# Investigation of nonreciprocal spin-wave dynamics in Pt/Co/W/Co/Pt
multilayers

Krzysztof Szulc<EMAIL_ADDRESS>Faculty of Physics, Adam
Mickiewicz University, Poznań, Uniwersytetu Poznańskiego 2, 61-614 Poznań,
Poland  Simon Mendisch  Department of Electrical and Computer Engineering,
Technical University of Munich (TUM), Arcisstr. 21, 80333 Munich, Germany
Michał Mruczkiewicz  Institute of Electrical Engineering, Slovak Academy of
Sciences, 841 04 Bratislava, Slovakia  Centre for Advanced Materials
Application (CEMEA), Slovak Academy of Sciences, Dúbravská cesta 5807/9, 845
11 Bratislava, Slovakia  Francesca Casoli  Istituto dei Materiali per
l’Elettronica ed il Magnetismo (IMEM-CNR), I-43124 Parma, Italy  Markus
Becherer  Department of Electrical and Computer Engineering, Technical
University of Munich (TUM), Arcisstr. 21, 80333 Munich, Germany  Gianluca
Gubbiotti  Istituto Officina dei Materiali del CNR (CNR-IOM), Sede Secondaria
di Perugia, c/o Dipartimento di Fisica e Geologia, Università di Perugia,
I-06123 Perugia, Italy

###### Abstract

We present a detailed study of the spin-wave dynamics in single Pt/Co/W and
double Pt/Co/W/Co/Pt ferromagnetic layer systems. The dispersion of spin waves
was measured by wavevector-resolved Brillouin light scattering spectroscopy
while the in-plane and out-of-plane magnetization curves were measured by
alternating gradient field magnetometry. The interfacial Dzyaloshinskii-Moriya
interaction induced nonreciprocal dispersion relation was demonstrated for
both single and double ferromagnetic layers and explicated by numerical
simulations and theoretical formulas. The results indicate the crucial role of
the order of layers deposition on the magnetic parameters. A significant
difference between the perpendicular magnetic anisotropy constant in double
ferromagnetic layer systems conduces to the decline of the interlayer
interactions and different dispersion relations for the spin-wave modes. Our
study provides a significant contribution to the realization of the
multifunctional nonreciprocal magnonic devices based on ultrathin
ferromagnetic/heavy-metal layer systems.

##  I Introduction

High demand for improvement in the storage and computing devices and decrease
of their power consumption leads to continued interest in spintronic
phenomena. Recently, the interfacial Dzyaloshinskii–Moriya interaction (iDMI)
[1] brought the attention of the researchers as it permits to stabilize
topological magnetic solitons, e.g., skyrmions and radial vortices [2]. The
iDMI is an asymmetric exchange interaction and can be induced in ultrathin
multilayer systems where the inversion symmetry is broken between both
interfaces of the ferromagnetic layer. It is induced by large spin-orbit
coupling between a ferromagnet and heavy-metal atoms at one of the interfaces
of an ultrathin ferromagnet. The energy contribution of iDMI is minimized when
spins are aligned perpendicularly in specific direction, described by the
equation
$E_{\rm{DMI}}=-\sum_{i,j}\mathbf{D}_{ij}\cdot(\mathbf{S}_{i}\times\mathbf{S}_{j})$,
where $\mathbf{D}_{ij}$ is the Dzyaloshinskii–Moriya vector. Therefore, the
orientation of the $\mathbf{D}_{ij}$ determines whether right-handed or left-
handed rotation sense between neighboring spins is the configuration of lower
energy. Even if the iDMI favors noncollinear alignment of spins when it is
strong, the single-domain state can be achieved at high magnetic fields. Then,
the chiral property of the iDMI is exhibited in nonreciprocal spin-wave
dynamics [3, 4, 5, 6] and can be used to tailor the magnon dispersion
relation, and thus used to extend the functionality of the magnonic devices
[7].

The iDMI value is one of the highest in Pt/Co systems, which are also
characterized by strong perpendicular magnetic anisotropy (PMA). Thus, many of
the iDMI systems are basing on Pt/Co ultrathin films with broken inversion
symmetry, e.g., Pt/Co/AlOx [8, 9], Pt/Co/MgO [10] Pt/Co/Ta [11],
Pt/Co/(W,Ta,Pd) [12], Pt/Co-Ni/Ta [13], Ir/Fe/Co/Pt [14], Pt/Co/Cu/AlOx [15],
Pt/Co/Os/Pt [16], Pt/Cu/Co/Pt [17]. In Ref. [18] the implications of
asymmetric multilayers [Pt/Co/Ir]5 with broken inversion symmetry on domain
wall chirality, skyrmion stability, and its dynamics were reported.
Interestingly, weak iDMI was also present in symmetric Pt/Co/Pt multilayers
[19] due to different quality of the Co interfaces. The influence of the
surface quality can also have a significant impact on the anisotropy of the
sample [20].

Most of the studies, also cited above, considered structures with sandwich
multilayers, where the unit Pt/Co/X was repeated $n$ times, and magnetic
parameters of Co layers had negligible differences. Nevertheless, the stack of
layers with deliberately different magnetic properties of magnetic materials
across the thickness might also have interesting properties especially related
to the magnetization and spin-wave dynamics, useful for applications in
spintronics and magnonics as indicated by recent studies. For example, in the
antiferromagnetic-exchange-coupled symmetric bilayer CoFeB/Ru/CoFeB, the
measured Ru thickness-dependent nonreciprocity was related to the difference
between perpendicular interface anisotropy of the bottom and top CoFeB layer
[21]. Thus, in this paper, we will investigate the spin-wave properties in
systems composed of two ferromagnetic layers, i.e., double ferromagnetic layer
(DFL) systems.

DFL systems with opposite sign of iDMI in the limit of noninteracting layers
shall exhibit two nonreciprocal dispersion-relation branches, that are mirror
images at wavevector $k=0$. Therefore, having a dispersion resembling the
electronic Rashba splitting is expected [22, 23, 24]. Additionally, the
coupling strength between the layers can be tuned by Ruderman-Kittel-Kasuya-
Yosida (RKKY) interaction or dipolar interaction [25, 26]. Also, interlayer
DMI interaction in the DFL system, competing with RKKY interaction, was
recently shown [27]. These works point out that magnonic dispersion can be
tailored in many ways in the DFLs and multilayers with varied iDMI, magnetic
properties of the sublayers, and the coupling strength between them.

The strength of iDMI can be quantified by several methods, such as domain-wall
velocity [28, 29], asymmetric hysteresis loop method [30] and magnetic force
microscopy [31]. A detailed review of the different techniques used to measure
iDMI in ultrathin films has been recently published by Kuepferling  _et al._
[32]. Among them, Brillouin light scattering (BLS) spectroscopy has
demonstrated to be a powerful and reliable technique since it combines the
high sensitivity to detect signals from spin waves in magnetic monolayers [33,
34, 35, 36, 37, 38], and the possibility to explore a wide range of
wavevectors
($0-$100\text{\,}\mathrm{rad}\mathrm{/}\mathrm{\SIUnitSymbolMicro}\mathrm{m}$$)
and frequencies ($1-500$ GHz). The estimation of iDMI constant from
experimental measurements was studied also for complex multilayers [39].

In this work, we study Pt/Co/W/Co/Pt DFL systems and, as the reference
samples, the Pt/Co/W single ferromagnetic layer (SFL) systems. Hysteresis
loops were measured using the alternating gradient force magnetometer (AGFM).
BLS is used to measure the dispersion relation of spin waves and to extract
the iDMI constant by measuring the frequency asymmetry ($\Delta f$) between
the spin waves propagating in opposite directions. The numerical simulation in
the time and frequency domain provides an interpretation of the experimental
results and allows us to extract effective magnetization and anisotropy
constant of the Co layers. In particular, we found that in DFL samples, the Co
layers have an opposite sign of iDMI due to the inversion of interfaces and
significantly different anisotropies due to a different order of the layers
deposition. With these properties, we aim to demonstrate systems with two,
almost independent spin-wave dispersion relations possessing nonreciprocal
properties.

##  II Experimental methods

The characterized thin films were deposited at room temperature via confocal
rf-magnetron sputtering (base pressure
$<$2\text{\times}{10}^{-7}\text{\,}\mathrm{mbar}$$) onto $n^{-}$ doped silicon
$(100)$ substrates with an in-house grown thermal oxide (thickness
$\approx$20\text{\,}\mathrm{nm}$$). Before the deposition, residual water was
removed from the samples using a $300\text{\,}\mathrm{eV}$ Ar+ ion beam. All
materials were deposited at a constant argon pressure
$4\text{\,}\mathrm{\SIUnitSymbolMicro bar}$
($\approx$3\text{\,}\,\mathrm{m}\mathrm{T}\mathrm{o}\mathrm{r}\mathrm{r}$$)
except for the Ta adhesive, which was deposited at
$2\text{\,}\mathrm{\SIUnitSymbolMicro bar}$
($\approx$1.5\text{\,}\,\mathrm{m}\mathrm{T}\mathrm{o}\mathrm{r}\mathrm{r}$$).
The rf-power applied to the 2-inch targets was identical for all materials
($40\text{\,}\mathrm{W}$). To reduce contaminants the dead times between
elements during the automated deposition were generally kept below
$1\text{\,}\mathrm{s}$. All multilayer stacks feature a standard adhesive
($1.5\text{\,}\mathrm{nm}$ Ta), seed ($6\text{\,}\mathrm{nm}$ Pt), and capping
($3\text{\,}\mathrm{nm}$ Pt) layer. The stacks are, therefore, solely
addressed by their magnetic layer compositions with thicknesses given in
nanometers (e.g., Co(1.6)/W(0.95)/Co(1.95)). Single ferromagnetic Co layers
having a thickness of 1.6 and $1.95\text{\,}\mathrm{nm}$ have also been grown
on Pt films and used as reference samples. The set of four fabricated samples
is listed in Table 1.

