Pressure-induced spin transition and site-selective metallization in CoCl2

The interplay between spin states and metallization in compressed CoCl2 is investigated by combining diffraction, resistivity and spectroscopy techniques under high-pressure conditions and ab-initio calculations. A pressure-induced metallization along with a Co2+ high-spin (S = 3/2) to low-spin (S = 1/2) crossover transition is observed at high pressure near 70 GPa. This metallization process, which is associated with the p-d charge-transfer band gap closure, maintains the localization of 3d electrons around Co2+, demonstrating that metallization and localized Co2+ -3d low-spin magnetism can coexist prior to the full 3d-electron delocalization (Mott-Hubbard d-d breakdown) at pressures greater than 180 GPa.


Results
The Co 2+ (3d 7 ) Tanabe-Sugano diagram describing the electronic states' energy in terms of the octahedral crystal field (in Racah parameter B units, Fig. 1) shows that, for CoCl 2 (B ≈ 80 meV at 50 GPa 15,30 ), the HS-LS ( 4 T 1 , S = 3/2 → 2 E, S = 1/2) transition should occur at Δ SCO = 1.7 eV. Importantly, the LS state may be affected by a strong Jahn-Teller effect, providing an additional lattice relaxation energy which, in principle, could reduce the SCO crystal-field strength triggering metallization at unexpectedly low pressure 19,30 . Alternatively, high pressure could, in turn, suppress the Jahn-Teller distortion causing the HS-LS to occur at higher pressures than expected, or even disappear if CoCl 2 transforms into a fluorite-type structure (d 3 -like Co 2+ ) 20 .
XRD shows that CoCl 2 exhibits nearly-degenerate layered structures at ambient conditions. The CoCl 2 pressure-induced phase transition sequence as determined experimentally with support of DFT calculations is indicated in Fig. 1. The three represented layered structures are more stable than the rutile, cotunnite, and fluorite phases at all pressures up to 100 GPa. This result, which is confirmed by both single-crystal and powder XRD experiments at high pressure, demonstrates the stability of the hexagonal layered structure of CoCl 2 and thus the Co 2+ sixfold coordination in a wide pressure range (0-60 GPa), in a way similar to FeCl 2 14 and MgCl 2 26 and contrary to CoF 2 10,20 . The stability of the given CoCl 2 structures, which involve the different packing sequence of layers of face-sharing CoCl 6 octahedra, is a consequence of the subtle competition of inter-layer van der Waals interactions. The CoCl 2 equation-of-state can be phenomenologically described by two Murnaghan's equations: one above and one below 14 GPa (see Supplementary Figs S1-S3). Figure 2 shows the pressure dependence of the optical absorption spectra of CoCl 2 around the charge-transfer band gap (a) and in the sub-gap Co 2+ d-d crystal-field region (b). Besides the gap energy, these spectra allow us to determine the excited-state electronic structure in the transparency window of CoCl 2 (≈50 GPa). At ambient conditions, the main sub-gap absorption peaks within the D 3d (nearly O h ) CoCl 6 4− octahedron 7,8 correspond to crystal-field transitions 4 T 1 (F) → 4 T 2 (F), 4 A 2 (F), and 4 T 1 (P) and are located at 0.79, 1.66 and 2.10 eV, respectively. In terms of the Tanabe-Sugano diagram for d 7 ions (Fig. 1b) 32,33 , the transition energies at ambient pressure correspond to Δ = 0.87 eV and B = 97 meV with Δ/B = 9.0 (see Supplementary Table S1) 15,30,32 . According to this diagram the crystal-field strength required to induce the SCO is (Δ/B) SCO = 21. Interestingly, the SCO also involves crossing of the 4 T 2 (F) and 2 T 1 (G) excited states, hence these states, which are well observed by optical absorption, can be used to efficiently probe the HS-LS transition. www.nature.com/scientificreports www.nature.com/scientificreports/ The variation of the absorption spectra with pressure shows that the band gap energy decreases linearly with pressure at a rate of −43 meV/GPa (Fig. 3). Such a large shift is responsible for the intense piezochromism exhibited by CoCl 2 (Fig. 2a). The pressure-induced redshift of the bandgap follows a quadratic dependence with the crystal volume yielding gap closure at V = 17.5 Å 3 /Co (V/V 0 = 0.56) -i.e. 80 GPa-(see Supplementary Fig. S5(c)). This redshift is produced by the hybridization enhancement of the Cl − -p and Co 2+ -d orbitals with pressure which in turn causes a broadening of the mainly 3p-and 3d-orbital valence band and an energy decrease of the mainly 3d-orbital intermediate band both reducing the p-d charge-transfer bandgap. DFT reproduces the decrease in the band gap of HS state (P < 67 GPa) reasonably well (see Supplementary Fig. 6(c)). The plots of the electron band and density of states certainly show a clear energy delocalization of the d-orbital manifolds with pressure yielding band broadening (see Supplementary Fig. S7(c,d)). Concurrently, the increasing crystal-field energy as obtained from the optical spectra, and the reduction of B from 97 to 82 meV in the 0-50 GPa range yield a Δ/B variation from 9.0 to 18.5, which implies an almost doubled splitting between e and t 2 orbitals, Δ, from 0.87 to 1.52 eV (see Supplementary Table S1 and Fig. S5).
As Figs 2 and 3 show, the variation of the absorption spectrum and its associated peak energies with pressure reveal that Co 2+ has a HS state in the crystal transparency range. However, extrapolating the linear dependence of the transition energies with pressure we obtain a HS to LS [ 4 T 1 (F) ↔ 2 E(G)] transition at 67 GPa. It is worth noting that the SCO is observed in the DFT + U results using a Coulomb correlation energy U = 3 eV (Figs 3 and 4). As indicated in the Methods section, this method cannot capture the evolution of the Coulomb correlation parameter upon volume changes and could underestimate the SCO pressure for high pressure regime 31,34,35 . However, the essence of the electronic and magnetic properties before and after the transition is valid. The spectroscopic determination of the 3d-electron structure together with the DFT estimates make CoCl 2 a reference system to validate theories dealing with SCO phenomena and metallization processes in transition-metal systems 25,[36][37][38][39][40][41][42][43] . Figure 3 plots the calculated magnetic moment as a function of pressure. According to DFT calculations, the Co 2+ magnetic moment abruptly decreases from HS, μ eff = 2.6 μ B , to LS, μ eff = 0.9 μ B , at around 67 GPa with a hysteresis of 8 GPa. The experimental SCO pressure and the crystal and electronic structures demonstrate that the Jahn-Teller coupling is not involved in the stabilization of the LS ground state, 2 E. This contrasts with one of the hypotheses given elsewhere 30,31 , that the high-pressure conditions required for SCO could be relaxed by the strong Jahn-Teller effect in the LS 2 E state down to 35 GPa if we consider a Jahn-Teller coupling similar to those measured in the CuCl 6 system 44 . The lack of a HS-LS transition at ≈35 GPa in CoCl 2 indicates that the Jahn-Teller effect is unable to distort the Co 2+ environment in the severe high-pressure conditions required for SCO.
The pressure dependence of the optical gap, E GAP , allows us to infer that the p-d charge-transfer gap closure (metallization) takes place at 80 GPa. This result is confirmed by electrical resistance measurements under pressure (inset of Fig. 3 and Supplementary Fig. S12). Its pressure dependence R(P) unveils two distinct regions corresponding to HS and LS states. The associated SCO pressure, P SCO = 70 GPa, is close to that derived from optical absorption. Interestingly, the progressive decrease of R(P) in LS shows a change of slope for P > 80 GPa indicating the metallization onset. Spin density-and DOS simulations indicate that the charges are mainly localized at the Co 2+ site and small p-d hybridized ones can be observed at Cl − sites for HS. For P > 67 GPa (LS) a progressive decrease of the localized charges at Co 2+ occurs due to hybridization increase. However, the hybridized spin density spreads out over the entire crystal for P > 80 GPa (E GAP = 0) in the Cl − plane, while it is strongly localized at Co 2+ , indicating that metallization mainly involves Cl − sublattices rather than the Co 2+ ones. Furthermore, a full electron delocalization is completed for P > 180 GPa (Fig. 4). This result is noteworthy since it correlates two

