# Short-range Crystalline Order-Tuned Conductivity in Cr2Si2Te6 van der Waals
Magnetic Crystals

Yu Liu  †,♯,∗ Resta A. Susilo  ¶,♭ Yongbin Lee  ♢ A. M. Milinda Abeykoon  ∥
Xiao Tong  § Zhixiang Hu  †,‡ Eli Stavitski  ∥ Klaus Attenkofer  ∥,¶ Liqin Ke
♢ Bin Chen  ¶ and Cedomir Petrovic †,‡,∗<EMAIL_ADDRESS><EMAIL_ADDRESS>[

###### Abstract

Two-dimensional magnetic materials (2DMM) are significant for studies on the
nature of 2D long range magnetic order but also for future spintronic devices.
Of particular interest are 2DMM where spins can be manipulated by electrical
conduction. Whereas Cr2Si2Te6 exhibits magnetic order in few-layer crystals,
its large band gap inhibits electronic conduction. Here we show that the
defect-induced short-range crystal order in Cr2Si2Te6 on the length scale
below 0.6 nm induces substantially reduced band gap and robust semiconducting
behavior down to 2 K that turns to metallic above 10 GPa. Our results will be
helpful to design conducting state in 2DMM and call for spin-resolved
measurement of the electronic structure in exfoliated ultrathin crystals.

BNL] †Condensed Matter Physics and Materials Science Department, Brookhaven
National Laboratory, Upton, New York 11973, USA
¶Center for High Pressure Science and Technology Advanced Research, Pudong,
Shanghai 201203, China
♢Ames Laboratory, U.S. Department of Energy, Ames, Iowa 50011, USA
∥National Synchrotron Light Source II, Brookhaven National Laboratory, Upton,
New York 11973, USA
§Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton,
New York 11973, USA
‡Materials Science and Chemical Engineering Department, Stony Brook
University, Stony Brook, New York 11790, USA

KEYWORDS: van der Waals ferromagnet, Cr2Si2Te6, short-range crystalline order,
insulator-metal transition, electronic structure

##  1 Introduction

Intrinsic ferromagnetic (FM) semiconductors are of great interest for
fundamental studies of magnetism and for future spintronic technology 1. In
particular, due to use in nanoscale devices, significant effort is devoted
towards computational predictions and discovery of crystals with layered
structure with van der Waals (vdW) bonds 2. First-principles calculations,
Raman experiments and electronic transport indicated that FM state in Cr2X2Te6
(X = Si, Ge) survives even in mono- and few-layer crystals and indeed this is
experimentally observed in bilayer Cr2Ge2Te6 and related CrI3 2DMMs 3, 4, 5,
6. This presents potential opportunity for fundamental studies of 2D magnetism
and further magneto-electronic device design. In particular, due to magneto-
elastic coupling in Cr2Si2Te6, ferromagnetic spin exchange via Te-to-Cr charge
transfer can be manipulated by ultrafast optical pulses that excite coherent
phonon oscillations 7. Furthermore, of high interest are conducting electronic
states in 2D materials that can be used for spin-charge conversion in
spintronic devices 8, 9, 10, 11.

Cr2Si2Te6 orders ferromagnetically below 32 K and features band gap of 0.4 eV
12, 13. Cr2Ge2Te6 has FM $T_{\textrm{c}}$ of 61 K and band gap of 0.7 eV 14,
15. FM correlations along the $c$-axis vanish above 50 K in Cr2Si2Te6 but in-
plane short-range FM correlations persist up to room temperature. In addition,
there is strong spin-phonon coupling 16. Whereas spin-phonon interaction is
robust on chemical alloying and vacancies, application of high-pressure
induces metallic state above 8 GPa and superconductivity 17, 18.

On the other hand, different forms of crystalline imperfections have been
predicted by the first-principle calculations to tune both magnetic and
conducting states in Cr2X2Te6. Surface Ge vacancies lead to metallic state by
closing the band gap in Cr2Ge2Te6 multilayer, causing a magnetic anisotropy
energy rise 19. Strain in Cr2Ge2Te6 monolayer can raise ferromagnetic
$T_{\textrm{c}}$ close to room temperature 20. Of particular interest is
theoretical consideration of crystalline imperfection engineering in Cr2Si2Te6
monolayer. Defects are predicted to result in fully spin polarized current
arising from bipolar magnetic semiconducting state where reversible spin
direction of opposite spin-polarized conduction and valence bands state may be
tuned by the gate voltage 21. This is favored over external magnetic field
switching of single spin direction in standard half-metals and semiconductors;
moreover bipolar magnetic semiconductors could also be used for separation and
detection of entangled states in superconductors, of interest for quantum
computing 22, 23, 24.

In this work we successfully synthesized exfoliable crystals of Cr2Si2Te6 with
defect-induced short-range crystalline order imperfections on the length scale
below 1 nm. This suppresses the 0.4 eV gap in the charge insulating state
above magnetic $T_{c}$ 25 and gives rise to semiconducting current that can be
tuned to a good metal at high pressure. We observe considerably lower thermal
conductivity when compared to previous reports 13 arising from possible
stacking faults and higher magnetic entropy released below the magnetic
transition which implies not only increased phonon scattering but also
perturbation of phonon modes and possibly of magnetoelastic coupling. Enhanced
conduction suggests that Cr2Si2Te6 exfoliable crystals may be of interest for
future spintronic devices, calling for investigation of spin-polarized
electronic structure and spin-polarized current in epitaxially strained
Cr2Si2Te6 nanostructures.

