# Spin and electronic excitations in 4f atomic chains on Au(111) substrates

David Facemyer<EMAIL_ADDRESS>Department of Physics and Astronomy and
Nanoscale and Quantum Phenomena Institute, Ohio University, Athens, OH 45701
Naveen K. Dandu  Materials Science Division, Argonne National Laboratory,
Lemont, IL 60439  Chemical Engineering Department, University of Illinois at
Chicago, Chicago, IL 60608  Vijay R. Singh  Materials Science Division,
Argonne National Laboratory, Lemont, IL 60439  Chemical Engineering
Department, University of Illinois at Chicago, Chicago, IL 60608  Anh T. Ngo
Materials Science Division, Argonne National Laboratory, Lemont, IL 60439
Chemical Engineering Department, University of Illinois at Chicago, Chicago,
IL 60608  Sergio E. Ulloa  Department of Physics and Astronomy and Nanoscale
and Quantum Phenomena Institute, Ohio University, Athens, OH 45701

###### Abstract

High spin systems, like those that incorporate rare earth 4f elements (REEs),
are increasingly relevant in many fields. Although research in such systems is
sparse, the large Hilbert spaces they occupy are promising for many
applications. In this work, we examine a one-dimensional linear array of
europium (Eu) atoms on a Au(111) surface and study their electronic and
magnetic excitations. Ab initio calculations using VASP with PBE+U, spin-orbit
coupling, and the HSE hybrid functional are employed to study the structure.
We find Eu atoms to have a net charge when on gold, consistent with a net
magnetic momemt of $\simeq 3.5\mu_{B}$. Examining various spin-projection
configurations, we can evaluate first and second neighbor exchange energies in
an isotropic Heisenberg model between spin-$\frac{7}{2}$ moments to obtain
$J_{1}\approx-0.9\,\mathrm{K}$ and $J_{2}\approx 4.3\,\mathrm{K}$ for the
relaxed-chain atomic separation of $a\approx 5$ Å. These parameters are used
to obtain the full spin excitation spectrum of a physically realizable four-
atom chain. The large $J_{2}/|J_{1}|\simeq 4.8$ ratio results in a singlet
ground state with dimer-like antiferromagnetic correlations between second
neighbors. The seemingly small $J_{1}$ values significantly affect the
spectra, underscoring the important role that nearest-neighbor coupling plays
in this system, including possible Dzyaloshinskii-Moriya interactions. Spin-
flip excitations are calculated to extract differential conductance profiles
as those obtained by scanning tunneling microscopy techniques. We uncover
interesting behavior for local higher spin excitations, especially as we track
their dispersion with applied magnetic fields.

##  I Introduction

The study of low dimensional arrays of localized magnetic moments, generally
referred to as spin chains, is ubiquitous in physics. The simplicity of such
systems resides only in their spatial dimension, however. The classical nature
of spin chains is complex enough, but quantum mechanical effects enrich these
systems even more. Many models and experiments have allowed us to gather
information about the magnetic properties of spin chains, including their
ground state and excitations, thermal magnetic properties, and possible phase
transitions [1, 2]. The last decade has also uncovered new exotic phenomena in
atomic chains, such as building unique Kondo configurations [3] or creating
Yu-Shiba [4] or Majorana edge states [5, 6, 7] whenever magnetic atoms are
placed in proximity to superconducting substrates. In addition to the
fundamental questions on the behavior of such interesting systems, a great
deal of current research is rooted in technological advancement and possible
applications, including quantum computing, the transmission of quantum
information, and sensing [1, 8].

Much of this work, however, has been focused on spin-$\frac{1}{2}$ systems,
while larger-spin arrays have received much less attention. We consider here
spin-$\frac{7}{2}$ magnetic moments as those associated with some lanthanide
($4f$) atoms. The sorts of challenges and promises that come with these
systems are easily recognized. Their Hilbert space grows rapidly with
increasing site number (chain or cluster size), making them computationally
expensive on classical computers. In contrast, these large Hilbert spaces may
provide robust computational bases for quantum computation or information
storage and a rich state manifold for complex dynamical behavior [9, 10].

Scanning tunneling microscopy (STM) is a versatile and powerful tool for
imaging atomic clusters or molecules on metallic surfaces. STM can further
manipulate individual atoms or molecules on a substrate [11, 12], allowing the
design and construction of spin chains and clusters with precision, as well as
the extraction of single-atom and collective electronic and magnetic
properties [13, 1]. The theoretical work we present here is motivated in part
by these extraordinary capabilities, and it aims to provide insight into
possible experiments on these deceptively simple structures.

Rare earth elements are natural physical implementations of large-spin
systems. For example, $Gd^{+3}$ ions in $GdRh_{2}Si_{2}$ are well described
experimentally as a pure spin-$\frac{7}{2}$ system [14]. Dynamic magnetic
properties of core-shell nanowires of such material were studied using an
Ising model [15], while thermodynamic response functions were obtained in a
three-state Blume-Capel model [16]. Similarly, magnetic properties of
$La$-substituted $Gd_{1-x}La_{x}RhIn_{5}$ were well characterized using a
$\frac{7}{2}$-Heisenberg model for $x\leq 0.5$ [17]. Beautiful recent
experiments exploring lanthanide atoms on thin insulating layers have been
able to modify [18] or sense [19] the magnetic moment of individual atoms,
paving the way for many fundamental and practical questions using such
systems.

A wide range of linear array candidates and the means for onsite manipulation
also suggest deeper investigations into the realm of quantum information
processing. A carefully tuned spin chain with strongly inhomogeneous couplings
is predicted to exhibit perfect quantum information transfer [20]. Likewise,
perfect state transmission over many chain sites was demonstrated in both XY
and Heisenberg systems with local magnetic fields [21]. And quantum state
transfer with high fidelity was predicted for large Heisenberg ferromagnetic
chains [22]. To accurately substantiate such behavior in future experimental
work, we must accurately obtain model parameters from a rather complex but
experimentally realizable system, such as high-spin Eu ions on a Au(111)
surface.

