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Structural, magnetic and electronic properties of CrO2 at multimegabar pressures

As the only half-metallic ferromagnetic material in 3d transition metal dioxides, CrO2 has attracted great scientific interest from materials science to physical chemistry. Here, an investigation into the structural, magnetic and electronic properties of CrO2 under high pressure has been conducted by first-principles calculations based on density functional theory. Static calculations have predicted that CrO2 undergoes structural transitions with the sequence of rutile-type → CaCl2-type → pyrite-type → Pnma → (Fe2P-type→) I4/mmm at high pressures. In addition, a transition from the ferromagnetic state to the non-magnetic state with the magnetic collapse of Cr is observed in CrO2 at the pyrite–Pnma transition. This transition also delocalizes the 3d electrons of Cr and leads to a metallic character of CrO2. The equation of state, elasticity and band gap for each energetically favorable phase of CrO2 are determined. Our results not only bridge the gap about the high-pressure behavior of CrO2 in previous studies but also extend our understanding of its properties up to multimegabar conditions. According to previous data and present results, we further discuss and summarize the high-pressure behavior of various AO2 compounds. This can contribute to investigating properties of other AO2 compounds or exploring novel materials at high pressures.


Introduction
The high-pressure behavior of AO 2 compounds, especially transition metal dioxides such as TiO 2 , VO 2 , CrO 2 and FeO 2 , has attracted considerable interest in the eld of materials science, condensed matter physics and geoscience. [1][2][3][4][5][6][7][8][9][10] For example, as a very important technological wide-gap semiconductor widely applied in photo-catalysts and electrochemical solar cells, 1,3 the band gap of TiO 2 can be modied by pressure, which extends its application in the industry. [11][12][13] The possibility to quench highpressure forms of AO 2 compounds with different properties to ambient conditions is also potentially important to explore novel materials. 14 In addition, pressure-induced structural and electronic transitions of the simple compound VO 2 provide a good example to deeply understand and interpret the complicated Mott-like metal-insulator transition. 15,16 On the other hand, pressure-induced phase transitions of transition metal dioxides can serve as lower-pressure analogs to SiO 2 , a critical component in the Earth's interior, especially when investigating ultrahigh-pressure polymorphs of SiO 2 in super-Earths' or extrasolar planets' interiors. [17][18][19][20] In particular, CrO 2 attracts special interest since it is the only half-metallic (HM) ferromagnetic (FM) material in 3d transition metal dioxides. At ambient conditions, CrO 2 adopts the tetragonal rutile-type structure consisting of distorted edge-sharing CrO 6 octahedra similar to other transition metal dioxides [ Fig. 1(a)]. Due to the crystal eld of distorted CrO 6 octahedra, Cr t 2g states are split into d xy with lower energy and d yz -d xz with higher energy. The double-exchange interaction between the localized 3d electron occupying the d xy state and the delocalized 3d electron occupying half of the d yz -d xz state near the Fermi level accounts for its HM and FM nature. The previous Andreev reection experiment demonstrated that the spin polarization of the conduction electrons was more than 90%. 21 The saturation magnetization at 10 K was experimentally determined to be 1.92 mB per Cr. 22 Compared with other half-metals, the FM CrO 2 possesses a high Curie temperature of 390 K, which is also of technological importance to develop spintronic devices. 23 It is thus evident that these intriguing technological applications are associated with the structural, magnetic and electronic congurations of CrO 2 . The properties are originated from the arrangement and interaction of electrons of CrO 2 within a typical structure.