Hysteresis loops were measured by the AGFM, applying a magnetic field up to 15
kOe in the directions parallel and perpendicular to the film plane.

Figure 1: Schematic drawing of the BLS scattering geometry in the Damon-
Eshbach configuration. The incident light makes an angle $\theta$ with respect
to the sample normal. Measurements are performed in the backscattering
configuration, where the same camera objective is used to focus laser light
upon the sample surface and to collect scattered light sent to the
interferometer for the frequency analysis. A magnetic field $H$ is applied in
the sample plane and perpendicular to the incidence plane of light.

BLS spectra were recorded at room temperature in the backscattering
configuration using a (3+3)-tandem Sandercock-type interferometer [40]. About
200-mW p-polarized monochromatic light from a solid-state laser
$\lambda=$532\text{\,}\mathrm{nm}$$ was focused onto the sample surface. An
in-plane magnetic field $H$ was applied parallel to the sample surface and
perpendicular to the plane of incidence of light in the so-called Damon-
Eshbach configuration. A schematic representation of the scattering geometry
is represented in Fig. 1. Due to in-plane momentum conservation, the
wavevector $k$ of spin waves entering into the scattering process is given by
$k=(4\pi/\lambda)\sin\theta$. Spin waves traveling in the $-x$ and $+x$
directions appear as peaks in the Stokes and anti-Stokes side of the spectra,
respectively. BLS measurements were performed in two different configurations:
1) by changing the magnitude of the external magnetic field applied in the
sample plane at normal incidence of light upon the sample surface
($\theta=$0\text{\,}\mathrm{\SIUnitSymbolDegree}$$), i.e. $k=0$; 2) by
sweeping the wavevector $k$ in the range from 0 to
$20\text{\,}\mathrm{rad}\mathrm{/}\mathrm{\SIUnitSymbolMicro}\mathrm{m}$ at
fixed applied field $H=\pm 5.5$ kOe [41]. Reversing the direction of the
external magnetic field from $+5.5$ to $-5.5$ kOe is equivalent to reverse the
direction of the propagating spin waves. The frequency asymmetry induced by
iDMI is proportional to the sine function of the in-plane angle $\phi$ between
the applied field and the wavevector direction [5]. In the Damon-Eshbach
configuration ($\phi=$90\text{\,}\mathrm{\SIUnitSymbolDegree}$$), $\Delta f$
is maximum.

##  III Theoretical and numerical methods

Spin-wave dynamics are calculated numerically using the finite-element method
in COMSOL Multiphysics [42]. Motion of the spin is described by the Landau-
Lifshitz equation:

$\frac{\partial\textbf{M}}{\partial
t}=-\gamma\mu_{0}\textbf{M}\times\textbf{H}_{\text{eff}},$ (1)

where $\textbf{M}=(m_{x},m_{y},m_{z})$ is the magnetization vector, $\gamma$
is the gyromagnetic ratio, $\mu_{0}$ is the magnetic permeability of vacuum,
and $H_{\text{eff}}$ is the effective magnetic field, which is given as
follows:

$\begin{split}\textbf{H}_{\text{eff}}=H\mathbf{\hat{z}}+\frac{2A_{\text{ex}}}{\mu_{0}M_{\text{S}}^{2}}\nabla^{2}\textbf{M}+\frac{2D}{\mu_{0}M_{\text{S}}^{2}}\,\mathbf{\hat{z}}\times\frac{\partial\textbf{M}}{\partial
x}+\\\
+\frac{2K_{u}}{\mu_{0}M_{\text{S}}^{2}}m_{y}\mathbf{\hat{y}}-\nabla\varphi,\end{split}$
(2)

where $H$ is the external magnetic field, $M_{\text{S}}$ is the saturation
magnetization, $A_{\text{ex}}$ is the exchange stiffness constant, $D$ is the
iDMI constant, $K_{u}$ is the PMA constant, and $\varphi$ is the magnetic
scalar potential fulfilling Poisson-like equation

$\nabla^{2}\varphi=\nabla\cdot\textbf{M}.$ (3)

In the DFL structures, the RKKY interaction is applied as the boundary
conditions on the inner interfaces of the ferromagnetic layers [43] along with
the boundary condition for the exchange interaction

$\begin{split}0=2A_{\text{ex}}\mathbf{\hat{z}}\times\frac{\partial\mathbf{M}_{1(2)}(y)}{\partial
y}\bigg{|}_{y=y_{1(2)}^{\text{in}}}-\\\
-J\mathbf{\hat{z}}\times(\mathbf{M}_{2(1)}-\mathbf{M}_{1(2)}(y_{1(2)}^{\text{in}})),\end{split}$
(4)

where $J$ is the RKKY constant and subscripts numerate bottom and top layers
in DFL samples. The boundary condition on the outer interfaces consist only of
the exchange interaction term

$0=2A_{\text{ex}}\mathbf{\hat{z}}\times\frac{\partial\mathbf{M}_{1(2)}(y)}{\partial
y}\bigg{|}_{y=y_{1(2)}^{\text{out}}}$ (5)

Eqs. (1) and (3) are solved in the linear approximation, i.e., assuming
$m_{x},m_{y}\ll m_{z}\approx M_{S}$. Time-domain simulations were used to
simulate the hysteresis loops of the DFL system. Frequency-domain simulations
were carried out to calculate the spin-wave dispersion relation of the DFL
system. Triangular mesh with a maximum element size of 1 nm inside the
ferromagnetic layers and a growth rate of 1.15 outside of the ferromagnetic
layers was used.

In the SFL system, the spin-wave dispersion relation was fitted using the
analytical formula [44, 45]

$f=\frac{\gamma\mu_{0}}{2\pi}\left(\sqrt{\left(H+M_{\text{S}}\frac{d|k|}{2}+\frac{2A_{\text{{ex}}}}{\mu_{0}M_{\text{S}}}k^{2}\right)\left(H+M_{\text{S}}\left(1-\frac{d|k|}{2}\right)+\frac{2A_{\text{ex}}}{\mu_{0}M_{\text{S}}}k^{2}-\frac{2K_{u}}{\mu_{0}M_{\text{S}}}\right)}+\frac{2D}{\mu_{0}M_{\text{S}}}k\right).$
(6)

The frequency difference between the Stokes and anti-Stokes peaks $\Delta f$
can be derived from Eq. (6) as

$\Delta f=f_{+k}-f_{-k}=\frac{\gamma}{2\pi}\frac{4D}{M_{\text{S}}}k.$ (7)

The field dependence of the frequency was measured at normal-incidence angle
$\theta=$0\text{\,}\mathrm{\SIUnitSymbolDegree}$$, therefore, Eq. (6)
simplifies to the following formula

$f=\frac{\gamma\mu_{0}}{2\pi}\sqrt{H\left(H+M_{\text{S}}-\frac{2K_{\text{u}}}{\mu_{0}M_{\text{S}}}\right)}.$
(8)

Basing on Eq. (8), the effective magnetization $M_{\text{eff}}$ can be defined
as

$M_{\text{eff}}=M_{\text{S}}-\frac{2K_{\text{u}}}{\mu_{0}M_{\text{S}}}.$ (9)

$M_{\text{S}}$ values are extracted from the out-of-plane magnetization curves
obtained by Mendisch  _et al._ [46]. For Co(1.6) is
$M_{\text{S}}=$1050\text{\,}\mathrm{k}\mathrm{A}\mathrm{/}\mathrm{m}$$ while
for Co(1.95) is
$M_{\text{S}}=$1100\text{\,}\mathrm{k}\mathrm{A}\mathrm{/}\mathrm{m}$$.

##  IV Results

###  IV.1 AGFM hysteresis loops

Table 1: Magnetic parameters of the SFL and DFL samples. Abbrev. | Sample |  $M_{\text{S}}$ (kA/m) [46] |  $M_{\text{eff}}$ (kA/m) |  $K_{\text{u}}$ (kJ/m3) |  $D$ (mJ/m2)
---|---|---|---|---|---
SFL1 | Co(1.95)/W(0.95) | 1100 | 28 | 741 | 0.74
SFL2 | Co(1.6)/W(0.95) | 1050 | -235 | 848 | 0.84
DFL1 | Co(1.6)/W(0.95)/Co(1.95) | 1100 | 774 | 225 | -0.64
1050 | -194 | 821 | 0.72
DFL2 | Co(1.6)/W(0.95)/Co(1.6) | 1050 | 626 | 280 | -0.49
1050 | -246 | 855 | 0.84
Figure 2: AGFM hysteresis loops measured in the in-plane configuration and
out-of-plane configuration. The purple dashed lines represent the fitting
using the numerical simulations. In the inset plots, the zoom to low external
fields is shown. On top of the figure, the schematic representation of the
samples is shown.

The AGFM hysteresis loops measured in the film plane (green curves) and
perpendicular to the plane (blue curves) are shown in Fig. 2. The results were
used to determine $M_{\text{eff}}$ values of the layers in all of the samples.
Hard-axis hysteresis loops were fitted with the numerical simulations. The
saturation field values obtained from the simulations should be consistent
with the $M_{\text{eff}}$ values. The beginning of the magnetization reversal
process is sharp, so the extracted $M_{\text{eff}}$ values are considered to
be well defined. At this point, the effect of the RKKY interaction between the
layers is neglected. Its effect is explained in Section IV.3. Using the
predefined $M_{\text{S}}$ from Ref. [46], we also determined the PMA constant
$K_{\text{u}}$ using Eq. (9). They are collected in Table 1.