To explore such realistic systems, we utilize a combination of theoretical
methods. Density functional theory (DFT), an indispensable tool to study the
electronic structure of materials, provides us with the characteristic
interactions between rare earth atoms such as Eu, deposited on a Au(111)
surface. DFT finds a sizable charge and magnetic moment on each atom,
compatible with spin-$\frac{7}{2}$, and allows us to extract nearest and next-
nearest neighbor exchange energies in a Heisenberg model. Once these
parameters are established, we explore a more experimentally realistic
structure of an open-ended linear array of Eu atoms on the gold substrate. The
low energy magnetic excitation spectrum is obtained by exact diagonalization,
which allows us to analyze the STM spectroscopy for site-specific spin-
excitations and their dependence on applied magnetic fields, as well as
spatial correlations of the magnetic moments in the chain. The high symmetry
of such a system results in highly degenerate manifolds with interesting
magnetic field dependence. As strong fields cause increasing polarization of
an otherwise singlet ground state, the field-induced transitions are
accompanied by characteristic changes in the differential conductance curves.
Such behavior can be easily identified in experiments, providing a direct
approach to the energetics of the system and benchmarking of system
parameters. We also study the role of a possible non-colinear exchange
interaction between magnetic moments, and how they would affect the
differential conductance curves. As the different interactions compete with
one another in defining the excitation spectrum, they leave signatures that
would hopefully assist in the full characterization of the overall Hamiltonian
of the system.

##  II Methods

###  II.1 First principles calculations

Relaxation of a linear chain of Eu atoms on an Au(111) surface was carried out
using the Vienna Ab Initio Simulation Package (VASP) [23]. The valence
electrons were described in terms of Kohn-Sham orbitals, expanded in a plane-
wave basis with an energy cutoff of 500 eV. A $\Gamma$-centered $k$-point mesh
of $8\times 8\times 8$ is used for all calculations with two different
functionals. We have used three set of calculations, PBE + U [24], HSE and
HSE+SOC hybrid functional [25]. Atoms were allowed to relax until the net
force per atom was less than 0.01 eV/Å. Moreover, within the HSE06 approach
[25], different values of exact Hartree-Fock (HF) nonlocal exchange ($\alpha$)
were tested (25% and 20%). The screening parameter (which controls the extent
of the range of the exchange interactions) was also tuned for two values of
$\alpha$ (5% and 25%).

The simulated system has a supercell of four Eu-atoms on the gold film with
three atomic layers, all Eu atoms arranged in a way that make the cell repeat
periodically, as illustrated in the insets of Fig. 1. The bottom gold layer is
kept fixed at the bulk lattice parameters, while the rest of the structure is
allowed to relax. The electronic projected density of states (PDOS) near the
Fermi level of the system indicates that all Eu ions have a well-defined
magnetic moment (we find $\mu\simeq 3.5\mu_{B}$) as well as a Bader charge
consistent with a 3+ ion – see Fig. 1. Figure S1 (see SI [26]) represents the
PDOS of the same system using PBE+U method, with two different values of U: 3
and 7.2 eV. Increasing the value of U kept the value of the magnetic moment
unaltered.

Figure 1: Projected density of states near the Fermi level of model system for
Eu and Au atoms using the HSE method. Notice spin polarization of Eu
$f$-orbital. Top inset shows side view of Eu atom linear chain on a Au(111)
surface. Bottom inset shows top view (two cells) of the system. Supercell has
four Eu atoms and a gold slab with three layers; Eu-Eu average distance is
4.98 Å; Eu-Au distance is 3.68 Å.

Considering different magnetic configurations for the Eu ions along the chain,
we find that the double-period Néel arrangement has the lowest energy,
followed by the ferromagnetic configuration, while the single-period Néel has
the highest energy, as shown in Table 1 – U and D indicate maximal moment
projections $\pm\frac{7}{2}$, respectively.

Magnetic configuration | Total energy difference $\Delta E$ [meV]
---|---
$\mathrm{UDUD}$ | 39.4
$\mathrm{UUUU}$ | 31.6
$\mathrm{UUDD}$ | 0
Table 1: Energy differences per unit cell with respect to the ground state
magnetic configuration, double period Néel (UUDD), for Eu-ion linear chain on
Au(111).

###  II.2 Heisenberg model

In order to extract effective exchange coupling constants, we consider an
isotropic Heisenberg Hamiltonian and neglect local magnetic anisotropy [13,
1]. The Hamiltonian is then

$\hat{H}=\sum_{i<j}{\hat{\vec{S}}_{i}\cdot\mathrm{J}_{ij}\cdot\hat{\vec{S}}_{j}},$
(1)

where $\mathrm{J}_{ij}$ is the full magnetic exchange tensor that couples
different pairs of effective moments. We consider first and second-nearest-
neighbor exchange coupling, so that the Hamiltonian takes the form

$\displaystyle\hat{H}$ $\displaystyle=J_{1}\sum_{\langle
ij\rangle}{\hat{\vec{S}}_{i}\cdot\hat{\vec{S}}_{j}}+J_{2}\sum_{\langle\langle
ij\rangle\rangle}{\hat{\vec{S}}_{i}\cdot\hat{\vec{S}}_{j}}$
$\displaystyle=J_{1}\bigg{(}\sum_{\langle
ij\rangle}{\hat{\vec{S}}_{i}\cdot\hat{\vec{S}}_{j}}+\alpha\sum_{\langle\langle
ij\rangle\rangle}{\hat{\vec{S}}_{i}\cdot\hat{\vec{S}}_{j}}\bigg{)},$ (2)

where $\alpha=\frac{J_{2}}{J_{1}}$. Recall that $J_{ij}<0$ corresponds to
interacting moments favoring parallel alignment, i.e. ferromagnetic, and
$J_{ij}>0$ favors antiparallel (antiferromagnetic) alignment. One can estimate
the coupling constants by evaluating the energy of corresponding
configurations in Table 1. Considering the energy for the four-atom supercell,
one obtains

$\displaystyle E_{F}$
$\displaystyle=\langle\mathrm{UUUU}|\hat{H}|\mathrm{UUUU}\rangle=49J_{1}\bigg{(}\alpha+1\bigg{)}$
$\displaystyle E_{N}$
$\displaystyle=\langle\mathrm{UDUD}|\hat{H}|\mathrm{UDUD}\rangle=49J_{1}\bigg{(}\alpha-1\bigg{)}$
$\displaystyle E_{dN}$
$\displaystyle=\langle\mathrm{UUDD}|\hat{H}|\mathrm{UUDD}\rangle=-49J_{2}\,.$
(3)

The energy difference between different configurations are then

$\displaystyle\Delta E_{1}$ $\displaystyle=E_{N}-E_{F}=-98J_{1}$
$\displaystyle\Delta E_{2}$ $\displaystyle=E_{dN}-E_{F}=-49J_{1}(1+2\alpha).$
(4)

These equations, together with the corresponding energy differences from Table
1, allow the determination of exchange energies,
$J_{1}\approx-0.08\;\mathrm{meV\approx-0.9\;\mathrm{K}}$ and
$J_{2}\approx+0.37\;\mathrm{meV\approx 4.3\;\mathrm{K}}$. With these exchange
parameters, we can employ full diagonalization of the Hamiltonian for
different systems and explore their characteristics – we use QuSpin [27], and
focus here on an open chain with four Eu ions on the gold surface. Notice that
the Hilbert space for $N$ sites (magnetic moments) grows as $8^{N}$ due to the
different spin projections, i.e., $m=\\{\pm 7/2,...,\pm 1/2\\}$. The $N=4$
chain with open boundary conditions allows us to capitalize on the inversion
symmetry of the Hamiltonian and attain reasonable computational times. We can
calculate the full magnetic excitation spectrum and corresponding eigenstates,
as we discuss below. See [26] for spectral results for $N=3$ and $N=4$.

