# Anisotropic magnetic properties and tunable conductivity in two-dimensional
layered NaCrX2 (X=Te,Se,S) single crystals

Jiale Huang  Bingxian Shi  Feihao Pan  Jinchen Wang  Juanjuan Liu  Daye Xu
Hongxia Zhang  Tianlong Xia  Peng Cheng<EMAIL_ADDRESS>Laboratory for
Neutron Scattering and Beijing Key Laboratory of Optoelectronic Functional
Materials and MicroNano Devices, Department of Physics, Renmin University of
China, Beijing 100872, China

###### Abstract

Monolayer NaCrX2 (X=Te,Se,S) were theoretically proposed to be two-dimensional
intrinsic ferromagnetic semiconductors while their physical properties have
not been thoroughly investigated in bulk single crystals. We report the
single-crystal growth, structural, magnetic and electronic transport
properties of NaCr(Te1-xSex)2 ($0\leqslant x\leqslant 1$) and NaCrS2. For
NaCr(Te1-xSex)2, the strong perpendicular magnetic anisotropy of NaCrTe2 can
be gradually tuned to be a nearly isotropic one by Se-doping. Meanwhile, a
systematic change in the conductivity with increasing $x$ is observed,
displaying a doping-induced metal-insulator-like transition. Under magnetic
field larger than 30 kOe, both NaCrTe2 and NaCrSe2 can be polarized to a
ferromagnetic state. While for NaCrS2, robust antiferromagnetism is observed
up to 70 kOe and two field-induced metamagnetic transitions are identified
along H$\parallel$ab. These intriguing properties together with the potential
to be exfoliated down to few-layer thickness make NaCrX2 (X=Te,Se,S) promising
for exploring spintronic applications.

##  I Introduction

Magnetism in two dimensions has been a fascinating topic in condensed matter
physics for decades. From the initial investigations on thin-film magnets to
the recent discovery of two-dimensional (2D) magnetic order in ultra-thin van
der Waals (vdW) materials, a wide range of possibilities for both spintronic
applications and fundamental research have been opened upBurch  _et al._
(2018); Li  _et al._ (2019); Cortie  _et al._ (2020). For few-layer vdW
crystals, 2D magnetism has been realized in metallic Fe3GeTe2Deng  _et al._
(2018); Fei  _et al._ (2018), semiconducting CrI3/Gr2Ge2Te6Huang  _et al._
(2017); Gong  _et al._ (2017) and insulating FePS3Lee  _et al._ (2016); Wang
_et al._ (2016) due to the large magnetic anisotropy which could counteract
thermal fluctuations. These materials can serve as different building blocks
of vdW heterostructures depending on their conductivity and exploring
potential applications in novel magneto-electronic devices. Therefore magnetic
anisotropy and conductivity are two key properties of 2D magnetic materials.
Finding new 2D materials and ways to tune these properties would be quite
important in the research of 2D magnetism.

Bulk CrTe2 with 1$T$ phase is a vdW ferromagnet with in-plane magnetic
anisotropy and Curie temperature of 310 KFreitas  _et al._ (2015). Remarkably,
in untra-thin flakes or films, the easy axis of CrTe2 changes from in-plane to
out-of-plane and room-temperature ferromagnetism is retainedSun  _et al._
(2020); Zhang  _et al._ (2021); Meng  _et al._ (2021); Fabre  _et al._ (2021).
Moreover, a recent study identified a zigzag type antiferromagnetic order in
monolayer CrTe2Xian  _et al._ (2022), demonstrating the intricacy of 2D
magnetism in this material. On the other hand, the intercalations of metal
atoms into the vdW gap of CrX2 (X=Te,Se,S) can form plenty of new phases.
Although the structures of these intercalated CrTe2 phases are non-vdW type,
many of them are still able to be exfoliated into nanosheets while keep
intriguing physical properties. For example, the room-temperature
ferromagnetism in 10 nm-thick Cr-intercalated CrTe2Huang  _et al._ (2021) and
the superionic behavior in 1.1 nm-thick AgCrS2Peng  _et al._ (2021) have been
reported recently. Especially for the latter, the structure of so-called
AgCrS2 monolayer consists of one Ag layer sandwiched between two [CrS2] layers
with actual formula AgCr2S4, which has been shown to be stable
experimentallyPeng  _et al._ (2021).

The Na-intercalated NaCrX2 (X=Te,Se,S) are recently proposed to be a class of
monolayer ferromagnetic semiconductors by first-principles calculationsXu  _et
al._ (2020). Although the crystal structures are non-vdW type, their cleavage
energies are comparable with other 2D materials. It also should be mentioned
that, in previous research the vdW magnetic material CrTe2 is mainly made by
deintercalating the alkali metal of KCrTe2. However the physical properties of
NaCrTe2 have not been thoroughly investigated until recently. Experimentally,
NaCrTe2 is determined to be an $A$-type antiferromagnet with TN=110 K and
perpendicular magnetic anisotropyKobayashi  _et al._ (2016); Wang  _et al._
(2021). With applied magnetic field, spin-flip-driven giant negative and
angle-dependent magnetoresistance are observed for single crystals of
NaCrTe2Wang  _et al._ (2021). For NaCrSe2 and NaCrS2, although their
antiferromagnetic transition temperature and structure have already been
determinedEngelsman  _et al._ (1973), the anisotropic and field-induced
magnetic properties are still unclear due to the lack of single crystals.
Furthermore, chemical doping has been proved to be an effective way to tune
the magnetic and transport properties of layered magnetic materialsTian  _et
al._ (2019); Sheng  _et al._ (2020); Tian  _et al._ (2020); Lee  _et al._
(2021). It would be interesting to explore the Se-doping effect on NaCrTe2.

Figure 1: (a) Crystal structure of NaCrTe2 (up) and top view (down) of CrTe2
layer. The blue dotted lines represent the unit cell. (b) Crystal structure of
NaCrSe2 and NaCrS2. (c,d) Lattice parameters obtained by fitting single
crystal x-ray diffraction data for NaCr(Te1-xSex)2. (e,f) Atomic force
microscopy images and height profile step of NaCrSe2 and NaCrTe2 nano-flakes
mechanically-exfoliated onto a 300 nm SiO2/Si substrate.

In this paper, we report the successful growth of single crystals of
NaCr(Te1-xSex)2 and NaCrS2. These crystals show intriguing magnetic and
transport properties, including field-induced spin-flip transitions, giant
negative magnetoresistance, chemical doping controlled magnetic anisotropy and
conductivity. Our findings suggest the NaCrX2 series are promising candidates
for further investigations in 2D limit.

##  II methods

Single crystals of NaCr(Te1-xSex)2 and NaCrS2 were grown by melting
stoichiometric elements. High-purity Na, Cr, Te and Se/S were mixed in the
mole ratio 1:1:2(1-$x$):2$x$. These reagents were mixed in alumina crucibles
and sealed into an evacuated quartz tube. The assembly was heated up to
$1050\,^{\circ}\mathrm{C}$ and maintained at this temperature for 24 h. Then
it was slow-cooled to $800\,^{\circ}\mathrm{C}$ at a rate of
$3\,^{\circ}\mathrm{C}$/h and annealed at this temperature for one day before
furnace-cooled to room temperature. In order to make the reaction adequate,
before heating to $1050\,^{\circ}\mathrm{C}$, the assembly would stay for ten
hours at the temperatures slightly below the melting or boiling point of each
reactant. The plane size of the obtained NaCr(Te1-xSex)2 single crystals is up
to 6 mm$\times$6 mm, while the size of NaCrS2 is smaller which is typically 1
mm$\times$1 mm. NaCrTe2 is air-sensitive, its shinning surface could be
oxidized and discolored after being put in the air for a few hours. With Se-
doping, the crystal become less air-sensitive and it takes about two days for
NaCrSe2 to become degenerative in the air. NaCrS2 is air-stable.