##  2 RESULTS AND DISCUSSION

Cr2Si2Te6 [Fig. 1(a)] was previouly synthesized by Ouvrard _et al._ 26, which
is a layered material with Si-Si pairs. Cr atoms make honeycomb lattice in
planes separated by vdW bonds with Si in hexagon center. Each Cr is
octahedrally coordinated by Te, Si-Si bonds make dimers which form Si2Te6
groups 26, 27, 28. Dimers of Si-Si are a peculiarity when compared with CrI3,
whereas different electronegativity of constituent atoms suggests variable
character of chemical bonds in planes separated by vdW force. Magnetic
interaction in planes are FM, arising by Cr-Te-Cr superexchange through nearly
90∘ angle and is stronger than antiferromagentic (AFM) Cr-Cr direct exchange.
The exchange interactions from the next-nearest- and third-nearest- besides
the nearest-next (NN) couplings also contribute to its magnetic ground state
29. XRD $2\theta$ scan [Fig. 1(b)] reveal only $(00l)$ peaks, indicating
layered structure. XRD powder pattern taken at NSLS II synchrotron is fitted
with main phase of $R\overline{3}h$ space group Cr2Si2Te6 with $\sim$ 1.7%
SiTe2 impurity [Fig. 1(c)]. Room temperature unit cell parameters of Cr2Si2Te6
are $a=b=6.7607(2)$ Å and $c=20.6650(4)$ Å 26.

Figure 1(d,e) presents the XANES and the corresponding Fourier transform
spectra of the EXAFS for the Cr and Te $K$-edge of Cr2Si2Te6, respectively, at
the room temperature. The XANES spectra indicate Cr3+ and Te2+ states in
Cr2Si2Te6 30, 31, 32. The local structural information is revealed in the
EXAFS of Cr2Si2Te6 measured at room temperature. By the EXAFS equation, which
in the single-scattering approximation takes the form 33:

$\displaystyle\chi(k)=\sum_{i}\frac{N_{i}S_{0}^{2}}{kR_{i}^{2}}f_{i}(k,R_{i})e^{-\frac{2R_{i}}{\lambda}}e^{-2k^{2}\sigma_{i}^{2}}sin[2kR_{i}+\delta_{i}(k)].$

Here $N_{i}$ is the number of surrounding atoms from the central
photoabsorbing atom at a distance of $R_{i}$. $S_{0}^{2}$ is the reduction
factor for passive electrons, $f_{i}(k,R_{i})$ describes backscattering
amplitude, $\delta_{i}$ and $\lambda$ are phase shift and mean free path of
photoelectron, respectively. The $\sigma_{i}^{2}$ is Debye-Waller factor. The
local chemical bond distances from 1.5 to 4.0 Å (Table I) show that local
environment of Cr atoms consists of six Te atoms with two close distances
[2.81(9) Å and 2.86(9) Å]; the three Cr atoms are further away [3.91(49) Å].
For the Te site, the NN are one Si [2.35(26) Å] and two Cr with close
distances [2.81(27) Å and 2.86(27) Å] whereas two Si [3.68(26) Å] and six Te
[3.89(12) Å and 3.94(12) Å] are further away. The obtained results from
different element EXAFS analysis agree well with each other. First
coordination shell bond distances seen from EXAFS do not indicate difference
from previously published bond distances seen by the average crystal structure
where Cr NN Te atoms are at 2.81 Å and 2.86 Å away and Te NN atoms are Si at
2.34 Å and Cr at 2.81 Å and 2.86 Å 34.

For further insight into change of interatomic distances beyond first
coordination shell we studied scanning tunneling microscope (STM) as well as
local and average crystal structure from total scattering. The surface of Te
atomic layer is easily exposed by crystal cleaving 35. Figure 1(h) presents
the STM topography obtained on the surface of cleaved Cr2Si2Te6 crystal. An
ordered honeycomb lattice of bright spots is observed; each spot is a surface
Te atom. It should be noted that a large number of darker spots (defects) were
also observed [Fig. 1(h) upper panel], which tunes the local electronic
structure. Figure 1(i) shows the comparison of the spatially-averaged dI/dV
spectrum of bright and dark areas measured at the room temperature. As we can
see, there is a small energy gap around $E_{\textrm{F}}$, which is more narrow
in the dark area [Fig. 1(i)]. A similar defects feature was also observed in
Cr2Ge2Te6, which is explained by assuming the replacement of Cr by Ge atoms
35. The local energy gap between maximum of valence band and Fermi level is
about $\sim$ 0.16(1) eV from the Ultraviolet Photoelectron Spectroscopy (UPS).
The bright surface domains/areas, though, appear long range order in atomic
structure, but are randomly “waved” as shown in large scale STM images. The
randomly waved/corrugated top atomic layers are causing the interlayer
distance to vary randomly, which may cause random variation of the the
interlayer electrical coupling in the real space. Thus, in momentum space,
there could be changes in band dispersion in the Brillouin zone (BZ) that
affect electron correlation. This is similar to twisted or pressed bi- or
multi-layer graphene where the interlayer electrical coupling can be
dramatically changed by converting linearly dispersive Dirac cones into flat
bands at some magic twist angle or pressure, giving rise to correlated
electronic liquid that may exhibit skyrmions in ferromagnetic state or
unconventional superconductivity 36, 37. On other hand, the randomly
distributed dark areas could act as electron scattering centers, resulting in
the Anderson localization, less dispersive and more correlated conducting
bands. This implies that the dark features in STM may posses unique crystal
structure with different coordinate lattice environment when compared to
defects-free surface area.