High pressure, as one important thermodynamic parameter provides a unique way to decipher materials' structural, magnetic and electronic properties. The previous synchrotron X-ray diffraction (XRD) experiment and rst-principle simulations both conrmed a second-order structural transition of CrO 2 from rutile-type to CaCl 2 -type at $12 GPa. [24][25][26] Theoretical computations predicted a further transition to the CaF 2 -type structure at 89.6 GPa. 25 Recently, Wu et al. 27 predicted a pressure-induced phase transition sequence of rutile-type / CaCl 2 -type / pyrite-type / CaF 2 -type for CrO 2 whereas calculated results by the GGA method demonstrated that CrO 2 underwent a transition sequence of rutile-type / CaCl 2 -type / PbO 2 -type / pyrite-type at high pressures. 28 Obviously, there exists considerable discrepancy between different computational studies on CrO 2 . It is worthwhile to note that heretofore the highest coordination number of Cr of various CrO 2 phases considered in previous investigations is eight whereas denser structures with higher coordination number are not included. In terms of magnetic properties of CrO 2 at high pressures, Kuznetsov et al. 29 predicted a magnetic transition from the FM state to the non-magnetic (NM) state accompanied by a halfmetal to metal transition at $53 GPa. Whereas another theoretical study showed that the energetically favorable pyrite-type CrO 2 kept FM and HM up to $100 GPa. 28 In the meanwhile, Kim et al. 26 indicated that the phonon soening led to the FM-NM transition across a structural transition from the CaCl 2 -type to a monoclinic structure at $61 GPa. Beyond $89 GPa, the CaF 2type structure had the lowest enthalpy and correspondingly CrO 2 became a FM insulator. Therefore, the effect of pressure on the magnetic and electronic properties of CrO 2 still remains elusive and the physical properties of CrO 2 with much denser structures are poorly understood.
In this paper, we have performed rst-principle calculations based on density functional theory (DFT) to fully investigate the structural, magnetic and electronic properties of CrO 2 at high pressures aiming to bridge the gap about the high-pressure behavior of CrO 2 between previous studies. Furthermore, we extend the pressure range to investigate stable structures and properties of CrO 2 up to multimegabar conditions. Finally, comparing previous data with present results, we summarize the high-pressure behavior of various AO 2 compounds such as the phase transition sequence, elasticity and electronic properties.

Methods
High pressure can generally reduce bond distances and lead to the structural transition of one compound to form a denser structure. In addition, transition metal dioxides might undergo a similar phase transition sequence upon compression due to similar properties of transition metal elements. Thus, based on this empirical rule of the high-pressure crystal chemistry and extensive experimental and computational data, twelve candidate structures (rutile-type (P4 2 /mnm), CaCl 2 -type (Pnnm), PbO 2type (Pbcn), pyrite-type (Pa 3), CaF 2 -type (Fm 3m), Pnma, Fe 2 P-type (P 62m), CuAl 2 -type (I4/mcm), R 3m, I4/mmm, AlB 2 -type (P6/mmm), and Ni 2 In-type (P6 3 /mmc)) for CrO 2 were considered in the present study. First-principle calculations were performed based on DFT with the projected augmented wave method (PAW) implemented in Vienna ab-initio simulation package (VASP). [30][31][32] The Perdew-Burke-Ernzerhof (PBE) version of the generalized gradient approximations (GGA) was selected to treat the exchange correlation potential. 33 The kinetic energy cut-off was set to 1000 eV. The energy convergence criterion for the electronic self-consistent calculation was 10 À6 eV. The total energy difference was converged to 1 Â 10 À5 eV per formula unit (f.u.) with respect to the energy cutoff or k-points. The force difference was converged to 1 Â 10 À3 eVÅ À1 (less than 0.1 GPa). The spin-polarization of Cr without spin-orbit coupling in CrO 2 with various structures was included in the present study to obtain accurate physical information of CrO 2 . The calculated sub-lattice magnetic moment per Cr in the rutile-type CrO 2 at 0 GPa was 2.04 mB in agreement with previous results and the HM property of the rutile-type CrO 2 could be accurately depicted. 