##  III Magnetic excitations and spectroscopy

###  III.1 Magnetic excitation spectrum

The large ratio $J_{2}/|J_{1}|\simeq 4.8$ of this system suggests that it can
be qualitatively understood as a chain of antiferromagnetic next-nearest-
neighbor dimer pairs which appear for $J_{1}\simeq 0$, i.e., a double-Nèel
interspersed chain, with an overall singlet ground state and highly degenerate
excitation manifolds 111See Supplemental Information LINK. The first excited
manifold is a sextuplet (two degenerate $S=1$ triplets), followed by two
degenerate ($S=2$) quintuplets. Despite $J_{1}$ having a relatively small
magnitude, its action perturbs significantly the dimer states and splits
degeneracies. The ground state is unaffected to first-order in $J_{1}$, while
low-energy excited states show nonzero first-order shifts [26]. The supplement
shows that the resulting spin correlations of the ground state are consistent
with this picture [26].

Using the DFT-obtained parameters from the Eu-on-gold chain, the full magnetic
excitation spectrum for the open four-atom chain in Fig. 2 shows that the
system has in fact an antiferromagnetic singlet ground state. The nearest-
neighbor coupling results in splittings of the excited states, producing
triplet and quintuplet excitations at nearly $J_{2}/2$ and $3J_{2}/2$ values
above $E_{\rm grnd}$, as seen in Fig. 2.

\begin{overpic}[width=244.69386pt]{first_spectrum.png}\put(520.0,120.0){\framebox(0.0,0.0)[bl]{\includegraphics[width=116.65646pt]{full_spectrum.png}}}\end{overpic}
Figure 2: Magnetic excitation spectrum for an open four-site spin chain of
$S=7/2$ magnetic moments with nearest and next-nearest neighbor exchanges,
$J_{1}=-0.08\;\mathrm{meV}$ and $J_{2}=0.37$ meV. Ground state is a singlet.
Inset shows full spectral range. Energies in units of $J_{2}$.

###  III.2 STM spectroscopy

The rich structure of the magnetic excitation spectrum can be explored using
experimental probes. Ideally suited to carry this out is the differential
spectroscopy technique using STM. By increasing bias voltage $V$ while the STM
tip is placed at different sites along the chain, one is able to excite
different spin configurations that have a local overlap at that site, which
are reflected in differential conductance features as peaks in $d^{2}I/dV^{2}$
versus bias [28, 13, 1].

We can estimate theoretically what such an experiment will yield by
considering the repeated action of the spin-raising (or lowering) operator on
different sites of the chain [28]. If the experiment is carried out at low
temperatures, the system can be assumed in its ground state $|\Psi_{\rm
grnd}\rangle$. As the tunneling electrons go from tip to substrate (or vice
versa), they can rise ($S^{+}$), lower ($S^{-}$) or leave unchanged ($S^{z}$)
the magnetic moment of the structure they are tunneling through [28]. Notice
that each tunneling electron can only provide angular momentum changes of $\pm
1\,(\hbar)$ on the adsorbed species, so that higher ‘spin-flips’ require
repeated electron scatterings before relaxation, and correspondingly higher
tunneling currents. Considering that $(S^{\pm}_{i})^{n}|\Psi_{\rm
grnd}\rangle=|\psi_{i}^{(n)}\rangle$ represents a local (on site $i$) magnetic
excitation that can be seen as composed from different excited eigenstates
$|\lambda\rangle$, one can write
$|\psi_{i}^{(n)}\rangle=\sum_{\lambda}b_{\lambda}{|\lambda\rangle}$. The
effect of the first-few spin-raising operator actions ($n=1,...,4$) on the
first atom of the chain are shown in Fig. 3, that shows the weights
$|b_{\lambda}|^{2}$ as a function of excitation energy. This gives an
‘excitation weight profile’ for the system, directly related to the
differential conductance curves (when one assumes the excitation yield to be
constant for all the $\lambda$-eigenstates 222As mentioned, the visibility of
spin excitations will depend on the tunneling current intensity as $\simeq
I^{n}$, so that higher spin ‘flips’ will require higher current intensity to
occur with sufficient amplitude. Variation of STM set points can provide
information on these features.) [30]. As the ground state of the chain is a
singlet, successive ‘flips’ create excitations along the chain with one-
quantum larger or smaller spin overall. Larger flips typically involve higher
energy, which provides distinct spectral signatures, as seen by the different
color curves in the top left inset of Fig. 3 for different $n$ values in the
case of the spin-raising operator $(S^{+}_{i})^{n}$. The associated change in
current versus bias voltage as different spin-flip channels are open can be
easily identified in experiments [31, 29].

It is interesting to notice that tunneling onto different sites along the
chain changes the differential conductance signatures. The first- and second-
sites of the chain have nearly identical spectral yield for low energy.
However, the amplitudes of various peaks are slightly higher (by 10 to 20%)
when tunneling onto site 2. At higher energy, excitations have drastically
different site-signatures [26]. We emphasize that higher energy excitations
would be produced less likely at low tunneling current, resulting in an
overall decaying probability envelope for higher energies [29]. Also note that
the spatial inversion symmetry of the chain ensures the same results for
tunneling onto the fourth and third sites, correspondingly. Similar behavior
is seen for $(S^{-})^{n}$ on different sites, as expected for an overall
singlet ground state.

As mentioned, the full $d^{2}I/dV^{2}$ features need to consider all spin-flip
scattering events, as electrons tunnel. Before presenting those results, we
consider the effect of Zeeman fields on the system.

\begin{overpic}[width=244.69386pt]{site_1_first_flips_diff_cond.png}\put(620.0,420.0){\framebox(0.0,0.0)[bl]{\includegraphics[width=88.2037pt]{site_1_flips_diff_cond.png}}}\put(250.0,420.0){\framebox(0.0,0.0)[bl]{\includegraphics[width=88.2037pt]{spin_flip_contributions.png}}}\put(465.0,320.0){\sf
SITE 1}\end{overpic} Figure 3: Excitation profile for repeated spin raising on
the first site of the Eu-four-atom chain on its ground state. Left inset shows
contributions to main panel by successive spin ’flips’ on site 1 – higher $n$
appear at higher excitation energy. Right inset shows higher energy region.
Weights are displayed using Gaussian broadening with FWHM$=0.25J_{2}$. All
horizontal axes show excitation energy in units of $J_{2}$.