Theoretical calculations predict Cr(Si) but also Si(Cr) antisite defects that
are energetically favorable in monolayer Cr2Si2Te6, which has lower formation
energy than other vacancies and/or interstitial defects 21. The defect
engineering has been predicted to give rise to bipolar magnetic semiconducting
state with highly spin polarized current; in such state a gate voltage control
of reversible spin detection is possible. For insight into nanoscale crystal
structure we present the Rietveld and pair distribution function (PDF) result
from total scattering. Long-range order (LRO) atomic structure of Cr2Si2Te6
[Fig. 1(c)] features relatively large atomic displacement parameters (ADPs)
(see Supplementary Materials) and the noticeable diffuse scattering component
in background subtracted data suggested short-range ordered (SRO) structural
modulations. The PDF analysis was further performed to confirm this
observation. Not surprisingly, LRO model can explain crystal structure on the
(6.2 - 25) Å length-scale but shows a rather poor agreement on (1.5 - 6.2) Å
of PDF refinement [Fig. 1(k)]. Further refinement of the LRO model on the PDF
length scale (1.5 - 6.2) Å resulted in noticeably different bond lengths and
angles. SRO at distances below 6.2 Å is well fitted with the same trigonal
symmetry but with somewhat different unit cell dimensions $a=b=6.76151(1)$ Å
and $c=20.6138(1)$ Å that introduce changes in local environment of Cr atoms.
The detailed refinement can be found in Supplementary Materials that is
considered as a distorted structure in the DFT calculations (see below).

The $M(T)$ of our Cr2Si2Te6 crystal is nearly isotropic above 40 K for both
directions but a large magnetic anisotropy sets in below 40 K. For
$\mathbf{H\parallel ab}$, a clear two-step transition occurs, not present in
$M(T)$ measured in higher fields 38, and the splitting of ZFC and FC was
observed below 26 K. To probe anisotropy of the two-stage transition 39, we
performed ac magnetization measurements. An obvious kink (satellite
transition) at $T^{*}$ $\sim$ 26 K was further confirmed in real part of ac
susceptibility $m^{\prime}(T)$ in addition to the upturn around
$T_{\textrm{c}}$ $\sim$ 35 K [Fig. 2(a) inset]. For $\mathbf{H\parallel c}$,
the ZFC - FC splitting below $T_{\textrm{c}}$ is due to the anisotropic FM
domain effect. The clear peak at $T_{\textrm{c}}$ $\sim$ 35 K was also
verified in $m^{\prime}(T)$ [inset in Fig. 2(b)]. A clear $\lambda$-type peak
in heat capacity [Fig. 2(c)] corresponds to the ferromagnetic transition
observed at 37 K in zero field. The $C_{\textrm{p}}(T)$ below 12 K can be
described by $C_{\textrm{p}}(T)=\gamma T+\beta T^{3}+\delta T^{3/2}$, where
first two terms describe electronic and phonon contributions and $\delta
T^{3/2}$ is the spin-wave contribution 40. The $\gamma$ is negligible, $\beta$
= 1.18(3) mJ mol-1 K-4 and $\delta$ = 36(1) mJ mol-1 K-5/2. The Debye
temperature from $\Theta_{\textrm{D}}=(12\pi^{4}NR/5\beta)^{1/3}$ = 254(2) K
with $N=10$. We obtain magnetic entropy $S(T)=\int_{0}^{T}C_{p}(T,H)/TdT$ =
3.1 J mol-1 K-1 in (25-45) K range, higher when compared to previously
observed but still far below expected $R$ln(2$S$+1) = 11.53 Jmol-1K-1 expected
total magnetic entropy 13. The magnetic entropy change $\Delta
S_{\textrm{M}}(T,H)=S_{\textrm{M}}(T,H)-S_{\textrm{M}}(T,0)$, assuming
adiabatic process of field change and electronic and phonon contributions are
field independent. The $\Delta T_{\textrm{ad}}$, adiabatic temperature change
induced by magnetic field change is $\Delta
T_{\textrm{ad}}(T,H)=T(S,H)-T(S,0)$. Here $T(S,H)$ and $T(S,0)$ are the
temperatures at constant total entropy $S$ in magnetic field and in the
absence of magnetic field, respectively. $-\Delta S_{\textrm{M}}$ and $\Delta
T_{\textrm{ad}}$ [Fig. 2(d)] show maximum around $T_{c}$ and rise with
magnetic field increase. $-\Delta S_{\textrm{M}}$ and $\Delta T_{\textrm{ad}}$
show maximum values of 6.77 J kg-1 K-1 and 3.0 K in 9 T, somewhat higher when
compared to magnetic entropy change estimated from magnetization curves up to
5T 38, and also larger than those of CrX3 (X = Cl, Br, I) and Cr2Ge2Te6 11.

