High-pressure Raman spectroscopy and lattice-dynamics calculations on scintillating MgWO4: A comparison with isomorphic compounds

Raman scattering measurements and lattice-dynamics calculations have been performed on magnesium tungstate under high pressure up to 41 GPa. Experiments have been carried out under a selection of different pressure-media. The influence of non-hydrostaticity on the structural properties of MgWO4 and isomorphic compounds is examined. Under quasi-hydrostatic conditions a phase transition has been found at 26 GPa in MgWO4. The high-pressure phase has been tentatively assigned to a triclinic structure similar to that of CuWO4. We also report and discuss the Raman symmetries, frequencies, and pressure coefficients in the low- and high-pressure phases. In addition, the Raman frequencies for different wolframites are compared and the variation of the mode frequency with the reduced mass across the family is investigated. Finally, the accuracy of theoretical calculations is systematically discussed for MgWO4, MnWO4, FeWO4, CoWO4, NiWO4, ZnWO4, and CdWO4.

wolframites undergo, in addition to the expected phase transition around 31 GPa, another one around 17 GPa [6]. From combined Raman spectroscopic and ab initio calculations [8,9] it has been established that the monoclinic -fergusonite structure (space group C2/c, SG: 13) could be the most probable HP phase for these compounds.
In addition, a triclinic structure (space group 1 P , SG: 2) similar to that of CuWO 4 is energetically competitive with the wolframite and -fergusonite phases. This fact has been used to explain the additional phase transition observed by means of powder XRD in MgWO 4 and ZnWO 4 .
In order to further understand and explain the structural behavior of wolframites under compression we have performed a combined Raman spectroscopy and theoretical study of MgWO 4 up to 41 GPa. Experiments were carried out using various pressuretransmitting media (PTM) including neon, methanol-ethanol, spectroscopic paraffin, and no PTM at all. This study will provide us not only with a better knowledge of its vibrational properties but also the possibility to correlate the general trends of wolframites at high pressure.

II. EXPERIMENTAL DETAILS
Five series of Raman measurements were performed on 10 m-thick platelets cleaved from MgWO 4 single crystals (or with micron-sized powders grounded from the crystals) using three different Raman spectrometers in backscattering geometry. Single crystals were prepared using the flux growth technique developed at the Institute for Scintillation Materials (Kharkov, Ukraine) [12]. A stoichiometric mixture of MgO and

III. CALCULATIONS DETAILS
In the last years ab initio methods have allowed detailed studies of the energetics of materials under high pressures [14]. In this work total-energy calculations were done within the framework of the density-functional theory (DFT), the Kohn-Sham equations were solved using the projector-augmented wave (PAW) [15,16] method as implemented in the Vienna ab initio simulation package (VASP) [17]. We used a planewave energy cutoff of 520 eV to ensure accurate and high precision in the calculations.
The exchange and correlation energy was described within the GGA in the PBE [18] prescription for MgWO 4 . The Monkhorst-Pack (MP) [19] grid used for Brillouin-zone integrations ensured highly converged results for the analyzed structures (to about 1 meV per formula unit). It has been pointed out in different studies of transition metal compounds that GGA often yields incorrect results for systems with high correlated electrons. The implementation of the DFT+U method has been found to have some influence on transition metal compounds [20]. The GGA+U method was used to account the strong correlation between the electrons in the d orbitals on the basis of Dudarev's method [20] [22]. Consequently, these two e rized in Fig. 4 and Table I.
By means of the harmonic approximation, if we consider that the atoms are bonded by means of springs then it can be stated that the frequency of the oscillations is directly proportional to the inverse square root of the reduced mass of the cations. In our case for simplicity we will consider that our system consists on two separate blocks one  inverse proportional relation between the frequencies of the external modes and the square root of the reduced mass . In particular, the B g mode located at 405 cm -1 for MgWO 4 is extremely sensitive to the mass of the divalent cation. Indeed, in Fig. 5 and Table II it can be seen that the mode-frequency () sequence in the 350 -400 cm -1 region changes from  Bg > ´B g >  Ag in MgWO 4 to´B g >  Ag >  Bg in CdWO 4 (the quotation mark is used to differentiate between different B g modes). We would like to note here that these three modes have very similar pressure coefficients in the three compounds. It is also interesting that the influence of the atomic mass of the divalent cation on the phonon frequencies of the external modes, which we observed in nonmagnetic wolframites, is similar to that found in alkaline-earth tungstates [25]. In contrast, the external-mode frequencies of MnWO 4 , FeWO 4 , CoWO 4 , and NiWO 4 show the opposite behavior as they increase with the divalent-cation mass. This different behavior could be caused by the influence of magnetic interactions and second-order Jahn-Teller effects which induce strong distortions of the WO 6 and AO 6 octahedra. Actually these effects could even become strong enough to induce triclinic distortion, as is the case for CuWO 4 [10]. It is interesting to note that the Raman spectrum of wolframite-type CuWO 4 , which is obtained at 10 GPa after undergoing a phase transition, resembles that of magnetic wolframites (see Table II) [10]. This fact supports the hypothesis described above. Nevertheless, the discussion of the influence of magnetic and Jahn-Teller effects on the lattice vibrations of wolframites is beyond the sco ith the fact that MgWO 4 is the nd among the wolframite family. respectively. These magnetic structures agree with neutron-diffraction studies and x-ray absorption experiments [26 -28]. The obtained magnetic order and moments are also comparable with results reported for antiferromagnetic MnWO 4 [23]. In Table III (Table II). To conclude this section, it is interesting to note that in contrast with scheelite-structured oxides [25] no phonon softening occurs in C. Hig wolframites upon compression.

