# Optical fingerprints of the electronic band reconstruction in van der Waals
magnetic materials

M. Corasaniti† R. Yang† Laboratorium für Festkörperphysik, ETH - Zürich, 8093
Zürich, Switzerland  Y. Liu‡ Condensed Matter Physics and Materials Science
Department, Brookhaven National Laboratory, Upton NY 11973, USA  C. Petrovic
Condensed Matter Physics and Materials Science Department, Brookhaven National
Laboratory, Upton NY 11973, USA  L. Degiorgi∗ Laboratorium für
Festkörperphysik, ETH - Zürich, 8093 Zürich, Switzerland

(August 29, 2024)

###### Abstract

We report a broadband study of the charge dynamics in the van der Waals (vdW)
magnetic materials 2H-$M_{x}$TaS2 ($M$ = Mn and Co), which span the onset of
both long-range antiferromagnetic (AFM) and ferromagnetic (FM) order,
depending on the intercalation $M$ and its concentration $x$. We discover a
spectral weight ($SW$) shift from high to low energy scales for FM
compositions, while reversely $SW$ is removed from low towards high spectral
energies for AFM compounds. This maps the related reconstruction of the
electronic band structure along the crossover from the FM to AFM order, which
restores an occupation balance in the density of states between spin majority
and minority bands of the intercalated 3$d$ elements.

Understanding the physical mechanism as well as functionalities of van der
Waals (vdW) heterostructures and electronic/spintronic devices is at present a
central topic of the ongoing solid state physics research activities Zhang
_et al._ (2019). In this context, Fe3GeTe2 and MnSe2 are prototype examples
Deng  _et al._ (2018); O’Hara  _et al._ (2018) of two-dimensional vdW magnets.
The discovery of such a long-range magnetism lately boosted the several
decades long investigation of the (mostly non-magnetic) vdW transition-metal
dichalcogenides (TMDCs) with appropriate magnetic intercalations. This
enlarges the fundamental studies of low-dimensional magnetism and provides a
platform for questing the nature of the critical behaviour of the spin
interactions, ranging from Heisenberg and XY to Ising type Zhang  _et al._
(2019).

The TMDC materials of general formula TX2 (e.g., with T = Nb, Ta and X = Se,
S) consist of layered-like sandwiches held together by relatively weak forces
across the vdW gaps, within which intercalation may occur. The latter is
notably accompanied by charge transfer between the intercalated species and
the host layer but is not supposed to change the local bonding within the
sandwich layers, so that the electronic properties of the host TMDC materials
could be treated within the rigid-band model and consequently be fine-tuned
depending on the effective $d$-bands filling. Such a controllable degree of
band filling seems to be a feature quite unique to low-dimensional structures
Parkin and Friend (1980); Friend and Yoffe (1987).

In this work, we focus our attention on the 2H-$M_{x}$TaS2 compounds with $M$
= Co and Mn. While the possibility to intercalate TMDCs with magnetic 3$d$
elements $M$, exhibiting diverse magnetic properties, is known since the
eighties, their physical properties have been only addressed recently Liu  _et
al._ (2021a, b, 2022). Any intercalation with atoms, that tend to preserve
local moment when embedded in a metallic host, induces long range magnetic
order Zhang  _et al._ (2021); Hatanaka  _et al._ (2022). This is different
from the simple charge transfer that occurs upon intercalation of non-magnetic
atom such as Pd or Li, and which commonly perturbs the charge-density-wave
(CDW) and enhances superconductivity Bhoi  _et al._ (2016); Liu  _et al._
(2021c). The pristine 2H-TaS2 compound is in fact a familiar CDW material
Harper  _et al._ (1977) and the peculiarities with respect to its broken-
symmetry ground state are amply documented in the literature. The (magnetic)
Co and Mn intercalation (Fig. S1 in Supplemental Material (SM) SM ), besides
removing the CDW transition, expands the vdW gap of the 2H-$M_{x}$TaS2
crystals along the $c$-axis (i.e., orthogonal to the layers) and should result
in an electronic doping via hybridization with atoms around the vdW gap Liu
_et al._ (2022). This induces a ferromagnetic (FM) state with an easy-plane
anisotropy in 2H-MnxTaS2 Hinode  _et al._ (1995); Onuki  _et al._ (1986); Li
_et al._ (2011); Shand  _et al._ (2015); Zhang  _et al._ (2018); Liu  _et al._
(2021b). For Co-intercalation, ferromagnetism with strong uniaxial anisotropy
in 2H-Co0.22TaS2 Liu  _et al._ (2021a) and a three-dimensional
antiferromagnetic (AFM) state in 2H-Co0.34TaS2 Van Laar  _et al._ (1971) have
been firmly established. The evolving FM to AFM transition promoted by the Co-
intercalation and the related sign-change of the ordinary Hall coefficient
hint to an electronic multi-band occurrence and its reconstruction based on
the magnetic ground state Liu  _et al._ (2022). The temperature-dependent
electrical resistivity ($\rho(T)$) displays an overall metallic behaviour for
all samples (Fig. S2 in SM SM ). A clear kink in $\rho(T)$, a weak anomaly in
thermal conductivity, as well as a slope change in thermopower were yet
observed at the magnetic transitions for 2H-Mn0.28TaS2 ($T_{C}\sim$ 82 K) and
2H-Co0.34TaS2 ($T_{N}\sim$ 36 K), albeit weaker for crystals with lower
concentration $x$ Liu  _et al._ (2022).