22 The structural, elastic and magnetic properties of the rutile-type CrO 2 at 0 GPa could be reproduced by means of the GGA method. But Korotin et al. 34 suggested that the correlated effect of 3d electrons should be considered in CrO 2 . Whether this system is strongly correlated is still an open question. On the one hand, comparing DFT results with low-temperature experimental data, Toropova et al. 35 concluded that the ordered phase of CrO 2 was weakly correlated. On the other hand, the calculated band gap of the rutile-type CrO 2 at 0 GPa was $1.3 eV by the GGA method, much lower than the normal value $2 eV. 34 Thus, in the present study, we used both the GGA and GGA + U methods to perform electronic density of state (DOS) calculations. 36 We applied U ¼ 3 eV (the on-site Coulomb interaction parameter) and J ¼ 0.9 eV (the Hund coupling constant) for Cr in GGA + U calculations as previous simulations did. 34,37 For each crystalline phase, the atomic positions, unit-cell parameters and individual magnetic moments were allowed to relax at each given volume to obtain the minimum total energy. Energy-volume results were then tted to the third-order Birch-Murnaghan equation of state (EoS) to obtain the corresponding parameters (volume per formula unit (V 0 ), bulk modulus (K 0 ), its pressure derivative ðK 0 0 Þ and energy (E 0 ) at zero pressure). 38,39 In addition, the enthalpy (H ¼ E + PV) of each phase was compared with each other to identify the most stable structure at the given pressure. Furthermore, the DOS of various CrO 2 phases under selected pressure conditions were obtained by the static calculation, utilizing the tetrahedral smearing method with Blöchl corrections. The k-points grids were set as 12 Â 12 Â 20 for rutile-type, 12 Â 12 Â 20 for CaCl 2 -type, 16 Â 16 Â 16 for pyrite-type, 16 Â 24 Â 12 for Pnma, 13 Â 13 Â 29 for Fe 2 P-type and 24 Â 24 Â 12 for I4/mmm CrO 2 in DOS calculations. The phonon dispersion was calculated using the phonopy code by the supercell method. 40 2 Â 3 Â 2, 2 Â 2 Â 3 and 3 Â 3 Â 2 supercells were constructed for the Pnma, Fe 2 P-type and I4/ mmm CrO 2 , respectively. The k-points grids in phonon calculations were set as 3 Â 5 Â 3 for Pnma, 3 Â 3 Â 5 for Fe 2 P-type and 5 Â 5 Â 3 for I4/mmm CrO 2 , respectively.

Structural stability and phase transitions
The corresponding EoS parameters of various candidate phases of CrO 2 are listed in Table 1. The present results of the FM rutile-type CrO 2 are consistent with previous high-pressure XRD data. 24 Calculated static enthalpy differences among various candidate phases of CrO 2 are plotted in Fig. 2 as a function of pressure up to 700 GPa based on aforementioned parameters. The present static calculations predict that CrO 2 will undergo ve structural transitions upon compression with the sequence of rutile-type / CaCl 2 -type / pyrite-type / Pnma / Fe 2 P-type / I4/mmm. Calculated lattice constants and atomic coordinates of six phases at selected pressures are listed in Table 2.
The predicted rutile-CaCl 2 transition at 12 GPa is consistent with the experimental observation at 12 AE 3 GPa by highpressure XRD and Raman spectroscopy. 24 The second Table 1 Calculated parameters of the third-order Birch-Murnaghan equation of state (energy per formula unit E 0 , volume per formula unit V 0 , bulk modulus K 0 and its pressure derivative K 0 0 at zero pressure) of different CrO 2 phases. FM and NM represent ferromagnetic and non-magnetic, respectively. The previous experimental and theoretical data are extracted for comparison  Fig. 2 presents that the enthalpy difference between the PbO 2 -type and pyrite-type CrO 2 is marginal, our results imply a direct transition from CaCl 2 -type to pyrite-type. This can be also supported by the previous high-pressure XRD experiment, which has revealed that the CaCl 2 -type CrO 2 is stable up to about 50 GPa. 24 In addition, previous studies simply considered the CaF 2 -type structure as the high-pressure post-pyrite phase of CrO 2 neglecting other structures. 25 The present simulation demonstrates that neither the FM CaF 2 -type nor the NM CaF 2type is a stable high-pressure phase. Instead, the Pnma structure becomes energetically favorable compared with the pyrite-type structure above 124 GPa. We further predict that at ultra-high pressures the Fe 2 P-type and I4/mmm structures are energetically stable for CrO 2 , both of which have been also identied as the post-Pnma phases for many AX 2 compounds. [17][18][19][41][42][43] It is to be noted that neither the AlB 2 -type nor Ni 2 In-type CrO 2 is an energetically stable phase compared with the ten-fold coordinated I4/mmm structure in the calculated pressure range. The enthalpy difference between AlB 2 -type (or Ni 2 In-type) and I4/ mmm is considerable. That is there is no tendency to transform to a structure where the coordination number of Cr is beyond 10 up to at least 700 GPa.
