of crystallinity in the samples as the laser power is increased is clearly
visible in the XRD measurements shown in Figure 8(a) & 8(e).5061 It can be
observed that even though a partial crystallization of th films can be
observed for laser fluences between $15mJ/cm^{2}$ and $36mJ/cm^{2}$ in the
optical reflectivity contrast measurements, this cannot be observed in the XRD
spectra.50 With the increase in the laser fluences from $36mJ/cm^{2}$ to
$98mJ/cm^{2}$ a gradual but proportional increase in the volume of the
crystalline fraction can be seen.50 It is also seen that femtosecond pulses
$(500fs)$ show a threshold power for crystallization at $13mJ/cm^{2}$ compared
to $36mJ/cm^{2}$ for nanosecond pulses $(20ns)$, indicating the possibility
for ultra-fast low power switching.5063 Figure 8(b) shows the grain size as a
function of laser power for both $ns$ and $fs$ pulses. 50

Annealing of $GST$ films and the crystal growth velocity $(v_{g})$ has also
been studied extensively at different temperatures and laser fluences using
both $DFT$ and experimental studies.6164 It is apparent that the crystalline
phase dominates the fraction of the solid as the temperature is increased and
maintained above $T_{g}\sim 150^{o}C$ as seen from the XRD measurements and
the crystal fraction measurements at different annealing temperatures.6164 We
can observe that $v_{g}$ increases with the laser power, this is to be
expected with an increase in the rate of crystallization.61 The cooling rate
also plays an important role in the crystallization kinetics, by saturating
$v_{g}$ at high laser powers and promoting amorphization at high enough
values.61 $v_{g}$ also increases with an increase in temperature till about
$527^{o}C$ when the crystalline nucleus becomes too unstable to propagate.61
The theoretical maximum value for $v_{g}$ predicted by $DFT$ studies is $\sim
1.5m/s$ at $\sim 427^{o}C$ which is in close agreement with the experimentally
measured value of $\sim 1.7m/s$.6164

Studies have also looked at how doping iso-electronic species, such as other
chalcogens like $Se$ affects the switching speed in $GST-225$, observing an
improved performance in $Ge-Sb-Se-Te$ $(GSST)$, which similar to $GST$ forms a
metastable cubic phase $(c-GSST)$ and a stable hexagonal phase $(h-GSST)$.6566
The optimized addition of $Se$ to $GST-225$ can significantly reduce the
optical loss in the near-IR to mid-IR range, where $GSST$ shows a broadband
transparency from $\lambda\sim 1\mu m$ to $1.85\mu m$ while offering a $\Delta
n\sim 2$ without loss penalty $(\Delta k\approx 0)$, maximizing the figure of
merit $(FOM)=\Delta n/\Delta k$.65 The reason for this optical contrast
according to $DFT$ simulations of random addition of $Se$ atoms to the $GST$
structure is the widening of the band gap leading to a smaller loss in the IR
regime, which has been experimentally confirmed.2865 $GSST$ also shows a
smaller density of states near the band edge due to the narrowing of the
conduction and valence band in the $E-k$ diagram, which reduces the free
carrier absorption in the IR range.65 The electronic excitations due to laser
stimulation are also suppressed in $GSST$ compared to $GST$, where the
creation of non-equilibrium photo-generated charge carriers are crucial for
bond rupture.32 Photo-generated carriers occupy these weak states in the
longer $Ge-Te$ bond making them more susceptible to thermal vibration induced
dislocations.32

It is also seen that increasing the $Se$ content monotonically increases the
crystallization temperature, making the $c-GSST$ phase more stable and the
crystallization process slower $(t\sim 3\mu$ at $25\%$ $Se)$ compared to $GST$
$(t\sim 20ns)$.3165 This also makes the effect of the preconditioning pulse
weaker, pushing the system towards nucleation driven kinetics which is
inherently sluggish.3165

(a) $AgIn$-doped $Sb_{2}Te$ and $Ge_{12}Sb_{88}$

(b) $Ge_{1}Sb_{2}Te_{4}$ and $Ge_{2}Sb_{2}Te_{5}$

Figure 9: (a) Rim to Centre Growth. (b) Nucleation and subsequent Crystal
Growth.12

### Rim to Center Crystallization

One of the possible mechanisms for the $a-GST\rightarrow c-GST$ transformation
to occur is rim to centre crystallization, where the crystal grows from the
rim of the melted $a-GST$ spot toward the centre, hence its name.12 The
primary reason for why this might occur would be if the edges of the spot
cooled faster than the centre, then this would promote crystal growth in the
inwards direction.1221 This is only possible if heat is extracted fast enough
and evenly at the rim-ambient interface and not the spot-substrate interface,
forming a thermal gradient between rim and centre, like in the case of
$AgIn-$doped $Sb_{2}Te_{3}$ where a direct correlation between the size of the
spot and crystallization time is observed, characteristic of such a mechanism,
confirmed by irradiation experiments of $AgIn-$doped $Sb_{2}Te_{3}$ observing
the same between radius of the spot $(R_{s})$ and crystallization time
$(t_{r\rightarrow c}\sim 600ns)$.12 In such materials the crystal growth
velocity $(v_{g})$ is a exponential function of the temperature.126164