From a spectroscopic point of view, these materials are still not
comprehensively scrutinised. Here, we investigate the temperature ($T$)
dependence of the (in-plane) absorption spectrum Dressel and Gruner (2002)
over a broad spectral range of both Co-and Mn-intercalated 2H-$M_{x}$TaS2.
2H-CoxTaS2 harbour a distinct and reverse spectral weight ($SW$) reshuffling
with regard to the FM and AFM transition at $T_{C}$ and $T_{N}$, respectively.
The overall optical response of the FM Co-intercalated materials (i.e.,
$x\leq$ 0.22) copies with the data collected on the Mn compositions, which all
refer to a FM state. We supply arguments, which favour a reconstruction of the
electronic band structure upon crossing over from the FM to AFM order with
increasing Co-concentration, bearing testimony to the progressive lifting of
the occupation imbalance in the density of states between spin majority and
minority bands of the intercalated 3$d$ elements.

Figure 1: (a-c) In-plane $\sigma_{1}(\omega)$ below 4$\times$104 cm-1 (1 eV =
8.06548$\times$103 cm-1, please note the logarithmic energy scale) at 5 or 10
and 300 K together with their respective total Drude-Lorentz fit (thick dashed
line) after Eq. S1 in SM SM , and (d-f) $T$ dependence of the $SW$ relative
variation with respect to 300 K, i.e., $\Delta SW(T)=SW(T)-SW$(300 K) for
selected fit components (see legend in panels (a-c)) of 2H-$M_{x}$TaS2 ($M$ =
Mn and Co): (a,d) $x$ = 0.09 (FM) Mn-concentration, and (b,e) $x$ = 0.22 (FM)
as well as (c,f) $x$ = 0.34 (AFM) Co-concentration. Panels (a-c) explicitly
show all fit components: the total Drude and Lorentz (Li, i = 1 to 9) HOs SM .
The coloured shaded areas emphasise $SW$ encountered by each component
(reddish and blueish colours refer to 300 and 5 or 10 K, respectively, while
the grey shaded area corresponds to $SW$ being $T$-independent). The rounded
arrows in panels (a-c) highlight the direction in energy of the $SW$
reshuffling upon lowering $T$, which is stronger with thicker arrows. The
inset in panel (d) is a blow-up of $\Delta SW$ for the total Drude term and
HOs L1 and L2. The vertical dashed and dotted lines in panels (d-f) mark
$T_{C}$ and $T_{N}$ (see Table I in SM SM ), respectively. The error bars in
$\Delta SW(T)$ correspond to the direct propagation of the error in the HOs
strength, estimated numerically within the non-linear least-squares fit
technique. The vertical black arrows in panels (d-f) indicate $T^{*}$, as the
onset of the faster $\Delta SW(T)$ variation upon lowering $T$. Additional
data with similar analysis are available in Fig. S7 in SM SM .

We launch first the survey about the $T$ dependence of the real part
($\sigma_{1}(\omega)$) of the optical conductivity, shown in Figs. 1(a-c) for
three selected Mn- and Co-concentration in the energy interval spanning the
far- (FIR), mid- (MIR) and near- (NIR) infrared up to the visible spectral
ranges at 5 or 10 and 300 K. We refer to SM in Ref. SM,  for further details
and additional data for other concentrations. The selected compositions are
particularly pertinent, since they encompass both the FM and AFM magnetic
phase transitions for the Co-intercalation and address a representative Mn
compound towards its FM one (Table I in SM SM ). There is a metallic Drude-
like component, which gets narrow as well as robust upon lowering $T$ (i.e.,
it generally gains $SW$, see below). It merges into a broad and $T$-dependent
MIR absorption between 1000 and 3000 cm-1 SM .

