Abstract
Transition metal phosphorous trichalcogenides, MPX3 (M and X being transition metal and chalcogen elements, respectively), have been the focus of substantial interest recently because they are unusual candidates undergoing Mott transition in the two-dimensional limit. Here we investigate material properties of the compounds with M=Mn and Ni employing ab initio density functional and dynamical mean-field calculations, especially their electronic behavior under external pressure in the paramagnetic phase. Mott metal-insulator transitions (MIT) are found to be a common feature for both compounds, but their lattice structures show drastically different behaviors depending on the relevant orbital degrees of freedom, i.e., t2g or eg. Under pressure, MnPS3 can undergo an isosymmetric structural transition within monoclinic space group by forming Mn-Mn dimers due to the strong direct overlap between the neighboring t2g orbitals, accompanied by a significant volume collapse and a spin-state transition. In contrast, NiPS3 and NiPSe3, with their active eg orbital degrees of freedom, do not show a structural change at the MIT pressure or deep in the metallic phase within the monoclinic symmetry. Hence NiPS3 and NiPSe3 become rare examples of materials hosting electronic bandwidth-controlled Mott MITs, thus showing promise for ultrafast resistivity switching behavior.
| Original language | English (US) |
|---|---|
| Article number | 236401 |
| Journal | Physical review letters |
| Volume | 123 |
| Issue number | 23 |
| DOIs | |
| State | Published - Dec 3 2019 |
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- Physics and Astronomy(all)
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Mott Metal-Insulator Transitions in Pressurized Layered Trichalcogenides. / Kim, Heung Sik; Haule, Kristjan; Vanderbilt, David.
In: Physical review letters, Vol. 123, No. 23, 236401, 03.12.2019.Research output: Contribution to journal › Article › peer-review
TY - JOUR
T1 - Mott Metal-Insulator Transitions in Pressurized Layered Trichalcogenides
AU - Kim, Heung Sik
AU - Haule, Kristjan
AU - Vanderbilt, David
N1 - Funding Information: https://orcid.org/0000-0003-0691-7605 Kim Heung-Sik 1,2 Haule Kristjan 1 Vanderbilt David 1 Department of Physics and Astronomy, 1 Rutgers University , Piscataway, New Jersey 08854-8019, USA Department of Physics, 2 Kangwon National University , Chuncheon 24341, Korea 3 December 2019 6 December 2019 123 23 236401 17 September 2019 27 August 2018 © 2019 American Physical Society 2019 American Physical Society Transition metal phosphorous trichalcogenides, M P X 3 ( M and X being transition metal and chalcogen elements, respectively), have been the focus of substantial interest recently because they are unusual candidates undergoing Mott transition in the two-dimensional limit. Here we investigate material properties of the compounds with M = Mn and Ni employing ab initio density functional and dynamical mean-field calculations, especially their electronic behavior under external pressure in the paramagnetic phase. Mott metal-insulator transitions (MIT) are found to be a common feature for both compounds, but their lattice structures show drastically different behaviors depending on the relevant orbital degrees of freedom, i.e., t 2 g or e g . Under pressure, MnPS 3 can undergo an isosymmetric structural transition within monoclinic space group by forming Mn-Mn dimers due to the strong direct overlap between the neighboring t 2 g orbitals, accompanied by a significant volume collapse and a spin-state transition. In contrast, NiPS 3 and NiPSe 3 , with their active e g orbital degrees of freedom, do not show a structural change at the MIT pressure or deep in the metallic phase within the monoclinic symmetry. Hence NiPS 3 and NiPSe 3 become rare examples of materials hosting electronic bandwidth-controlled Mott MITs, thus showing promise for ultrafast resistivity switching behavior. National Science Foundation 10.13039/100000001 DMR-1629059 Kangwon National University 10.13039/501100002507 National Supercomputing Center of Korea KSC-2019-CRE-0036 Since the first identification of the Mott metal-insulator transition (MIT) by Mott and Peierls in 1937 [1] and the suggestion of the canonical Hubbard model in 1963 [2] , many systems showing the Mott MIT have been found. They can be broadly classified into two