We characterized all samples with energy dispersive x-ray spectroscopy (EDS,
Oxford X-Max 50). For NaCr(Te1-xSex)2 with x=0.1 and x=0.2, the EDS value is
quite close to the nominal value. For x$\textgreater$0.3, the doping
concentration may slightly deviate from the nominal value (the estimated error
is about 20%). In order to be accurate, all measured samples have been
carefully checked by EDS. The descriptions in this paper about doping level
$x$ all refer to the EDS values.

X-ray diffraction (XRD) of the samples were collected from a Bruker D8 Advance
X-ray diffractometer and a Bruker D8 VENTURE single-crystal diffractometer
using Cu Kα radiation. Magnetization and electrical transport measurements
were carried out in Quantum Design MPMS3 and PPMS-14T, respectively. The
dimensions of exfoliated NaCrTe2 and NaCrSe2 nanoflakes were checked by a
Bruker edge dimension atomic force microscope.

Figure 2: (a)-(e) The temperature dependent magnetic susceptibilities measured
on NaCr(Te1-xSex)2 ($0\leqslant x\leqslant 0.42$) under magnetic field applied
along $ab$-plane or $c$-axis. (f)-(j) Magnetization isotherms measured on the
same crystals at $T$=2 K. For $x$=0 and $x$=0.10, the hysteresis loops are
presented.

##  III Results and discussions

###  III.1 Crystal structure of NaCrX2

As shown in Fig. 1(a) and confirmed by XRD analysis, NaCrX2 crystallizes in a
hexagonal structure with the space group of $P$-3$m$1 for X=Te and $R$-3$m$
for X=Se/S, same as previous reportsEngelsman  _et al._ (1973); Kobayashi  _et
al._ (2016); Wang  _et al._ (2021). The crystal structure of NaCrTe2 can be
considered as the intercalation of Na atoms between 1$T$-CrTe2 layers. Na and
Cr atoms stack alternately along the $c$-axis in the same site. The Cr atoms
form a triangular lattice in the $ab$-plane. When Te was substituted by Se or
S, the major change in crystal structure is the interlayer stacking order.
Comparing with NaCrTe2, for NaCrSe2 and NaCrS2, both Na- and Cr-triangular
lattice layers are stacked along the $c$-axis with (1/3 1/3) translation in
the $ab$-plane. So the $c$-lattice parameter has almost tripled. These two
different structures are referred as ’Te-phase’ and ’Se-phase’ respectively in
the following descriptions.

For NaCr(Te1-xSex)2 ($0\leqslant x\leqslant 1$), the lattice parameters were
obtained by refining the single crystal x-ray diffraction data and plotted in
Fig. 1(c) and (d). The results show that the samples with $x\leqslant 0.5$
maintain the Te-phase while the samples with $x\geqslant 0.68$ are confirmed
to have the Se-phase. Therefore the phase boundary may exist near $x$=0.6,
although it has not been accurately determined. The precession images from the
single crystal x-ray diffraction data display streaking features for most
doped samples, especially for the heavily doped ones. This indicates that
notable stacking disorders and possible phase separations may exist in
NaCr(Te1-xSex)2 (Figure S2 in Supplementary MaterialsSup ). In the Te-phase
zone, both the $a$\- and $c$-lattice parameters do not follow a monotonic
change with increasing $x$. Compare with NaCrTe2, there is a 7% shrinkage for
the $a$-axis of NaCrSe2. The $c$-lattice parameter for NaCrS2 is 19.485$\AA$ ,
which decreases about 4% compared with that of NaCrSe2.

Previous calculations of the cleavage energies suggest that NaCrX2 can be
exfoliated to a thickness of a few layersXu  _et al._ (2020). We performed the
mechanical exfoliation of bulk NaCrX2 single crystals using Scotch tape.
Nanosheets of NaCrTe2 and NaCrSe2 with thickness 20-30 nm could be obtained,
which is demonstrated by the atomic force microscopy images in Fig. 1(e) and
(f). Recently Jing Peng $et~{}al.$ demonstrated that isostructural AgCrS2 can
be exfoliated into 1.1 nm nanosheet which consists of one Ag-layer sandwiched
between two CrS2-layersPeng  _et al._ (2021). Therefore this class of
materials are promising 2D materials for further investigations. Future
investigation on whether NaCrX2 is stable under similar exfoliation method as
AgCrS2 could be stimulated.

###  III.2 Magnetic properties of NaCr(Te1-xSex)2

The temperature dependent magnetic susceptibility $\chi$(T) and isothermal
magnetization M(H) of NaCr(Te1-xSex)2 single crystals are shown in Fig. 2.
Demagnetization corrections with methods used in our previous publication have
been applied on the $H\parallel c$ data and the applied magnetic field Happ in
$M(H)$ curve is replaced by the internal field HintTian  _et al._ (2020). For
NaCrTe2, $\chi$(T) curve under H$\parallel$c exhibits a sharp drop down to
nearly zero below TN=110 K in contrast to the weak cusp and plateau-like
feature under H$\parallel$ab. This suggests the development of an $A$-type
antiferromagentic order (ferromagnetic intralayer and antiferromagnetic
interlayer couplings) with moment aligned along $c$-axis. The Curie-Weiss fit
on the high-temperature paramagnetic susceptibility reveals
$\mu_{eff}/Cr=3.8~{}\mu_{B}$ and $\theta_{CW}=155~{}K$. The large positive
$\theta_{CW}$ value indicates the strong intralayer ferromagnetic
correlations. The hysteresis loops at 2 K under H$\parallel$c and
H$\parallel$ab demonstrate the strong perpendicular magnetic anisotropy (PMA)
and a spin-flip transition to the ferromagnetic state near Hab=30 kOe. These
observations are similar as previous reportWang  _et al._ (2021). The
saturation moment for NaCrTe2 is $2.6~{}\mu_{B}/Cr$, which is a bit lower than
the theoretical value $3.0~{}\mu_{B}$ for Cr3+ in a localized model.

For x=0.1, TN decreases to 78 K while the features of $A$-type
antiferromagnetic order and perpendicular magnetic anisotropy still persist.
The spin-flip transition near 30 kOe also exists but with a much larger
hysteresis comparing with that of $x$=0. An important modification of magnetic
anisotropy is that the PMA seems to get weakened with Se-doping. If we choose
the ratio Mc/Mab at H=60 kOe and T=2 K as a criterion, it decreases from 2.3
for $x$=0 to 1.5 for $x$=0.10.

With increasing doping concentration $x$, TN continuously shifts to lower
temperature and the spin-flip transition gradually vanishes as shown in Fig.
2(c)-(d) and (h)-(j). The Mc/Mab at 60 kOe and 2 K also gradually decreases
from 1.4 ($x$=0.19) to 1.2 ($x$=0.30), and finally to 0.95 ($x$=0.42). This
means the magnetic anisotropy gradually evolves from PMA to a slightly
preferred in-plane magnetization. On the other hand, for $x\geqslant 0.19$ ,
there is a bifurcation between zero-field-cooling (ZFC) and field-cooling (FC)
magnetization below TN, which implies the emergence of a spin-glass state. In
addition, the Curie-Weiss fit on the doped samples reveals similar values of
effective moment but lower $\theta_{CW}$ values (131 K-106 K), suggest a
slightly weakened ferromagnetic correlations.