In the Co(1.95)/W(0.95) (SFL1) sample [Fig. 2(a)], the parallel loop has a
square shape while the perpendicular loop has the typical S-shape behavior
characterized by an almost linear dependence on the applied field, indicating
an in-plane easy axis. The magnetic saturation in the perpendicular direction
is reached in a field much lower than $\mu_{0}M_{S}$, thus indicating that a
strong PMA is present in this sample, which competes with the shape
anisotropy. $K_{u}$ is slightly lower than the value required to get a change
from an in-plane to an out-of-plane easy magnetization axis, which is 760
kJ/m3, and the sample remains in the in-plane configuration in the remanence.
In-plane and perpendicular coercivity values are low, but both loops close at
higher field values, i.e., around 0.2–0.3 kOe.

The Co(1.6)/W(0.95) (SFL2) sample [Fig. 2(b)] shows a clear PMA contribution,
which dominates over the magnetostatic in-plane contribution, giving rise to
an easy magnetization direction perpendicular to the film plane. The
hysteresis loop measured with the field applied in the film plane shows a
transcritical shape with a saturation field around 3 kOe, low coercivity, but
an open loop up to a higher field (approximately 1.2 kOe). The latter feature
might depend on a secondary phase with a tilted easy magnetization axis. The
hysteresis loop measured in the perpendicular direction shows a square shape
with a larger coercive field compared to the in-plane direction.

---
Figure 3: (a-d) The sequence of BLS spectra measured at $k=0$
($\theta=$0\text{\,}\mathrm{\SIUnitSymbolDegree}$$) and different magnitudes
of the externally applied field for all the investigated samples. (e-h) The
spin-wave frequency measured by BLS in the function of the external field $H$
and fitting with the theoretical formula in Eq. (8).

In the DFL samples [Figs. 2(c,d)], the PMA contribution is evident. The
hysteresis loops along the in-plane and perpendicular directions clearly show
the contribution of two magnetic components: one with an easy magnetization
axis in the film plane and the other with an easy magnetization axis
perpendicular to the film plane. In the Co(1.6)/W(0.95)/Co(1.95) (DFL1) sample
[Fig. 2(c)], the in-plane easy-axis part appears to have a larger magnetic
moment, indicating that it is associated with the Co(1.95) layer, while the
out-of-plane easy-axis is present in the Co(1.6) layer. In the
Co(1.6)/W(0.95)/Co(1.6) (DFL2) sample [Fig. 2(d)], the in-plane and out-of-
plane parts carry the same magnetic moment because of the same thicknesses of
the ferromagnetic layers. Also, comparing the magnetic parameters in the DFL
and SFL samples, we can ascribe a larger $K_{u}$ value to the bottom Co layer
and smaller $K_{u}$ to the top Co layer. We associate this effect with the
order of the layers deposition. Even though the Co layer has the same vicinity
(Pt and W), the effect on the magnetic parameters is different if the material
plays the role of the seed or capping layer [47] as well as depends on the
growth conditions [48]. Moreover, in both DFL samples, the coercive field
values are larger in the perpendicular direction.

###  IV.2 Field-dependent BLS measurements

Figs. 3(a-d) present the sequences of measured BLS spectra and Figs. 3(e-h)
present the frequency values plotted as a function of $H$ at $k=0$ for all of
the investigated samples. BLS spectra were measured starting from $H=8$ kOe
and decreasing it down to zero, i.e., along the descending branches of the in-
plane loops in Fig. 2. For SFL samples, only one peak is observed. For the
SFL1 sample, it has a monotonic dependence on $H$, while for the SFL2 sample,
it first decreases, reaching a minimum at 2.4 kOe, and then increases again.
For DFL samples, two peaks are visible on both the Stokes and anti-Stokes
sides of the spectra. Here, the field dependence is more complicated since the
frequency of high-frequency mode monotonously decreases with decreasing $H$
while the low-frequency peak first decreases, reaches a minimum, and then
increases again. Since the spectra are measured at $k=0$, the frequency
position of the peaks are symmetric ($f_{\text{S}}=f_{\text{AS}}$) on both the
Stokes and anti-Stokes sides of the spectra.. Basing on PMA constants derived
from the AGFM hysteresis loops, we used Eq. (8) to determine the gyromagnetic
ratio $\gamma$ of the analyzed samples. We reached satisfying fitting for
$\gamma=$192\text{\,}\mathrm{rad}\mathrm{/}\mathrm{(}\mathrm{T}\cdot\mathrm{s}\mathrm{)}$$,
as shown in Figs. 3(e-h) with solid lines. These results, together with the
values of the saturation fields derived from the AGFM measured loops, permit
to unambiguously affirm that above 4 kOe, the magnetization is saturated and
aligned parallel to the sample plane. Therefore, we performed the wavevector-
dependent measurements for an externally applied field of $\pm 5.5$ kOe.

###  IV.3 Role of RKKY interaction in DFL samples

The numerical simulations were used to check the presence of the RKKY
interaction in the DFL samples. First, $K_{\text{u},1}$ and $K_{\text{u},2}$
were fitted to the hysteresis loops from Fig. 2 in the function of the RKKY
constant $J$. The results show that the difference between $K_{\text{u},1}$
and $K_{\text{u},2}$ increases with the RKKY constant. However, the hysteresis
loop does not change its character. The shape is identical to the shape of the
loop of the noninteracting layers. The possible cause is the large difference
between $M_{\text{eff}}$. In the next step, the RKKY constant (along with
related to it $K_{\text{u},1}$ and $K_{\text{u},2}$) was fitted to the field
dependence of the frequency results obtained from the BLS measurements shown
in Figs. 3(e-h). The gyromagnetic ratio $\gamma$ was used to fit the low-
frequency mode, and the RKKY constant was fitted to the high-frequency mode.
The value of the RKKY constant for DFL1 equals
$-100\text{\,}\mathrm{\SIUnitSymbolMicro}\mathrm{J}\mathrm{/}\mathrm{m}^{2}$
for
$\gamma=$195\text{\,}\mathrm{rad}\mathrm{/}\mathrm{(}\mathrm{T}\cdot\mathrm{s}\mathrm{)}$$
and for DFL2 equals
$20\text{\,}\mathrm{\SIUnitSymbolMicro}\mathrm{J}\mathrm{/}\mathrm{m}^{2}$ for
$\gamma=$190\text{\,}\mathrm{rad}\mathrm{/}\mathrm{(}\mathrm{T}\cdot\mathrm{s}\mathrm{)}$$.
However, the best fit assuming the absence of the RKKY is as far as 1 GHz from
the satisfactory fit. It lies within the error range, which considers the
reading of $M_{\rm{eff}}$ from the hysteresis loops and instrument errors. In
general, the frequency shift is small even for a large value of the RKKY
constant (exceeding
$\pm$100\text{\,}\mathrm{\SIUnitSymbolMicro}\mathrm{J}\mathrm{/}\mathrm{m}^{2}$$).
Moreover, the shape of the hysteresis loops and the field dependence of the
frequency with RKKY are identical to the case of the noninteracting layers.
Therefore, the presence of the RKKY interaction can not be confirmed when the
difference between $M_{\text{eff}}$ of the layers in the bilayered structure
is too large, and thus the RKKY interaction in DFL samples is assumed to be
negligible.

###  IV.4 Wavevector-dependent BLS measurements

---
Figure 4: (a-d) Measured BLS spectra at
$k=$18.1\text{\,}\mathrm{rad}\mathrm{/}\mathrm{\SIUnitSymbolMicro}\mathrm{m}$$
($\theta=$50\text{\,}\mathrm{\SIUnitSymbolDegree}$$) and for two different
orientation of the external field: $H=+5.5$ and $-5.5$ kOe. Black points
represent the measured spectra, while red curves are the Lorentzian fitting of
the peaks. (e-h) Dispersion relations measured by the BLS spectroscopy in the
external field of $\pm 5.5$ kOe and fitted using finite-element method
simulations. (i-l) Frequency asymmetry plots measured by the BLS spectroscopy
with the linear regression fitting basing on Eq. (7).

In order to derive the iDMI constant, we measured the BLS spectra for
different wavevector values in the range from 0 to
$20\text{\,}\mathrm{rad}\mathrm{/}\mathrm{\SIUnitSymbolMicro}\mathrm{m}$ for
$H$ fixed at $+5.5$ and $-5.5$ kOe. Typical BLS spectra measured at these
fields for
$k=$18.1\text{\,}\mathrm{rad}\mathrm{/}\mathrm{\SIUnitSymbolMicro}\mathrm{m}$$
are shown in Fig. 4(a-d) for all the investigated samples. Because of the
small sample thickness, both the Stokes and anti-Stokes peaks, corresponding
to spin waves propagating in opposite directions, are simultaneously observed
with slightly different intensity. Frequencies of the spin-wave modes were
extracted by fitting the peaks in the BLS spectra (displayed in Figs. 4(a-d)
by the red curves) with Lorentzian functions and were plotted as a function of
their respective wavevectors $k$ in Figs. 4(e-h). It is noteworthy that on
reversing the direction of the applied magnetic field, the respective center
frequencies and intensities of the Stokes and anti-Stokes peaks interchanges
due to the fact that reversing the magnetization is equivalent to a reversal
operation. For that reason, the following discussion will pertain to the
results in positive external magnetic field. The dispersions were calculated
by the finite-element method simulations in COMSOL Multiphysics. We set the
exchange stiffness
$A_{\text{ex}}=$15\text{\,}\mathrm{p}\mathrm{J}\mathrm{/}\mathrm{m}$$. The
values of $M_{\text{S}}$ and $K_{u}$ used in simulations are written in Table
1. The iDMI constant $D$ was the free parameter in the fitting procedure for
each sample separately.