categories, (i) the filling-controlled MITs, such as in the doped cuprates [3] , or (ii) the bandwidth-controlled MITs, such as in the rare-earth nickelates R NiO 3 ( R being a rare-earth element) [4,5] or vanadium oxides V 2 O 3 [6–8] and VO 2 [6,9] . Considering applications to electronic resistive switching devices, the filling-controlled MIT of type (i) is not favorable due to the inevitable strong inhomogeneity at the atomic scale introduced by the chemical doping. The bandwidth-controlled MITs of type (ii), on the other hand, are typically coupled strongly to the structural degrees of freedom, as for examples in the bond disproportionation between the short and long Ni-O bonds in R NiO 3 [10–13] and the dimerization of vanadium atoms in VO 2 [14,15] . Such involvement of slow lattice dynamics in the MIT is also not favorable for fast switching. Hence, systems with electronic bandwidth-controlled MITs (i.e., weak or no lattice distortions involved) are desirable for fast resistive switching [16,17] . Surprisingly, there are very few solids that are known to undergo purely electronic and bandwidth-controlled MITs, as was originally envisioned by Hubbard. From the theoretical side, there is growing evidence that starting from the metallic side, the MIT would not have occurred in any of above three systems ( R NiO 3 , V 2 O 3 , and VO 2 ) in the absence of a simultaneous structural distortion. Even less common are such transitions in two-dimensional materials, which might be useful for ultrathin electronic and spintronic applications, and to our knowledge there is no known example of an electronically driven MIT among the van der Waals (vdW) materials except the recently discovered Mott phase and superconductivity in twisted bilayer graphene [18,19] . Here we propose new candidates for the electronic bandwidth-controlled MIT without significant structural distortion among the emerging class of two-dimensional vdW materials. Our target is a series of transition metal phosphorous trichalcogenides M P X 3 ( M = Mn , Ni, X = S , Se) [20–22] . To incorporate the electronic and structural degrees of freedom on an equal footing, we employ the state-of-the-art embedded dynamical mean-field theory combined with density functional theory (EDMFT), which implements forces on atoms and allows relaxation of internal atomic coordinates [23] . For the optimization of the size and shape of unit cells we use density functional theory (DFT) augmented by the on site Coulomb repulsion U ( DFT + U ), after which optimizations of internal atomic coordinates are performed both in EDMFT and DFT + U yielding consistent results [24] . We mainly focus on paramagnetic phases of MnPS 3 and NiP { S , Se } 3 above their Néel temperatures ( T N = 78 and 154 K for MnPS 3 and NiPS 3 , respectively [31–33] ), with disordered local Mn 2 + ( d 5 ) S = 5 / 2 and Ni 2 + ( d 8 ) S = 1 moments, although the behavior of their MITs in the magnetic phases is discussed in the Supplemental Material [28] . We will show that the recently discovered MIT in MnPS 3 falls under the family of transitions coupled to structural changes, in which the dimerization plays a crucial role, therefore bearing a resemblance to the MIT in VO 2 [20] . On the other hand, theoretical simulations in NiPS 3 and NiPSe 3 suggest that the MIT in these two vdW compounds occurs at even lower pressure, and does not involve a simultaneous structural transition. Therefore they become rare examples of electronic bandwidth-controlled transitions with a potential for very fast resistive switching. Crystal structures versus pressure.— Figures 1(a) and 1(b) show DFT + U results on the pressure-induced change of the three lattice parameters ( a / a 0 , b / b 0 , and c / c 0 , where { a , b , c } 0 denote their zero-pressure values) for NiPS 3 and MnPS 3 , respectively. Note that here we focus on the monoclinic C 2 / m structure as shown in Fig. 1(c) . Because both of the compounds are vdW-type layered systems, the interplane lattice parameter c shows a steeper decrease compared to the in plane a and b , and the threefold symmetry within each layer forces b ≃ 3 a in the low- P regime. The resulting volume decrease under pressure is substantial: 40% of volume reduction at ∼ 50 GPa compared to the ambient pressure volume, as shown in the inset of Fig. 1(b) . 