### Crystal Nucleation & Subsequent Growth

The second, more probable mechanism for the $a-GST\rightarrow c-GST$
transformation occurring is nucleation followed by crystal growth.1255 Such a
mechanism requires the laser irradiated $GST$ spot not losing heat fast enough
to induce rim to centre growth, but instead causing the formation of randomly
distributed crystal nucleation sites, facilitated by low thermal conductivity
of the rim-ambient interface, spot-substrate interface and $GST$ alloys in
general.31 This is observed in $GST-415$, $GST-124$ and $GST-225$ where the
crystallization time $t_{n}$ is independent of the radius of the spot, which
is expected of such a mechanism.316367

The rate at which nucleation sites are formed inside the irradiated spot is
dependent on the temperature, which in-turn is determined by the laser power
and pulse width.316164 This points at the existence of a optimum temperature
for nucleation $(T\sim 175-180^{o}C)$ to occur, when crystallization is
fastest in the time-temperature transformation $(t-T)$ diagram.31 The
temperature dependence of the steady state homogeneous nucleation rate is
strong and drops rapidly over a small temperature range. Thus when the laser
power is sufficient to reach this optimum temperature, the crystallization is
uniform and reproducible over a large number of cycles.3161

Nucleation is generally accepted to be the time limiting step in such a
process, making it the bottleneck for achieving fast switching speeds,
especially when using as-deposited $a-GST$.31 The crystallization of as-
deposited $a-GST$ films is dominated by nucleation, making the
$a-GST\rightarrow c-GST$ orders of magnitude slower compared to melt-quenched
$GST$ $(t\sim 3\mu m)$, which contain sub-critical crystalline domains left
over from when $c-GST$ undergoes the laser amorphization process. These
domains allow us to bypass nucleation and proceed with the crystal growth
dominated step, making the process significantly faster $(t\sim 20ns)$.315255
Higher laser powers than the optimum often lead to a random distribution of
nucleation centres, but also a higher probability of ablation which is
undesirable and results in the loss of information stored in the memory
cell.52545860

Crystallization time may also be much larger than the duration of the laser
pulse in cases where the substrate on which the $GST$ spots are made has a
cooling time much larger than the pulse itself, leading to the slow cooling
and better crystallization of the $GST$.121721 This usually happens when the
thermal conductivity of the substrate is significantly less compared to the
$GST$, for example $GST$ films on $SiO_{2}$ and $Al_{2}O_{3}$ substrates which
show a high degree of crystallinity due to the cooling time for $SiO_{2}$ and
$Al_{2}O_{3}$ being of the order of nanoseconds $(t\sim 10ns)$.1221 Thus the
cooling time for the substrate is an important factor which limits the laser
pulse widths that can be utilized for crystallization.12162131

## Atomistic Mechanism of Phase Transformation

Now that we have looked into the various phases of $GST-225$ as well as the
macroscopic kinetics of the phase transformation upon optical stimulation, we
turn our attention to the atomic mechanism for the $c-GST\rightarrow a-GST$
transformation.

### Atomic Migrations & Bond breaking

It is evident from our earlier description of the $c-GST$ unit cell, which
crystallizes in a distorted rock-salt cubic structure, that there exist three
long $(\sim 3.20$Å$)$ and three short $(\sim 2.84$Å$)$ $Ge-Te$ bonds.1432 This
in-turn results in weaker $(E_{b}\sim 396.7kJ/mol)$ and stronger $(E_{b}\sim
402kJ/mol)$ $Ge-Te$ bonds, determined by their bond dissociation
energies.193268 Upon laser stimulation, the longer bonds are broken but not
the shorter bonds as a result of which the $Ge$ in the distorted octahedral
centre is pulled into a tetrahedral void in one of the corners by the shorter
$Ge-Te$ bonds as shown in Figure 6(b).3247 This is clear as the measured co-
ordination number for $Ge$ in $a-GST$ $\approx 4$ and the simulated XANES
spectra for this process and the measured data are in good agreement as seen
in Figure 7(b) & (c).32 As the direction in which these longer and shorter
bonds exist depends on the surrounding atomic layers , and the $8$ fold $3D$
symmetry of a cubic unit cell adds even more randomness as to which of the
four tetrahedral centres the $Ge$ will be pulled towards, this creates a loss
of long range order in the crystal and causes amorphization.3132 The train of
thought that has been presented herein is also applicable to a octahedral
centre containing a $Sb$ atom where the longer $(\sim 3.10$Å$)$ and shorter
$(\sim 2.95$Å$)$ $Sb-Te$ bond display a similar behaviour.324750