To investigate the dynamic stability of three new phases predicted here, the Pnma, Fe 2 P-type and I4/mmm structures at ultra-high pressures, we have performed ab initio latticedynamics calculations (Fig. 3). The resultant phonon spectra, lacking any imaginary frequencies imply that the Pnma and I4/ mmm phases are dynamically stable. But for the Fe 2 P-type phase, the phonon soens below zero around the gamma point in the Brillion zone indicating that it is dynamically unstable. Combining H-P relations and phonon spectra, we might modify the high-pressure phase transition sequence of CrO 2 with rutile-type / CaCl 2 -type / pyrite-type / Pnma / I4/mmm. It is worthwhile to mention that although recent rstprinciple calculations have shown that the energetically favorable Fe 2 P-type ZrO 2 is dynamically unstable, 44 the high-pressure and high-temperature XRD experiments have successfully synthesized the Fe 2 P-type ZrO 2 . 43 This may indicates that the Fe 2 P-type phase is dynamically unstable at 0 K, and it can be stable at high temperature and quenched to the ambient temperature. Furthermore, the recent high-pressure experiment has found that VO 2 partially undergoes the Pnma-Fe 2 P transition at $100 GPa at room temperature without laser heating. 45 Thus, the Fe 2 P-type structure can still be a candidate as an intermediate high-pressure phase between the Pnma and I4/ mmm phases. It denitely requires further experimental verication.  24,27 Our results are generally larger than those obtained by experiments and calculated from simulations. It is widely accepted that GGA tends to overestimate the experimental volume whereas LDA underestimates it. In addition to different exchange correlation potentials, the spin-polarization of Cr is introduced in the present study, which can also cause a larger calculated volume of one compound.

Equation of state and elasticity
The volume reduction through the rutile-CaCl 2 transition is marginal, specically less than 0.5%, corresponding to the strain-driven distortive phase transition [ Fig. 1(a) and (b)]. 24 This can also be supported by the calculated average Cr-O bond distance (d av ) shown in Fig. 5, where the evolution of Cr-O bond distances is continuous through the rutile-CaCl 2 transition at 12 GPa. (The average bond distance is dened as d av ¼ P j d j exp½1 À ðd j =d av Þ 6 P j exp½1 À ðd j =d av Þ 6 . 46,47 d av is obtained selfconsistently.). The volume collapse is 5.1% for the CaCl 2 - pyrite transition, and 7.7% for the pyrite-Pnma transition (Fig. 4). It indicates that two transitions are both rst-order. Fig. 5 and Table 2 demonstrate that the large volume collapse at the CaCl 2 -pyrite transition is due to the reconstruction of ions but not to the compression of the nearest-neighbor Cr-O distances [ Fig. 1  at high pressures leads to the abrupt volume change at the pyrite-Pnma transition [ Fig. 1(d Though the volume reduction is typically smaller than the aforementioned ones, it may have important contributions to stabilize the high-pressure polymorphs of CrO 2 . As displayed in Fig. 5, both the dense polyhedral packing and the compression of the nearest-neighbor Cr-O bond distances contribute to the volume variation [ Fig. 1(e) and (f)].

(b) and (c)]. The compression of Cr-O distances
As for the zero-pressure bulk modulus K 0 of different polymorphs of CrO 2 , none of them are less than 200 GPa (Table 1). K 0 of CrO 2 generally increases aer transforming into a new high-pressure phase except K 0 of the CaCl 2 -type CrO 2 . The distortion of the CaCl 2 -type structure upon compression mainly accounts for such a reduction. It is worthwhile to note that K 0 of the ten-fold coordinated I4/mmm CrO 2 exceeds 300 GPa, which might be a potential super-hard material or could be utilized to explore novel super-hard materials.

Magnetic and electronic properties
As reported by previous studies, the rutile-type CrO 2 is FM at ambient conditions. 23 CrO 2 keeps FM through the rutile-CaCl 2pyrite transition upon compression up to about 120 GPa (Fig. 6).