h-pressure phase
As was already mentioned in section A, the occurrence of a phase transition is observed by the appearance of an additional Raman mode at a wavelength slightly smaller than the most intense mode of wolframite at different pressures between 17 and 30 GPa depending on the PTM used (Figs. 2, 3). The phase transition is reversible with little hysteresis in all the experiments. In the experiment performed using Ne as PTM ( Fig. 2), the appearance of the new mode at 25.8 GPa is followed by a quick increase of its intensity and the appearance of extra Raman bands. A total of 18 emerging modes are observed at 38 GPa. Simultaneously, a decrease in relative intensity of the other modes is observed, which fully disappear at 38 GPa. In the experiment performed without using any pressure medium ( Fig. 3 (a)), the same process happens at a higher pressure of 29.6 GPa but more gradually. Finally, in the experiment with spectroscopic paraffin (see Fig. 3  that the transition is detected at the lowest pressure when the experiment is performed with paraffin suggests that beyond 10 GPa paraffin becomes stiffer than the wolframites. A similar behavior has already been observed previously for ZnWO 4 [6,8] indicating that non-hydrostatic conditions in wolframites accelerate the transition onset. The effect of non-hydrostaticity on MgWO 4 becomes further visible from the analysis of the pressure dependence of the full-width at half maximum (FWHM) for some Raman modes. In Fig. 8  GPa in the methanol-ethanol experiment. It is known that the methanol-ethanol mixture provides better quasi-hydrostatic conditions compared to paraffin [22,35]. Similar conclusions have been drawn recently from x-ray diffraction studies in the related material BaWO 4 [36]. Therefore, all the above described facts suggest that nonhydrostaticity could play a key role on the acceleration of the phase transition in wolframites. These results explain why in previous x-ray diffraction experiments performed on MgWO 4 in silicone oil [6], the onset of the transition from wolframite to the HP phase occurs around 11 GPa lower compared to the Ne experiments of this study; i.e., the results obtained using silicone oil are similar to those obtained using paraffin because of the lack of good hydrostaticity of both PTM above 10 GPa. It is commonly accepted the use ruby fluorescence to check hydrostaticity in DAC experiments [22]. Therefore, to further check the non-hydrostaticity hypothesis, we have also followed the FWHM of the fluorescent R 1 Table IV. According to Table IV, it seems reasonable to affirm that the high pressure phase of MgWO 4 better resembles the triclinic structure than the monoclinic (C2/c) one. In particular, the calculated low-and high-frequency modes match well with the experimentally measured ones within 5%.
The same accounts for the pressure coefficients. However, the agreement is not so good for the modes of intermediate frequencies.
In Fig. 9, we compare Raman spectra of the HP phases of Mg, Zn, and Cd wolframites with that of the triclinic phase of CuWO 4 at ambient pressure. We have also added ticks corresponding to the calculated modes for       Arrows indicate the appearance of the strongest band of the HP phase and the strongest band of the wolframite phase after the transition onset. All spectra are measured upon pressure increase with the exception of those denoted by (r), which correspond to pressure release.