1 10.1103/PhysRevLett.123.236401.f1 FIG. 1. (a), (b) Evolution of DFT + U -optimized lattice parameters [ a , b , and c as depicted in (c), (d)] as a function of pressure, where (a) and (b) panels show results from NiPS 3 and MnPS 3 , respectively. Inset in (b) shows a volume versus pressure plot for MnPS 3 , where black and gray curves represent ground-state and metastable structures, respectively. Thick vertical dashed lines in both plots indicate the values of critical pressure where the MIT happens. The thin dotted line in (a) shows the pressure where the a / a 0 and b / b 0 begin to branch in NiPS 3 (i.e., b ≠ 3 a ) due to the enhanced monoclinicity by pressure. Note that, the critical pressure for MnPS 3 reported in Ref. [20] is around 30 GPa, as depicted in the figure. (c) Crystal structures for NiPS 3 and MnPS 3 at the ambient pressure. (d) MnPS 3 structure when P > 64 GPa , where the Mn dimer is formed parallel to b . Both compounds show MIT and structural phase transitions under pressure, but the nature of their transition is drastically different. As shown in Fig. 1(a) , the MIT and the structural transition in NiPS 3 occur at very different pressures, around 31 and 57 GPa, respectively, while they coincide in MnPS 3 . Remarkably, theoretical simulations suggest that the MIT in NiPS 3 accompanies no significant structural distortion (discontinuous structural changes, for example), and is thus a rare example of an electronically driven bandwidth-controlled MIT. On the other hand, in MnPS 3 the isosymmetric structural transition (i.e., structural transition within the same space group symmetry) with a volume collapse at 63 GPa is crucial for the occurrence of the MIT; hence the transition is better classified as the structurally assisted MIT [see Fig. 1(b) ]. We note that the theoretical critical pressure of 63 GPa is somewhat overestimated compared to the experimentally reported value of ∼ 30 GPa [20] . However, we show in the Supplemental Material [28] that within EDMFT, spinodal lines extend down to a much lower pressure of 40 GPa with a much reduced energy barrier between the metallic and insulating solutions compared to the DFT + U results. Inclusion of the phonon free energy and the lattice zero-point energy, which is neglected here, could then move the position of the transition significantly (see the Supplemental Material for further details). In addition to the volume collapse, mostly from the discontinuous change of a , DFT + U simulations of MnPS 3 show a Mn-Mn dimerization along the b direction with the tilting of the P 2 dimer as shown in Fig. 1(d) . The Mn-Mn bond lengths between the dimer and nondimer bonds are 2.42 and 3.10 Å at 63 GPa, respectively, which is a rather large difference. This Mn dimer formation is attributed to the direct d - d overlap between the Mn t 2 g orbitals, pointing directly towards the nearest-neighbor Mn as shown in the inset of Fig. 1(d) . Note that the previous experimental study suggested the formation of Mn zigzag chains in the high- P phase [20] , in contrast to our DFT + U and EDMFT results. NiPS 3 , on the other hand, shows no such intermetallic dimerization or chain formation at the MIT or beyond the structural transition pressure, because the partially filled Ni e g orbitals point towards the S atoms. This makes NiPS 3 more sensitive to the p - d hybridization, yielding a smaller MIT pressure in NiPS 3 compared to MnPS 3 . Such a stark contrast between NiPS 3 and MnPS 3 , originating from the difference in their orbital physics, affects the nature of the structural behavior of their MIT as shown below. Note that the structural transition in NiPS 3 at 57 GPa is not orbital in nature and comes purely from the reduced interlayer distance and the large overlap between the layers. We note that the two compounds show markedly different pressure dependence of the lattice parameters even before the structural transition. By comparing Figs. 1(a) and 1(b) it is evident that the compression of c under pressure is stronger in NiPS 3 than in MnPS 3 ; while a / a 0 - c / c 0 in MnPS 3 at 60 GPa is about 0.03 [see Fig. 1(b) ], in NiPS 3 it is about 0.15 [Fig. 1(a) ] despite the similar volume change. In other words, it is much easier to compress NiPS 3 along the layer-normal direction compared to MnPS 3 . Because the kinetic energy scale set by the hopping integrals between the t 2 g (for MnPS 3 ) and e g (for NiPS 3 ) orbitals show different anisotropy, the t 2 g and e g yield strong in plane d - d and interplane d - p - p - d overlaps, respectively (see the Supplemental Material [28] ). As a result, while the t 2 g orbitals favor in plane compression for the larger in plane kinetic energy gain, the e g orbitals prefer to reduce the interplane distance, yielding the tendency shown in Figs. 1(a) and 1(b) . Electronic MIT in NiPS 3 .