In order to focus the discussion on the impact of the magnetic phase
transition on the electronic properties, we propose their phenomenological
Drude-Lorentz fit SM , which is singled out for the spectra at 5 or 10 and 300
K in Figs. 1(a-c). The chosen layout of the collected data allows to emphasise
the $SW$ redistribution and its evolution as a function of $T$ among the
Lorentz (Li, i = 1 to 9) harmonic oscillators (HO). In general, $SW$ of the
optical conductivity corresponds to its integral
$SW(T)=\frac{Z_{0}}{\pi^{2}}\int_{\omega_{1}}^{\omega_{2}}\sigma_{1}(\omega^{\prime};T)d\omega^{\prime}$,
expressed in units of cm-2 ($Z_{0}$ = 376.73 $\Omega$, being the impedance of
free space) Dressel and Gruner (2002). $\omega_{i}$ ($i$ = 1 and 2) define the
energy interval, relevant for the $SW$ estimation. Ahead, we alternatively
propose to identify specific energy intervals via the phenomenological fit
components, for which the related $SW$ corresponds to the square of the
(Drude) plasma frequency or of the (Lorentz) HO strength (i.e.,
$\omega_{p,Di}^{2}$ or $\Omega_{j}^{2}$ in Eq. (S1) in SM SM ). As elaborated
in SM SM , the metallic part of $\sigma_{1}(\omega)$ necessitates of two Drude
terms for the Co-intercalated materials, thus spotting the multiband nature of
their electronic structure, while the Mn-intercalated compositions feature a
single Drude component. The resulting global Drude $SW$ (i.e.,
$SW=\sum_{i}\omega_{p,Di}^{2}$, $i$ ranging over the number of contemplated
Drude terms) will be anyhow at the centre of our attention.

The main findings of our work are summarised in Fig. 1(d-f). First, in all
compounds the $T$ dependence of the plasma frequencies (Fig. S8 in SM SM ) is
such that the total Drude $SW$ either barely changes or moderately increases
upon lowering $T$. For the Co-compositions, this also pairs with an additional
$SW$ accumulating into the high frequency tail of the purely metallic response
(represented by HO L1, Figs. 1(b-c) and S7(b) in SM SM ). Such an enhancement
results from a shift of $SW$ from higher energy scales. For the Mn-compounds,
the Drude tail is given by the combination of HO L1 and L2 (Fig. 1(a) and
S7(a) in SM SM ), which equally suffer a $SW$ reordering among them and in
favour of the Drude term. The $SW$ reshuffling affecting the Drude term and
eventually its high-energy tail turns out though to be rather residual,
compared to the $SW$ redistribution at higher energies (as e.g. emphasised by
the inset in Fig. 1(d) as well as in Fig. S7(c) in SM SM ). Second and even
more relevant for our discussion, there is an opposite and strong
redistribution of $SW$ between HO L2 and L3 depending on whether a FM or AFM
transition (Figs. 1(b-c)) takes place for the Co-intercalated compounds. For
the Co-concentration $x$ = 0.22, HO L3 losses $SW$, which merges almost
totally in HO L2 upon crossing $T_{C}$ (Fig. 1(e)). The trend in the $SW$
removal and reallocation across the FM transition as observed in the Co-
intercalated composition is similarly confirmed by the observations in the Mn-
intercalated ones (e.g., for $x$ = 0.09 and 0.19 in Fig. 1(d) and Fig. S7(c)
in SM SM , respectively). On the contrary, for the AFM Co-concentration $x$ =
0.34 we principally encounter a progressive and gradual shift of $SW$ from HO
L2 towards HO L3 upon approaching $T_{N}$ from high $T$ (Fig. 1(f)). An
equivalent incidence is observed for the $x$ = 0.26 Co-intercalation (Fig.
S7(d) in SM SM ), so that the $SW$ reshuffling for the AFM transition is fully
exploited and leans towards a constant behaviour pattern below $T_{N}$.
Summarising, we overall discern a mostly incremental $SW$ redistribution at
FIR and MIR-NIR energy intervals upon approaching the magnetic phase
transition from high $T$, which then tends to saturate into the magnetic state
(i.e., at $T<T_{N}$ or $T_{C}$). Additionally, a change of slope in $\Delta
SW(T)$ is observed in all compositions at $T$ ranging between $\sim$ 100 and
250 K. This is noted by $T^{*}$ (black arrows in Figs. 1(d-f) and S7(c-d) in
SM SM ). The resulting kink in $\Delta SW(T)$ is smooth in the Mn-intercalated
materials and rather abrupt and sudden in the Co-ones (at least for $x$ = 0.22
(Fig. 1(e)) and 0.26 (Fig. S7(d) in SM SM ) and somehow stepwise for $x$ =
0.34 (Fig. 1(f)). These observations fairly agree with similar findings (as
kink or upturn around $T^{*}$) in the measured $T$ dependence of the in-plane
thermopower and total thermal conductivity as well as Hall resistivity Liu
_et al._ (2022). The origin of these peculiarities and their link to the
advanced multiband nature of these materials need to be better understood, as
offered here from the optical perspective.