### Peierl’s Distortion & Umbrella Flip Distortion

Though the $c-GST\rightarrow a-GST$ transformation involves the longer $Ge-Te$
bond rupturing upon laser stimulation, it is important to note that the solid
can not be considered conventionally molten due to the shorter $Ge-Te$ bonds
remaining unbroken.313247 Thus the overall transformation from
$c-GST\rightarrow a-GST$ can be thought of as a flip of the $Ge/Sb$ atom from
a octahedral position to a tetrahedral position, which involves the rupture of
the longer bonds and a direction change of the shorter bonds similar to the
ribs of an umbrella flipping during strong winds.1432 This type of distortion
is therefore aptly named the umbrella flip distortion.32 In actuality it is
more similar to a localized Peierls distortion of the lattice, which involves
atoms in a chain coming close to one of their neighbours, which in this case
would be the $Ge$ atom coming close to the $Te$ atoms on the face-centre and
the corner as seen in Figure 6(b).3247 These distortions of the lattice are
the primary reason for the change in the band gap of the solid upon
stimulation, the loss in the long range order and formation of dangling bonds
also results in the formation of an Urbach-Martienssen tail in their
absorption spectra characteristic of amorphous materials as seen in Figure
3(d).2938

(a)

(b)

Figure 10: (a) $c\rightarrow a$ and $a\rightarrow c$ process under a beam
intensity of $6$ x $10^{23}e^{-}/m^{2}s$. (b) $c\rightarrow a$ process under a
beam energy of $200keV$.40

### Effect of charge carriers

The laser pulse not only heats the material but also excites non equilibrium
charge carriers that weaken the longer $Ge-Te$ bonds significantly.3140 Since
the density of states in these bonds is lower, the carriers more easily
populate these states making hem more vulnerable to thermal vibrations and
dislocations.143865 Thus the presence of these electronic interactions is
critical to the phase transformation. This can be most clearly demonstrated by
a study where a similar phase change was observed when a electron beam was
used instead of a laser, indicating that carrier interactions with the lattice
play a major role in the overall process.40 The study conducted employed a
$200keV$ electron source with a electron density of $6$ x
$10^{23}e^{-}/m^{2}s$ which was used to irradiate a $80nm$ $a-GST$ film.40 The
films were exposed to the beam for $5$ $min$ when multiple crystal domains
began to appear which were confirmed by SAED. On increasing he exposure time
to $15$ $min$ th crystallite size grows to $10-20nm$ and SAED shows sharp and
bright diffraction rings.40 The study also confirmed the existence of a
threshold beam intensity $(1.6$ x $10^{23}e^{-}.m^{2}s)$ below which no
transformation was observed however long the beam remains irradiated on the
sample.40 Amorphization is also possible by increasing the beam intensity to
about $1.1$x $10^{24}e^{-}/m^{2}s$.40 This was confirmed as being due to the
electron beam by performing the same experiments on thermally amorphized
samples.40 The threshold intensity for amorphization was found to be $8$ x
$10^{23}e^{-}.m^{2}s$. This radiation amorphized $GST$ can be recrystallized
by adjusting the electron beam intensity.40 Irradiation induced amorphization
was also found to be continuous with no abrupt changes in the structural
patterns, which indicates a non thermal component to th phase change. 40 The
temperature increase due to irradiation is calculated using the expression
$\Delta T=\frac{{1}}{\pi\kappa e}\frac{\Delta E}{d}\ln\frac{b}{a}$, which
gives us a result around $220^{o}C$ nowhere close to $\sim 650^{o}C$ needed
for thermal amorphization.40 It was also observed that the intensity of the
electron beam, voltage, and irradiation time had a major impact on the degree
of phase change that was observed in the sample, making us conclude that the
collisions of the electrons with the lattice plays an important role in
triggering $a\rightarrow c$ transformation, which can be localized by
decreasing beam area, additionally electronic states also change from $p-type$
bonding to a $sp^{3}$ thus leading to optical contrast between the two
phases.323840 In order for the absorbed energy to be dissipated non-
radiatively, a large number of phonon’s have to be emitted which is
facilitated by the presence of large number of atomic sites near these states,
enabling us to selectively heat these areas to a higher temperature.133146

## Conclusion

In this term paper, we have investigated the $c\rightarrow a$ ans
$a\rightarrow c$ transformation of $GST-225$ under optical stimulation by a
laser source. We first looked at the three structural phases of $GST$ namely
$c-GST$ (rock-salt), $h-GST$ (hexagonal) and $a-GST$ (amorphous), their band
structures, vacancy distributions and atomic and bond lengths and arrangements
which play a major role in their stability, phase transformation as well as
electrical and optical contrast. Then the role of laser power, pulse duration,
temperature, doping as well as the distribution of electronic states and
carriers and their effect on the macroscopic kinetics and the mechanism of
phase transformation was explored. It was found out that the transformation
prefers a nucleation mechanism followed by subsequent crystal growth due to
the combined thermal characteristic of both the $GST$ and the substrate, as
well as laser power and pulse width.