Thermal conductivity $\kappa(T)$ [Fig. 2(e)] is smaller below room temperature
from previously observed 13. The $\kappa(T)$ is contributed by the electronic
term $\kappa_{\textrm{e}}$ and the lattice part $\kappa_{\textrm{L}}$, i. e.,
$\kappa=\kappa_{\textrm{e}}+\kappa_{\textrm{L}}$. From Wiedemann-Franz law we
can calculate the $\kappa_{\textrm{e}}=L_{0}T/\rho$ from the measured
resistivity $\rho$ with $L_{0}$ = 2.45 $\times$ 10-8 W $\Omega$ K-2. As
depicted in the inset in Fig. 2(e), $\kappa_{\textrm{e}}$ is about ten times
smaller than $\kappa_{\textrm{L}}$. An anomaly was observed at
$T_{\textrm{c}}$ (red dashed line) for both $\kappa_{\textrm{e}}$ and
$\kappa_{\textrm{L}}$, confirming the strong spin-phonon coupling 13, 17.
Magnetic field-dependent $\kappa(T)$ in Cr2Si2Te6 exhibits visible deviation
from the zero-field $\kappa$($T$) due to magnetic correlations above
$T_{\textrm{c}}$, in agreement with entropy 13 and neutron scattering results
16. $\kappa(T)$ in [Fig. 2(e)] increases in magnetic field, suggesting
possible phonon scattering off RuCl3-like Kitaev-Heisenberg excitations as
discussed in Cr2X2Te6 ($X$ = Si, Ge) 41, 42, 43. The $S(T)$ [Fig. 2(f)] is
positive with $S$(300 K) =180 $\mu$V K-1. The $S(T)$ is almost linear in high
temperature. Assuming energy-independent relaxation time in the free electron
model $S=\pi^{2}k_{\textrm{B}}^{2}T/3eE_{\textrm{F}}$. Hence, fit result
$dS/dT$ = 0.492(6) and 0.526(3) $\mu$V K-2 derives the Fermi energy
$E_{\textrm{F}}$ = 49.7(6) and 46.4(3) meV in 0 and 9 T, respectively. The
$S(T)$ shows a kink at $T_{\textrm{c}}$ $\sim$ 34 K in zero magnetic field, in
agreement with the $\kappa(T)$ measurement, which is suppressed in 9 T. The
low temperature $S(T)$ is well fitted by
$S(T)=(k_{\textrm{B}}/e)(A+E_{\textrm{S}}/k_{\textrm{B}}T)+BT^{1/2}$ [inset in
Fig. 2(f)] 44, 45, where $E_{\textrm{S}}$ $\sim$ 30(1) $\mu$eV is the
activation energy whereas $A$ is constant, the second term is attributed to
the variable-range hopping (VRH) conduction.

Resistivity $\rho(T)$ of Cr2Si2Te6 at ambient pressure is presented in Fig.
3(a). It increases on cooling from the room temperature, showing a typical
semiconducting behaviour. Below 50 K, $\rho(T)$ increases faster with a weak
shoulder at $T_{\textrm{c}}$. The temperature-derivative curve shows an
anomaly at 37 K, consistent with the $T_{\textrm{c}}$ observed from the
magnetization and specific heat data. Therefore the weak shoulder in the
$\rho(T)$ data is associated with the FM transition. Above 40 K, resistivity
is explained by the thermally activated model in the presence of disorder-
induced localization of the electronic wavefunction: $\rho(T)$ = $\rho$0 \+
$A$exp($E_{\rho}$/$k_{\textrm{B}}$$T$) - $B$$T^{0.5}$, where $\rho$0 is
residual resistivity, prefactors $A$ and $B$ denote relative contribution of
activated and localization scattering mechanism whereas $E_{\rho}$ is the band
gap 46, 47. The fit yields $E_{\rho}$ $\sim$ 18.0(1) meV activation energy,
$A$ = 10(2)$\times$10-5 and $B$ = 1.77(3)$\times$10-3, which shows that
electronic transport is dominated by disorder-induced localization. The
$\rho(T)$ below magnetic transition can be fitted with the same equation used
for paramagnetic state but where band conduction yields to adiabatic small
polaron hopping, i.e. temperature activated term
$A$exp($E_{\rho}$/$k_{\textrm{B}}$$T$) is replaced by
$CT$exp($E$ρ/$k_{\textrm{B}}$$T$) 44. The derived $E_{\rho}$ $\sim$ 0.30(2)
meV, $C$ = 2.3(2)$\times$10-3 and $D$ = 43(1)$\times$10-3. The
$E_{\textrm{S}}$ $<$ $E_{\rho}$ is consistent with polaron contribution to
transport mechanism, since $E_{\textrm{S}}$ is associated with carrier
hopping, whereas energy to both create and activate the hopping of carriers
are in $E_{\rho}$ 44. It should be noted, though, that disorder-induced
localization is dominant in paramagnetic state as well below magnetic order,
which shows high correlation between electronic transport and inhomogeneous
nanoscale short range crystallographic distortions.

The electronic transport in Cr2Si2Te6 can be further tuned by pressure. The
pressure-dependent resistance at 300 K [Fig. 3(a) inset] significantly drops
from $10^{3}$ $\Omega$ below 1 GPa to values less than $10^{-1}$ $\Omega$
around 10 GPa and above. The giant drop in resistance signals pressure-induced
semiconductor-metal transition as observed in the isostructural Cr2Ge2Te6 48.
This critical value of pressure ($\sim$ 10 GPa) agrees well with the
theoretical prediction of pressure-induced semiconductor-metal transition
($\sim$ 10.4 GPa) in distorted Cr2Si2Te6 (see below). In order to confirm this
semicondutor-metal transition, we measured the temperature-dependent data at
different pressures [Fig. 3(b)]. At 5.7 GPa, a hump in the resistivity
emerges, proposed to be related to the insulator-metal transition (IMT) 18. On
increasing pressure, the hump shifts towards high temperature and
simultaneously weakens in high pressure. The resistivity behavior above 9 GPa
suggests that Cr2Si2Te6 approaches a metallic state. Indeed, the resistivity
at 12.5 GPa falls below the Mott-Ioffe-Regel (MIR) limit 49, 50,
$\rho_{\textrm{MIR}}=\hbar c/e^{2}~{}\sim~{}9\times 10^{-4}~{}\Omega$ cm,
where $c$ is the lattice constant ($\sim 20.5$ Å). Above 20 GPa, the
resistance decreases with decreasing temperature which indicates the
metallization of compressed Cr2Si2Te6. Note that no obvious resistivity drop,
which signals superconducting transition, was observed from the resistivity
data measured above 9 GPa. This is in contrast with the pressure-induced
superconductivity in Cr2Si2Te6 above $\sim$ 8 GPa reported previously,
implying that short-range structural details [Fig. 1(k)] are detrimental for
the high-pressure superconducting state 18.