Figure 3: Anisotropic magnetization data for NaCrSe2 single crystal: (a) The
temperature dependent magnetic susceptibilities at $H$=5 kOe. (b) Magnetic
hysteresis loops at $T$=2 K. (c) and (d) Magnetization isotherms measured at
selected temperatures under $H\parallel c$ and $H\parallel ab$, respectively.
Figure 4: (a) The temperature dependent resistivity of NaCr(Te1-xSex)2 with
$x$=0.1 under zero field. (b) Isothermal magnetoresistance (MR) of $x$=0.1
under $H\parallel c$.

The samples with $0\leqslant x\leqslant 0.42$ discussed above all belongs to
the Te-phase. Our XRD analysis reveal that at least from $x$=0.68,
NaCr(Te1-xSex)2 enters the Se-phase. Let us first discuss the magnetic
properties of NaCrSe2 which is shown in Fig. 3. A cusp at TN=39 K is observed
in the $\chi(T)$ curve indicating an antiferromagnetic transition. On the
other hand, fitting the high-temperature paramagnetic data to the Curie-Weiss
law yields $\mu_{eff}/Cr=3.8~{}\mu_{B}$ and $\theta_{CW}=108~{}K$. The
positive $\theta_{CW}$ temperature indicates ferromagnetic correlations are
still strong in each individual layer, while the interlayer coupling is
antiferromagnetic, similar as NaCrTe2 and many other 2D layered magnetic
materials.

Figure 5: (a) Temperature dependent resistivity data for NaCr(Te1-xSex)2
($H$=0). (b) Ln$\rho$ versus T-1 plot of $x$=1 for all measured temperatures.
The inset shows same plots for $x$=0.42 and $x$=0.76. (c,d) Low temperature
Ln$\rho$ versus T-1/(ν+1) plots of $x$=0.76 and $x$=0.42, respectively. $\nu$
is the parameter from VRH formula.

In contrast to the strong anisotropic magnetization under H$\parallel$c and
H$\parallel$ab for NaCrTe2, the magnetic anisotropy of NaCrSe2 is much
smaller. Without applying a demagnetization correction, NaCrSe2 appears to
have essentially zero anisotropy. After the correction, a weak PMA could be
identified from the M(H) curves at 2 K [Fig. 3(b)]. Under $H\geqslant
30~{}kOe$ for both directions and $T$=2 K, the magnetization becomes saturated
with a saturation moment of $3.0~{}\mu_{B}/Cr$, which is larger than that of
NaCrTe2 and accurately equals to the theoretical value of Cr3+ in a localized
model. It should be noted that, before reaching saturated value, the
magnetization increases quickly and linearly with increasing field along both
directions. This indicate that although the spins of NaCrSe2 are
antiferromagnetically aligned at low field, they could be continuously canted
along the field direction with increasing field. Fig. 3(c) and (d) show the
M(H) curves at different temperatures. The saturation moment gradually
decreases with increasing temperature. At 50 K which is well above TN, the
M(H) curve still exhibits a nonlinear curvature and a large moment ($\sim
2.2~{}\mu_{B}/Cr$) at 60 kOe. In addition, the M(T) curve also deviates from
Curie-Weiss behavior below 200 K, which are actually observed for all NaCrX2
(X=Te,Se,S) samples. These observations suggests that strong magnetic
fluctuations or short-range magnetic order may develop well above TN.

For $x$=0.68 and $x$=0.79 with Se-phase, the spin-glass behavior are quite
similar as $x$=0.42 with Te-phase. The related magnetization data is not shown
here but the results are plotted in the phase diagram of Fig. 6. Further
discussions about the evolution of anisotropic magnetic properties of
NaCr(Te1-xSex)2 will be presented in the following section with the phase
diagram.

###  III.3 Tunable conductivity in NaCr(Te1-xSex)2

Previously, NaCrTe2 was reported to exhibit a metal-insulator-like transition
due to the formation of $A$-type antiferromagnetic orderingWang  _et al._
(2021). Similarly, the resistivity of $x$=0.1 sample has a typical metallic
behavior above 130 K [Fig .4(a)], while a sharp jump appears at TN=78 K with
deceasing temperature which should result from the localization of charge
carriers by long-range antiferromagnetic order. With further deceasing
temperature, the resistivity continues to increase with a smaller slope which
might be attributed to the impurity scattering effect by chemical-doping.
Under magnetic field along $c$-axis, a giant negative magnetoresistance
appears with maximal value up to 48% at 5 K and 70 kOe. This behavior is
directly associated with the field-induced spin-flip transition and due to the
reduced spin scattering to the electrons in the ferromagnetic state comparing
with that in the antiferromagnetic states.

Comparing with the previously reported resistivity of NaCrTe2Wang  _et al._
(2021), we noticed that the value for $x$=0.1 approximately increases by an
order of magnitude. As shown in Fig. 5(a), intriguingly, with further
increasing Se-doping concentration $x$, the temperature dependent resistivity
of NaCr(Te1-xSex)2 becomes fully semiconducting-like and the absolute value of
resistivity continuously increases by several orders. For NaCrSe2 with $x$=1,
the resistivity is about $\sim$ 10 $\Omega.cm$ and the data below 95 K cannot
be obtained due to the upper limit of PPMS measurement. Thus a Se-doping
induced metal-insulator transition is observed for NaCr(Te1-xSex)2.

Density functional theory calculations have shown that both NaCrTe2 and
NaCrSe2 are semiconductors, their band gaps are 0.59 eV and 0.77 eV
respectivelyXu  _et al._ (2020). In order to check whether the doping
controlled conductivity is due to the gradual increasing of the band gap, we
have tried to fit the resistivity data using the thermal activation model as
described by $\rho$=$\rho_{0}$exp(Ea/2kBT). Where $E_{a}$ is the energy gap
and $k_{B}$ is the Boltzmann constant. Therefore a fine fitting result using
this formula can only be obtained when ln$\rho$ and T-1 follows a linear
relationship. However, as shown in Fig. 5(b), there are not well defined
linear relations between ln$\rho$ and T-1 for all samples, especially for
$x$=0.42 and $x$=0.76.

Figure 6: Temprature versus doping phase diagram for NaCr(Te1-xSex)2
($0\leqslant x\leqslant 1$).

For chemical doped samples, the doping-induced strong disorder potential might
trap itinerant electrons and lead to a metal-insulator transition, which is
the famous Anderson localizationAnderson (1958). For an Anderson insulator at
low temperatures, there are electronic states trapped in the vicinity of the
Fermi surface and the hopping transport by localized electrons would be
described by the variable range hopping (VRH) model
$\rho$=$\rho_{0}$exp(T0/T)1/(ν+1)Ying  _et al._ (2016). In this formula,
$\nu$=0 denotes the traditional insulator with band gap (same as thermal
activation model described above). $\nu$=1, 2 and 3 correspond to one-, two-,
and three-dimensional material with Anderson localization, respectively. In
Fig. 5(c) and (d), the ln$\rho$ versus T-1/(ν+1) plots for $x$=0.42 and 0.76
from 2 K to 10 K are presented. Although a perfect straight line is not
observed, the formula using $\nu$=2 or $\nu$=3 would clearly give a much
better fitting results comparing with that using $\nu$=0, especially for
$x$=0.76. Our results indicate that the significant enhancement of resistivity
in NaCr(Te1-xSex)2 may partially originate from the Anderson localization.
Besides, the tuning of band gap by Se-doping would also be possible. The
electronic transport properties of NaCr(Te1-xSex)2 may contains contributions
from these two aspects.