Then we delved into the atomic mechanism of the phase transformation using
both experimental evidence from literature in tandem with $DFT$ calculations
to figure out the cause for the transformation. This analysis points to the
primary cause for the $c\rightarrow a$ transformation being the atomic
migration of the $Ge/Sb$ atoms from the octahedral to the tetrahedral centre,
causing a loss in the long range order in the arrangement i.e. amorphization.
The rupture of the longer $Ge-Te/Sb-Te$ bonds, which leads to a umbrella-flip
distortion (Peierls distortion) pulling the $Ge/Sb$ from a $6$\- fold co-
ordination $(octahedral)$ site to $4$-fold co-ordination $(tetrahedral)$ site
in a semi-random manner, was found to be the root cause. The importance of the
role played by charge carriers and their interactions with the lattice in
causing the phase transformation is also highlighted. In conclusion, we have
attempted to provide a comprehensive picture of the macroscopic kinetics of
the phase switching behaviour observed in $GST-225$ and the parameters that
affect the stability of the phases as well as the speed of the phase
switching. We also present a atomistic picture of the phase transformation by
studying the interactions between the constituent atoms, their movement and
behaviour in the crystal structure to pinpoint as reason for the phase change
behaviour.

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††thanks: Correspondence to<EMAIL_ADDRESS>and
<EMAIL_ADDRESS>
# Oblique spin injection to graphene via geometry controlled magnetic
nanowires

Jesus C. Toscano-Figueroa  These authors contributed equally to the work.
Department of Physics and Astronomy, University of Manchester, Manchester M13
9PL, United Kingdom  Consejo Nacional de Ciencia y Tecnología (CONACyT), Av.
Insurgentes Sur 1582, Col. Crédito Constructor, Alcaldía Benito Juarez, C.P.
03940, Ciudad de México, México  Daniel Burrow  These authors contributed
equally to the work.  Department of Physics and Astronomy, University of
Manchester, Manchester M13 9PL, United Kingdom  Victor H. Guarochico-Moreira
Department of Physics and Astronomy, University of Manchester, Manchester M13
9PL, United Kingdom  Facultad de Ciencias Naturales y Matemáticas, Centro de
Investigación y Desarrollo en Nanotecnología, Escuela Superior Politécnica del
Litoral, ESPOL, Campus Gustavo Galindo, Km. 30.5 Vía Perimetral, Guayaquil,
090902, Ecuador  Chengkun Xie  Department of Physics and Astronomy, University
of Manchester, Manchester M13 9PL, United Kingdom  Thomas Thomson  Department
of Computer Science, University of Manchester, Manchester M13 9PL, United
Kingdom  Irina V. Grigorieva  Department of Physics and Astronomy, University
of Manchester, Manchester M13 9PL, United Kingdom  Ivan J. Vera-Marun
Department of Physics and Astronomy, University of Manchester, Manchester M13
9PL, United Kingdom

(August 28, 2024)

###### Abstract

We exploit the geometry of magnetic nanowires, which define 1D contacts to an
encapsulated graphene channel, to introduce an out-of-plane component in the
polarisation of spin carriers. By design, the magnetic nanowires traverse the
angled sides of the 2D material heterostructure. Consequently, the easy axis
of the nanowires is inclined, and so the local magnetisation is oblique at the
injection point. As a result, when performing non-local spin valve
measurements we simultaneously observe both switching and spin precession
phenomena, implying the spin population possesses both in-plane and out-of-
plane polarisation components. By comparing the relative magnitudes of these
components, we quantify the angle of the total spin polarisation vector. The
extracted angle is consistent with the angle of the nanowire at the graphene
interface, evidencing that the effect is a consequence of the device geometry.
This simple method of spin-based vector magnetometry provides an alternative
technique to define the spin polarisation in 2D spintronic devices.

††preprint: APS/123-QED

##  I Introduction

Efficient generation of spin accumulation in an appropriate transport medium,
and control over the consequent diffusive spin signals, are two of the most
crucial elements of spintronic devices [1, 2]. Graphene is an ideal material
for spin transport, owing to its high electron mobility, low spin orbit
coupling strength, and gate tuneable carrier density [3, 4, 5, 6, 7].
Furthermore, encapsulating graphene between two layers of hexagonal-boron
nitride (hBN), an insulating isotrope of graphite, is known to greatly
increase its quality as both a charge and spin transport medium, with
significant improvements to electron mobility and spin diffusion lengths
reported [8, 9, 10, 11, 12, 13]. Making a Van der Waals heterostructure
comprising insulating outer layers, inherently presents challenges in
contacting graphene, with conventional top contacts no longer a viable option.
A promising alternative is the use of one-dimensional (1D) edge contacts,
where electrodes make contact with the graphene channel only along its atomic
edge [14]. Such contacts have been shown to be far less invasive than top
contacts [15, 16, 17], and have recently been implemented, in the case of
magnetic nanowire electrodes, for efficient spin injection and long range spin
transport [18].