In the SFL samples [Figs. 4(e,f)], the frequency dependence is close to linear
and has a positive slope. A more detailed analysis of Eq. (6) allows
explaining the character of the dispersion relation. First, the effect of the
dipolar interaction is significantly weakened by the PMA as
$M_{\text{S}}\approx 2K_{u}/\mu_{0}M_{\text{S}}$ and so $M_{\text{eff}}\approx
0$. In fact, when $M_{\text{eff}}<0$, the surface wave propagates backward,
and the dispersion relation has a negative slope even with the absence of
iDMI, until the effect of the exchange interaction starts to dominate. The
small thickness of the layer leads to the additional flattening of the
dispersion. In the BLS range of the wavevector, the effect of the exchange
interaction is small, and so the dispersion relation is close to linear. The
slope of the dispersion is directly connected to the iDMI.

The dispersion relation of the DFL samples [Figs. 4(g,h)] shows two branches
of a different character. Comparing the dispersion relations with the systems
of noninteracting layers, the frequency is changing by less than 100 MHz,
indicating very weak dipolar coupling between the layers. The weakening of the
dipolar coupling is caused by the large difference between the PMA of the
layers. Interestingly, it allows us to use the approximation of the
noninteracting layers, even for separations as small as 1 nm. The low-
frequency mode is close to linear with the positive slope. Its character is
identical to the single-layer dispersion confirming the connection with the
bottom layer. The high-frequency mode is flat on the positive wavevectors’
side and has a negative slope on the negative wavevectors’ side. The
flattening is the result of the compensation of dynamic dipolar interaction by
the iDMI.

Figs. 4(i-l) shows the frequency difference $\Delta f$ between the Stokes and
the anti-Stokes peaks measured as a function of the wavevector $k$. The values
for positive wavevectors represents the measurements in the positive external
field and negative wavevectors – in the negative external field. The frequency
asymmetry exhibits a linear dependence as a function of $k$, agreeing with the
theoretical prediction of Eq. (7). The frequency difference plots were fitted
using the linear regression method based on Eq. (7), and the values of iDMI
constant $D$ are collected in Table 1. The values are in agreement with values
presented in the literature for the similar thickness of Co layer [9], where
the iDMI constant is about
$1\text{\,}\mathrm{m}\mathrm{J}\mathrm{/}\mathrm{m}^{2}$ for
$1.6\text{\,}\mathrm{nm}$ Co thickness and lower for larger thicknesses of Co.

In the DFL samples [Figs. 4(k,l)], the frequency asymmetry always has a linear
dependence on $k$, but for the two modes, it has an opposite sign since the Co
layers have Pt as a bottom or top layer. However, the iDMI constants in the
layers differ. This effect can come from the different thicknesses of the Pt
layers, as well as, in the DFL1 sample [Fig. 4(k)], from the different
thicknesses of the Co layers. The sputtering order of the layers can also
affect the iDMI constant absolute value, as it is observed for the PMA
constant.

##  V Conclusions

We have studied the iDMI and spin-wave dynamics in Pt/Co/W/Co/Pt DFL
structures with the opposite arrangement of Co and Pt layers and Pt/Co/W SFL
samples. AGFM hysteresis loops show a strong PMA contribution, leading to a
resultant out-of-plane easy magnetization axis in Co(1.6) layer and in-plane
easy magnetization axis in Co(1.95) layer with small effective magnetization.
Hysteresis loops of DFL samples indicate both in-plane and out-of-plane
anisotropy contributions, also pointing at a significant difference between
the PMA constants of the Co layers. Field-dependent measurements of the BLS
spectra at normal incidence confirm the presence of strong PMA in the Co
layers. Numerical simulations were made to check the presence of the RKKY
interaction through the W spacer. We find that AGFM and BLS results can be
fitted without this interaction taken into account, which does not confirm the
presence of the RKKY interaction in the DFL samples.

Wavevector-dependent BLS measurements were made in a large external field of
$\pm 5.5$ kOe to reach the in-plane configuration of magnetization. The
results show the iDMI-dominated linear dispersion in SFL samples and two-mode
dispersion in DFL samples related to the two Co layers in the studied system.
The strong asymmetry between the Stokes and anti-Stokes peaks is present. In
the DFL samples, the slope of the two branches and thus the signs of the iDMI
constant are opposite due to the opposite arrangement of Co and Pt layers. The
iDMI constant values vary between 0.49 and
$0.84\text{\,}\mathrm{m}\mathrm{J}\mathrm{/}\mathrm{m}^{2}$, being in line
with the values known from the literature.

In DFL samples, the linear low-frequency mode is dominated by iDMI and
resembles the dispersions measured in SFLs. The asymmetric high-frequency mode
consists of a flat branch for positive wavevectors and a strongly dispersive
branch for the negative wavevectors at the selected orientation of the
external magnetic field. A comparison with the system of noninteracting layers
points out a significant weakening of the interlayer coupling via the dynamic
dipolar field. This uncoupling of spin waves between the Co layers separated
by only 0.95-nm-thick nonmagnetic spacer arises from the significantly
different frequencies of oscillations in both layers, with the difference
equaling 15.5 GHz at $k=0$ for both DFL1 and DFL2 samples. Such a significant
difference in frequencies in nominally very similar Co films is attributed to
the different PMAs originating in different deposition sequences for the
bottom and top Co layers.

To sum up, we design the system based on ultrathin layers composed of the same
set of materials, operating at two frequency ranges, both possessing
nonreciprocal spin-wave dispersion relations but with different
characteristics, indicating interesting properties for magnonics, especially
for the design of the multifunctional spin-wave devices.

## Acknowledgements

The authors thank Maciej Krawczyk for a fruitful discussion. K.S. acknowledges
the financial support from the National Science Center of Poland, project no.
UMO-2018/30/Q/ST3/00416. S.M. and M.B. acknowledge the financial support by
the German Research Foundation (DFG), priority program SPP2137 project no.
403505866, as well as the TUM International Graduate School of Science and
Engineering (IGSSE), project no. GSC 81-24184165. M.M. acknowledges funding
from the Slovak Grant Agency APVV, no. APVV-16-0068 (NanoSky) and APVV-19-0311
(RSWFA). This study was performed in the frame of the implementation of the
project Building-up Centre for Advanced Materials Application of the Slovak
Academy of Sciences, ITMS project code 313021T081 supported by Research &
Innovation Operational Programme funded by the ERDF. G.G. acknowledges the
financial support by the European Metrology Programme for Innovation and
Research (EMPIR) under the Grant Agreement 17FUN08 TOPS.