The $SW$ distribution and its evolution upon crossing $T_{C}$ or $T_{N}$ seems
to be a common property for both Co or Mn intercalations and is exclusively
driven by the targeted, final magnetic state (i.e., independent of the element
choice). Moreover, the encountered shift of $SW$ occurs at FIR-MIR energy
scales up to the NIR spectral range, while at visible and ultra-violet
frequencies $SW$ is constant at any $T$ (grey shaded areas in Figs. 1(a-c) and
Figs. S7(a-b) in SM SM ). This also means that the full recovery of $SW$ is
achieved at about 1 eV. Nonetheless, the opposite $SW$ allocation discovered
upon lowering $T$ through either a FM or AFM transition (see rounded arrows in
Figs. 1(a-c) and Figs. S7(a-b) in SM SM ) calls for a yet different
reconstruction of the related electronic band structure, upon which we wish to
argue for the rest of our paper.

Figure 2 schematically depicts the density-of-states (DOS), factual for the
alleged progression of the interband transition probability upon lowering $T$
across the FM and AFM transitions. The charge dynamics and the evolution of
its stored $SW$ convey the presence of interband transitions grouping within
two distinct spectral intervals, i.e., at FIR resonance energies between 50
and 200 meV (i.e., involving the blue bands in Fig. 2) as well as at MIR-NIR
ones between 300 and 500 meV (i.e., involving the red bands in Fig. 2). These
ranges are described by the combination of HOs L3-L4 and L5-L6 for the Mn-
intercalated material and L2 and L3 for the Co-intercalated compositions
(Figs. 1(a-c)), respectively. The thickness of the coloured (vertical) arrows
in Fig. 2 mimics the strength (i.e., $SW$) of those two possible interband
transitions, which alike discriminate between the two magnetic states. Below
$T_{N}$, the (convoluted) MIR-NIR transition is stronger than the lower FIR
one, while the opposite seems to apply below $T_{C}$.

Figure 2: Proposal for DOS particularly emphasising the interband transitions
grouping around the characteristic FIR energy scales of 0.05-0.2 eV (i.e.,
between the blue bands) and MIR-NIR ones of 0.3-0.5 eV (i.e., between the red
bands). The trend in the related transition probability (i.e., $SW$
redistribution of the proposed interband excitations) is indicated by the
arrows thickness (violet vertical arrows for the FM state and green vertical
arrows for the AFM state). The colour code of the arrows is in accord with the
convention used for the $SW$ reshuffling in the AFM and FM state of Figs.
1(a-c) and Figs. S7(a-b) in SM SM .

The characteristic ingredients pertinent to the reconstruction of the
electronic band structure, depicted in Fig. 2 and then driving the $SW$
redistribution observed in $\sigma_{1}(\omega)$ (Fig. 1 and Fig. S7 in SM SM
), embrace several findings and achieved knowledge on related, sister
materials. First of all and from a general perspective, the FM state in both
Mn- and Co-intercalated 2H-TaS2 has been tentatively reconciled within a
Ruderman-Kittel-Kasuya-Yosida interaction scenario Liu  _et al._ (2021a, b,
2022), in which the local spins of intercalated Mn and Co ions align
ferromagnetically through the itinerant Ta 5$d$ electrons, as initially
proposed for the related Co-intercalated 2H-NbS2 material Barišić  _et al._
(2011). Further, it is speculated that Co atoms tend to hybridise more
strongly with the electronic states associated with covalently bonded
structural subunit (i.e., Ta and S) when intercalated in the vdW gap. By
enlarging the Co concentration, this leads to a suppression of the spontaneous
magnetic moment and to a stronger tendency for AFM exchange coupling
parameters Liu  _et al._ (2022); Polesya  _et al._ (2019).