####  III.2.1 Zeeman field effects

Applying magnetic fields during STM spectroscopy experiments provides a
powerful tool to obtain further information on the system. A modest field of
$h_{z}=0.1|J_{1}|\approx 0.14\;\mathrm{T}$ splits degeneracies in the Eu-chain
for the low excitation energy manifolds, as shown in Fig. 4. The field
splittings are linear, as the perturbing Hamiltonian is
$\hat{H}_{Z}=-h_{z}\hat{S}_{z}$, associated with the corresponding $S_{z}$
total-spin projection of each state, and displayed for the low-energy
excitations in Fig. 5. Notice that for $h_{z}\gtrsim 3.1\;\mathrm{T}$ the
ground state of the chain is polarized from $S_{z}=0$ to $1$, and increasing
$S_{z}$ projections as $h_{z}$ increases (to $S_{z}=2$ at $\approx 6.2$ T,
etc.).

\begin{overpic}[width=244.69386pt]{first_spectrum_h=01.png}\put(520.0,120.0){\framebox(0.0,0.0)[bl]{\includegraphics[width=113.81102pt]{full_spectrum_h=01.png}}}\end{overpic}
Figure 4: Energy excitation spectrum for the four-site spin chain with Zeeman
field $h_{z}=0.1|J_{1}|\simeq 0.14$ T. Notice slight splitting of degenerate
multiplets, as compared with those in Fig. 2.
\begin{overpic}[width=244.69386pt]{zeeman_splitting.png}\end{overpic} Figure
5: Low-lying eigenstates for increasing applied Zeeman field. Linear
dependence illustrates $S_{z}$ projection of each state. Ground state is
increasingly polarized from $S_{z}=0$ to 1, 2, etc. at $h_{z}\simeq 3.1$, 6.2,
etc.

To explore the role of the Zeeman field on the differential conductance
features, we calculate the excitation weight profile on the first and second
sites of the chain as a function of field. As seen in the spectrum above, the
Zeeman coupling results in clear shifts with increasing field, reflected also
in the excitation weight profile, shown for site 1 and 2 in Fig. 6a and b,
respectively. The low-energy profiles for the different site excitations are
rather similar, with features shifting linearly in field, as expected [30].
However, for the multiplet with excitation $\Delta E/J_{2}\simeq 3$, the
coincidence of multiple contributions results in different field dependence
for the two sites. While the left-most twin peak at $\Delta E\simeq 2.6J_{2}$
shifts equally to the first peak at 0.5, the right-most twin peak ($\Delta
E\simeq 2.9J_{2}$ at zero field) shifts in field at triple the rate of the
other, and this is seen for both sites 1 and 2. However, site 1 exhibits a
shoulder feature on the right, $\Delta E\simeq 3.4J_{2}$ at 2.5 T, absent for
site 2. This behavior reflects the origin of the corresponding eigenstates,
and the associated larger $S_{z}$ spin projection component when a larger rate
of change is seen in Fig. 6, produced by higher order spin flips on a site
[29].

\begin{overpic}[width=244.69386pt]{site_1_flips_diff_cond_h_varies_vert_heatmap.png}\put(4.0,650.0){(a)}\end{overpic}

\begin{overpic}[width=244.69386pt]{site_2_flips_diff_cond_h_varies_vert_heatmap.png}\put(4.0,650.0){(b)}\end{overpic}

Figure 6: Heatmap of excitation weight profile ($\simeq$ differential
conductance signatures) for increasing Zeeman field strength and corresponding
energy (bias). We plot $I=2|b_{z}|^{2}+|b_{+}|^{2}+|b_{-}|^{2}$ to account for
all different scattering processes for tunneling electrons. (a) Results for
tunneling through first and (b) second site.

###  III.3 Non-collinear exchange effects

It is reasonable to expect a Dzyaloshinskii-Moriya interaction (DMI) may also
appear in the spin system due to the strong Rashba spin-orbit effect measured
on the gold surface [32]. This interaction results in the antisymmetric
Hamiltonian
$H_{DMI}=\sum_{ij}\vec{D}\cdot\hat{\vec{S}}_{i}\times\hat{\vec{S}}_{j}$, that
can qualitatively change the ground state configuration as well as the rest of
the excitation spectrum [33, 34]. To assess its effect on STM spectroscopy, we
consider the likely dominant $z$-component of the DMI vector $\vec{D}$. Figure
7 displays the resulting spectrum with $D_{z}=0.71|J_{1}|$, showing that the
ground state remains a singlet, while the excitation multiplets are split more
strongly the larger their $|S_{z}|$ values – notice that the $\pm S_{z}$
degeneracies in the spectrum remain. Figure 8 shows how the excitation
spectrum changes for larger $D_{z}$ values, shifting all energies down as
$D_{z}$ increases, splitting degenerate manifolds, and producing nonlinear
changes in the excitation spectrum with $D_{z}$ (main panel).

\begin{overpic}[width=244.69386pt]{first_spectrum_d=1T.png}\put(520.0,110.0){\framebox(0.0,0.0)[bl]{\includegraphics[width=113.81102pt]{full_spectrum_d=1T.png}}}\end{overpic}
Figure 7: Low energy and (inset) full excitation spectrum for the four-site
spin chain with $h_{z}=0$ and $D_{z}=0.71J_{1}$. Compare with Fig. 2.
\begin{overpic}[width=244.69386pt]{dmi_splitting_delta.png}\put(160.0,400.0){\framebox(0.0,0.0)[bl]{\includegraphics[width=113.81102pt]{dmi_splitting.png}}}\end{overpic}
Figure 8: Main panel shows excitations for Eu-chain as $D_{z}$ increases.
Inset shows corresponding low-lying states, all for $h_{z}=0$.
\begin{overpic}[width=227.62204pt]{zeeman_splitting_with_d=1.png}\end{overpic}
Figure 9: Low-lying eigenstates for increasing applied Zeeman field and
$D_{z}=0.71J_{1}$.