Figure 1: Characterisation of device A. (a) Optical image of device. The blue
strip is the hBN graphene encapsulated channel, while the yellow bars are
Co/Au nanowires. Scale bar is 10 $\mu$m. The non-local measurement
configuration is shown, with the injector ($I$) and detector ($D$) electrodes,
as well as the back gate connection ($V_{BG}$), indicated. $L$ is the channel
length in the non-local measurement. (b) AFM scan of a magnetic nanowire,
taken from the region enclosed by the box in panel (a). Cyan and red bars
indicate the location of profiles taken from the scan. Scale bar is 200 nm.
(c) Height profiles of the stack and magnetic nanowire, taken from panel (b).
The angle of inclination of the nanowire is found to be $42\pm 8\degree$. (d)
Schematic illustration of the device profile, showing the hBN/graphene/hBN
heterostructure with a Co/Au magnetic nanowire laid over the top. The angled
magnetisation at the injection point is indicated.

Here, we investigate how the geometry of these magnetic nanowires can be
exploited to define the polarisation of a spin population injected into a high
quality graphene device [19]. The magnetic nanowires are engineered with
considerable shape anisotropy (Figure 1a), such that the easy axis points
along their length. Moreover, as the nanowires cross the 2D material
heterostructure the easy axis tilts out-of-plane at the interface with the
graphene (Figure 1d). As such, the local magnetisation vector is oblique at
the point of spin injection; in other words, it is described by both in-plane
and out-of-plane components (Figure 1d). To explore the effect of the
magnetisation angle on diffusive spin transport through the graphene channel,
we conduct standard spin valve (magnetic field in-plane) and Hanle spin
precession (magnetic field out-of-plane) measurements [20, 5, 21]. We find the
spin valve response displays a Hanle-like line shape, implying that the
oblique magnetisation transmits an out-of-plane component to the polarisation
of the injected spin population, which precesses around the in-plane magnetic
field. By analysing the precession curve observed in our spin valve
measurements, and comparing the results to those extracted from standard Hanle
spin precession data, we quantify the relative magnitudes of in-plane and out-
of-plane spin polarisation and use this information to reconstruct the angle
of the total polarisation vector. The extracted angle is consistent with the
inclination of the magnetic nanowire at the graphene interface, evidencing
that the effect is geometric in nature. Previous demonstrations of generation
of out-of-plane injected spin polarisation in lateral devices, have utilised
complex physics such as the anomalous spin Hall effect [22],
magnetocrystalline anisotropy within Van der Waals magnets [23], or generation
within graphene itself via proximity-induced spin-orbit coupling [24]. Hence,
exploiting device geometry provides an alternative, and relatively simple,
technique for defining spin polarisation in spintronic devices.

##  II Fabrication and characterisation

We fabricate a total of four devices (A-D) in line with the methods used in
our previous work [18]. Individual flakes of 2D material (both hBN and
graphene) are isolated via mechanical exfoliation, then subsequently stacked
into hBN/graphene/hBN heterostructures via the dry peel transfer technique [8,
25]. Reactive ion etching is used, along with a polymer hard mask, to engineer
a long, narrow transport channel out of the heterostructure (Figure 1a). After
etching, the sides of the stack are angled and a small ledge of graphene is
left exposed at the edges (Figure 1b,c). This permits one-dimensional
electrical contact to the heterostructure by deposition of ferromagnetic metal
nanowires [26, 16]. The nanowire pattern is defined in a polymer layer via
electron beam lithography, before metal is deposited via electron beam
evaporation; materials used for all devices are 60 nm Cobalt (Co) with a 20 nm
Gold (Au) capping layer.

Devices fabricated using this methodology have previously shown high
electronic quality, with charge carrier mobilities $>10$ m2 V-1 s-1, and
demonstrated efficient spin transport with spin relaxation lengths $>10$
$\mu$m [18]. One aspect of this architecture that remains unexplored, is the
geometry of the magnetic nanowires that form the 1D contacts. The nanowire
design results in an easy axis dictated by shape anisotropy, which points
along the length of the wire. Therefore, switching of the in-plane
magnetisation, $M_{||}$, can be achieved with relatively low magnetic fields,
as expected for Co nanowires with dominant shape anisotropy [27]. However,
owing to the geometry of the nanowires as they traverse the sides of
heterostructure, the easy axis is inclined and the magnetisation gains a small
out-of-plane component, $M_{\perp}$, at the injection point (Figure 1d).

A further consideration in this geometric treatment, is the role of the
heterostructure thickness, $t$, which is determined entirely by the
encapsulating hBN layers. The thicknesses of our four heterostructures are
varied by selection of hBN flakes (thickness decreases from A-D), while the
thickness of the Co layer in the nanowires is kept constant across all devices
(60 nm). Figures 1a and 1b show optical and AFM images of device A,
respectively. Profiles taken from the AFM scan show the total height of this
heterostructure to be $\sim 50$ nm (Figure 1c), which is comparable to the
thickness of the Co within the nanowire $\sim 60$ nm. Aside from protecting
the graphene from environmental contamination and giving rise to high charge
mobilities, using thicker flakes of hBN ($>20$ nm) is expected to lead to a
greater magnitude of $M_{\perp}$ in the nanowires, relative to a given
thickness of Co. It should be noted that the etching process used has to be
optimised for thicker flakes. Using AFM profile data for device A, the angle
of inclination of the nanowires is found to be $\theta=42\pm 8\degree$.