Conclusions
In summary, with various types of experimental and theoretical approaches, we have thoroughly analysed the physics of the pressure-induced spin-state transition and metallization phenomena in CoCl 2 . We have shown that the layered structure of CoCl 2 , and hence the Co 2+ sixfold coordination, is stable in the 0-200 GPa range, in contrast to CoF 2 , whose high-pressure phases involve increasing coordination numbers (6 → 8 → 9). We demonstrate that pressure-induced metallization is associated with p-d charge-transfer band gap, closing at about 80 GPa. Although the HS-to-LS transition (67 GPa) can trigger insulator-to-metal transition, DFT calculations also show that after the SCO metallization Co 2+ preserves the local character of the 3d-electrons and that Mott-Hubbard-electron breakdown takes place for P > 180 GPa in LS. In consequence, this work demonstrates that metallization with involvement of Cl − planes and localized Co 2+ -3d LS magnetism can coexist prior to Mott-Hubbard breakdown in CoCl 2 . These results unveil the complex metallization mechanism of CoCl 2 under compression with Cl − and Co 2+ layers exhibiting site-dependent electrical and magnetic behaviours. Especially, the intermediate phase with metallic magnetism is rarely observed in a system with local moment such as transition metal complexes. We believe these findings provide new insight into unforeseen electronic properties of multilayer 2D systems and highlight the importance of high-pressure studies as a route to novel electronic and magnetic phases.