We calculate the excitation weight profile as function of Zeeman field for a
system with $D_{z}=0.7J_{1}$, with field dependence shown in Fig. 9. Notice
that the ground state changes from a singlet ($S_{z}=0$) to a $S_{z}=1$ at a
lower field ($\simeq 2$ T), and that the first excited singlet occurs at
around 1.8$J_{2}$. These and other level splittings introduced by the DMI
perturbation are naturally reflected in the weight profile shown in Fig. 10,
for tunneling through the site 1. In this case (not shown), tunneling through
site 2 produces essentially the same differential conductance profile,
indicating that the DMI interaction has effectively involved all sites in this
low-energy regime.

\begin{overpic}[width=241.84842pt]{site_1_flips_diff_cond_d=07_h_varies_vert_heatmap.png}\end{overpic}
Figure 10: Heatmap of excitation weight profile (akin to differential
conductance signatures) for increasing Zeeman field strength and corresponding
energy (bias) for system with $D_{z}=0.7J_{1}$ – Fig. 9. We plot
$I=2|b_{z}|^{2}+|b_{+}|^{2}+|b_{-}|^{2}$ to account for different scattering
processes for tunneling electrons. Results for tunneling through first site of
chain.

##  IV Conclusions

The advent of atomic-site manipulation via STM has heralded a new era of
materials science and engineering. One can not only design quantum systems,
but precisely assemble them and measure their electronic and magnetic
characteristics at the level of a single atom or molecular entity. Spin
chains, with a great history of deep insights into the physics of interacting
systems, garner ever increasing interest as they naturally interface with
growing fields of quantum information transmission, computing, and sensing.
Our proposal to assemble large-spin systems to highlight their rich behavior
has focused on a four-atom chain of effective Eu+3 ions on a Au(111) surface.
First principles calculations of realistic systems allow us to extract
magnetic excitation spectra and resulting differential conductance profiles
with site-specific excitations. Experimental realization of this system would
provide us with the interesting opportunity of not only benchmarking our model
and specific exchange parameters, but would be the next step in exploring
quantum information transfer down long chains.

###### Acknowledgements.

We thank S.-W. Hla and E. Masson for helpful discussions and acknowledge
financial support from the U.S. Department of Energy, Office of Science,
Office of Basic Energy Sciences, Materials Science and Engineering Division.

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11institutetext:  National Observatory of Athens, Institute for Astronomy,
Astrophysics, Space Applications and Remote Sensing, Ioannou Metaxa and
Vasileos Pavlou GR-15236, Athens, Greece 22institutetext: Department of
Astrophysics, Astronomy & Mechanics, Faculty of Physics, University of Athens,
Panepistimiopolis, GR-15784 Zografos, Athens, Greece 33institutetext: LLR
(Laboratoire Leprince-Ringuet), CNRS, Ãcole Polytechnique, Institut
Polytechnique de Paris, Palaiseau, France 44institutetext: School of Physics
and Astronomy, Cardiff University, Queenâs Buildings, The Parade, Cardiff,
CF24 3AA, UK 55institutetext: AIM, CEA, CNRS, Université Paris-Saclay,
Université Paris Diderot, Sorbonne Paris Cité, 91191 Gif-sur-Yvette, France
66institutetext: Univ. Grenoble Alpes, CNRS, Grenoble INP, LPSC-IN2P3, 53,
avenue des Martyrs, 38000 Grenoble, France 77institutetext: Université Paris-
Saclay, CNRS, Institut d’astrophysique spatiale, 91405, Orsay, France
88institutetext: Institut Néel, CNRS, Université Grenoble Alpes, France
99institutetext: Institut de RadioAstronomie Millimétrique (IRAM), Grenoble,
France 1010institutetext: Aix Marseille Univ, CNRS, CNES, LAM (Laboratoire
d’Astrophysique de Marseille), Marseille, France 1111institutetext:
Sterrenkundig Observatorium Universiteit Gent, Krijgslaan 281 S9, B-9000 Gent,
Belgium 1212institutetext: Department of Physics and Astronomy, University
College London, Gower Street, London WC1E 6BT, UK 1313institutetext:
Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 5,
I-00185 Roma, Italy 1414institutetext: Univ. Grenoble Alpes, CNRS, IPAG, 38000
Grenoble, France 1515institutetext: Institute for Research in Fundamental
Sciences-IPM, Larak Garden,19395-5531 Tehran, Iran 1616institutetext: Centro
de Astrobiología (CSIC-INTA), Torrejón de Ardoz, 28850 Madrid, Spain
1717institutetext: Instituto de Radioastronomía Milimétrica (IRAM), Granada,
Spain 1818institutetext: LERMA, Observatoire de Paris, PSL Research
University, CNRS, Sorbonne Université, UPMC, 75014 Paris, France
1919institutetext: School of Earth and Space Exploration and Department of
Physics, Arizona State University, Tempe, AZ 85287, USA Laboratoire de
Physique de lâÉcole Normale Supérieure, ENS, PSL Research University, CNRS,
Sorbonne Université, Université de Paris, 75005 Paris, France
2020institutetext: Department of Physics and Astronomy, University of
Pennsylvania, 209 South 33rd Street, Philadelphia, PA, 19104, USA
2121institutetext: Institut d’Astrophysique de Paris, Sorbonne UniversitÃ,
CNRS (UMR7095), 75014 Paris, France 2222institutetext: Kavli Institute for
Astrophysics and Space Research, Massachusetts Institute of Technology,
Cambridge, MA 02139, USA 2323institutetext: Caltech, Pasadena, CA 91125, USA
2424institutetext: Instituto de AstrofÃsica de Canarias, VÃa Lâactea S/N,
38205 La Laguna, Spain