## References

  * Moriya [1960] T. Moriya, Anisotropic superexchange interaction and weak ferromagnetism, Phys. Rev. 120, 91 (1960).
  * Finocchio  _et al._ [2016] G. Finocchio, F. Büttner, R. Tomasello, M. Carpentieri, and M. Kläui, Magnetic skyrmions: from fundamental to applications, J. Phys. D: Appl. Phys. 49, 423001 (2016).
  * dos Santos  _et al._ [2020a] F. J. dos Santos, M. dos Santos Dias, and S. Lounis, Nonreciprocity of spin waves in noncollinear magnets due to the Dzyaloshinskii-Moriya interaction, Phys. Rev. B 102, 104401 (2020a).
  * Udvardi and Szunyogh [2009] L. Udvardi and L. Szunyogh, Chiral asymmetry of the spin-wave spectra in ultrathin magnetic films, Phys. Rev. Lett. 102, 207204 (2009).
  * Cortés-Ortuño and Landeros [2013] D. Cortés-Ortuño and P. Landeros, Influence of the Dzyaloshinskii–Moriya interaction on the spin-wave spectra of thin films, J. Phys. Condens. Matter 25, 156001 (2013).
  * Mruczkiewicz and Krawczyk [2016] M. Mruczkiewicz and M. Krawczyk, Influence of the Dzyaloshinskii-Moriya interaction on the FMR spectrum of magnonic crystals and confined structures, Phys. Rev. B 94, 024434 (2016).
  * Szulc  _et al._ [2020] K. Szulc, P. Graczyk, M. Mruczkiewicz, G. Gubbiotti, and M. Krawczyk, Spin-wave diode and circulator based on unidirectional coupling, Phys. Rev. Appl. 14, 034063 (2020).
  * Belmeguenai  _et al._ [2015] M. Belmeguenai, J.-P. Adam, Y. Roussigné, S. Eimer, T. Devolder, J.-V. Kim, S. M. Cherif, A. Stashkevich, and A. Thiaville, Interfacial Dzyaloshinskii-Moriya interaction in perpendicularly magnetized ${\text{Pt/Co/AlO}}_{x}$ ultrathin films measured by Brillouin light spectroscopy, Phys. Rev. B 91, 180405 (2015).
  * Cho  _et al._ [2015] J. Cho, N.-H. Kim, S. Lee, J.-S. Kim, R. Lavrijsen, A. Solignac, Y. Yin, D.-S. Han, N. J. Van Hoof, H. J. Swagten, B. Koopmans, and C.-Y. You, Thickness dependence of the interfacial Dzyaloshinskii–Moriya interaction in inversion symmetry broken systems, Nat. Commun. 6, 1 (2015).
  * Boulle  _et al._ [2016] O. Boulle, J. Vogel, H. Yang, S. Pizzini, D. de Souza Chaves, A. Locatelli, T. O. Menteş, A. Sala, L. D. Buda-Prejbeanu, O. Klein, M. Belmeguenai, Y. Roussigné, A. Stashkevich, S. M. Chérif, L. Aballe, M. Foerster, M. Chshiev, S. Auffret, I. M. Miron, and G. Gaudin, Room-temperature chiral magnetic skyrmions in ultrathin magnetic nanostructures, Nat. Nanotechnol. 11, 449 (2016).
  * Woo  _et al._ [2016] S. Woo, K. Litzius, B. Krüger, M.-Y. Im, L. Caretta, K. Richter, M. Mann, A. Krone, R. M. Reeve, M. Weigand, P. Agrawal, I. Lemesh, M.-A. Mawass, P. Fischer, M. Kläui, and G. S. D. Beach, Observation of room-temperature magnetic skyrmions and their current-driven dynamics in ultrathin metallic ferromagnets, Nat. Mater. 15, 501 (2016).
  * Zhang  _et al._ [2017] B. Zhang, A. Cao, J. Qiao, M. Tang, K. Cao, X. Zhao, S. Eimer, Z. Si, N. Lei, Z. Wang, X. Lin, Z. Zhang, M. Wu, and W. Zhao, Influence of heavy metal materials on magnetic properties of Pt/Co/heavy metal tri-layered structures, Appl. Phys. Lett. 110, 012405 (2017).
  * Yu  _et al._ [2016] J. Yu, X. Qiu, Y. Wu, J. Yoon, P. Deorani, J. M. Besbas, A. Manchon, and H. Yang, Spin orbit torques and Dzyaloshinskii-Moriya interaction in dual-interfaced Co-Ni multilayers, Sci. Rep. 6, 1 (2016).
  * Soumyanarayanan  _et al._ [2017] A. Soumyanarayanan, M. Raju, A. G. Oyarce, A. K. Tan, M.-Y. Im, A. P. Petrović, P. Ho, K. Khoo, M. Tran, C. Gan, F. Ernult, and C. Panagopoulos, Tunable room-temperature magnetic skyrmions in Ir/Fe/Co/Pt multilayers, Nat. Mater. 16, 898 (2017).
  * Kim  _et al._ [2017] N.-H. Kim, J. Cho, J. Jung, D.-S. Han, Y. Yin, J.-S. Kim, H. J. M. Swagten, K. Lee, M.-H. Jung, and C.-Y. You, Role of top and bottom interfaces of a Pt/Co/AlOx system in Dzyaloshinskii-Moriya interaction, interface perpendicular magnetic anisotropy, and magneto-optical Kerr effect, AIP Adv. 7, 035213 (2017).
  * Tolley  _et al._ [2018] R. Tolley, S. A. Montoya, and E. E. Fullerton, Room-temperature observation and current control of skyrmions in Pt/Co/Os/Pt thin films, Phys. Rev. Mater. 2, 044404 (2018).
  * Parakkat  _et al._ [2016] V. M. Parakkat, K. R. Ganesh, and P. S. Anil Kumar, Copper dusting effects on perpendicular magnetic anisotropy in Pt/Co/Pt tri-layers, AIP Adv. 6, 056122 (2016).
  * Legrand  _et al._ [2018] W. Legrand, J.-Y. Chauleau, D. Maccariello, N. Reyren, S. Collin, K. Bouzehouane, N. Jaouen, V. Cros, and A. Fert, Hybrid chiral domain walls and skyrmions in magnetic multilayers, Sci. Adv. 4 (2018).
  * Wells  _et al._ [2017] A. W. J. Wells, P. M. Shepley, C. H. Marrows, and T. A. Moore, Effect of interfacial intermixing on the Dzyaloshinskii-Moriya interaction in Pt/Co/Pt, Phys. Rev. B 95, 054428 (2017).
  * Danilov  _et al._ [2018] A. P. Danilov, A. V. Scherbakov, B. A. Glavin, T. L. Linnik, A. M. Kalashnikova, L. A. Shelukhin, D. P. Pattnaik, A. W. Rushforth, C. J. Love, S. A. Cavill, D. R. Yakovlev, and M. Bayer, Optically excited spin pumping mediating collective magnetization dynamics in a spin valve structure, Phys. Rev. B 98, 060406 (2018).
  * Belmeguenai  _et al._ [2017] M. Belmeguenai, H. Bouloussa, Y. Roussigné, M. S. Gabor, T. Petrisor, C. Tiusan, H. Yang, A. Stashkevich, and S. M. Chérif, Interface Dzyaloshinskii-Moriya interaction in the interlayer antiferromagnetic-exchange coupled Pt/CoFeB/Ru/CoFeB systems, Phys. Rev. B 96, 144402 (2017).
  * dos Santos  _et al._ [2020b] F. J. dos Santos, M. dos Santos Dias, and S. Lounis, Modeling spin waves in noncollinear antiferromagnets: Spin-flop states, spin spirals, skyrmions, and antiskyrmions, Phys. Rev. B 102, 104436 (2020b).
  * Costa  _et al._ [2010] A. T. Costa, R. B. Muniz, S. Lounis, A. B. Klautau, and D. L. Mills, Spin-orbit coupling and spin waves in ultrathin ferromagnets: The spin-wave Rashba effect, Phys. Rev. B 82, 014428 (2010).
  * Henry  _et al._ [2019] Y. Henry, D. Stoeffler, J.-V. Kim, and M. Bailleul, Unidirectional spin-wave channeling along magnetic domain walls of Bloch type, Phys. Rev. B 100, 024416 (2019).
  * Grimsditch  _et al._ [1996] M. Grimsditch, S. Kumar, and E. E. Fullerton, Brillouin light scattering study of Fe/Cr/Fe (211) and (100) trilayers, Phys. Rev. B 54, 3385 (1996).
  * Fuchs  _et al._ [1997] P. Fuchs, U. Ramsperger, A. Vaterlaus, and M. Landolt, Roughness-induced coupling between ferromagnetic films across an amorphous spacer layer, Phys. Rev. B 55, 12546 (1997).
  * Fernández-Pacheco  _et al._ [2019] A. Fernández-Pacheco, E. Vedmedenko, F. Ummelen, R. Mansell, D. Petit, and R. P. Cowburn, Symmetry-breaking interlayer Dzyaloshinskii–Moriya interactions in synthetic antiferromagnets, Nat. Mater. 18, 679 (2019).
  * Karnad  _et al._ [2018] G. V. Karnad, F. Freimuth, E. Martinez, R. Lo Conte, G. Gubbiotti, T. Schulz, S. Senz, B. Ocker, Y. Mokrousov, and M. Kläui, Modification of Dzyaloshinskii-Moriya-interaction-stabilized domain wall chirality by driving currents, Phys. Rev. Lett. 121, 147203 (2018).
  * Shahbazi  _et al._ [2019] K. Shahbazi, J.-V. Kim, H. T. Nembach, J. M. Shaw, A. Bischof, M. D. Rossell, V. Jeudy, T. A. Moore, and C. H. Marrows, Domain-wall motion and interfacial Dzyaloshinskii-Moriya interactions in $\mathrm{Pt}/\mathrm{Co}/\mathrm{Ir}({t}_{\mathrm{Ir}})/\mathrm{Ta}$ multilayers, Phys. Rev. B 99, 094409 (2019).
  * Han [2016] W. Han, Perspectives for spintronics in 2D materials, APL Mater. 4, 032401 (2016).
  * Samardak  _et al._ [2018] A. Samardak, A. Kolesnikov, M. Stebliy, L. Chebotkevich, A. Sadovnikov, S. Nikitov, A. Talapatra, J. Mohanty, and A. Ognev, Enhanced interfacial Dzyaloshinskii-Moriya interaction and isolated skyrmions in the inversion-symmetry-broken Ru/Co/W/Ru films, Appl. Phys. Lett. 112, 192406 (2018).
  * Kuepferling  _et al._ [2020] M. Kuepferling, A. Casiraghi, G. Soares, G. Durin, F. Garcia-Sanchez, L. Chen, C. H. Back, C. H. Marrows, S. Tacchi, and G. Carlotti, Measuring interfacial Dzyaloshinskii-Moriya interaction in ultra thin films (2020), arXiv:2009.11830 .
  * Krams  _et al._ [1992] P. Krams, F. Lauks, R. L. Stamps, B. Hillebrands, and G. Güntherodt, Magnetic anisotropies of ultrathin Co(001) films on Cu(001), Phys. Rev. Lett. 69, 3674 (1992).
  * Madami  _et al._ [2004] M. Madami, S. Tacchi, G. Carlotti, G. Gubbiotti, and R. L. Stamps, In situ Brillouin scattering study of the thickness dependence of magnetic anisotropy in uncovered and Cu-covered Fe/GaAs(100) ultrathin films, Phys. Rev. B 69, 144408 (2004).
  * Nembach  _et al._ [2015] H. T. Nembach, J. M. Shaw, M. Weiler, E. Jué, and T. J. Silva, Linear relation between Heisenberg exchange and interfacial Dzyaloshinskii–Moriya interaction in metal films, Nat. Phys. 11, 825 (2015).
  * Di  _et al._ [2015] K. Di, V. L. Zhang, H. S. Lim, S. C. Ng, M. H. Kuok, J. Yu, J. Yoon, X. Qiu, and H. Yang, Direct observation of the Dzyaloshinskii-Moriya interaction in a Pt/Co/Ni film, Phys. Rev. Lett. 114, 047201 (2015).
  * Tacchi  _et al._ [2017] S. Tacchi, R. E. Troncoso, M. Ahlberg, G. Gubbiotti, M. Madami, J. Åkerman, and P. Landeros, Interfacial Dzyaloshinskii-Moriya interaction in $\mathrm{Pt}/\mathrm{CoFeB}$ films: Effect of the heavy-metal thickness, Phys. Rev. Lett. 118, 147201 (2017).
  * Kumar  _et al._ [2020] A. Kumar, A. K. Chaurasiya, N. Chowdhury, A. K. Mondal, R. Bansal, A. Barvat, S. P. Khanna, P. Pal, S. Chaudhary, A. Barman, and P. K. Muduli, Direct measurement of interfacial Dzyaloshinskii–Moriya interaction at the MoS2/Ni80Fe20 interface, Appl. Phys. Lett. 116, 232405 (2020).
  * Bouloussa  _et al._ [2018] H. Bouloussa, Y. Roussigné, M. Belmeguenai, A. Stashkevich, S. M. Chérif, J. Yu, and H. Yang, Spin-wave calculations for magnetic stacks with interface Dzyaloshinskii-Moriya interaction, Phys. Rev. B 98, 024428 (2018).
  * Sandercock [1982] J. R. Sandercock, Light scattering in solids III (Springer-Verlag, 1982) p. 173.
  * Carlotti and Gubbiotti [2002] G. Carlotti and G. Gubbiotti, Magnetic properties of layered nanostructures studied by means of Brillouin light scattering and the surface magneto-optical Kerr effect, J. Phys. Condens. Matter 14, 8199 (2002).
  * Graczyk  _et al._ [2018] P. Graczyk, M. Zelent, and M. Krawczyk, Co- and contra-directional vertical coupling between ferromagnetic layers with grating for short-wavelength spin wave generation, New J. Phys. 20, 053021 (2018).
  * Klingler  _et al._ [2018] S. Klingler, V. Amin, S. Geprägs, K. Ganzhorn, H. Maier-Flaig, M. Althammer, H. Huebl, R. Gross, R. D. McMichael, M. D. Stiles, S. T. B. Goennenwein, and M. Weiler, Spin-torque excitation of perpendicular standing spin waves in coupled $\mathrm{YIG}/\mathrm{Co}$ heterostructures, Phys. Rev. Lett. 120, 127201 (2018).
  * Gubbiotti  _et al._ [1997] G. Gubbiotti, G. Carlotti, G. Socino, F. D’Orazio, F. Lucari, R. Bernardini, and M. De Crescenzi, Perpendicular and in-plane magnetic anisotropy in epitaxial Cu/Ni/Cu/Si(111) ultrathin films, Phys. Rev. B 56, 11073 (1997).
  * Moon  _et al._ [2013] J.-H. Moon, S.-M. Seo, K.-J. Lee, K.-W. Kim, J. Ryu, H.-W. Lee, R. D. McMichael, and M. D. Stiles, Spin-wave propagation in the presence of interfacial Dzyaloshinskii-Moriya interaction, Phys. Rev. B 88, 184404 (2013).
  * Mendisch  _et al._ [2019] S. Mendisch, G. Žiemys, V. Ahrens, A. Papp, and M. Becherer, Pt\Co\W as a candidate for low power nanomagnetic logic, J. Magn. Magn. Mater. 485, 345 (2019).
  * Chowdhury  _et al._ [2012] P. Chowdhury, P. D. Kulkarni, M. Krishnan, H. C. Barshilia, A. Sagdeo, S. K. Rai, G. S. Lodha, and D. V. Sridhara Rao, Effect of coherent to incoherent structural transition on magnetic anisotropy in Co/Pt multilayers, J. Appl. Phys. 112, 023912 (2012).
  * Mallick  _et al._ [2018] S. Mallick, S. Mallik, B. B. Singh, N. Chowdhury, R. Gieniusz, A. Maziewski, and S. Bedanta, Tuning the anisotropy and domain structure of Co films by variable growth conditions and seed layers, J. Phys. D: Appl. Phys. 51, 275003 (2018).