##  III Oblique spin injection

Figure 2:  Defining Hanle and spin valve (SV) measurement configurations. (a)
Illustration spin injection and Hanle measurement. The magnetic field,
$B_{\perp}$ (purple arrow), points along the z-axis, causing the precession of
the in-plane spin component, $P_{||}$ (red arrow). The total polarisation
vector, $P$ (blue arrow), of the injected spin population follows the
magnetisation vector of the nanowire, $M$ (black arrows). (b) Illustration of
a SV measurement, for which the magnetic field, $B_{||}$ (purple arrow), is
directed along the easy-axis of the nanowires (y-axis). Due to the geometry of
these devices an out-of-plane spin component, $P_{\perp}$ (white arrow), is
injected, which precesses around the $B_{||}$. (c) Hanle response for the
cases of parallel ($\uparrow\uparrow$) and anti-parallel
($\uparrow\downarrow$) alignment of the magnetisation for the injector and
detector electrodes. (d) SV response of the device, with switches between the
$\uparrow\uparrow$ and $\uparrow\downarrow$ states at $B_{||}\sim\pm 40$ mT
(indicated by empty black and red squares). A Hanle-like line shape is visible
in the SV signal associated with the $\uparrow\uparrow$ state (indicated by
filled red and black squares). When the magnetisation state switches to
$\uparrow\downarrow$, the line shape is inverted, implying the effect is spin
dependent (indicated by empty green and blue circles).

We investigate the effect of the nanowire geometry on diffusive spin
transport, by performing non-local (Figure 1a) spin precession (Hanle) and
spin valve (SV) measurements, on device A [5, 28]. For Hanle measurements, a
magnetic field, $B_{\perp}$, is applied along the z-axis, perpendicular to the
plane of the channel, causing precession of the in-plane component of the spin
polarisation, $P_{||}$, as the carriers diffuse through the channel (Figure
2a). The observed Hanle response is characteristic of spin precession through
the graphene channel (Figure 2c). When ${B_{\perp}}=0$ there is a peak in the
non-local signal, $R_{NL}$, as the spin polarisation is fully co-linear with
the magnetisation of the electrode. As $B_{\perp}$ increases, $R_{NL}$
decreases to a minimum, at $B_{\perp}\sim\pm 100$ mT, implying a full
$\pi$-rotation of the spin polarisation at the detector electrode. For
$B_{\perp}>\pm 100$ mT, $R_{NL}$ flattens out, suggesting the spin signal is
fully dephased before reaching the detector. This effect is inverted for the
two relative orientations of the injector-detector magnetisations: parallel
($\uparrow\uparrow$) and anti-parallel ($\uparrow\downarrow$) (Figure 2a,c).

Figure 3:  Magnetisation angle reconstruction from spin transport (a)
Comparison of spin-precession phenomena in terms of spin signal, $R_{s}$, at
charge carrier density $n=$1.5\text{\times}{10}^{12}$$
$\mathrm{c}\mathrm{m}^{-2}$. Black squares represent the full Hanle precession
signal, while red squares represent the Hanle-like background from Figure
2(d), with the $\uparrow\downarrow$ switches removed. Both data sets are
presented with a linear background removed and offset corrections. A coloured
line through each precession curve indicates a fit to the data. (b) Spin
diffusion length, as a function of carrier density, extracted by fitting data
from the two separate precession experiments over a range of carrier
densities: Hanle ($\lambda_{||}$) and SV ($\lambda_{\perp})$. The value and
trend of $\lambda_{s}$ from the two precession phenomena are consistent across
most of the carrier density range. (c) Spin polarisation as a function of
carrier density, also extracted from fits to the two data sets; $P_{||}$ from
Hanle data, and $P_{\perp}$ from SV data. We observe the same trend for both
precession phenomena, indicating they describe the same system. The
resistivity of the channel, $\rho$, is shown superimposed (right axis). (d)
Inclination angle of the nanowire magnetisation, reconstructed from
$\theta=\arctan(P_{\perp}/P_{||})$. The average angle across the data range is
reported along with the standard deviation (shown as an error band). Error
bars on data points in (b-d) come from individual fits to spin precession data
as shown in (a).