Figure 7: Anisotropic magnetization data for NaCrS2 single crystal: (a) The
temperature dependent magnetic susceptibilities at $H$=5 kOe. (b) Magnetic
hysteresis loops at $T$=2 K. (c) and (d) Magnetization isotherms measured at
selected temperatures under $H\parallel c$ and $H\parallel ab$, respectively.
(e) Contour plot of $dM/dH$ as a function of temperature and field along
$H\parallel ab$. (f) The temperature dependent magnetic susceptibilities under
different applied field near the antiferromagnetic transition.

###  III.4 Discussion on the phase diagram of NaCr(Te1-xSex)2

The $T$-$x$ phase diagram of NaCr(Te1-xSex)2 is presented in Fig. 6, which
summarizes the major experimental results above. Three features should be
mentioned about this phase diagram. Firstly, considering either from Se-doped
NaCrTe2 or Te-doped NaCrSe2, the antiferromagnetic transition temperature
gradually decreases and the system enters a spin-glass state with increasing
doping concentration. Secondly, the magnetic anisotropy can be effectively
tuned by chemical doping in this system. NaCrTe2 possesses a strong PMA and it
continuously gets weakened and evolves into a nearly isotropic magnetic
behavior at $x$=0.42 while maintain the Te-phase. For NaCrSe2 at the other
end, a weak PMA is identified. Thirdly, A systematic change in the
conductivity of NaCr(Te1-xSex)2 occurs on increasing $x$, from bad metallic
behavior in NaCrTe2 to the semiconducting or insulating behavior in NaCrSe2.

The doping-induced disorder effect and stacking faults should be responsible
for the emergence of the spin glass stateBinder and Young (1986). It also may
play an important role in tuning the magnetic anisotropy in NaCr(Te1-xSex)2.
In previous investigations on materials for high-density magnetic recording
media, chemical disorder has been shown to have important influence on the
magnetocrystalline anisotropy energy (MAE)Aas  _et al._ (2011); Si  _et al._
(2021); Neise  _et al._ (2011). It may either drastically reduce the MAE or
tune the MAE to a maximum valueAas  _et al._ (2011); Si  _et al._ (2021);
Neise  _et al._ (2011). For vdW material, recent studies reveal that
Ni1-xFexPS3 and Fe5(1-x)Co5xGeTe2 enable chemical tuning of easy-plane and
easy-axis anisotropiesLee  _et al._ (2021); Tian  _et al._ (2020); May  _et
al._ (2020). Magnetic anisotropy is a key property of 2D magnets, which is
required for counteracting thermal fluctuations. There have been reports about
pressure control of magnetic anisotropy on CrGeTe6Sakurai  _et al._ (2021) and
tensile strain-tunable magnetic anisotropy in monolayer CrX3 (x=Cl, Br,
I)Webster and Yan (2018). Our study provides a new example for chemical
disorder or stacking fault controlled magnetic anisotropy in 2D magnetic
material NaCr(Te1-xSex)2.

In addition, one should notice that the magnetic anisotropy also makes a big
difference between NaCrTe2 and NaCrSe2, both of them seem to have no evident
chemical disorder. A possible speculation is that, for NaCrSe2 with relatively
much lighter Se element, the spin-orbit coupling effect may become weak and
results in a weak PMAXue  _et al._ (2019). As we mentioned above, the
saturation moment of NaCrSe2 agrees well with the expectation of Cr3+ spin
$S$=3/2 model without orbital moment while that of NaCrTe2 has a notable
smaller value which might be due to the enhanced spin-orbital coupling.

The tuning of conductivity by chemical doping in 2D magnetic material has been
rarely reported. This effect found in NaCr(Te1-xSex)2, possibly due to
Anderson localization and the change of band structure, may have important
applications in designing novel spintronic devices. Particularly, the chemical
doping in NaCr(Te1-xSex)2 could simultaneously tune both the conductivity and
magnetic anisotropy.

.

###  III.5 Field-induced metamagnetic transitions in NaCrS2

For the magnetic properties of NaCrS2, so far as we know, there has not been
any investigations on the single crystals. We present the anisotropic
magnetization data on NaCrS2 single crystals in Fig. 7. The different
temperature dependent features of $\chi_{ab}$ and $\chi_{c}$ below TN=19 K
indicate the ordered magnetic moment should be confined within $ab$-plane
[Fig. 7(a)]. Fig. 7(b) present the magnetic hysteresis loops at 2 K. Under
magnetic field applied along the hard-axis ($H\parallel c$), a linear
relationship between magnetization and field is observed. But for field
applied along the easy $ab$-plane, a sudden magnetization jump is revealed at
around $25~{}kOe$ suggest the occurrence of field-induced metamagnetic
transition. From the magnetization isotherms at higher temperatures [Fig. 7
(c) and (d)], the linear behavior persists for $H\parallel c$ and the
magnetization jump gradually weakens with increasing temperature for
$H\parallel ab$. The contour plot of $dM_{ab}/dH$ in Fig. 7(e) reveals that
there are actually two metamagnetic transitions which appear at $H$=23 kOe and
$H$=29 kOe respectively. These two transitions gradually disappear near TN.
The transition at lower field slightly softens with increasing temperature
similar as that for a conventional spin-flop transition.

Early neutron diffraction result on NaCrS2 powders have determined its
magnetic structure to be a in-plane helical oneEngelsman  _et al._ (1973). The
spins of Cr have antiferromagnetic coupling along the $c$-axis, while in the
$ab$-plane they are aligned in a helimagnetic order with rotating angle
$\phi=33^{\circ}$ in adjacent (110) planesEngelsman  _et al._ (1973). This
ground state magnetic structure is consistent with the anisotropic magnetic
behavior of our single-crystal sample. It is interesting to point out that the
Curie-Weiss fit gives still positive $\theta_{CW}$ values (18 K for
$H\parallel ab$ and 31 K for $H\parallel c$) which suggests the ferromagnetic
correlations still exist. In addition, we noticed that the paramagnetic
susceptibility and corresponding fitted $\theta_{CW}$ values have large
anisotropy. Whether this really means the anisotropy on the exchange
interactions need further researches to clarify, as this kind of difference
can arise solely from the single-ion anisotropy even without exchange
interaction as in a previous theoretical researchJohnston (2017).

Furthermore, the observed field-induced metamagnetic transitions should have
significant influences on this complex helimagnetic order. Firstly, the
magnetic order under field above $30~{}kOe$ should also be antiferromagnetic-
like. This is supported by the cusp-like feature in the $\chi_{ab}-T$ curve at
TN, as shown in Fig. 7 (f). The antiferromagnetic transition seems to be quite
robust under field. TN only has a slight shift to 16 K under $H=70~{}kOe$. In
addition, M(H) curve follows a linear relationship up to 70 kOe with a small
value of moment ($\sim$ 0.7$\mu_{B}$/Cr) under this field. Secondly, for
$H_{ab}\leqslant 20~{}kOe$ the magnetic susceptibilities have a sharp drop
below TN. In contrast, for $H_{ab}=30~{}kOe$ and 70 kOe, the magnetic
susceptibilities exhibit a plateau below TN, which is a typical feature of
canted antiferromagnetic magnetic order. Therefore, new types of
antiferromagnetic order are expected under in-plane magnetic field, which
would be an interesting topic for further investigations using neutron
scattering.