∎

11institutetext: BeiHang University 22institutetext: 22email:
<EMAIL_ADDRESS>33institutetext: Beijing, 100191, China

# PLU-Net: Extraction of multi-scale feature fusion

Weihu Song

(Received: date / Accepted: date)

###### Abstract

Deep learning algorithms have achieved remarkable results in medical image
segmentation in recent years. These networks are unable to handle with image
boundaries and details with enormous parameters, resulting in poor
segmentation results. To address the issue, we develop atrous spatial pyramid
pooling (ASPP) and combine it with the Squeeze-and-Excitation block (SE
block), as well as present the PS module, which employs a broader and multi-
scale receptive field at the network’s bottom to obtain more detailed semantic
information. We also propose the Local Guided block (LG block) and also its
combination with the SE block to form the LS block, which can obtain more
abundant local features in the feature map, so that more edge information can
be retained in each down sampling process, thereby improving the performance
of boundary segmentation. We propose PLU-Net and integrate our PS module and
LS block into U-Net. We put our PLU-Net to the test on three benchmark
datasets, and the results show that by fewer parameters and FLOPs, it
outperforms on medical semantic segmentation tasks.

###### Keywords:

Semantic segmentation U-Net deep learning medical image

##  1 Introduction

The significance of image analysis is rising in parallel with the successful
application of imaging in clinical medicine. Image segmentation is a key image
analysis technology which plays an essential role in imaging medicine. Deep
learning technology, mainly based on deep convolutional neural network (DCNN),
have solved various semantic segmentation difficulties of medical images in
recent times.Although the performance of subsequent improved methods based on
the U-Net has improved, some issues have emerged, including such increasing
the parameters and FLOPs, and the network for image segmentation boundary and
details is not good enough.In this article, we propose PLU-Net, a simple and
effective network model which utilizes U-Net as a baseline to solve the
problems. To start, the LS block is employed to obtain rich local information
in order to improve boundary segmentation performance. Second, with its broad
and multi-scale receptive field, the PS module is added to the bottom of the
network to collect richer detail information. The combination of the two
modules allows for excellent image boundary and detail information
acquisition. Finally, the network depth is reduced by one layer, greatly
increasing the model’s interface speed.

##  2 Related work

Other CNN models appeared in the years after the ILSVRC Russakovsky et al.
(2015) competition began in 2012, including ALexNet Krizhevsky et al. (2012),
VGG Simonyan and Zisserman (2014), GoogLeNet Szegedy et al. (2015), ResNet He
et al. (2016), and SENet Hu et al. (2018). These models are mostly utilized in
image classification tasks at the image level, and many fields require more
detailed image classification. This is especially true in medical imaging,
where precision and speed are more important than other fields.

deep convolutional networks: In 2015, the Fully Convolutional Network (FCN)
Long et al. (2015) replaced the fully connected layer with the convolution
layers to output spatial mapping, allowing the model to handle images of
varying sizes and considerably boosting segmentation accuracy over traditional
methods. However, it still has significant flaws, such as the model’s poor
recognition efficiency in particular cases and the omission of global context
information. At this time, U-Net was born. It uses a completely symmetrical
model structure and uses an altogether new feature fusion technique than FCN:
concat. Meanwhile, it reduces the size of the model and delivers excellent
results with little training data, which is essential for medical
segmentation. More semantic segmentation models employ U-Net as the basis for
improvement because of its superior performance. U-Net++ Zhou et al. (2020)
improves accuracy by adding deep supervision to each layer’s sub-network and
better capturing some feature information lost in down-sampling and up-
sampling operations.

multi-scale feature extraction: PSPNetZhao et al. (2016) proposes to use the
pyramid pooling module to aggregate the context information of different
regions, so as to improve the extraction ability of feature information.
DeepLabChen et al. (2014) uses ASPP to aggregate more convolution kernels of
different scales to improve the multi-scale feature extraction ability.Res-
UNet Xiao et al. (2018) and Dense-UNet Huang et al. (2017), respectively,
incorporate ResNet and DenseNet concepts into the U-Net, ResNet’s residual
block and DenseNet’s dense block are used to effectively reduce feature
information loss during transmission.

attention modules: For each up-sampling, Attention U-Net Oktay et al. (2018)
inserts the attention gate into U-Net, which eliminates feature redundancy
caused by the repetitive employment of low-level features in multiple
convolution processing. R2U-Net Alom et al. (2018) combines the RNN and ResNet
structures into a U-Net structure, allowing the structure to gain more
characteristic information after each convolution. Additionally, because
transformer has a global receptive field and can acquire feature information
from all pixels in an image, numerous recent works Fan et al. (2022) Sha et
al. (2021) Chen et al. (2021) Petit et al. (2021) Lin et al. (2021) have
merged transformer and U-Net in various ways. The models performance has
improved to some level, but it has also introduced a slew of new issues. On
the one hand, a transformer structure will dramatically increase the size of
the model, stifling inference speed and necessitating higher hardware needs.
On the other hand, it frequently requires the blessing of the pre-trained
model, therefore a solid pre-trained model is critical to the model’s
performance. To summarize, the model’s accuracy can be enhanced by learning
additional feature information or lowering feature information loss during the
feature map calculation. In addition, during the model design process, the
long-running time induced by the growth of the model size must be taken into
account.

(a) LG block

(b) SE block

(c) LS block

Figure 1: Comparison of three different blocks.

##  3 Methodology

###  3.1 LS block

The Conv block in the original U-Net network consists of two 3x3 convolution
operations, two batch normalization operations, and two nonlinear activations
(ReLU). However, we notice that this structure has a loss of local
information, so we propose the local guided block (LG block, shown as Fig.1),
which is divided into two branches and is made up of two 3x3 dilated
convolution operations with dilated rates equal to 1 and 3, The results of two
dilated convolution operations are then concatenated to enhance feature
propagation. Then, to achieve cross-channel information fusion, a 1x1
convolution operation is employed, and nonlinear features are added on the
assumption that the size of the feature map remains unchanged. To achieve
channel information adaptation, we inserted SE block after LG block to make LS
block (shown as Fig.1), similar to PS module. LG block, as comparison to the
original convolution block, minimizes the amount of calculation while
obtaining richer feature information with a large receptive field thanks to
the addition of double branch structure and dilated convolution. It further
realizes the adaptation of channel feature information by adding SE block.