The variation of the magnetic moment per Cr is continuous through the rutile-CaCl 2 transition and there is slight increase of the magnetic moment by 0.08 mB at the CaCl 2 -pyrite transition. As shown in Fig. 6, the pressure slightly affects the magnetic moment of Cr of the FM state. Specically, the slopes of magnetic moment reductions versus pressure are À0.0028 for rutile-type, À0.0008 for CaCl 2 -type and À0.0014 for pyrite-type, respectively. A magnetic collapse where the sub-lattice magnetic moment per Cr drops from $1.95 mB to 0 mB is observed at the transition from pyrite-type to Pnma at 124 GPa indicating an FM-NM transition (Fig. 6). CrO 2 keeps NM up to 700 GPa considered in the present study. Our results do not support the FM-NM-FM transition proposed by Kim et al. 26 Comparing previous investigations with our data, we are able to nd out that magnetism affects not only the structural stability of CrO 2 at high pressures but also other physical properties such as elasticity. [26][27][28] The DOS of various energetically favorable CrO 2 phases at high pressures calculated by the GGA + U method are plotted in Fig. 7. In the rutile-type structure at ambient pressure [ Fig. 7(a) and 8], the total DOS in the spin-up state crosses the Fermi level  exhibiting metallic whereas there is a gap of 2.07 eV in the spindown state indicating the semiconducting property. These conrm the HM character of the rutile-type CrO 2 at ambient pressure. Upon compression, CrO 2 keeps its half-metallicity at the transition to CaCl 2 -type, even further to pyrite-type ( Fig. 7b  and c). There is no discontinuity in the variation of the gap in the spin-down state across the rutile-CaCl 2 transition (Fig. 8). The gap of the CaCl 2 -type CrO 2 drops $0.2 eV at $35 GPa. It may be related to the soening of the B 1g phonon mode as observed in the high-pressure Raman experiment. 24 The gap in the spindown state of the pyrite-type CrO 2 reduces gradually upon compression implying the decrease of its half-metallicity at high pressures. At the transition to the Pnma structure, CrO 2 becomes metallic demonstrating that its half-metallicity is destroyed by pressure [ Fig. 7(d) and 8]. The Fe 2 P-type and I4/ mmm CrO 2 still exhibit metallic at least in the calculated pressure range [ Fig. 7(e) and (f) and 8]. The contribution of 2p electrons of O to the conducting band is more pronounced in the Fe 2 P-type or I4/mmm structure than that in the Pnma structure. Compared with the rst three structures (rutile-type, CaCl 2 -type and pyrite-type), the 3d electrons of Cr and 2p electrons of O both become more delocalized within the last three structures (Pnma, Fe 2 P-type and I4/mmm) resulting in an enhancement of the hybridization between 3d electrons of Cr and 2p electrons of O. As mentioned above, an FM-NM transition with the magnetic collapse of Cr is observed at the pyrite-Pnma transition. In combination with the analysis of DOS of various CrO 2 phases, we may propose that with increasing pressure an FM-NM transition accompanied by a magnetic collapse delocalizes the 3d electrons of Cr leading to the metallic character of CrO 2 .

Comparison with other AO 2 compounds
Extensive experimental and theoretical simulations have been performed on AO 2 compounds to investigate their stable highpressure polymorphs. For the fourth main-group element  dioxides except CO 2 , they can undergo a transition to the Pnma structure at relevant high-pressure conditions. 42,48-51 SiO 2 and GeO 2 are predicted to undergo the Pnma-Fe 2 P transition upon further compression. 17,18,42 The Pnma-Fe 2 P transition of TiO 2 is predicted to occur at 161 GPa by the GGA method and conrmed by in situ XRD at 200 GPa and 3000 K. 41 Experimental and theoretical studies have also veried similar transitions in ZrO 2 . 43 According to these available data and our results, we have plotted the transition pressure to the Pnma or Fe 2 P-type structure (noted by P P or P F ) for AO 2 compounds versus the ionic radius of cations (noted by I r ) (Fig. 9). The ionic radius is the value of the six-fold coordinated cation with the chemical valence of +4. 