##  IV Conclusions

In summary, the physical properties of NaCrX2 (X=Te,Se,S) are investigated in
single-crystal form. For NaCr(Te1-xSex)2, a field-induced spin-flip transition
together with a giant negative magnetoresistance are observed at
$x\leqslant$0.1. At higher doping level, a spin glass state emerges. The most
prominent feature is that both the magnetic anisotropy and the conductivity
can be effectively tuned by $x$. For NaCrS2, two magnetic field induced
metamagnetic transitions are identified. We further demonstrate that these
crystals can be mechanically-exfoliated into nano-flakes. These properties
would make NaCrX2 a promising material playground for further investigations
on 2D magnetism and designing novel magneto-electronic devices. Furthermore,
our samples also provide a route to vdW layered Cr$X_{2}$ through
deintercalation.

## Acknowledgement

This work was supported by the National Natural Science Foundation of China
(No. 12074426, No. 11227906 and No. 12004426), the Fundamental Research Funds
for the Central Universities, and the Research Funds of Renmin University of
China (Grants No. 22XNKJ40).

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<EMAIL_ADDRESS>Leopold Talirz0000-0002-1524-5903 Luca M.
Ghiringhelli0000-0001-5099-3029 Berend Smit0000-0003-4653-8562 This LiveCoMS
document is maintained online on GitHub at
https://github.com/ltalirz/livecoms-atomistic-software; to provide feedback,
suggestions, or help improve it, please visit the GitHub repository and
participate via the issue tracker. 10.XXXX/YYYYYYY <volume> <issue> <number>
Day Month Year Day Month Year

# Trends in atomistic simulation software usage [1.3]

Leopold Talirz  Laboratory of Molecular Simulation (LSMO), Institut des
Sciences et Ingenierie Chimiques, Valais, École Polytechnique Fédérale de
Lausanne, CH-1951 Sion, Switzerland  Theory and Simulation of Materials
(THEOS), Faculté des Sciences et Techniques de l’Ingénieur, École
Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland  Luca M.
Ghiringhelli  The NOMAD Laboratory at the Fritz Haber Institute of the Max
Planck Society and Humboldt University, Berlin, Germany  Berend Smit
Laboratory of Molecular Simulation (LSMO), Institut des Sciences et Ingenierie
Chimiques, Valais, École Polytechnique Fédérale de Lausanne, CH-1951 Sion,
Switzerland  National Centre for Computational Design and Discovery of Novel
Materials (MARVEL), École Polytechnique Fédérale de Lausanne, CH-1015
Lausanne, Switzerland

(<year>)

###### Abstract

Driven by the unprecedented computational power available to scientific
research, the use of computers in solid-state physics, chemistry and materials
science has been on a continuous rise. This review focuses on the software
used for the simulation of matter at the atomic scale. We provide a
comprehensive overview of major codes in the field, and analyze how citations
to these codes in the academic literature have evolved since 2010. An
interactive version of the underlying data set is available at
https://atomistic.software.

##  1 Introduction

Figure 1:  Performance of the top 500 supercomputers in the world from 1993 to
2020 in solving linear equations (Linpack benchmark), measured in 64bit
floating point operations per second (FLOP/s). Shown are the sum of the entire
list (green dots), the performance of the top machine (brown triangles), and
performance of the bottom of the list (blue squares), together with least
squares fits. Adapted from top500.org/statistics/perfdevel.

Scientists today have unprecedented access to computational power. This
statement would be unremarkable, were it not for the extent to which
computational power has exploded. Figure 1 shows the performance ranking of
the top 500 supercomputers in the world over the last decades, including the
performance of the top-ranked machine, the machine at the bottom of the list,
and the sum of all 500. Remarkably, the least-squares fit to the sum (green
line) corresponds to a growth rate of ${\sim}75\%$ per year, which translates
to a performance increase of more than one _million_ times over the last 25
years. Similar improvements in commodity hardware mean that many of 2020’s
laptop computers would have made the top 500 list of the early 2000s [1].

First versions of quantum-chemistry codes, such as Gaussian [2], were already
released in the 1970s, followed by force-field codes, such as GROMOS [3], and
periodic density-functional theory (DFT) codes, such as CASTEP [4], in the
1980s and 1990s. In other words, many of these atomistic simulation engines
have been around during this explosion of computational power, continuously
evolving to take advantage of new algorithms, processor architectures,
increasing parallelism and, more recently, dedicated accelerator hardware.
Over time, they have developed from instruments for specialists to proven and
tested tools in the arsenal of practitioners in physics, chemistry, and
materials science.

Title | Authors | Journal | # cited
---|---|---|---
Generalized gradient approximation made simple | Perdew, Burke, Ernzerhof | PRL (1996) | $108\,099$
Development of the Colle-Salvetti correlation-energy formula … | Lee, Yang, Parr | PRB (1988) | $77\,473$
Efficient iterative schemes for ab initio total-energy calculations … | Kresse, Furthmüller | PRB (1996) | $58\,176$
Projector augmented-wave method | Blöchl | PRB (1994) | $43\,455$
Self-consistent equations including exchange and correlation … | Kohn, Sham | PR (1965) | $42\,795$
From ultrasoft pseudopotentials to the projector augmented-wave … | Kresse, Joubert | PRB (1999) | $42\,485$
Special points for Brillouin-zone Integrations | Monkhorst, Pack | PRB (1976) | $41\,232$
Density-functional exchange-energy approximation with correct … | Becke | PRA (1988) | $41\,142$
Inhomogeneous electron gas | Hohenberg, Kohn | PRB (1964) | $35\,445$
Ab initio molecular dynamics for liquid metals | Kresse, Hafner | PRB (1993) | $23\,192$
Table 1:  Top ten most highly cited articles published by the American
Physical Society, all of which deal with density functional theory and its
practical application. Data collected from the Web of Science on June 16th,
2021.

Records of the pervasive use of these tools can be found in the scientific
literature. In a 2014 survey, van Noorden et al. found that 12 of the top 100
most cited papers of all time were on density-functional theory [5]. As with
other examples in van Noorden’s list, the flood of citations are indicative of
papers being cited by the many practitioners (here: of density-functional
theory) rather than the few method developers. If one focuses the analysis on
articles published in physics journals, the footprint of density-functional
theory grows even further: For example, table 1 shows the top ten most cited
papers published by journals of the American Physical Society. All of them are
related to density-functional theory and its application.

Software | Version | Main language | Contributors 2020 | Lines of code
---|---|---|---|---
NWChem [6] | 7.0.2 | Fortran | 11 |  $5\,034\,139$*
LAMMPS [7] | 27May2021 | C++ | 51 | $1\,039\,872$
CP2K [Kuhne2020a] | 8.2 | Fortran | 38 | $911\,367$
ABINIT [9] | 9.4.2 | Fortran | 21 | $719\,048$
Quantum ESPRESSO [10] | 6.7.0 | Fortran | 43 | $604\,666$
GROMACS [11] | 2021.2 | C++ | 25 | $589\,108$
Psi4 [12] | 1.3.2 | C++ | 34 | $496\,858$
SIESTA [13] | 5.0.0-alpha | Fortran | 4 | $411\,829$
Octopus [14] | 10.5 | Fortran | 10 | $297\,825$
OpenMM [15] | 7.5.1 | C++ | 21 | $256\,452$
xtb [16] | 6.4.1 | Fortran | 18 | $124\,344$
Linux kernel | 5.13 | C | >4000 [17] | $20\,904\,410$

Table 2:  Counting lines of code for 11 popular open-source atomistic
simulation engines (and the Linux kernel for comparison), using the latest
releases as of June 2021. Line counts are determined by cloc v1.6.0 [18] and
exclude blank lines, comments, and markup languages (detailed reports in the
supporting information). Contributors for the year 2020 were determined by
counting the number of different committers to the source code from January
1st 2020 to January 1st 2021 (numbers for the Linux kernel are from 2019). *
Roughly 3 million lines of code of NWChem are computer-generated.