Structural properties of Cr2Si2Te6 at high pressures have been investigated
recently by Cai et al. 18 and Xu et al. 51. However, both reports arrived at
different conclusion regarding whether Cr2Si2Te6 transforms into another high
pressure phase on compression. Here, we used Raman spectroscopy to probe the
vibrational properties of Cr2Si2Te6 under pressure up to 20 GPa connected with
the putative structural transition Fig. 3(c). It is known that many Te-
containing materials experience easy surface oxidation, which is also
problematic in the case of Cr2Si2Te6 since Te-oxide (TeOx) shows very strong
Raman signals. In order to minimize surface oxidation, we used a freshly
cleaved crystal in glovebox and attempted to load the crystal into the diamond
anvil cell in less than 5 minutes. As shown in Fig. 3(d), a contribution to
the Raman spectra of Cr2Si2Te6 due to the TeOx impurities can be excluded.
Group theory analysis revealed that the Raman tensor is represented by five
$A_{g}$ and five doubly degenerate $E_{g}$ modes, i.e. $\Gamma=5A_{g}+5E_{g}$
52. Raman spectrum of Cr2Si2Te6 at smallest pressure of 0.3 GPa features two
peaks at around 117 cm-1 and 147 cm-1 which are assigned to $E_{g}^{3}$ and
$A_{g}^{3}$ modes, respectively [Fig. 3(d)]. Both the $E_{g}^{3}$ and
$A_{g}^{3}$ modes shift to high frequencies with increasing pressure without
apparent anomalies [Fig. 3(e,f)]. No peaks splitting or the appearance of new
Raman mode was observed, implying no crystal structure changes in Cr2Si2Te6 up
to 18 GPa, consistent with the high pressure XRD data by Xu et al. 51. The
intensities of both modes weaken above 12 GPa and completely disappear at 20
GPa probably due to metallization of Cr2Si2Te6 as revealed from the resistance
data in Fig. 3(b). It is also possible that the Raman modes vanishing is due
to the loss of long-range order due to the formation of amorphous phase
reported to occur above 24 GPa 51. Given that Raman spectroscopy probes local
atomic vibrations, thus it is also sensitive to the short range crystalline
structure, we also carried out another run on another batch of sample prepared
with the same method. The evolution of $E_{g}^{3}$ and $A_{g}^{3}$ modes [Fig.
3(e,f)] is consistent between different samples which indicates that such
short range crystalline order is reproducible in our grown samples.

To comprehend the implications of structural distortion, we further performed
the band structure calculation as well as calculations of conductivity in
undistorted and distorted (SRO) structures. The band structures [Fig. 4(a)]
show flat bands with similar energies between $T$ and $\Gamma$, and the
maximum of valence band (VBM) is in between $T$ and $\Gamma$ points. In
comparison, the valence bands of the undistorted structure have higher energy
than the bands of the distorted structure near the Fermi energy
($E_{\text{F}}$). For the conduction band, while the undistorted structure
shows a minimum in conduction band (CBM) between H2 and $T$ Brillouin zone
points, the distorted one shows three CBMs between H2 and $T$, between $L$ and
H0, and between $\Gamma$ and S0 points. The CBMs between H2 and $T$ have
similar energy in both structures, and these bands are majority-spin dominant
bands. The other two CBMs of the distorted structure are minority-spin
dominant bands, and corresponding bands of the undistorted structure have
higher energies. The undistorted structure has a bandgap of 0.45 eV without
spin-orbit coupling (SOC); including SOC decreases the gap size to 0.27 eV.
Similar SOC effects on bandgap have been found in other magnetic 2D vdW
materials 53. The distorted structure has slightly different bandgaps that are
0.47 eV and 0.25 eV without and with SOC, respectively. These bandgaps are all
indirect.

To understand the pressure-induced IMT in Cr2Si2Te6, we investigated how
electronic structures and transport properties evolve with the decreasing of
lattice constants using DFT. For simplicity, we keep the $c/a$ constant
(adopted from the experimental value) while changing the volume. Compared to
the experimental values at ambient pressure, DFT slightly overestimates the
lattice parameters by $1.8\%$ and $1.2\%$ in the undistorted and distorted
structures, respectively. To qualitatively relate the volume change to
pressure and compare it with experiments, we also fit the $E$(V) curve, where
$E$ is the total energy and $V$ is the volume, by Birch-Murnaghan equation of
state (EOS) 54. Figure 4(b) shows the calculated bandgap as functions of
volume in undistorted and distorted Cr2Si2Te6. With decreasing lattice
parameters, the bandgap decreases in the distorted structure, while the gap in
the undistorted structure slightly increases and then decreases. The
semiconductor-metal transition occurs at $\Delta V=-10\%$ and $-15\%$ for the
distorted and undistorted structures, respectively. This volume change
corresponds to about the pressure value of 10.4 (18.6) GPa for the distorted
(undistorted) structure. The calculated transition pressure of 10.4 GPa for
the distorted structure agrees well with the experimental observed value. This
shows that local distortion can affect the semiconductor-metal transition
pressure.