—Below we take a closer look into the nature of the MIT in NiPS 3 . Note that all the spectra presented hereafter are EDMFT results, where the ( DFT + U )-optimized cell parameters and estimated pressure values are employed. Figure 2(a) shows projected densities of states (PDOS) of NiPS 3 with varying pressure from 0 to 88 GPa. It is clear that the t 2 g states ( a g and e g ′ ) are mostly occupied, while the e g states are partially filled and show a narrow dip at the Fermi level at 30.4 GPa. The self-energies of the e g orbitals show poles at the Fermi level (see the Supplemental Material [28] ), confirming the presence of the paramagnetic Mott phase. Previously, it was suggested that NiPS 3 is a negative charge-transfer (NCT) insulator with a d 9 L _ 1 configuration ( L _ denoting a S p -ligand hole) [21] . However, our EDMFT results show that when the Ni occupation is close to n d ≈ 9 , where the d 9 L _ 1 configuration is dominant, the Mott insulating state cannot be stabilized; i.e., the material is metallic. The experimentally observed Mott insulating behavior can only be achieved with the Ni occupancy of n d ≈ 8 , where the high-spin S = 1 configuration is dominant, i.e., corresponding to approximately half-filled e g states [see Fig. 2(b) for the probability distribution in the insulating and metallic states]. This observation is corroborated by x-ray absorption spectroscopy, indicating that NiPS 3 is close to the NCT regime, but is still dominated by the d 8 S = 1 configuration, consistent with our EDMFT results [34] . 2 10.1103/PhysRevLett.123.236401.f2 FIG. 2. (a) Projected density of states (PDOS) in the paramagnetic phase of NiPS 3 at T = 232 K , calculated by EDMFT with the increasing pressure from the ambient condition (top panel) to 88 GPa (lowest). (b) Monte Carlo probabilities for the d 8 | S z | = 0 (purple dashed line), d 7 , 9 | S z | = 1 / 2 (red dash dotted), and d 8 | S z | = 1 (black solid) as a function of pressure. (c) Pressure dependence of the size of PM Ni spin moment | 2 S z | from PM EDMFT results at T = 232 K . Note a cusp at P = 30.4 GPa where the MIT happens. Figure 2(b) shows the valence histogram for the few most important Ni d configurations versus pressure at T = 232 K . The Mott insulating state is stable as long as the high-spin state ( | S z | = 1 ) of the Ni- d 8 configuration is dominant. Note that we report S z values rather than S values, because of our choice of an Ising-type approximation of the Coulomb interaction in the EDMFT impurity solver [35] . Around 31 GPa the | S z | = 1 / 2 states (of d 9 and d 7 configurations) become equally probable, at which point the Mott state collapses and a narrow metallic quasiparticle peak appears [see the third panel in Fig. 2(a) ]. Despite the enhanced charge fluctuation, the change of Ni d -orbital occupation ( n d ) across the transition is negligible: n d = 8.15 and 8.19 at P = 0 and 88 GPa, respectively. The increase of charge fluctuations with increasing pressure has an additional effect of unlocking the | S z | = 0 sector of the d 8 configuration, which is favored in the itinerant low spin regime at large pressure. Note that the increase of the probability for | S z | = 0 at the expense of the | S z | = 1 state has a large effect on the size of the fluctuating moment | 2 S z | , which is plotted in Fig. 2(c) . Its zero-pressure value is around 1.6 μ B , which is quite reduced from the maximum atomic value of 2 μ B , and once it is reduced below 1.4 μ B it drops very suddenly and takes values of ≤ 1.3 μ B in the metallic state. We note that the change between 30.4 and 31.8 GPa is abrupt, which is likely associated with a first-order transition, for which a coexistence of both solutions is expected. However the hysteresis was not observed, probably because it is too narrow at the temperature studied ( T = 232 K ). We mention that the MIT was carefully checked by employing beyond-Ising Coulomb interaction terms (spin-flip and pair-hopping types) at a lower temperature of T = 116 K , but neither a hysteretic behavior nor a discontinuity in the energy-volume curve were found, signifying very weak coupling between the lattice and charge degrees of freedom in NiPS 3 (see Sec. III. A in the Supplemental Material [28] and Fig. S3 therein for more details). MIT driven by uniaxial pressure in NiPSe 3 .