For spin valve measurements, the magnetic field, $B_{||}$, is applied along
the y-axis, co-linear with the easy axis of the magnetic nanowires (Figure
2b,d). The SV response seen here is unique to the geometry of our devices. The
expected switches between the $\uparrow\uparrow$ and $\uparrow\downarrow$
states are observed at $B_{||}\sim\pm 40$ mT (open squares, Figure 2d).
However, the non-local signal associated with the $\uparrow\uparrow$ state,
outside of the switching region, features a line shape reminiscent of that of
a Hanle measurement (filled squares, Figure 2d). We define this line shape as
the Hanle-like background of the spin valve measurement. This phenomenon
arises from the precession of an out-of-plane component in the spin
polarisation, $P_{\perp}$, imprinted on the injected spin population by the
magnetisation of the magnetic nanowire at the injection point. This component
is also injected during Hanle measurements but will not precess in this case,
as it is co-linear with the applied magnetic field. To determine whether the
Hanle-like background is truly spin-dependent (i.e magnetic in origin), we
perform a minor hysteresis loop, by reversing the direction of the magnetic
field as soon as a switch occurs between the $\uparrow\uparrow$ and
$\uparrow\downarrow$ states. The result of this process is shown in Figure
2(d) by the open green and blue circles. The curve between the switches is
inverted depending on whether the nanowire magnetisations are arranged
parallel or antiparallel, as is the case for precession measurements, implying
that the observed line shape is indeed spin-dependent. Therefore, providing
additional evidence that the detected Hanle-like background arises from the
precession of the out-of-plane component of injected spins.

##  IV Electronic angle reconstruction

Figure 4: Connection between heterostructure thickness, $t$, and observed
Hanle-like background. (a-c) Optical microscope images of device B-D, arranged
from thickest (B) to thinnest (D). The optical contrast can be used as a
metric for stack thickness, with thinner flakes appearing darker in colour.
White scale bars are 10 $\mu$m. (d-f) Height profiles taken from AFM scans at
device edges. Stack thicknesses, from top to bottom, are: $\sim 52.0$ nm (B),
$\sim 27.5$ nm (C), and $\sim 14.8$ nm (D). Insets show the AFM images that
profiles are extracted from, with the cyan bar illustrating profile locations
(white scale bars are all 200 nm). (g-i) Spin valves taken from devices B
(top), C (middle), and D (bottom), all at a temperature of 20 K. Red and black
lines indicate the direction of the magnetic field sweep. A Hanle line shape
is visible for device B. Magnitudes of in-plane and out-of-plane spin signals
are indicated ($R_{s-||}$ and $R_{s-\perp}$ respectively). Stack C displays a
subtle Hanle-like background, while stack D does not show any. All spin valve
measurements are taken at a carrier density far from the neutrality point.

Figure 3a shows representative spin precession data for two types of
experiments: i) full Hanle signal, defined as
$R_{s-||}=(R_{NL\uparrow\uparrow}-R_{NL\uparrow\downarrow})/2$, representing
precession of a large in-plane spin component and ii) the Hanle-like
background from the SV experiment, with the switches removed, representing
precession of a small out-of-plane spin component ($R_{s-\perp}=R_{NL}$). We
use a DC voltage, $V_{BG}$, applied between the silicon substrate, which acts
as a global back gate (Figure 1a), and the graphene channel, to control the
carrier density in graphene, $n$ [3, 4]. The data is taken at a fixed charge
carrier density where the non-local signal is maximum ($n=1.5\times 10^{12}$
cm-2; $V_{BG}=20$ V). A linear background is removed from both data sets,
which arises due to Hall effect in the presence of a magnetic field. Both spin
precession signals are fitted to the steady state solution to the Bloch
equation, as has been discussed elsewhere [29, 5, 30, 31, 28]. This process is
repeated for data taken over a range of carrier densities ($n=0.5-2.5\times
10^{12}$ cm-2), which enables estimations of the spin relaxation time,
$\tau_{s}$, spin diffusion coefficient, $D_{s}$, and contact polarisation,
$P$. These values allow us to quantify the spin diffusion length,
$\lambda_{s}=\sqrt{D_{s}\tau_{s}}$, the value of which is consistent across
the two separate measurement techniques, with an average of
$\lambda_{s}=6.8\pm 0.4$ $\mu$m (Figure 3b).

The polarisation vector, $P$, is useful for studying the geometry of the
device, as it is formed from orthogonal components of different magnitudes,
$P_{\perp}$ and $P_{||}$. It relates to the non-local signal measured in the
channel, $R_{NL}$, as [5],

$R_{NL}=\frac{\rho P^{2}\lambda_{s}}{2W}e^{-L/\lambda_{s}},$ (1)