Figure 4(c) shows the spin-projected density of states (DOS) calculated with
various volumes in undistorted structure. The minority spin band gap is larger
than the majority spin band gap at ambient pressure. However, the majority-
and minority-spin bands respond to pressure differently. The majority-spin
bandgap slightly increases with increasing pressure while the minority-spin
gap decreases. This results in the bandgap increase with pressure in a small
pressure region until the minority-spin bandgap becomes smaller than the
majority-spin bandgap (see Fig. S2). The actual bandgap is determined by the
smaller bandgap in two spin channels. Pressure promotes the hybridization
between Cr and Te atom by reducing inter-atomic distance and the
delocalization of Cr-$d$ states 55. Cr-$d$ states are the dominant states
filling the gap. In comparison to non-SOC calculations, SOC reduces the size
of the bandgap, resulting in a smaller IMT transition pressure value (see Fig.
S2). Figure 4(d) shows the spin-projected DOS in the distorted structure.
Compared to the undistorted structure, the distorted structure has a slightly
smaller gap in the majority spin, and a much smaller gap in the minority spin
channel. As a result, the distorted structure has a lower IMT transition
pressure than the undistorted one. Since electronic conductivities adopt
changes in electronic band structures, they display a similar character of IMT
transition with increasing pressure. For example, at 20 K, the conductivity in
distorted structure with $\Delta V=-12\%$ and the undistorted structure with
$\Delta V=-16\%$ increase by $\sim 180$ and $\sim 108$ times, respectively,
compared to their ambient structures (see Fig. S4).

The present plain DFT description of the pressure effects on bandstructure and
the calculated IMT transition pressure compare well with experimental results.
Future theoretical investigation can explore the pressure-dependent structures
and bandgaps with more comprehensive approaches. For example, more accurate
descriptions of the pressure-dependent structure of vdW materials can be
obtained by employing proper vdW density functionals 56. However, the best
choice of vdW functional often depends on the material investigated, and a
more comprehensive structure study can be helpful. Moreover, it will also be
interesting to use more sophisticated ab-initio methods beyond DFT 53 for a
better description of the bandgap.

##  3 Conclusions

Defects, dislocations and other crystalline imperfections in 2D materials
beyond graphene often bring interesting physics and useful functionality 57.
In this work we have experimentally observed defects-induced short-range
crystallographic order on the length scale 0.6 nm in van der Waals magnet
Cr2Si2Te6 where conductivity is dominated by polaron hopping, and also
discussed by the DFT calculations. Moreover, metallic state emerges at high
pressure without change of the crystal lattice symmetry. It is of high
interest to further nanofabricate ultrathin crystals of Cr2Si2Te6 with short
range order for transport or to tune its properties by epitaxial strain in
thin films which could be used for spin-charge conversion in nanoscale
devices.

##  4 Material and Methods

Cr2Si2Te6 crystals with defects were made using flux method 38. Cr2Si2Te6
stoichiometry of raw materials was sealed in fused silica tube in about 2 Torr
Argon gas pressure. The tube was heated to 1100 ∘C in 20 h. After keeping the
tube at 1100 ∘C for 3 h, it was cooled to 680 ∘C in 1 ∘C/h. Crystals were
decanted in centrifuge from flux and immediately quenched in ice water. The
transport and magnetic properties as well as high pressure Raman data are
reasonably repeatable in samples from two different batches. The average
chemical composition was investigated by energy-dispersive x-ray spectroscopy
(EDS) on several points on the crystal surface using JEOL LSM-6500 scanning
electron microscope (SEM). The result was consistent with 1 : 1 : 3
stoichiometry. Wide angle X-ray scattering and PDF experiments used pulverized
sample in a capillary in transmission mode and 74.5 keV ($\lambda$ = 0.1665
${\AA}$) of 28-ID-1 (PDF) beamline of the National Synchrotron Light Source II
(NSLS II) at Brookhaven National Laboratory (BNL). The data were integrated
using pyFAI software, and reduced to obtain experimental PDFs
(Q${}_{\textrm{max}}$ = 25 Å-1) using the xPDFsuite whereas Rietveld and PDF
analysis were performed by GSAS-II and PDFgui software 58, 59, 60, 61.

Scanning tunneling microscope (STM) experiments were performed at room
temperature in Scienta Omicron VT STM XA 650 with Matrix SPM Control System in
$\sim$ 2 $\times$ 10-10 torr UHV chamber on a fresh surface obtained by
cleaving. The topography was obtained with positive bias in the constant
current mode. STM images were analyzed using SPIP software. In scanning
tunneling spectroscopy (STS) experiments, the current (I)-voltage (V) curves
are recorded at selected spots while the feedback loop is turned off. Each I-V
curve is the average of about 40 individual I-V curves, and then the dI/dV
curve was generated. For Ultraviolet Photoelectron Spectroscopy (UPS)
measurements a $<$ 2 $\times$ 10-9 Torr UHV system was used and hemispherical
electron energy analyzer (SPECS, PHOIBOS 100) and ultraviolet source (SPECS,
10/35). He(I) at 21.2 eV radiation was used. The spectra were calibrated by
the Fermi edge of Au(111) crystal.