# Exploring the millimetre emission in nearby galaxies:

analysis of the edge-on galaxy NGC 891

S. Katsioli Exploring the millimetre emission in nearby galaxies:Exploring the
millimetre emission in nearby galaxies:Exploring the millimetre emission in
nearby galaxies:Exploring the millimetre emission in nearby galaxies:
<EMAIL_ADDRESS>R. Adam Exploring the millimetre emission in nearby
galaxies:Exploring the millimetre emission in nearby galaxies: P. Ade
Exploring the millimetre emission in nearby galaxies:Exploring the millimetre
emission in nearby galaxies: H. Ajeddig Exploring the millimetre emission in
nearby galaxies:Exploring the millimetre emission in nearby galaxies: P. André
Exploring the millimetre emission in nearby galaxies:Exploring the millimetre
emission in nearby galaxies: E. Artis Exploring the millimetre emission in
nearby galaxies:Exploring the millimetre emission in nearby galaxies: H.
Aussel Exploring the millimetre emission in nearby galaxies:Exploring the
millimetre emission in nearby galaxies: A. Beelen Exploring the millimetre
emission in nearby galaxies:Exploring the millimetre emission in nearby
galaxies: A. Benoît Exploring the millimetre emission in nearby
galaxies:Exploring the millimetre emission in nearby galaxies: S. Berta
Exploring the millimetre emission in nearby galaxies:Exploring the millimetre
emission in nearby galaxies: L. Bing Exploring the millimetre emission in
nearby galaxies:Exploring the millimetre emission in nearby galaxies: O.
Bourrion Exploring the millimetre emission in nearby galaxies:Exploring the
millimetre emission in nearby galaxies: M. Calvo Exploring the millimetre
emission in nearby galaxies:Exploring the millimetre emission in nearby
galaxies: A. Catalano Exploring the millimetre emission in nearby
galaxies:Exploring the millimetre emission in nearby galaxies: I. De Looze
Exploring the millimetre emission in nearby galaxies:Exploring the millimetre
emission in nearby galaxies:Exploring the millimetre emission in nearby
galaxies:Exploring the millimetre emission in nearby galaxies: M. De Petris
Exploring the millimetre emission in nearby galaxies:Exploring the millimetre
emission in nearby galaxies: F.-X. Désert Exploring the millimetre emission in
nearby galaxies:Exploring the millimetre emission in nearby galaxies: S. Doyle
Exploring the millimetre emission in nearby galaxies:Exploring the millimetre
emission in nearby galaxies: E. F. C. Driessen Exploring the millimetre
emission in nearby galaxies:Exploring the millimetre emission in nearby
galaxies: G. Ejlali Exploring the millimetre emission in nearby
galaxies:Exploring the millimetre emission in nearby galaxies: M. Galametz
Exploring the millimetre emission in nearby galaxies:Exploring the millimetre
emission in nearby galaxies: F. Galliano Exploring the millimetre emission in
nearby galaxies:Exploring the millimetre emission in nearby galaxies: A. Gomez
Exploring the millimetre emission in nearby galaxies:Exploring the millimetre
emission in nearby galaxies: J. Goupy Exploring the millimetre emission in
nearby galaxies:Exploring the millimetre emission in nearby galaxies: A. P.
Jones Exploring the millimetre emission in nearby galaxies:Exploring the
millimetre emission in nearby galaxies: A. Hughes Exploring the millimetre
emission in nearby galaxies:Exploring the millimetre emission in nearby
galaxies: F. Kéruzoré Exploring the millimetre emission in nearby
galaxies:Exploring the millimetre emission in nearby galaxies: C. Kramer
Exploring the millimetre emission in nearby galaxies:Exploring the millimetre
emission in nearby galaxies:Exploring the millimetre emission in nearby
galaxies:Exploring the millimetre emission in nearby galaxies: B. Ladjelate
Exploring the millimetre emission in nearby galaxies:Exploring the millimetre
emission in nearby galaxies: G. Lagache Exploring the millimetre emission in
nearby galaxies:Exploring the millimetre emission in nearby galaxies: S.
Leclercq Exploring the millimetre emission in nearby galaxies:Exploring the
millimetre emission in nearby galaxies: J.-F. Lestrade Exploring the
millimetre emission in nearby galaxies:Exploring the millimetre emission in
nearby galaxies: J.-F. Macías-Pérez Exploring the millimetre emission in
nearby galaxies:Exploring the millimetre emission in nearby galaxies: S. C.
Madden Exploring the millimetre emission in nearby galaxies:Exploring the
millimetre emission in nearby galaxies: A. Maury Exploring the millimetre
emission in nearby galaxies:Exploring the millimetre emission in nearby
galaxies: P. Mauskopf Exploring the millimetre emission in nearby
galaxies:Exploring the millimetre emission in nearby galaxies:Exploring the
millimetre emission in nearby galaxies:Exploring the millimetre emission in
nearby galaxies: F. Mayet Exploring the millimetre emission in nearby
galaxies:Exploring the millimetre emission in nearby galaxies: A. Monfardini
Exploring the millimetre emission in nearby galaxies:Exploring the millimetre
emission in nearby galaxies: M. Muñoz-Echeverría Exploring the millimetre
emission in nearby galaxies:Exploring the millimetre emission in nearby
galaxies: A. Nersesian Exploring the millimetre emission in nearby
galaxies:Exploring the millimetre emission in nearby galaxies:Exploring the
millimetre emission in nearby galaxies:Exploring the millimetre emission in
nearby galaxies: L. Perotto Exploring the millimetre emission in nearby
galaxies:Exploring the millimetre emission in nearby galaxies: G. Pisano
Exploring the millimetre emission in nearby galaxies:Exploring the millimetre
emission in nearby galaxies: N. Ponthieu Exploring the millimetre emission in
nearby galaxies:Exploring the millimetre emission in nearby galaxies: V.
Revéret Exploring the millimetre emission in nearby galaxies:Exploring the
millimetre emission in nearby galaxies: A. J. Rigby Exploring the millimetre
emission in nearby galaxies:Exploring the millimetre emission in nearby
galaxies: A. Ritacco Exploring the millimetre emission in nearby
galaxies:Exploring the millimetre emission in nearby galaxies:Exploring the
millimetre emission in nearby galaxies:Exploring the millimetre emission in
nearby galaxies: C. Romero Exploring the millimetre emission in nearby
galaxies:Exploring the millimetre emission in nearby galaxies: H. Roussel
Exploring the millimetre emission in nearby galaxies:Exploring the millimetre
emission in nearby galaxies: F. Ruppin Exploring the millimetre emission in
nearby galaxies:Exploring the millimetre emission in nearby galaxies: K.
Schuster Exploring the millimetre emission in nearby galaxies:Exploring the
millimetre emission in nearby galaxies: S. Shu Exploring the millimetre
emission in nearby galaxies:Exploring the millimetre emission in nearby
galaxies: A. Sievers Exploring the millimetre emission in nearby
galaxies:Exploring the millimetre emission in nearby galaxies: M. W. L. Smith
Exploring the millimetre emission in nearby galaxies:Exploring the millimetre
emission in nearby galaxies: F. Tabatabaei Exploring the millimetre emission
in nearby galaxies:Exploring the millimetre emission in nearby
galaxies:Exploring the millimetre emission in nearby galaxies:Exploring the
millimetre emission in nearby galaxies: C. Tucker Exploring the millimetre
emission in nearby galaxies:Exploring the millimetre emission in nearby
galaxies: E. M. Xilouris Exploring the millimetre emission in nearby
galaxies:Exploring the millimetre emission in nearby galaxies: R. Zylka
Exploring the millimetre emission in nearby galaxies:Exploring the millimetre
emission in nearby galaxies:

###### Abstract

New observations of the edge-on galaxy NGC 891, at 1.15 and 2 mm obtained with
the IRAM 30-m telescope and the NIKA2 camera, within the framework of the
IMEGIN (Interpreting the Millimetre Emission of Galaxies with IRAM and NIKA2)
Large Program, are presented in this work. By using multiwavelength maps (from
the mid-IR to the cm wavelengths) we perform SED fitting in order to extract
the physical properties of the galaxy on both global and local ($\sim$kpc)
scales. For the interpretation of the observations we make use of a state-of-
the-art SED fitting code, HerBIE (HiERarchical Bayesian Inference for dust
Emission). The observations indicate a galaxy morphology, at mm wavelengths,
similar to that of the cold dust emission traced by sub-mm observations and to
that of the molecular gas. The contribution of the radio emission at the NIKA2
bands is very small (negligible at 1.15 mm and $\sim 10\%$ at 2 mm) while it
dominates the total energy budget at longer wavelengths (beyond 5 mm). On
local scales, the distribution of the free-free emission resembles that of the
dust thermal emission while the distribution of the synchrotron emission shows
a deficiency along the major axis of the disc of the galaxy.

##  1 Introduction

Nearby galaxies have provided a great piece of knowledge in the field of
galaxy formation and evolution. Their proximity allows us to study galaxies at
high resolution and to derive their properties on local (sub-kpc/kpc) scales.
The current study is part of the IMEGIN Large Program (P.I.: S. Madden), a
NIKA2 guaranteed time program of 200 hours allocated telescope time with the
aim of mapping 22 nearby galaxies (distances of < 30 Mpc) at 1.15 and 2 mm
using the NIKA2 continuum camera at the IRAM 30-m telescope
(NIKA2-performance, ; NIKA2-general, ; NIKA2-instrument, ; NIKA2-electronics,
). The main objective of the project is to explore the emission at millimetre
wavelengths originating from nearby galaxies, a complex wavelength regime with
contributions from a mix of different emission mechanisms (free-free,
synchrotron, and dust thermal emission). This is the first time that nearby
galaxies are being observed in the continuum at mm wavelengths at resolutions
of 11.1′′ and 17.6′′ ($\sim 0.5$ kpc, and $\sim 0.8$ kpc at a distance of 10
Mpc) at 1.15 and 2 mm respectively. At these scales it is possible to
disentangle the contribution of the different emission mechanisms in different
environments inside the galaxies (disc, halo, HII regions, etc).

As a pilot study, we analyze the NIKA2 observations of the edge-on galaxy NGC
891, a SA(s)b type galaxy 2013AJ….145..137K . Due to its proximity (D = 9.6
Mpc; 2004ApJ…606..829S ) and its edge-on orientation (i $\cong$ 89.8∘;
1999A&A…344..868X ), NGC 891 is one of the most observed and well studied
galaxies of the Local Universe (e.g. 1999A&A…344..868X ; hughes ; mulcahy ;
yoon ).

##  2 Observations and Analysis

Figure 1: NIKA2 high-resolution millimeter observations of NGC 891 at 1.15
(top panel) and 2 mm (bottom panel). The maps are presented in their native
resolution (11.1′′ and 17.6′′ at 1.15 and 2 mm respectively; indicated by the
white circles in each panel) and they are rotated by 22.9∘ (the position angle
of the galaxy). Their sky RMS values are 1.0 mJy beam-1 and 0.3 mJy beam-1 at
1.15 mm and 2 mm. The surface brightness contours correspond to 3.5, 8, 15 and
30 $\times$ RMS.

The NIKA2 observations of NGC 891 were obtained between October 2019 and
January 2020 with a total on-source integration time of 7 hours. The maps of
the galaxy at 1.15 and 2 mm were reduced using the
GILDAS/PIIC111https://publicwiki.iram.es/PIIC/ (version of 29.04.2020)
software (2013ascl.soft03011Z, ) and are shown in Fig. 1 (top and bottom
panels respectively). The edge-on orientation of the galaxy and the high
resolution of the maps allow us to discern different regions along the major
axis with the main characteristics being a peak emission at the nucleus and
secondary maxima at $\sim 3$ kpc either side of the center. These emission
features closely resemble the distribution of the cold dust traced by sub-mm
observations 2011A&A…531L..11B  as well as of the molecular gas
(1993ApJ…404L..59S, ; 1992A&A…266…21G, ) which are possibly originating either
from a ring structure or limb brightening associated with spiral arms (see
1998ApJ…507L.125A ).

In our study we performed a Spectral Energy Distribution (SED) analysis of NGC
891 using multiwavelength data ranging from 3.4 $\mu$m to 5 cm. We used
archival data from the WISE telescope (3.4, 4.6, 11.6 and 22.1 $\mu$m), the
Spitzer telescope (3.6, 4.5, 5.8, and 24 $\mu$m), as well as the Herschel
telescope (70, 100, 160, 250, and 350 $\mu$m). Along with the NIKA2
observations at 1.15 and 2 mm we also used centimeter data from the AMI (2 cm)
and EVLA (5 cm) radio telescopes. The archival data have been retrieved from
the DustPedia222http://dustpedia.astro.noa.gr/ and
NED333https://ned.ipac.caltech.edu/ databases. The maps were all convolved
(using Gaussian Kernels) to the same angular resolution of 25′′ corresponding
to the resolution of the 350 $\mu$m SPIRE map. This resolution corresponds to
$\sim 1.1$ kpc at the distance of NGC 891. All maps have also been regridded
into a common reference frame with a pixel size of 8′′. Fitting the continuum
emission of the galaxy, we had to remove the background sources from the near-
IR maps as well as to correct the 1.15 mm map (see NIKA2-performance  for the
NIKA2 transmission curves) from the CO(2-1) line contamination following the
procedure described in CO_line . In order to compute the global fluxes at each
wavelength we used an elliptical aperture centered at
RA${}_{J2000}=2^{h}22^{m}33^{s}$,
DEC${}_{J2000}=+42^{\circ}20^{\prime}53^{\prime\prime}$ 2007AJ….134.1019O
with major and minor axes of 5′ and 48′′ respectively and positional angle of
22.9∘, so as to encompass the bulk of the emission originating from the disc
of the galaxy. Additional global photometry at radio wavelengths (from Planck,
100-m Effelsberg, OVRO, WSRT and GBT telescopes) were also culled from the
literature.