There used to be a time when it was commonplace for computational condensed-
matter physicists and quantum chemists to write their own electronic-structure
code, and many of the atomistic-simulation engines that are in broad use today
have started this way. Over the years, however, many of these engines have
developed into complex software distributions. Table 2 shows counts for the
lines of code in some of today’s popular open-source simulation engines: they
range from hundreds of thousands to millions of lines of code, typically
written in Fortran or C++, with similar numbers being reported for commercial
packages [19]. While statistics like these are by no means accurate measures
of code complexity (and developers follow different approaches to packaging
and outsourcing of functionality to external libraries), they nevertheless
suggest that many of these code bases are too large to be sustained by any
single person.

This poses important questions for how to sustain these software projects
going forward: questions of funding, business models, and software licenses.
Proponents of the open-source route argue that it democratizes research and
education by removing barriers for both users and developers, and that science
carried out with commercial software is harder to verify and reproduce [20,
21, 1]. The open-source model can also be adopted irrespective of the size of
a code’s target user group, while commercial activity tends to require a
minimal market size. On the other hand, the strong focus on innovation and
development often found in open-source scientific software can negatively
impact usability and quality of documentation [22]. Proponents of commercial
licenses argue that making academic software accessible to a broader community
is a technical task best left to professional software engineers, and that the
resulting gain in scientific productivity can easily outweigh the license fees
that pay for it [19]. We note that open-source and commercial activity do not
necessarily exclude each other: numerous software companies are built around
an open-source core, and we start seeing first examples in atomistic modelling
as well (e.g. Molcas/OpenMolcas [23]). Overall, it has been suggested that
“scientific publications are a more sound metric [of the scientific impact of
software] than either the price of a product or whether its source code is
available in the public domain” [19]. Providing a peek into this citation
record is one of the reasons for creating the atomistic.software collection.

The other reason is a practical one: When young scientists start their first
research project in atomistic simulations, they often have no grasp of the
extent of this software ecosystem, let alone of current trends in the field –
at least this is the personal experience of the authors of this review.
Software choices in research groups are therefore often informed by what other
members of the group already use. This makes sense: colleagues have vetted the
code for the type of problems the research group is working on, and built up
expertise around which of the many knobs to turn in order to find the sweet
spot between efficiency and accuracy.

But what if that code is no longer actively developed? What if there was
another code that was better suited to solve the specific research problem at
hand? That had a larger user/developer community? Was free instead of
commercial? Was open source instead of closed source? The goal of the
atomistic.software collection is to provide a comprehensive overview of all
major atomistic simulation engines (cf. Figure 2), and to help newcomers to
the field as well as experienced practitioners and software developers find
better answers to some of these questions.

Readers interested mainly in the results are invited to go straight to the
atomistic.software web site that displays the data discussed in this review.
For those wanting to know more, the following sections provide details on the
methodologies used, and discuss some of the trends that can be observed.

##  2 The atomistic.software collection

###  2.1 Overview

Figure 2:  Highly cited atomistic simulation engines in the scientific
literature. Font size scaled (approximately) by the number of citations during
the year 2020 as reported by Google Scholar.

The atomistic.software collection draws upon existing lists of atomistic
simulation codes [24, 25, 26, 27, 28], in particular the "Major codes in
electronic-structure theory, quantum chemistry, and molecular-dynamics" [29]
maintained by the NOMAD Centre of Excellence from 2017-2019. It enriches these
with annual citation data from the Google Scholar search engine, which
provides an overview of the current usage landscape as well as ongoing trends,
both at the level of individual codes and at the ecosystem level.

Figure 3:  Overview table of atomistic simulation engines, sorted by how often
they are referenced on Google Scholar during the previous year (here: 2020). A
drop-down menu provides access to annual citation data reaching back to the
year 2010.  Figure 4:  Filtering for density-functional theory codes with both
permissive (P) and copyleft (CL) open-source licenses.

The overview table Fig. 3 lists all codes in the data set, ordered by how
often they are referenced by articles indexed in Google Scholar. Clicking on
the citation count opens the corresponding query on Google Scholar, so users
can sift through the references one by one and discover what science is being
done with this software. Clicking on the name of the code instead opens the
code’s homepage for further information.

Users can filter codes by the methods or basis sets they use, and select only
codes that are commercial, free or open-source (Fig. 4). Hovering with the
mouse over any abbreviation in the list opens a tool-tip with an explanation.
Further metadata include information on which range of the periodic table the
code covers, available installation routes, support for
parallelization/acceleration, support for standard APIs, and the availability
of benchmarks. In order not to clutter the interface, not all metadata is
displayed by default but columns can be added/removed via the "View Columns"
button.

Besides the generic overview, each engine comes with a citation "trend" over
the last couple of years, which serves as an indicator of how its user
community has developed over time (Figure 5).

Figure 5:  Citation trend for the Quantum ESPRESSO code.

Finally, the statistics page looks at the top codes by citation growth,
indicating a rapidly growing user community. Ranking by absolute growth
naturally favors established codes, while considering relative growth provides
insight into the dynamics of new contenders in the list. Ideally, codes rank
highly in both metrics as is currently the case, e.g., for Desmond [30] and
OpenMM [15].

Figure 6:  2020 rankings for absolute and relative citation growth with
respect to the previous year.

A word of caution: The popularity of a code is a factor of many variables
(starting, e.g., with the size of the target audience) – please do not choose
the code for your next research project merely based on its ranking in this
list. atomistic.software links to the scholar query for the papers citing the
code, thus making it quick and easy to get an impression of the research the
code is currently used for. Yet, certain aspects of a code are likely to
correlate with popularity, such as how much used/tested the software is; how
many Q&A resources one is likely to find online or how much tooling there is
likely around this code, etc. From a software-developer perspective, knowing
the popularity of a code can be useful for gauging the potential impact of
supporting the code in your own tool (such as a workflow manager,
visualization software, …). And, finally, the citation trend provides an
interesting peek into the future – is the user community growing, stagnating
or decreasing?

###  2.2 Scope

atomistic.software uses the following working definition of an atomistic
simulation engine:

> A piece of software that, given two sets of atomic elements and positions
> (and, possibly, bond network), can compute their relative internal energies.
> In almost all cases, engines will also be able to compute the derivative of
> the energy with respect to the positions, i.e. the forces on the atoms, and
> thus be able to perform tasks like geometry optimizations or molecular
> dynamics.

This covers the Density-Functional Theory (`DFT`), Wave-Function Methods
(`WFM`), Quantum Monte Carlo (`QMC`), Tight-Binding (`TB`), and Force-Field
(`FF`) categories. Codes in the Spectroscopy (`S`) category are not
necessarily simulation engines in the above sense, but compute the response of
a given atomic structure to an external excitation (via photons, electrons,
…).

atomistic.software aims to be a _comprehensive_ list of all major atomistic
simulation engines, with annual updates going forward. Since there is a long
tail of simulation engines with a limited user base, a relevance criterion is
introduced in order to keep maintenance of the list manageable. The criterion
has been set to having at least one year with 100 citations or more. The value
of 100 is not set in stone and could be re-evaluated in the future, once the
list has had some time to consolidate. A "watch list" is kept of codes that do
not yet meet the criterion.

###  2.3 Methodology & Limitations

Approximate citation counts are obtained from Google Scholar as follows:

  1. 1.