Along this line of thoughts, the FM to AFM crossover, hither studied upon
changing the intercalation and contingently the concentration of the
intercalated Co atom, can be also achieved after two alternative ways: either
by differentiating the element-intercalation at given concentration or by
applying pressure on a selected intercalated compound. It is experimentally
known that the structurally equivalent 2H-NbS2 compound Str , intercalated
with 3$d$ elements Cr, Mn and Fe for the concentration 1/3, exhibits a variety
of magnetic states, (roughly) classified as FM for the Cr and similarly Mn
materials Hulliger and Pobitschka (1970); Miyadai  _et al._ (1983); Van Laar
_et al._ (1971); Kousaka  _et al._ (2009) and as AFM for the Fe composition
Van Laar  _et al._ (1971); Gorochov  _et al._ (1981); Yamamura  _et al._
(2004). The first-principles electronic band structure calculations that have
been performed using the fully relativistic Korringa-Kohn-Rostoker Green
function method Mankovsky  _et al._ (2016) have pointed out the complexity of
their magnetic ordering. For Cr1/3NbS2 and Mn1/3NbS2, the in-plane
magnetocrystalline anisotropy and Dzyaloshinskii-Moriya interactions give rise
to a helimagnetic structure along the $c$-axis, following the experimental
observations Hulliger and Pobitschka (1970); Miyadai  _et al._ (1983). On the
other hand, the negative exchange interactions in the Fe1/3NbS2 compound
result in a noncollinear frustrated magnetic structure if the
magnetocrystalline anisotropy is not taken into account. However, a strong
magnetocrystalline anisotropy along the $c$-axis does lead to a magnetic state
referred to as an ordering of the third kind, which was indeed determined
experimentally Van Laar  _et al._ (1971); Gorochov  _et al._ (1981); Yamamura
_et al._ (2004). This may be pinned down to the diverse DOS with respect to
the magnetic state in these series of compounds. For all compounds, DOS is
rather large for the majority-spin states at the Fermi energy ($E_{F}$). In
the case of minority-spin states of Cr1/3NbS2 and Mn1/3NbS2, one can however
observe a pseudogap between the occupied and unoccupied states Polesya  _et
al._ (2019); Mankovsky  _et al._ (2016). Such an imbalance then leads to the
FM ground state. In the case of Fe1/3NbS2, $E_{F}$ is located at the DOS
maximum corresponding to the Fe minority-spin $d$ states. DOS is thus finite
for both spin directions, which facilitates an AFM ground state Mankovsky  _et
al._ (2016). This latter trend is reflected in the isotropic exchange coupling
parameter for the three compositions, which is predominantly positive for the
Cr and Mn compounds (i.e., promoting FM) but negative (i.e., leading to AFM)
for Fe-Fe interactions at short distance Mankovsky  _et al._ (2016).