###  3.2 PS module

ASPP first was proposed in DeepLabv1 Chen et al. (2014) and then improved in
DeepLabv2 Chen et al. (2017a) and DeepLabv3 Chen et al. (2017b), as seen in
Fig.2. Deeplabv3’s ASPP, which comprises of one 1x1 convolution, three dilated
convolutions, and one global average pooling operation, is used as the
foundation. The employment of the global average pooling method in up-sampling
produces duplicate information and degrades prediction performance, according
to experimental verification. As a result, we remove the global average
pooling and replace the ordinary void convolution with the depthwise separable
convolution Sifre and Mallat (2014), resulting in a reduction of roughly five
times the number of parameters compared to the original ASPP. The ASPP’s
multi-scale structure allows it to gather more feature information and utilise
larger receptive fields, however more feature information may contain
duplicated data, lowering the performance of the system.To alleviate the
impact of redundant information, we choose to employ the SE block in SENet Hu
et al. (2018) to increase the weight of important channel information while
decreasing the weight of worthless channel information. The SE block uses
squeeze and excitation two processes to learn the importance of each channel’s
features, and then strengthens the relevant channel while weakening the idle
channel to achieve adaptive feature channel calibration. As a result, a PS
module is proposed (shown as Fig.2). After getting additional feature
information and employing the large receptive field, this module may combine
the advantages of the ASPP module and the SE block to suppress redundant
information and strengthen the important channel feature information.

(a) ASPP

(b) PS module

Figure 2: Comparison of different feature extractors.

###  3.3 Network Architecture

Our PLU-Net, as shown in Fig.3, improves on the original U-Net network
architecture by substituting the LS block for the convolution block in the
down-sampling and up-sampling pathways. The LS block’s double-branch structure
effectively ensures that information loss is minimized at each layer of
operation, while feature reuse and successful propagation are ensured by the
bigger receptive field. In addition, the U-Net network’s up-sampling and down-
sampling periods were reduced from four to three, and a PS module was added at
the end of the down-sampling. We may considerably minimize the calculation
amount and make the model more lightweight by reducing the number of down-
sampling and up-sampling channels in the last layer of the U-Net network,
which is 1024. We employ four branches and a greater dilation rate at the same
time to obtain a bigger receptive field and consequently richer feature
information. The up-sampling step that follows can be completed efficiently.
Our network structure can now achieve better performance with fewer parameters
and FlOPs because to the combination of these enhancements.

Figure 3: Proposed PLU-Net architecture.

(a) DSB2018

(b) CVC

(c) ISIC2018

Figure 4: Qualitative comparison of segmentation results for nuclei, colon,
and skin lesion datasets, from top to bottom are Image, U-Net, U-Net++,
MultiResUnet, DoubleUNet, PLU-Net, Ground Truth

##  4 Experiments and Results

###  4.1 Datasets

Because both the PS module and the LS block are modular, they can simply be
utilized to substitute convolution processes in various network architectures.
We designed three models, PU-Net (conv+PS module), LUNet(LS block), and PLU-
Net (LS block+PS module), to demonstrate the robustness of our model, in
addition to the original U-Net (conv+null here A+B means A for down-sampling
and up-sampling pathway and B for PS module, the same below.) We evaluated the
models on three biomedical image segmentation datasets in the study.

####  4.1.1 Polyp Segmentation

CVC-ClinicDBBernal et al. (2015)(CVC for short) is from colonoscopy videos and
contains 612 polyp images. We use the original size 384x288 of image and is
randomly split into train set ($60\%$), validation set ($20\%$), and test set
($20\%$). Also, we scale the original images equally (resize it from
$512\times 512$ to $256\times 256$).

####  4.1.2 Nuclei Segmentation

In most cancer grading schemes, nuclei segmentation has far-reaching
significance because nuclear morphology is one of the important components.
The dataset is derived from Kaggle 2018 Data Science
Bowl111https://www.kaggle.com/c/data-science-bowl-2018/data (DSB2018 for
short). It contains 670 nucleus images and is randomly split into train set
($60\%$), validation set ($20\%$), and test set ($20\%$). Also, we resize the
original images to $96\times 96$.

####  4.1.3 Skin Lesion Segmentation

Computer-aided automatic diagnosis of skin cancer is an inevitable trend, and
skin lesions segmentation as the first step is urgent. The dataset is from
MICCAI 2018 Workshop - ISIC2018: Skin Lesion Analysis Towards Melanoma
Detection Codella et al. (2019) Tschandl et al. (2018) (ISIC2018 for short).
It contains 2594 images and is randomly split into train set ($60\%$),
validation set ($20\%$), and test set ($20\%$). For better model training and
result display, we resize all the original images to $224\times 224$.

###  4.2 Experimental Setup

We use three datasets to compare the U-Net, PU-Net, LU-Net, U-Net++,
MultiResUnetIbtehaz and Rahman (2020), DoubleUNetJha et al. (2020), and PLU-
Net architectures. We chose U-Net because of its widespread use and relevance
in medical image segmentation, as well as the fact that it serves as the
foundation for numerous network architectures. The kernel size is set to
$3\times 3$ with dilation values of 1 and 3 correspondingly in the LS block,
followed by batch normalization and ReLU. Furthermore, the PS module employs
depth-wise separable convolution, the results of which are fed into four
atrous convolutions with kernel sizes of $3\times 3$ and dilation values of 1,
6, 12, and 18 respectively. The output size is determined by concatenating the
results of four atrous convolutions using 1x1 convolution. For the DSB2018
dataset, we used a batch size of 16, four for the ISIC2018 dataset, and two
for the CVC dataset. The optimizer is Adam Kingma and Ba (2014), and the two
momentum terms are $0.5$ and $0.999$, with a learning rate of 0.0003. The
epoch is set to 100, and the loss function is Binary CrossEntropy
Loss(BCELoss). All of the experiments are run on four NVIDIA TITAN V GPUs with
12GB of RAM each, using PyTroch Paszke et al. (2019).

Table 1: Evaluation of proposed PLU-Net

Dataset | Methods | PC | SE | F1 | JS | Params(M) | FLOPs(G)
---|---|---|---|---|---|---|---
DSB2018 | U-NetRonneberger et al. (2015) | 0.8965 | 0.9064 | 0.9014 | 0.8205 | 34.53 | 9.21
| U-Net++Zhou et al. (2020) | 0.8892 | 0.9184 | 0.9036 | 0.8237 | 36.62 | 19.41
| MultiResUnetIbtehaz and Rahman (2020) | 0.9432 | 0.8401 | 0.8887 | 0.7977 | 7.24 | 2.11
| DoubleUNetJha et al. (2020) | 0.8808 | 0.9298 | 0.9046 | 0.8249 | 18.84 | 6.21
| LU-Net | 0.9067 | 0.9015 | 0.9040 | 0.8258 | 29.29 | 6.79
| PU-Net | 0.8912 | 0.9157 | 0.9032 | 0.8234 | 38.19 | 9.32
| PLU-Net | 0.9025 | 0.9099 | 0.9062 | 0.8279 | 6.22 | 4.99
CVC | U-NetRonneberger et al. (2015) | 0.8001 | 0.9087 | 0.8509 | 0.7385 | 34.53 | 110.49
| U-Net++Zhou et al. (2020) | 0.7973 | 0.9632 | 0.8724 | 0.7706 | 36.62 | 232.92
| MultiResUnetIbtehaz and Rahman (2020) | 0.7929 | 0.9495 | 0.8641 | 0.7562 | 7.24 | 25.3
| DoubleUNetJha et al. (2020) | 0.8637 | 0.9222 | 0.8920 | 0.8249 | 18.84 | 74.52
| LU-Net | 0.8591 | 0.9351 | 0.8954 | 0.8102 | 29.29 | 81.42
| PU-Net | 0.8727 | 0.9096 | 0.8807 | 0.7979 | 38.19 | 111.85
| PLU-Net | 0.9139 | 0.8832 | 0.8983 | 0.8125 | 6.22 | 59.9
ISIC2018 | U-NetRonneberger et al. (2015) | 0.8449 | 0.9038 | 0.8734 | 0.7665 | 34.53 | 50.13
| U-Net++Zhou et al. (2020) | 0.8342 | 0.9156 | 0.8730 | 0.7688 | 36.62 | 105.68
| MultiResUnetIbtehaz and Rahman (2020) | 0.8223 | 0.9340 | 0.8746 | 0.7732 | 7.24 | 11.48
| DoubleUNetJha et al. (2020) | 0.8567 | 0.9007 | 0.8781 | 0.7779 | 18.84 | 33.18
| LU-Net | 0.8678 | 0.8933 | 0.8804 | 0.7802 | 29.29 | 36.94
| PU-Net | 0.8556 | 0.8981 | 0.8763 | 0.7771 | 38.19 | 50.75
| PLU-Net | 0.8774 | 0.9152 | 0.8959 | 0.8061 | 6.22 | 27.18

###  4.3 Result and Discussion

To better show the experimental results, we considered several performance
metrics, including Precision (PC, Eq.1), Sensitivity (SE, Eq.2), F1-score(F1,
which is also known as Dice coefficient, DC, Eq.3) and Jaccard similarity (JS,
Eq.4). Variables involved in these formulas are True Positive (TP), False
Positive (FP), True Negative (TN), False Negative (FN), Ground Truth (GT), and
Segmentation Result (SR).