Search for name of the code and the last name of a representative developer
who is a coauthor of all key publications on the software (vast majority of
codes). If no such coauthor exists, this is easily extended to searching for
the presence of one of multiple author names (or a company name for commercial
codes).

  2. 2.

When the name of the code is too common a search term, additional search terms
may be added or citations of a major reference article are counted (minority
of codes)

Google Scholar was chosen over alternative sources like the Web of Science or
Scopus, since it provides full-text search and is available for free, thus
enabling direct links to the queries. The supporting information contains a
case study comparing citation counts from the search-based Google Scholar
approach against counting the citations of reference papers (both in Google
Scholar and the Web of Science).

Owing to the lack of standardization in today’s software citation practices
[31, 32], the citation counts reported here are necessarily approximate.
Shortcomings include the following:

  * •

While spot checks have been performed to weed out false matches (and reports
on the ltalirz/atomistic-software GitHub repository are highly welcome),
details of the query can have significant impact on the number of results.
This means, in particular, that the ranking by absolute number of citations is
not set in stone and may be subject to change if more accurate search terms
are identified.

  * •

Citation counts reported by Google Scholar are not entirely static, even for
years that lie in the past. Reasons may include new publishers being indexed,
more text being extracted, different citations being disambiguated, or even
the heuristic evolving that predicts the total number of results. In our
experience, citation data for the previous year can be subject to significant
(upwards) fluctuation, while citation data for years further in the past are
quite stable. For this reason, for each data point the date of collection is
recorded in the source code repository.

  * •

Counting citations does not directly measure how often simulation codes are
_used_ but how often they are _referenced_ in the scientific literature. This
may involve some systematic bias, for example if popular codes are more likely
to be mentioned without being used, or if a software targets industrial users
who may be less likely to publish their results.

The caveats listed above mainly affect the _absolute_ number of citations
reported, and thus the ranking of codes. Citation trends on the individual
code level should be more robust, and potential shortcomings in that domain
(e.g. missing citations to a new reference paper with different authors) can
be addressed by adapting the corresponding query.

The categorization of codes in terms of methods, tags and licenses is an
evolution of the classification devised by the NOMAD list [29]. For the sake
of this data set, the following terminology has been adopted:

  * •

_commercial_ : payment required to obtain the software111This definition of
_commercial_ does not necessarily mean _for profit_ – research groups may
price software below the actual development costs. Furthermore, commercial
licenses may exempt specific groups from payment, e.g. based on country of
residence, membership in consortia, etc.

  * •

_free for academic use_ : free for academics around the world222Some academic
licenses may explicitly exclude researchers from specific countries.

  * •

_free_ : free to use for anyone, possibly after registration

  * •

_source available_ : source code available either for free or against payment

  * •

_open-source_ : open-source license approved by the Open Source Initiative
(OSI, https://opensource.org/)

We note that license terms can (and sometimes do) change over time. This is
currently not reflected in this data set (only the latest license terms are
recorded), but could be taken into account in future updates.

All data, as well as the source code of the web application running on
atomistic.software are hosted in the ltalirz/atomistic-software GitHub
repository. The data is released under version 4 of the Creative Commons
Share-Alike Attribution International License (CC-BY-SA). The web application
is written in JavaScript using the React framework (reactjs.org) and released
under version 3 of the Affero General Public License (AGPL).

###  2.4 Trends

Extensive cross-checks of atomistic.software against other lists [24, 25, 26,
27, 28] suggest that the collection is already fairly complete, and can thus
enable a look at the landscape of atomistic simulation software as a whole.
Today’s atomistic simulation engines are highly sophisticated pieces of
software that each take many human-years of development, and developers have
chosen different routes to support these efforts: from commercial to free,
from closed source to open, and many shades of grey in between. One question
we can ask is: How do commercial codes fare versus their free competitors?

Figure 7:  Citations of commercial vs free codes, including a breakdown into
those free for general use and those free for academic use only.

Figure 7 compares the compound citations to commercial and free codes. It
illustrates that commercial codes are alive and well: they are ahead in terms
of citations gathered, and have been ahead throughout the last decade, with
Gaussian [33] and VASP [34] together accounting for more than half of all
citations of the 23 commercial codes. At the same time, citations of the 40
free codes (including those that are only free for academic use) have been
growing roughly at the same _absolute_ rate, mostly driven by the codes that
are free for general use.

We note some caveats that apply to this statistic:

  * •

The current dataset only records the _latest_ license conditions, while some
codes (e.g. CASTEP [35] or Dalton [36]) have moved to more open license terms
over time, thus switching categories.

  * •

For codes that are free for academic use only, some researchers may prefer to
use the commercial version (e.g. using CASTEP through Biovia’s Materials
Studio software [37]).

It seems safe to conclude, however, that – while commercial codes remain
highly popular – free codes are slowly gaining market share.

Figure 8:  Citations by source code availability. "Source available" includes
all engines whose source code can be obtained for free or for a fee. "Open-
source" includes only OSI-approved licenses.

Another important question concerns source-code availability, which is
relevant for the ability of researchers to independently verify published
calculations and pin down bugs. Figure 8 shows that consistently at least
${\sim}90\%$ of citations went to engines whose source code is available,
strongly dominating over the 12 closed-source codes, whose citations have
stagnated333One notable exception is the closed-source ORCA code [38] that is
free for academic use. during the 2010s. We recall here that counting
citations in the scientific literature places a focus on the usage in
academia, and that usage patterns in industry may differ from the trends
identified here.

License | Version | Copyleft | Published
---|---|---|---
MIT |  |  | 1980s
GPL | 2 | X | 1991
LGPL | 2.1 | X | 1999
BSD 3-clause | 2 |  | 1999
Apache | 2 |  | 2004
GPL | 3 | X | 2007
LGPL | 3 | X | 2007
ECL | 2 |  | 2006
Table 3:  OSI-approved open-source licenses used in the collection. See the
SPDX license list at spdx.org/licenses for the full license terms
corresponding to the abbreviations.

While citations to source-available engines have grown by ${\sim}130\%$ since
2010, citations to the 24 open-source engines within that group rose by >300%
within the same time frame, gaining market share. In this context, it is
useful to recall that the development of several engines on the lists predates
the open-source movement and the creation of many of the open-source licenses
that are in broad use today (see Table 3). atomistic.software distinguishes
between

  * •

_copyleft_ open-source licenses, such as the GPL family, which require444Under
specific circumstances, which differ significantly between the GPL and the
LGPL. derivative software to be distributed under the same open-source license
(thus also called _share-alike_ or _viral_ licenses), and

  * •

_permissive_ licenses, such as the BSD, Apache, and MIT licenses, which permit
relicensing of derivative works.

The enforced sharing of improvements in derivative works can be a competitive
advantage of adopting a viral license. It can also be one path towards
financial revenue when companies seek a separate license agreement that allows
them to keep derivative works proprietary. Other developers may want to
maximize impact of their software by lowering the barrier for adoption across
the board, and thus prefer permissive licenses. Overall, the choice of license
is highly nuanced and an extensive discussion is beyond the scope of this
article (interested readers are referred to choosealicense.com) but it may be
instructive to observe the choices made by the codes in the collection.