Methods
Crystal structure: X-ray diffraction. Both single-crystal plates (100 × 80 × 30 μm 3 ) and powder of CoCl 2 (Merck) were used for high-pressure experiments. CoCl 2 crystallizes in the trigonal space group R3m at ambient conditions 45 . The evolution of the crystal structure with pressure was studied by x-ray diffraction (XRD) using the I15 beam station at the DIAMOND synchrotron under proposals 832, 1655 and 6078. The pressure was applied by means of Almax-Boehler and MALTA-type Diamond Anvil Cell (DAC). DACs were loaded with several Ruby 170-μ m-diameter holes were perforated with a BETSA motorized electrical discharge machine. The DAC was loaded with a CoCl 2 single crystal and ruby microspheres (10 μm diameter) as pressure probes 46 using silicone oil as pressure-transmitting medium in an argon atmosphere inside a globe box to avoid sample hydration. Optical absorption under high-pressure conditions was performed on a prototype fiber-optics microscope equipped with two 20× reflecting objectives mounted on two independent x -y -z translational stages for the microfocus beam, and the collector objective and a third independent x -y -z translational stage for the DAC holder (Fig. 5). Optical absorption data and images were obtained simultaneously with the same device. Spectra in the UV-VIS and NIR were recorded with Ocean Optics USB 2000 and NIRQUEST 512 monochromators using Si-and InGaAs-CCD detectors, respectively.
Unpolarized micro-Raman scattering measurements were performed with a triple monochromator Horiba-Jobin-Yvon T64000 spectrometer in subtractive mode backscattering configuration, equipped with a Horiba Symphony liquid-nitrogen-cooled CCD detector. The 514.5-nm and 647-nm lines of a Coherent Innova 70 Ar + -Kr + laser were focused on the sample with a 20× objective for micro-Raman, and the laser power was kept below 4 mW in order to avoid heating effects. The laser spot was 20 μm in diameter and the spectral resolution was better than 1 cm −1 . The Raman technique was used to check the sample structure through the characteristic first-order modes (A 1g and E g in the trigonal R3m CdCl 2 -type phase) 38 as well as to determine structural phase-transition pressures (see Supplementary Figs S10 and S11 and Table S3). The Raman high-pressure experiments were performed on the same CoCl 2 single crystals employed in the optical absorption measurements. electrical measurements at high pressure. The electrical resistance measurement under pressure up to 96 GPa was performed using diamond anvil cell with solid transmitting medium NaCl (diamond's culet diameter  (a-d). The corresponding spin density around the Fermi level on the (111) plane is shown in panels below with red and blue denoting up and down spin density. A schematic Co 2+ 3d bands associated with t 2g (e e′ , a 1g ) + e g in blue and red colors, respectively, illustrates the HS and LS states (e,f). It must be noted that spin density in LS is significantly localized around Co 2+ whereas it is more delocalized around Cl − in spite the electronic Fermi levels have about the same contributions from Cl − -p and Co 2+ -d orbitals (detailed information in Supplementary Figs S7-S10). Note that above 150 GPa, calculated pressures by DFT + U are overestimated as the Coulomb correlation energy was fixed to U = 3 eV. Indeed pressure should be corrected by about 20% in that range if U decreases by 20% due to ultrahigh pressure effects. The lattice structure of CoCl 2 is depicted in (g). Note that the green plane is (111) plane for spin density plot.
www.nature.com/scientificreports www.nature.com/scientificreports/ of 100 μm). Gasket consists of T301 and the insulate layer is cBN. Pressure was determined by ruby fluorescence method at low pressure and the shift of diamond's Raman peaks. Figure 6 shows a schematic view of the DAC.
Density functional theory: spin crossover and metallization. After clarifying structural phase transitions, we identified that the electronic and magnetic transitions occur in P3 m1 phase. Thus, employing the same symmetry, we investigated the SCO behaviors in detail. We further performed electronic-structure calculations within DFT + U www.nature.com/scientificreports www.nature.com/scientificreports/ scheme as implemented in Vienna Ab Initio Simulation Package (VASP) 47 . As for layered system, where the van der Waals interactions are important, frequently used generalized gradient approximation (GGA) functionals sometimes fails to predict the correct structural behaviors. We found van der Waals-corrected functions gives better description of the ground state volume such that the errors were 1.6% for many-body dispersion and 2.2% for Tkatchenko-Scheffler methods while D3 approach severely underestimates the volume by 8.2% 31,34,35 ). From GGA 48 , we found that PBEsol overperforms PBE (3.8% vs. 8.1%) with accuracy similar to van der Waals approach, which enables us to choose PBEsol scheme with safety. Note that in our previous reports, PBEsol successfully explained the spin-state transition behaviors for CoCl 2 31 . We also carefully tested various U parameters and found that U eff = 3.0 eV fits best in describing the experimental transition behaviors. To obtain the pressure evolution of the electronic structure and magnetic properties, we fully relaxed the atomic positions until the atomic forces are less than 0.001 eV/Å for each volume point. Once the transition volume is found, we have cross-checked the results employing full potential full relativistic code FPLO 49 , and further analyzed its partial density of states (see Supplementary Figs S6-S9).

Data Availability
All data generated or analysed during this study are included in this published article (and its Supplementary Information files).