X-ray absorption spectroscopy (XAS) was done in fluorescence mode at 8-ID
beamline of the NSLS II at BNL. XANES (X-ray absorption near edge structure
spectra) and EXAFS (extended X-ray absorption fine structure spectra) analysis
was done by Athena software. EXAFS signal was $k^{2}$-weighed and Fourier-
transformed from 2 to 10 Å-1 range to analyze data in $R$ space.

Magnetic, thermal and transport measurements were carried out in MPMS-XL5 and
PPMS-9. Electrical transport of Cr2Si2Te6 at high pressure were measured using
a Be-Cu diamond anvil cell (DAC) of 300 $\mu$m cullet size. A sample chamber
and insulating layer between gasket and electrodes was a mix of cubic boron
nitride (cBN) and epoxy. Measurements were done on 60 $\mu$m $\times$ 15
$\mu$m crystal using NaCl powder pressure medium which gives a quasi-
hydrostatic condition. For electrical resistance in DAC, Pt foil electrodes
and van der Pauw four probe method was used. The pressure was calibrated by
Ruby 62. Renishaw in Via Raman system and 532 nm laser wavelength were used to
obtain Raman spectra at 300 K in a 300 $\mu$m symmetric DAC. Small single
crystal with few Ruby balls with silicone oil as a pressure medium were put in
a 120 $\mu$m hole of stainless steel gasket.

Band structures were calculated using a full-potential linear augmented plane
wave (FP-LAPW) in Wien2K 63 with GGA approximation 64. We used
$R_{\text{MT}}K_{\text{max}}$ = 8.0 with muffin-tin (MT) radii $R_{\text{MT}}$
=2.3, 1.8, and 2.1 a.u. for Te, Si, and Cr, respectively, to generate self-
consistent potential and charge. We used 371 $k$-points in the irreducible
Brillouin zone, iterated until total energy difference is less than 0.01 mRy.
SOC is induced in the second-variational method. Transport properties are
calculated within the Boltzmann theory through a postprocessing procedure, as
implemented in BoltzTraP 65, using the eigenenergies of a self-consistent
wien2k calculation. The approximation of isotropic relaxation time ($\tau$) is
employed.

##  5 Supplementary materials

The Support Information is available free of charge online.

Further details of crystal structure, STM analysis, and DFT calculations.

##  6 Author information

###  6.1 Corresponding Authors

<EMAIL_ADDRESS>
<EMAIL_ADDRESS>

###  6.2 Present Addresses

♯ Los Alamos National Laboratory, Los Alamos, NM 87545, USA
♭ Department of Physics, Pohang University of Science and Technology, Pohang
37673, Korea
¶ ALBA Synchrotron Light Source, Cerdanyola del Valles, E-08290 Barcelona,
Spain

###  6.3 ORCIDs

Yu Liu: 0000-0001-8886-2876
Resta A. Susilo: 0000-0003-0799-7416
A. M. Milinda Abeykoon: 0000-0001-6965-3753
Xiao Tong: 0000-0002-5567-9677
Klaus Attenkofer: 0000-0003-1588-3611
Liqin Ke: 0000-0001-5130-9006
Cedomir Petrovic: 0000-0001-6063-1881

###  6.4 Author Contribution

Y.L. (Yu Liu), R.A.S. and Y.L. (Yongbin Lee) contributed equally to this work.
C.P. and B.C. conceive the research and designed the experiment. Y.L. (Yu
Liu), Z.H., E.S., K.A. and C.P. performed synthesis, transport, thermal, X-ray
absorbtion, magnetic measurements and data analysis. X.T. contributed STM
studies. M.A. contributed synchrotron powder X-ray Rietveld and PDF
measurements and analysis. R.S. and B.C. contributed high pressure Raman,
X-ray and transport measurements and analysis. Y.L. (Yongbin Lee) and L.K.
contributed the first principle calculations and analysis. Y.L. (Yu Liu) and
C.P. wrote the paper with contribution from all authors. All authors discussed
the results and commented on the manuscript.

###  6.5 Notes

The authors declare no competing financial interest.

Work at Brookhaven National Laboratory (BNL) is supported by the Office of
Basic Energy Sciences, Materials Sciences and Engineering Division, U.S.
Department of Energy (DOE) under Contract No. DE-SC0012704. This research used
the 28-ID-1 and 8-ID beamlines of the NSLS II, a U.S. DOE Office of Science
User Facility operated for the DOE Office of Science by BNL under Contract No.
DE-SC0012704. This research used resources of the Center for Functional
Nanomaterials (CFN), which is a U.S. DOE Office of Science Facility, at BNL
under Contract No. DE-SC0012704. First principle calculations were supported
by the U.S. Department of Energy, Office of Science, Office of Basic Energy
Sciences, Materials Sciences and Engineering Division. Ames Laboratory is
operated for the U.S. Department of Energy by Iowa State University under
Contract No. DE-AC02-07CH11358.