—While the critical pressure for the MIT in NiPS 3 can be reached in modern high-pressure experimental setups, a substitution of S by the more polarizable Se is expected to further reduce the critical pressure. Therefore the recently synthesized NiPSe 3 [36] can be a better candidate for realizing the pressure-driven MIT compared to NiPS 3 . Moreover, the collapse of the interlayer distance is expected to be sufficient to induce the MIT, which can even be achieved by the tip of an atomic-force microscope [37] . As a zeroth-order approximation, we simulate such layer-normal strain by varying the interlayer distance with fixed in plane lattice parameters, and allowing the internal coordinates to relax within EDMFT. In Fig. 3 we show the e g PDOS of NiPSe 3 where the MIT happens at the modest stress of 13 ≤ σ z ≤ 15 GPa at T = 58 K , suggesting NiPSe 3 as another promising electronic bandwidth-controlled Mott transition system among these layered vdW materials. 3 10.1103/PhysRevLett.123.236401.f3 FIG. 3. NiPSe 3 e g PDOS in the presence of an uniaxial stress σ z along the layer-normal z ^ direction from PM EDMFT results at T = 58 K (with varying σ z from 0 to 16.6 GPa). Blue and red curves are PDOS for insulating and metallic phases, respectively, when the MIT happens between σ z = 15.4 and 16.6 GPa. Volume collapse and MIT in MnPS 3 .—We now address the volume-collapse transition in MnPS 3 . We first checked that once the optimized lattice parameters from DFT + U are employed, both DFT + U and EDMFT optimizations for the internal coordinates yield practically the same result. Figure 4(a) shows the evolution of the fluctuating Mn moment | 2 S z | within the PM EDMFT at T = 580 K . We also show the ordered magnetic moment M (per Mn) within DFT + U in the Néel-type antiferromagnetic ordered state [20,31,38] (grey line in the plot). Perhaps not surprisingly, the two methods show very similar behavior: an insulating state of almost maximum spin S = 5 / 2 configuration in the low-to-intermediate- P regime, and a metallic state with strongly reduced Mn moments above P = 64 GPa . The inset of Fig. 4(a) schematically depicts the spin-orbital configuration below and above the transition. In the presence of strong external pressure, the orbitally inert high-spin S = 5 / 2 configuration becomes energetically unstable, and the low-spin S = 1 / 2 with the partially filled t 2 g orbital is stabilized with an octahedral volume collapse [39] . As a result, the t 2 g open shell in this edge-sharing geometry leads to a strong σ -like direct d - d overlap between the nearest-neighboring (NN) Mn sites, resulting in a strong tendency toward Mn dimerization [40] . At ambient pressure, because of the weak interlayer coupling, the three in plane NN bonds are essentially equivalent to each other. In the high-pressure regime, however, the monoclinicity originating from the layer stacking is no longer negligible. Therefore, the NN bond parallel to the b direction, which becomes nonequivalent to the other bonds, dimerizes as shown in Fig. 1(d) (see Sec. III. B in the Supplemental Material [28] for more details on inclusion of the beyond-Ising Coulomb terms). 4 10.1103/PhysRevLett.123.236401.f4 FIG. 4. (a) Pressure dependence of the size of Mn spin moment M from DFT + U (gray line) and | 2 S z | from paramagnetic EDMFT at T = 580 K (black), where both results show the spin-state transition at 63 GPa. The schematic spin-orbital configurations below and above the transition are shown in the inset. (b) PDOS from EDMFT, at P = 0 GPa (upper panel), 62 GPa (center), and 70 GPa (lower). Note that the choice of d orbital onto which the DOS are projected is different below and above the transition ( e g ′ and a 1 g below, and d x z , y z , x y above 63 GPa). Summary.