In turn, one can induce the crossover from the FM to AFM state in Mn1/4NbS2
upon applying pressure Polesya  _et al._ (2020). This possibility is
instrumental, in order to better justify and support our schematic proposal in
Fig. 2. Focusing the attention on the spin-resolved DOS on Mn sites, which is
foremost contributed by the $d$-orbitals, the majority-spin states are almost
occupied around both the $\Gamma$ and $K$ points in the Brillouin zone at
ambient pressure, while the minority-spin states, essentially around the $K$
point of the Brillouin zone, are unoccupied. This favors FM and further
implies a dominating hole-type character of the electric carriers and a
positive slope of the Hall resistivity Polesya  _et al._ (2020). Interband
transitions within the FIR energy interval (so roughly peaked at 100 meV) are
foreseen from the electronic band structure at both $\Gamma$ and $K$ points of
the Brillouin zone Polesya  _et al._ (2020) and should play the most prominent
role in $\sigma_{1}(\omega)$. Figure 2 catches a glimpse of such a trim for
our FM compositions (Figs. 1(a-b) and S7(a) in SM SM ). Conversely, the
pressure increase results in the broadening of the energy bands, which
premises an occupation of the bottom of the minority-spin states (having
mainly $d_{x^{2}-y^{2}}$ and $d_{xy}$ character) and a draining of the top of
minority-spin states (primarily of $d_{xz}$and $d_{yz}$ character) at the $K$
point of the Brillouin zone in Mn1/4NbS2 Polesya  _et al._ (2020). This is
accompanied by a decrease of the exchange splitting of the majority- and
minority-spin $d$-states of Mn, which potentially turns negative for the first
neighbour interaction, as the prerequisite for an AFM alignment of the
magnetic moments in the absence of any other interactions. In fact, such a
setting is translated into an electron-like character of the ordinary Hall
effect Polesya  _et al._ (2020). By inspecting the resulting electronic band
structure in the AFM state Polesya  _et al._ (2020), we recognise the most
cogent consequence for the excitation spectrum: namely, low energy FIR
interband transitions are less probable, while the probability for high energy
ones at MIR and NIR frequencies (i.e., settled around 400 meV) increases
sensitively, as evinced in $\sigma_{1}(\omega)$ (Figs. 1(c) and S7(b) in SM SM
) and as also sketched in Fig. 2 for our case. Therefore, we claim that the
band reconstruction in Mn1/4NbS2 upon applying pressure is implementable to
2H-CoxTaS2 with respect to the FM-AFM crossover as a function of $x$, as
backed up by the same sign-change of the ordinary Hall coefficient upon
varying the magnetic ground state Liu  _et al._ (2022); Polesya  _et al._
(2020).

In conclusion, the charge dynamics of 2H-$M_{x}$TaS2 ($M$ = Mn and Co) allows
to determine a distinct $SW$ redistribution and to shed light on the relevant
energy scales shaping the reconstruction of the electronic band structure upon
crossing over from the FM to AFM order with varying intercalation (i.e.,
element and/or its concentration). Our spectroscopic findings seem to be
consistent with dedicated first-principles calculations upon tuning element-
intercalation, pressure and/or magnetic field on similar intercalated
materials. The applicability of the proposed comparison is validated by the
fact, that the quoted calculations do tackle the impact of (similar) magnetic
transitions on the electronic band structure of equivalent materials,
seemingly reflected in the charge dynamics of our compositions, too.

Summing up, the significance of this work consists in the first instance in
the systematic investigation of 2H-TaS2 with different intercalations and
across distinct magnetic transitions, hence widening out a previous, more
restricted attempt Hu  _et al._ (2008) and possibly challenging the so far
broadly accepted implementation of the rigid-band model. Moreover, since the
continuous change of the dominant magnetic exchange controls the FM to AFM
switching and being its impact mapped onto the easily accessible FIR-MIR-NIR
spectral range, one may exploit our straightforward (broadband) experimental
tool also as a function of alternative tuneable variables than chemical-
intercalation, which would thoroughly flash on the overall consistency of the
emerging physical picture. Finally, the present work demonstrates a feasible
route towards understanding magnetism in low dimensions and may help in
revealing robust properties, relevant for the development of low-power spin-
logic circuits from layered materials Liu  _et al._ (2021a). The possibility
of integration of FM is generally of interest for spintronics, so that novel
fabrication of low-dimensional heterostructures might be envisaged and
motivated, as well; the few-layer graphene/2H-TaS2 heterostructures with
robust spin-helical state Li  _et al._ (2020) is already a promising
development and the recent discovery of one-dimensional vdW (yet non magnetic)
heterostructures Xiang  _et al._ (2020) and multi-walled 2H-TaS2 nanotubes Li
_et al._ (2010) may open new avenues. Since exotic phenomena such as skyrmions
and magnetic solitons Zhang  _et al._ (2022); Zheng  _et al._ (2021) were
recently discovered in 2H-TaS2-based vdW magnets, our results may therefore
help to efficiently tune their properties for further applications.

## Acknowledgements

Work at Brookhaven National Laboratory was supported by the U.S. Department of
Energy, Office of Basic Energy Science, Division of Materials Science and
Engineering, under Contract No. DE-SC0012704 (materials synthesis).

† Authors M.C. and R.Y. contributed equally to the work.

‡ Present address: Los Alamos National Laboratory, Los Alamos, New Mexico
87545

∗ Correspondence and requests for materials should be addressed to: L.
Degiorgi, Laboratorium für Festkörperphysik, ETH - Zürich, 8093 Zürich,
Switzerland; email<EMAIL_ADDRESS>
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