52 These dioxides can be divided into two groups: main-group element dioxides with unoccupied d orbitals and transition metal dioxides. As shown in Fig. 9, P P or P F for transition metal dioxides is much lower than that for maingroup element dioxides. For main-group element dioxides, P P decreases signicantly with I r compared with P F [ Fig. 9(a)]. For transition metal dioxides, P P or P F can be roughly considered to reduce linearly with I r [ Fig. 9(b)]. Either theoretical or experimental P F of VO 2 is much lower than that of TiO 2 or CrO 2 . At room temperature, VO 2 crystallizes in the monoclinic P2 1 /c structure, a distorted rutile-type form. The distortion signicantly affects the structural characteristics and physical properties of VO 2 upon compression. The quasi-hydrostatic or nonhydrostatic condition in high-pressure diamond anvil cell experiments may contribute to or even promote the transition to the Fe 2 P-type structure. 45 P P and P F of CrO 2 are a little larger. It may be related to the fact that CrO 2 have unpaired 3d electrons. The existence of magnetism in CrO 2 may stabilize the pyrite-type phase, postponing the transition to the Pnma phase. Xie et al. 45 also take the high-pressure structural evolution of RuO 2 as an example to illustrate the phase transition route of CaCl 2 -pyrite-CaF 2 . The difference of oxygen coordination between VO 2 and RuO 2 leads to different evolution patterns. In the present study, the FM CaF 2 -type CrO 2 is much more stable than the NM phase (Fig. 2). But the NM Pnma CrO 2 is energetically favorable compared with aforementioned two phases. The magnetic collapse of Cr can make contributions to favor the pyrite-Pnma transition rather than the pyrite-CaF 2 transition. The available data for the pressure-induced phase transition to the I4/mmm structure are too limited and there is no signicant relation between the transition pressure to the I4/ mmm structure and I r . In terms of FeO 2 in the recent study, we have predicted a transition sequence of pyrite-R 3m-I4/mmm at high pressures, different from present calculated results. 53 And the stable region of the R 3m FeO 2 has a span of $1200 GPa whereas the R 3m CrO 2 is energetically unfavorable in the present calculated pressure range. Therefore, this can serve as an indirect evidence that the chemical valence of iron cation is not +4 in FeO 2 under ultra-high pressure.
The EoS of the Pnma TiO 2 and ZrO 2 have been also obtained by means of high-pressure XRD experiments. 54,55 These results show that K 0 of either TiO 2 or ZrO 2 is larger than 400 GPa. However, recent rst-principle calculations or updated XRD data demonstrate that they are both smaller than 300 GPa, i.e. 250-290 GPa for TiO 2 and $286 GPa for ZrO 2 . 12,41,43 It is thus worthwhile to mention that K 0 of the Pnma phase slightly Fig. 9 Correlation plot between the transition pressure to the Pnma or Fe 2 P-type structure for AO 2 compounds and the ionic radius of cations. The ionic radius of the horizontal ordinate is the value of the six-fold coordinated cation with the chemical valence of +4. 51   increases with I r . As displayed in Fig. 5(b), ECoN of Cr in the Pnma phase is much smaller than nine. It increases rapidly upon compression, indicating the rapid compression of the longest Cr-O bond as a function of pressure. This may result in a smaller K 0 . Whereas those with high ECoN may have a larger K 0 .
As for the electronic property, the HM CrO 2 is predicted to become metallic through the pyrite-Pnma structural transition and keep its metallicity up to 700 GPa. Lyle et al. 19 have predicted the closure of the band gap in TiO 2 and SiO 2 through the Fe 2 P-I4/mmm transition at 650 GPa and 9800 GPa, respectively. While FeO 2 is metallic even in the deep lower mantle conditions. 10,56 These thus lead to the conclusion that many of the I4/ mmm AO 2 compounds can exhibit metallic, to some extent, independent of their chemical valence and ionic radii of cations. That is the structural character of I4/mmm itself strongly affects the electronic property of AO 2 compounds with the I4/mmm structure upon compression. This can provide an alternative method to explore and synthesize metallic AO 2 materials at high pressures.

Conclusions
In conclusion, the high-pressure behavior of CrO 2 has been studied based on rst-principle density functional theory. CrO 2 is predicted to undergo a structural transition sequence of rutile-type / CaCl 2 -type / pyrite-type / Pnma/ (Fe 2 Ptype/) I4/mmm at high pressures. Through the pyrite-Pnma transition, a magnetic collapse in CrO 2 where the magnetic moment drops from $2 mB to 0 mB is observed accompanied by a half-metal to metal crossover. The equation of state for different phases of CrO 2 are determined and the elasticity of CrO 2 at high pressures is also discussed in detail. Finally, we summarize the high-pressure behavior of various AO 2 compounds, such as the phase transition pressure, elastic and electronic properties.

Conflicts of interest
There are no conicts to declare.