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Table 1: Structural parameters obtained from the synchrotron powder XRD and local bond distances extracted from the EXAFS spectra fits with fixed CN for Cr2Si2Te6. CN is the coordination number based on crystallographic value, R is the interatomic distance, and $\sigma^{2}$ is the Debye Waller factor. Chemical: | Cr2Si2Te6 | Space group: | $R\bar{3}h$
---|---|---|---
$a$ (Å) | 6.7607(2) |  $\alpha$ (∘) | 90
$b$ (Å) | 6.7607(2) |  $\beta$ (∘) | 90
$c$ (Å) | 20.6650(4) |  $\gamma$ (∘) | 120
$V$ (Å3) | 817.98(3) | Weight fraction | 98.3%
Site | $x$ | $y$ | $z$ | Occ. | Uiso (Å2)
Te | -0.0028(4) | 0.3519(3) | 0.0832(1) | 1 | 0.0147(2)
Si | 0 | 0 | 0.0602(6) | 1 | 0.027(3)
Cr | 0 | 0 | 0.3385(3) | 1 | 0.012(2)
Center | Distance | CN | R (Å) |  $\Delta$R (Å) |  $\sigma^{2}$ (Å2)
Cr | Cr-Te.1 | 3 | 2.81 | 0.09 | 0.005
| Cr-Te.2 | 3 | 2.86 | 0.09 | 0.005
| Cr-Cr.1 | 3 | 3.91 | 0.49 | 0.036
Te | Te-Si.1 | 1 | 2.35 | 0.26 | 0.011
| Te-Cr.1 | 1 | 2.81 | 0.27 | 0.001
| Te-Cr.2 | 1 | 2.86 | 0.27 | 0.001
| Te-Si.2 | 1 | 3.68 | 0.26 | 0.011
| Te-Te.1 | 4 | 3.89 | 0.12 | 0.008
| Te-Te.3 | 2 | 3.94 | 0.12 | 0.008

Figure 1: (Color online) (a) Crystal structure of Cr2Si2Te6 (space group:
$R\bar{3}h$) shown from the side and top views. (b) Single crystal X-ray
diffraction (XRD) and (c) refinement of synchrotron powder XRD data of
Cr2Si2Te6 at room temperature. Normalized (d) Cr and (e) Te $K$-edge X-ray
absorption near edge structure (XANES) spectra. Fourier transform magnitudes
of the extended X-ray absorption fine structure (EXAFS) oscillations (symbols)
for (f) Cr and (g) Te $K$-edge with the phase shifts correction. The model
fits are shown as solid lines. Insets show the corresponding filtered EXAFS
(symbols) with $k$-space model fits (solid lines). (h) Scanning tunneling
microscope (STM) images. Upper: sample bias of 1 V and tunneling current of
0.8 nA; lower: 1.3 V and 0.8 nA, respectively. Individual atoms are
represented by green (Cr), blue (Si) and brown (Te) colors. (i) Comparison of
tunneling spectroscopy at the bright (defect-free) and dark (defect) areas.
(j) Ultraviolet Photoelectron Spectroscopy of Cr2Si2Te6 at room temperature.
(k) LRO model obtained from the Rietveld refinement showed a good agreement on
the PDF length scale (6.2 - 25) Å. However, it gave a poor agreement on the
PDF length scale (1.5 - 6.2) Å. (l) Structural model fit on PDF length scale
(1.5 - 6.2) Å suggested modulated bond lengths and angles. Blue circles, red,
and green solid lines represent data, structural model fits, and the fit
residues respectively.

Figure 2: (Color online) Temperature dependence of zero field cooling (ZFC)
and field cooling (FC) dc magnetization $M(T)$ measured at $H$ = 10 Oe for
Cr2Si2Te6 single crystal with (a) $\mathbf{H\parallel ab}$ and (b)
$\mathbf{H\parallel c}$, respectively. Insets show the real part
$m^{\prime}(T)$ of ac susceptibility measured with oscillated an ac field of
3.8 Oe and frequency of 499 Hz. Temperature dependence of (c) specific heat
$C_{p}(T)$ and (d) calculated magnetic entropy change $-\Delta S_{M}(T)$ in
various out-of-plane fields of Cr2Si2Te6 single crystal. Inset in (c) shows
magnetic specific heat and magnetic entropy released around the transition in
J mol-1 K-1. Inset in (d) shows the estimated adiabatic temperature $\Delta
T_{ad}(T)$. Temperature dependence of (e) thermal conductivity $\kappa(T)$ and
(f) thermopower $S(T)$ of Cr2Si2Te6 single crystal in zero field and 9 T.
Inset in (e) shows the calculated electronic thermal conductivity
$\kappa_{e}(T)$ and lattice part $\kappa_{L}(T)$ in W m-1 K-1. Inset in (f)
shows low-temperature $S(T)$ fit (see text).

Figure 3: (Color online) (a) Temperature dependence of in-plane electrical
resistivity $\rho(T)$ (top) and $d\rho/dT$ (bottom) in zero field of Cr2Si2Te6
single crystal. Inset exhibits the room temperature resistance of a bulk
Cr2Si2Te6 sample during compression and decompression. (b) Temperature
dependence of $\rho(T)$ at indicated pressures. (c) Raman spectra of Cr2Si2Te6
single crystal at various pressures. (d) Raman spectra of Cr2Si2Te6 compared
with that of TeOx at 0.3 GPa. Pressure-dependent Raman shift of (e)
$E^{3}_{g}$ and (f) $A^{3}_{g}$ modes of two different batches of sample
(solid and open symbols represent Samples 1 and 2, respectively).

Figure 4: (Color online) (a) Comparison between band structures of distorted
(SRO) and undistorted Cr2Si2Te6 in the ambient pressure. (b) Electronic band
gaps calculated as functions of volume change with pressure in distorted and
undistorted Cr2Si2Te6. The spin-orbit coupling is included. Spin-projected DOS
calculated using different lattice parameters in (c) undistorted and (d)
distorted structures. The minority spin states are more sensitive than the
majority spin states to pressure, and the bandgap is determined by minority
spin states.