To interpret the SED we used the SED fitting code HerBIE (Hierarchical
Bayesian Inference for dust Emission; 2018MNRAS.476.1445G ; 2021A&A…649A..18G
). In contrast to the commonly used least-squares fitting method, HerBIE
eliminates the noise-induced correlations between the parameters. The code
takes into account realistic optical properties and stochastic heating for the
dust grains by making use of the THEMIS dust model which is described in
detail in 2013A&A…555A..39J ; 2017A&A…602A..46J . Free-free and synchrotron
emission mechanisms are also implemented in the code. The global SED of the
galaxy, fitted by the HerBIE code, is presented in the left panel in Fig. 2.

Figure 2: Left panel: the global SED of NGC 891 with multiwavelength data
ranging from 3.4 $\mu$m to 6.3 cm. The curve passing through the photometric
data is the best fitted model with the width of the curve indicating the
uncertainty of the model along the spectrum. The emission components of the
total SED of the galaxy, stellar, dust and radio, are plotted with orange, red
and brown color respectively. The residuals between the observed and the model
predicted fluxes are given in the graph below the SED in dex. Right panel: An
emission decomposition plot for characteristic wavelengths in the spectral
range between 1 mm to 2 cm. The percentage of the dust emission is presented
with orange color, while red and blue colors are used for percentages of the
free-free and the synchrotron emission respectively.

With an angular resolution of 25′′ (see Sec. 2) the observations used in this
study allowed us to perform spatially resolved SED fitting within the galaxy
and create maps of the local physical properties associated with the dust and
radio emission. The maps presented in Fig. 3 show the total dust luminosity
map (left), the free-free luminosity at 2 cm (middle) and the synchrotron
luminosity at 2 cm (right).

##  3 Results

Modelling the SED of NGC 891 in the wavelength range from 3.4 $\mu$m to 6.3 cm
allows us to accurately determine the dust content, taking into account
emission from the aromatic features as well as from the continuum emission
from small and big grains, but also the radio emission composed by the free-
free and the synchrotron radiation. Our model predicts a total dust mass of
(4.18 $\pm$ 0.21) $\times\leavevmode\nobreak\ 10^{7}$ M⊙, while the mass
fraction of the small carbon grains over the total dust mass is 0.10 $\pm$
0.01. The total radio luminosity at 2 cm is (5.54 $\pm$ 0.24)
$\times\leavevmode\nobreak\ 10^{4}$ L⊙ with a fraction of 0.16 $\pm$ 0.11
originating in free-free radiation. The inferred value of the synchrotron
radiation index ($\mathbf{\alpha_{s}}$) is 0.78 $\pm$ 0.08 (in agreement with
other studies, e.g. mulcahy ).

Having modelled the SED we can now study the largely unexplored wavelength
range between $\sim 1$ mm and $\sim 2$ cm where a mix of emission mechanisms
exists. In the right panel of Fig. 2 we present the percentages to the global
emission of dust (orange color), free-free (red color) and synchrotron
emission (blue color) at 1, 2, 3, 5, 7 mm and 1, and 2 cm. From this plot it
is evident that the dust thermal emission dominates to up to $\sim 3$ mm where
the contributions of the free-free and synchrotron emission mechanisms become
almost equally significant to the dust emission. At longer wavelengths, these
latter emission mechanisms dominate with the synchrotron emission increasing
rapidly with values up to $\sim 84\%$ at 2 cm, while the free-free emission
reaches a maximum contribution of $\sim 26\%$ at $\sim 7$ mm and then drops
again.

Figure 3: Maps of the model-inferred luminosity for the dust emission (left
panel), the free-free luminosity at 2 cm (middle panel) and the synchrotron
luminosity at 2 cm (right panel).The colorbar on the right in each panel
indicates the luminosity in units of L⊙pc-2.

The spatial decomposition of the emission of the galaxy (see Fig. 3) allows us
to determine the places where the different emission mechanisms dominate. From
the dust luminosity map (left panel of Fig. 3) it is evident that the bulk of
the dust emission comes from the disc of the galaxy, as it is clearly seen
also from the NIKA2 observations (Fig. 1), but with significant amount also
coming from the dust halo at large distances from the disc. The free-free
emission at 2 cm (middle panel of Fig. 3) shows a similar distribution to that
of the dust emission, while the synchrotron luminosity (right panel of Fig. 3)
shows a different distribution with a deficiency along the galactic plane and
with the peak emission originating from the galactic center. One interesting
difference between the dust and the radio emission maps is the shape of the
halo which, in the dust case has an elliptical shape, while in the radio case
(and especially in the synchrotron component) has a more complex “peanut”-like
shape.

##  4 Conclusions

In this study we present new millimetre NIKA2 observations of the edge-on
galaxy NGC 891 at 1.15 and 2 mm. Using the NIKA2 observations and also
multiwavelength maps (from the mid-IR to the cm wavelengths) we construct the
galaxy’s SED and perform SED fitting analysis using the HerBIE SED fitting
code. The observations indicate a morphology similar to that of the cold dust
(detected at sub-mm) and of the molecular gas with the emission peaking at the
nucleus of the galaxy and with two secondary maxima at $\sim 3$ kpc either
side of the center. Emission at the NIKA2 bands is dominated by thermal dust,
while the radio emission becomes almost equally significant to the thermal
emission at $\sim 3$ mm. At longer wavelengths the radio emission dominates
with synchrotron emission reaching up to $\sim 84\%$ at 2 cm. On local scales
our analysis shows that the bulk of the dust thermal emission and the free-
free emission comes from the disc of the galaxy while there is a deficiency,
of the synchrotron emission, along the major axis of the disc of the galaxy.

## Acknowledgements

We would like to thank the IRAM staff for their support during the campaigns.
The NIKA2 dilution cryostat has been designed and built at the Institut Néel.
In particular, we acknowledge the crucial contribution of the Cryogenics
Group, and in particular Gregory Garde, Henri Rodenas, Jean Paul Leggeri,
Philippe Camus. This work has been partially funded by the Foundation
Nanoscience Grenoble and the LabEx FOCUS ANR-11-LABX-0013. This work is
supported by the French National Research Agency under the contracts "MKIDS",
"NIKA" and ANR-15-CE31-0017 and in the framework of the "Investissements
dâavenir" program (ANR-15-IDEX-02). This work has benefited from the support
of the European Research Council Advanced Grant ORISTARS under the European
Union’s Seventh Framework Programme (Grant Agreement no. 291294). F.R.
acknowledges financial supports provided by NASA through SAO Award Number
SV2-82023 issued by the Chandra X-Ray Observatory Center, which is operated by
the Smithsonian Astrophysical Observatory for and on behalf of NASA under
contract NAS8-03060. This work was supported by the Programme National
"Physique et Chimie du Milieu Interstellaire" (PCMI) of CNRS/INSU with INC/INP
co-funded by CEA and CNES.

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