Out of the 24 open-source codes in the atomistic.software collection, the
majority (20) adopt the GPL or LGPL license. The four codes that are
distributed under _permissive_ licenses (NWChem [6], OpenMM [15], RASPA [39]
and PySCF [40]) either switched to this licensing scheme in the late 2000s or
2010s or started being developed during that time. This indicates that the use
of permissive licenses is a recent phenomenon in the space of atomistic
simulation engines, and may follow in the footsteps of the open-source
community at large which is exhibiting a similar trend: according to an
analysis of over 4 million open-source packages by WhiteSource [41], the use
of permissive open-source licenses has nearly doubled from 41% in 2012 to 76%
in 2020, with the Apache and MIT licenses alone accounting for more than half
of all licenses that year.

So much about the differences between licensing models. Overall, citations of
atomistic simulation engines in the collection have grown at an annual
compound growth rate of ${\sim}8\%$, roughly twice the $4\%$ growth rate seen
in the publication of peer-reviewed articles in science and engineering over
the last decade [42]. While part of this difference may reflect changing
citation practises555According to Mammola et al., the length of reference
lists in ecology journals has been increasing by ${\sim}2\%$ per year over the
last two decades. [43], it likely indicates an increasing adoption of
(atomistic) computational materials science throughout the scientific
literature.

##  3 Conclusions & Outlook

At the time of writing, the atomistic.software collection contains over 60
simulation engines that each gather >100 citations per year, some several
hundreds or thousands. Overall, this review paints a bright future for the
field of atomistic simulation: a growing variety of both commercial and free
software to choose from, citation growth rates that substantially outpace the
rest of the scientific literature, and a forecasted trillion dollar market
potential for a digitally-driven materials revolution [44]. There are,
however, some challenges ahead as well.

The continued slowdown in single-core performance scaling666While
supercomputers have historically been able to escape this trend by driving up
parallelization, Figure 1 suggests that the era of exponentially scaling
supercomputer performance may also be coming to an end. creates a powerful
driving force for the specialization of computer hardware. Small- to medium-
size development teams often lack the expertise or the resources to adapt
their code base to an ever growing number of hardware accelerators and are at
risk of falling behind. One way of approaching this issue is to try and
identify low-level, performance-critical primitives that are needed by
multiple codes. These primitives can then be bundled into domain-specific
libraries, such as libxc [45], libint [46], ELSI [47], SIRIUS [48], M-A-D-N-E-
S-S [49], or TiledArray [50] that are ported to and optimized for the various
accelerator architectures by HPC specialists.

Another issue that requires attention is the one of software citation. With
the increasing role that software plays in advancing science, it is crucial
that credit for the creation of software is attributed adequately and
accurately. One reason why the citation counts in atomistic.software are
approximate is that software citation in the field of atomistic simulations
comes in many different forms:

  * •

references of papers that summarize recent developments of the software,

  * •

references of papers that describe the implementation of specific methods,

  * •

references to the home page of the code, or even just

  * •

mentioning the code by name in the main text, possibly followed by a key
author or company in parentheses,

similar to what has been found in the field of biology [51]. Furthermore,
there is no standardized way of expressing whether a specific version of the
software was used or whether the software was referenced as a general concept,
e.g. as part of an enumeration of different codes like in this review.

In order to encourage adoption of a consistent policy for software citation
across disciplines and venues, in 2016 the software citation working group of
the FORCE11 coalition (force11.org) issued detailed software citation
principles [52], which include the recommendation of citing a unique,
persistent identifier that indicates which version of the software has been
used. Today, the technological infrastructure for _creating_ these identifiers
is in place: for example, for software hosted on github.com, the Zenodo-GitHub
integration [53] automatically stores the source code of each software release
on the Zenodo repository operated by CERN, and mints a document object
identifier (DOI) for it.

Figure 9 illustrates how citing such a DOI works from the user’s perspective:
When code developers place the DOI badge offered by Zenodo in the "how to
cite" section of their documentation, users can click on it and be redirected
to the landing page of the accompanying Zenodo record. There, they select the
DOI corresponding to the version they used – or, if they are referring to the
software in general, they can cite the "concept DOI" of the software that
represents all versions and always resolves to the latest one. Finally, they
can select the desired citation style and copy the citation into their
manuscript or download the citation in a format supported by their reference
manager.

Figure 9:  User flow for citation via Zenodo-GitHub integration. (a) User
clicks on DOI badge in the README file of the source code repository or in the
documentation of the software. (b) User is redirected to the landing page of
the Zenodo software record, where they can pick the version they used. (c)
User enters the desired citation style and copies the citation [54] into their
manuscript or downloads the citation in a format supported by their reference
manager.

At least three codes in the atomistic.software collection (PySCF [40, 55],
OpenMM [15, 56], and xtb [16, 57]) have already enabled the Zenodo-GitHub
integration but none of them mention this in their citation recommendations
yet, effectively reducing the functionality of the integration to that of a
future-proof backup of individual software versions. This is a common theme
found across software records on Zenodo today [31]. Part of the reason may be
that Zenodo records are not (yet) indexed by the widely used scholarly search
engines, such as the Web of Science, Scopus or Google Scholar. But as
researchers are getting increasingly accustomed to using platforms like
Zenodo, the Open Science Framework (osf.io) or Figshare (figshare.com) for
depositing and citing _data sets_ , it seems to be just a matter of time until
analogous practices in software citation will reach the mainstream. Zenodo
already _does_ track citations of its records through publicly available
sources such as Crossref and Europe PubMedCentral (and displays them on the
record). Trailblazing developers can therefore recommend their users to cite a
version-specific Zenodo DOI in _addition_ to a review paper, and thereby get
valuable statistics on which versions of their software are being used in
return. It can also be a convenient way of making a new code citable before a
paper has been written on it.

As for the atomistic.software collection, this review only marks the
beginning. Going forward, the collection will receive annual updates,
including updates of this perpetual review when warranted. Possible directions
for further work include

  * •

adding any simulation engines that were missed,

  * •

recording the time evolution of licenses at the level of individual codes, and

  * •

potentially evolving the scope of the collection, e.g. to include software for
atomistic visualization or workflow management (although care would need to be
taken in order not to lose focus).

Suggestions for future directions as well as updates and corrections of engine
metadata (search keywords, tags, distribution channels, accelerator support,
supported APIs, benchmarks, …) are highly welcome, be it through public
discussions on the ltalirz/atomistic-software issue tracker, via pull requests
to the repository or via private communication to the authors.

##  4 Author Contributions

Leopold Talirz: Conceptualization, Methodology, Software and Data curation for
atomistic.software. Writing- Original Draft, Reviewing and Editing.
Luca M. Ghiringhelli: Conceptualization, Methodology and Data curation for the
original static version of the collection. Writing- Reviewing and Editing.
Berend Smit: Supervision, Writing- Reviewing and Editing, Funding acquisition

##  5 Other Contributions

The authors are grateful to Nicola Marzari and Matthias Scheffler for sharing
their original idea of a list of atomistic simulation codes combined with
citation data. Thanks also go to Nicola Marzari for providing the idea for
table 1 and to Kevin Jablonka for a careful reading of the manuscript.
Insightful discussions with Michele Ceriotti, Lars Holm Nielsen, Kevin
Jablonka, Nicola Marzari, and Paul Saxe have contributed to the development of
this work, as have numerous constructive suggestions by the anonymous
reviewers of the manuscript.

For a more detailed description of contributions from the community and
others, see the GitHub issue tracking and changelog at
https://github.com/ltalirz/livecoms-atomistic-software.

##  6 Potentially Conflicting Interests

The authors declare no competing interests.

##  7 Funding Information

This work was supported by the MARVEL National Centre for Competence in
Research funded by the Swiss National Science Foundation (grant agreement ID
51NF40-182892), and the “MaGic” project of the European Research Council
(grant agreement ID 666983).

## Author Information

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