$PC=\frac{TP}{TP+FP}$ (1)

$SE=\frac{TP}{TP+FN}$ (2)

$F1=2\frac{SE*PC}{SE+PC}=2\frac{|GT\cap SR|}{|GT|+|SR|}=DC$ (3)

$JS=\frac{|GT\cap SR|}{|GT\cup SR|}$ (4)

Table.1 illustrates the results of our experiments using our proposed model
and various state-of-the-art U-Net models, such as U-Net++, MultiResUnet, and
DoubleUNet, while Table.1 demonstrates the segmentation outcomes of three
different biomedical image segmentation tasks. Table.1 shows that our proposed
models LU-Net, PU-Net, and PLU-Net are all superior to U-Net. F1 in JS is
superior to U-Net among them. On CVC, our model outperforms U-Net by more than
6 and 8 points in F1 and JS, respectively, when compared to U-Net. LU-Net and
PU-Net results, on the other hand, reveal that they are superior than U-Net in
JS and F1, with PLU-Net outperforming all other models, proving the
superiority of LG Block and the capability of PS module. Furthermore, the
segmentation results of the three segmentation tasks in Fig.2 show the model’s
advantages. In nucleus segmentation, our model performs better on the edges,
and in Polyp Segmentation, the model presented in this paper greatly
outperforms other models in terms of segmentation performance. Unlike other
models with smooth boundary processing, our model has more refined boundary
processing in skin lesion segmentation.

##  5 Conclusion

In this paper, We propose an LS block for learning local feature information
from a big reception field and a PS module for learning more deep information
from a wider reception field. Furthermore, we design a lightweight network
PLU-Net with fewer parameters and FLOPs, which can handle boundaries and
details well for medical images, based on the Local Guided block and PS
module. Experiments on colon cancer, nuclei, and skin lesion segmentation
demonstrate the advantages of the suggested PLU-Net for generating high-
quality segmentation results.

## Conflict of interest

The authors report no conflict of interest.

## Data availability statement

The data that support the findings of this study are available from the
corresponding author upon reasonable request.

## References

  * Alom et al. (2018) Alom MZ, Hasan M, Yakopcic C, Taha TM, Asari VK (2018) Recurrent residual convolutional neural network based on u-net (r2u-net) for medical image segmentation. arXiv preprint arXiv:180206955
  * Bernal et al. (2015) Bernal J, Sánchez FJ, Fernández-Esparrach G, Gil D, de Miguel CR, Vilariño F (2015) Wm-dova maps for accurate polyp highlighting in colonoscopy: Validation vs. saliency maps from physicians. Computerized medical imaging and graphics : the official journal of the Computerized Medical Imaging Society 43:99–111
  * Chen et al. (2021) Chen J, Lu Y, Yu Q, Luo X, Adeli E, Wang Y, Lu L, Yuille AL, Zhou Y (2021) Transunet: Transformers make strong encoders for medical image segmentation. arXiv preprint arXiv:210204306
  * Chen et al. (2014) Chen LC, Papandreou G, Kokkinos I, Murphy K, Yuille AL (2014) Semantic image segmentation with deep convolutional nets and fully connected crfs. arXiv preprint arXiv:14127062
  * Chen et al. (2017a) Chen LC, Papandreou G, Kokkinos I, Murphy K, Yuille AL (2017a) Deeplab: Semantic image segmentation with deep convolutional nets, atrous convolution, and fully connected crfs. IEEE transactions on pattern analysis and machine intelligence 40(4):834–848
  * Chen et al. (2017b) Chen LC, Papandreou G, Schroff F, Adam H (2017b) Rethinking atrous convolution for semantic image segmentation. arXiv preprint arXiv:170605587
  * Codella et al. (2019) Codella N, Rotemberg V, Tschandl P, Celebi ME, Dusza S, Gutman D, Helba B, Kalloo A, Liopyris K, Marchetti M, et al. (2019) Skin lesion analysis toward melanoma detection 2018: A challenge hosted by the international skin imaging collaboration (isic). arXiv preprint arXiv:190203368
  * Fan et al. (2022) Fan CM, Liu TJ, Liu KH (2022) Sunet: Swin transformer unet for image denoising. arXiv preprint arXiv:220214009
  * He et al. (2016) He K, Zhang X, Ren S, Sun J (2016) Deep residual learning for image recognition. In: Proceedings of the IEEE conference on computer vision and pattern recognition, pp 770–778
  * Hu et al. (2018) Hu J, Shen L, Sun G (2018) Squeeze-and-excitation networks. In: Proceedings of the IEEE conference on computer vision and pattern recognition, pp 7132–7141
  * Huang et al. (2017) Huang G, Liu Z, Van Der Maaten L, Weinberger KQ (2017) Densely connected convolutional networks. In: Proceedings of the IEEE conference on computer vision and pattern recognition, pp 4700–4708
  * Ibtehaz and Rahman (2020) Ibtehaz N, Rahman MS (2020) Multiresunet: Rethinking the u-net architecture for multimodal biomedical image segmentation. Neural Networks 121:74–87
  * Jha et al. (2020) Jha D, Riegler MA, Johansen D, Halvorsen P, Johansen HD (2020) Doubleu-net: A deep convolutional neural network for medical image segmentation. In: 2020 IEEE 33rd International Symposium on Computer-Based Medical Systems (CBMS), pp 558–564
  * Kingma and Ba (2014) Kingma DP, Ba J (2014) Adam: A method for stochastic optimization. arXiv preprint arXiv:14126980
  * Krizhevsky et al. (2012) Krizhevsky A, Sutskever I, Hinton GE (2012) Imagenet classification with deep convolutional neural networks. Advances in neural information processing systems 25:1097–1105
  * Lin et al. (2021) Lin A, Chen B, Xu J, Zhang Z, Lu G (2021) Ds-transunet: Dual swin transformer u-net for medical image segmentation. arXiv preprint arXiv:210606716
  * Long et al. (2015) Long J, Shelhamer E, Darrell T (2015) Fully convolutional networks for semantic segmentation. In: Proceedings of the IEEE conference on computer vision and pattern recognition, pp 3431–3440
  * Oktay et al. (2018) Oktay O, Schlemper J, Folgoc LL, Lee M, Heinrich M, Misawa K, Mori K, McDonagh S, Hammerla NY, Kainz B, et al. (2018) Attention u-net: Learning where to look for the pancreas. arXiv preprint arXiv:180403999
  * Paszke et al. (2019) Paszke A, Gross S, Massa F, Lerer A, Bradbury J, Chanan G, Killeen T, Lin Z, Gimelshein N, Antiga L, Desmaison A, Kopf A, Yang E, DeVito Z, Raison M, Tejani A, Chilamkurthy S, Steiner B, Fang L, Bai J, Chintala S (2019) Pytorch: An imperative style, high-performance deep learning library. In: Wallach H, Larochelle H, Beygelzimer A, d'Alché-Buc F, Fox E, Garnett R (eds) Advances in Neural Information Processing Systems 32, Curran Associates, Inc., pp 8024–8035, URL http://papers.neurips.cc/paper/9015-pytorch-an-imperative-style-high-performance-deep-learning-library.pdf
  * Petit et al. (2021) Petit O, Thome N, Rambour C, Themyr L, Collins T, Soler L (2021) U-net transformer: Self and cross attention for medical image segmentation. In: International Workshop on Machine Learning in Medical Imaging, Springer, pp 267–276
  * Ronneberger et al. (2015) Ronneberger O, Fischer P, Brox T (2015) U-net: Convolutional networks for biomedical image segmentation. In: International Conference on Medical image computing and computer-assisted intervention, Springer, pp 234–241
  * Russakovsky et al. (2015) Russakovsky O, Deng J, Su H, Krause J, Satheesh S, Ma S, Huang Z, Karpathy A, Khosla A, Bernstein M, Berg AC, Fei-Fei L (2015) ImageNet Large Scale Visual Recognition Challenge. International Journal of Computer Vision (IJCV) 115(3):211–252, DOI 10.1007/s11263-015-0816-y
  * Sha et al. (2021) Sha Y, Zhang Y, Ji X, Hu L (2021) Transformer-unet: Raw image processing with unet. arXiv preprint arXiv:210908417
  * Sifre and Mallat (2014) Sifre L, Mallat S (2014) Rigid-motion scattering for texture classification. arXiv preprint arXiv:14031687
  * Simonyan and Zisserman (2014) Simonyan K, Zisserman A (2014) Very deep convolutional networks for large-scale image recognition. arXiv preprint arXiv:14091556
  * Szegedy et al. (2015) Szegedy C, Liu W, Jia Y, Sermanet P, Reed S, Anguelov D, Erhan D, Vanhoucke V, Rabinovich A (2015) Going deeper with convolutions. In: Proceedings of the IEEE conference on computer vision and pattern recognition, pp 1–9
  * Tschandl et al. (2018) Tschandl P, Rosendahl C, Kittler H (2018) The ham10000 dataset, a large collection of multi-source dermatoscopic images of common pigmented skin lesions. Scientific data 5(1):1–9
  * Xiao et al. (2018) Xiao X, Lian S, Luo Z, Li S (2018) Weighted res-unet for high-quality retina vessel segmentation. In: 2018 9th international conference on information technology in medicine and education (ITME), IEEE, pp 327–331
  * Zhao et al. (2016) Zhao H, Shi J, Qi X, Wang X, Jia J (2016) Pyramid scene parsing network. IEEE Computer Society
  * Zhou et al. (2020) Zhou Z, Siddiquee M, Tajbakhsh N, Liang J (2020) Unet++: Redesigning skip connections to exploit multiscale features in image segmentation. IEEE Transactions on Medical Imaging 39(6):1856–1867