where we assume $P_{i}=P_{d}=P$ ($P_{i}$ and $P_{d}$ are injector and detector
polarisation, respectively), $\rho$ is the resistivity of graphene, while $W$
and $L$ are the channel width and length, respectively. Hence, the observed
difference in magnitude between the precession data extracted from SV and
Hanle measurements, reflects the difference in the magnitude of the respective
components of the polarisation, $P_{\perp}$ and $P_{||}$. Figure 3c shows the
evolution of these two components of polarisation against carrier density,
with $P_{\perp}$ being consistently smaller than $P_{||}$ throughout. At high
density ($n\geq 2\times 10^{12}$ cm-2), the signal to noise ratio of $R_{NL}$
decreases, as it is proportional to $P^{2}$ and $\rho$ (Equation 1, both of
which decrease at high $|n|$ (Figure 3c) [18]. Hence, reliable fits are harder
to perform as $n$ increases, especially for Hanle-like backgrounds, which are
considerably smaller in magnitude than the full Hanle signal. So, only data up
to $n=2\times 10^{12}$ cm-2 are used in the angle calculation. From the ratio
$P_{\perp}/P_{||}$, we reconstruct the angle of the overall spin polarisation
vector, $\theta=\arctan(P_{\perp}/P_{||})$. Note that this method yields an
inclination angle which is insensitive to variations in the magnitude of the
polarisation from contact to contact, being only sensitive to variations on
its inclination. The extracted $\theta$ has an average value of $36.0\pm
3.0$$\mathrm{\SIUnitSymbolDegree}$, over the carrier density range explored
(Figure 3d). This agrees within experimental error with the angle of the
nanowire extracted from AFM profilometry. Furthermore, the calculated value of
$\theta$ remains constant with changing $n$, confirming that it reflects the
geometry of the magnetic nanowire. Hence, we demonstrate geometric control
over the spin polarisation injected into a graphene spin transistor.

We investigate the consistency of oblique spin injection across several
devices of varying heterostructure thickness, all with a 60 nm thick Co layer
in the nanowires. The right column of Figure 4 shows spin valve signals
measured from devices B, C, and D, with heterostructure thicknesses $t\approx
52.0$ nm, $t\approx 27.5$ nm, and $t\approx 14.8$ nm, respectively. In all
cases, the magnitude of charge carrier density is comparable to that of the
measurement on device A. Starting with the thickest of these stacks, device B
(Figure 4c), a Hanle-like background is observable in the spin valve signal,
with a magnitude $R_{s-\perp}\propto P_{\perp}$ (Equation 1). Likewise, the
magnitude of the switches is $2R_{s-||}\propto P_{||}$ (Figure 4c). Hence, the
ratio between these magnitudes can be used to approximate the inclination
angle of the nanowire, which, for device B is found to be $\theta\approx 28\pm
5\degree$. Moving to the middle case, device C, the spin valve background
shows a subtle line-shape, implying this thickness is a boundary for achieving
detectable out-of-plane spin polarisation. The angle extracted here is
$\theta\approx 20\pm 3\degree$. Finally, for the thinnest case, device D, the
spin valve background is mostly flat. Here, the only measurable feature is a
faint hysteresis loop around $B\sim-30$ mT, consistent with prior observation
of Hall signal close to 1D magnetic contacts [16]. As such, the angle of the
nanowire cannot be evaluated for this device, implying that any out-of-plane
component in the magnetisation of the nanowire is below the resolution of the
measurement. It is expected that using this approximate method should be less
accurate for evaluating the nanowire geometry than the full Hanle analysis
laid out above. Nevertheless, the angles follow the expected trend with
decreasing thickness. Hence, the role of heterostructure thickness, relative
to the Co layer thickness, is crucial in achieving a geometrically defined
out-of-plane component in the nanowire magnetisation and, in turn, the spin
polarisation.

##  V  Conclusions

In conclusion, we exploit spin transport in an encapsulated graphene spin
valve device to characterise the magnetisation vector of a magnetic nanowire
acting as a 1D edge contact. This relatively simple approach provides an
alternative method of spin vector magnetometry that relies only on pure spin
signal, enabling a quantitative analysis of a nanoscale magnetic region.
Importantly, we demonstrate that the geometry of Van der Waals
heterostructures can be engineered to define the angle of spin injection into
2D materials. The use of geometry to control the generation of out-of-plane
spin is comparatively simpler than alternative methods based on unconventional
spin-orbit effects [22, 24] and is generally applicable to any magnetic
material without the need of magnetocrystalline anisotropy [23]. Such
structures can potentially be applied for the study of spin anisotropy in low-
dimensional materials [32] via the use of a geometrically defined oblique spin
accumulation.

###### Acknowledgements.

UK participants in Horizon Europe Project “2D Heterostructure Non-volatile
Spin Memory Technology” (2DSPIN-TECH) are supported by UKRI grant number
[10101734] (The University of Manchester). We wish to acknowledge the support
of Noel Natera-Cordero and Christopher R. Anderson for providing helpful
insights towards the fabrication and characterisation of devices. D.B.
acknowledges the Engineering and Physical Sciences Research Council (EPSRC),
Doctoral Training Partnership (DTP) for funding the PhD project (U.K).
J.C.T.F. acknowledges support from the Consejo Nacional de Ciencia y
Tecnología (México). V.H.G.M. acknowledges support from the Secretaría
Nacional de Educación Superior, Ciencia y Tecnología (SENESCYT), for the Ph.D.
scholarship under the program “Universidades de Excelencia 2014” (Ecuador).
Research data are available from the authors upon request.

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