— We report a theoretical study of the Mott MIT induced by external pressure in strongly correlated layered vdW materials. We comment that the Mott phases in other metal trisulfides, such as FePS 3 [41] or CoPS 3 [42] , are also of great interest because of their partially filled t 2 g shells even under ambient conditions. Overall, this family of vdW-layered transition metal trichalcogenides can be an excellent platform for the study of strong electron correlations and their cooperation with spin and lattice degrees of freedom. We thank Matthew J. Coak, Michael O. Yokosuk, Nathan C. Harms, Kevin A. Smith, Sabine N. Neal, Janice L. Musfeldt, and Sang-Wook Cheong for helpful discussions. The work was supported by NSF DMREF Grant No. DMR-1629059. H. S. K. thanks the support of the research grant for new faculty members from Kangwon National University, and also the support of supercomputing resources including technical assistances from the National Supercomputing Center of Korea (Grant No. KSC-2019-CRE-0036) [1] 1 N. F. Mott and R. Peierls , Proc. Phys. 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The work was supported by NSF DMREF Grant No.DMR-1629059. H.S.K. thanks the support of the research grant for new faculty members from Kangwon National University, and also the support of supercomputing resources including technical assistances from the National Supercomputing Center of Korea (Grant No.KSC-2019-CRE-0036) Publisher Copyright: © 2019 American Physical Society.
PY - 2019/12/3
Y1 - 2019/12/3
N2 - Transition metal phosphorous trichalcogenides, MPX3 (M and X being transition metal and chalcogen elements, respectively), have been the focus of substantial interest recently because they are unusual candidates undergoing Mott transition in the two-dimensional limit. Here we investigate material properties of the compounds with M=Mn and Ni employing ab initio density functional and dynamical mean-field calculations, especially their electronic behavior under external pressure in the paramagnetic phase. Mott metal-insulator transitions (MIT) are found to be a common feature for both compounds, but their lattice structures show drastically different behaviors depending on the relevant orbital degrees of freedom, i.e., t2g or eg. Under pressure, MnPS3 can undergo an isosymmetric structural transition within monoclinic space group by forming Mn-Mn dimers due to the strong direct overlap between the neighboring t2g orbitals, accompanied by a significant volume collapse and a spin-state transition. In contrast, NiPS3 and NiPSe3, with their active eg orbital degrees of freedom, do not show a structural change at the MIT pressure or deep in the metallic phase within the monoclinic symmetry. Hence NiPS3 and NiPSe3 become rare examples of materials hosting electronic bandwidth-controlled Mott MITs, thus showing promise for ultrafast resistivity switching behavior.
AB - Transition metal phosphorous trichalcogenides, MPX3 (M and X being transition metal and chalcogen elements, respectively), have been the focus of substantial interest recently because they are unusual candidates undergoing Mott transition in the two-dimensional limit. Here we investigate material properties of the compounds with M=Mn and Ni employing ab initio density functional and dynamical mean-field calculations, especially their electronic behavior under external pressure in the paramagnetic phase. Mott metal-insulator transitions (MIT) are found to be a common feature for both compounds, but their lattice structures show drastically different behaviors depending on the relevant orbital degrees of freedom, i.e., t2g or eg. Under pressure, MnPS3 can undergo an isosymmetric structural transition within monoclinic space group by forming Mn-Mn dimers due to the strong direct overlap between the neighboring t2g orbitals, accompanied by a significant volume collapse and a spin-state transition. In contrast, NiPS3 and NiPSe3, with their active eg orbital degrees of freedom, do not show a structural change at the MIT pressure or deep in the metallic phase within the monoclinic symmetry. Hence NiPS3 and NiPSe3 become rare examples of materials hosting electronic bandwidth-controlled Mott MITs, thus showing promise for ultrafast resistivity switching behavior.
UR - http://www.scopus.com/inward/record.url?scp=85076619604&partnerID=8YFLogxK
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U2 - 10.1103/PhysRevLett.123.236401
DO - 10.1103/PhysRevLett.123.236401
M3 - Article
C2 - 31868467
AN - SCOPUS:85076619604
SN - 0031-9007
VL - 123
JO - Physical Review Letters
JF - Physical Review Letters
IS - 23
M1 - 236401
ER -