1. Introduction

High pressure research is nowadays recognized as one of the worldwide priority research lines in Europe, Japan and USA, with the recent creation of multidisciplinary research teams focused on the application of the high pressure techniques in many branches of physics, chemistry, and biology. This technique provides scientists with a powerful method of tuning in a controllable and reversible manner the volume of a sample and, hence, its properties. In this sense, one of its most fundamental goals is to reproduce processes and phenomena similar to those occurring in the interior of the Earth and other planetary objects, but it has also allowed the growth of novel applications in diverse technological areas, from materials science to food technology [1].

High pressure can be induced on the material with the help of opposed sapphire, moissanite or diamond anvil cells [1], in which a hole in a pre-indented gasket forms the hydrostatic sample chamber. The determination of the pressure and temperature (P-T) inside the chamber requires calibrated standards. Thanks to the transparency of the anvils to visible light, it is quite common to know the working pressure (P) and temperature (T) through an in situ indirect measurement of the P-T sensitive luminescence of an optically active ion. Ideally, an optical pressure sensor should have a single emission line, with no broadening or weakening, a large shift with pressure, a small temperature-dependent line shift and a small linewidth [2,3]. The Cr³⁺ in ruby is the most commonly used luminescence pressure sensor due to the strong ²E→⁴A₂ luminescence, its large line shift with pressure and easy excitation with commercial lasers (Argon or diodes), although its main drawback is the low pressure sensitivity below 1 GPa, in the range of interest for life-related high pressure research [3,4].

Less standardized is the method to measure the exact temperature of the sample in the hydrostatic chamber [1]. The common optical temperature determination is based on the existence of two emitting levels of an optically active ion close enough in energy to be considered in quasi-thermal equilibrium. The fluorescence intensity ratio (R), as defined in [5] of these two closely spaced energy levels can be calibrated as a function of temperature and is proportional to their transition energies, emission cross-sections and population distributions, which follows a Boltzmann-type distribution, i.e. R∝exp(E_G/K_BT), and can be easily measured with the same equipment used for pressure calibration. For temperature up to1000 K in situ luminescent materials can still be used, although since the ruby lines broaden excessively and their intensities diminish above 700 K other promising luminescent hosts such as Sm³⁺:YAG garnet [3] can be used.

Thus new sensors should solve these problems, but preserving the advantages of ruby. In this sense, special attention has been paid to the rare-earth ions since they show sharp absorption and emission lines in the optical range with large P-T sensitivity line shifts and relative intensity changes [3,6]. Taking into account the Nd³⁺ emission in the near-infrared in garnet crystals, the possible application of this active medium as a P-T sensor in high pressure experiments can be inferred [7]. In this work, the co-doped Cr³⁺,Nd³⁺:Gd₃Sc₂Ga₃O₁₂ (GSGG) crystal is proposed as a new P-T sensor. It has been used for a long time as a solid-state laser material [8] and high pressure Nd³⁺ luminescence experiments have been already carried out [9,10], although no attention was paid to the emissions below 11,100 cm⁻¹ and its possibilities as temperature sensor have not been explored. This work focuses on the ⁴F_3/2→⁴I_9/2 emission of the Nd³⁺ ions ranging from 10,500 cm⁻¹ up to 11,500 cm⁻¹ as a function of pressure (0-12 GPa) and temperature (13-300 K), in which the R_1,2→Z_1,5 emissions can meet the requirements of a good optical P-T sensor, and with the ease of laser pump excitation due to the combined absorption bands of the Cr³⁺ and Nd³⁺ ions. Since the emission properties of the Nd³⁺: ⁴F_3/2→⁴I_9/2 transition are not affected by the excitation wavelength, the Cr³⁺→Nd³⁺ energy transfer has not been considered in this paper.

2. Experimental details

The luminescence of the Nd³⁺ ions was measured exciting with the 488 nm line of an Ar⁺ laser and recorded using a 0.75 m monochromator equipped with a NIR extended photomultiplier. Five different high pressure experiments were performed with a diamond anvil cell in a sample chamber of dimensions Ø = 150 μm and h = 70 μm made from a pre-indented Inconel-750 gasket. The sample chamber was filled with a 16:4:1 methanol-ethanol-water mixture as the pressure transmitting medium, which ensures the hydrostatic regime up to 15 GPa [6]. A 20 μm ruby sphere as the pressure gauge and was used.

3. Results and discussion

Garnet crystals belong to the cubic space group Ia-3d and in doped GSGG crystal, Cr3 + ions have preference for the Sc3 + octahedral sites, while the Nd3 + ions substitute mainly for the dodecahedral Gd3 + sites [11,12], with an orthorhombic D2 local symmetry site. Since the luminescence properties of the rare earth ions are ruled by the symmetry of its local site in the host, the D2 crystal-field interaction completely removes the degeneracy of the 2S + 1LJ multiplets, giving rise to the R1 and R2 Stark levels of the 4F3/2 multiplet and the ZN (N = 1-5) Stark levels of the 4I9/2 ground state (see Fig. 1 ).

 

Fig. 1 Emission spectra associated to the ⁴F_3/2(R_1,2)→⁴I_9/2(Z_1-5) transition as a function of pressure at RT. Partial energy level diagram of the Nd³⁺ ion in the GSGG garnet crystal and emission transitions between the Stark levels of the ⁴F_3/2 lowest emitting and the ⁴I_9/2 ground multiplets.

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The emission spectrum of the ⁴F_3/2→⁴I_9/2 transition of the Nd³⁺ in GSGG at ambient conditions consists in eight well defined narrow bands that can be easily assigned to the R_i→Z_N transitions [9,10]. Figure 1 shows the spectra taken upon pressure up to 14.4 GPa, in which each spectrum covers an interval of around 900 cm⁻¹, ranging from 10650 cm⁻¹ to 11550 cm⁻¹ with two distinct regions, one corresponding to the R_1,2→Z_1,2,3,4 transitions, which show slight pressure changes, and the other, with an energy gap of around 300 cm⁻¹, to the R_1,2→Z₅ transition composed by two lines with high linear pressure coefficients of −8.8 cm⁻¹/GPa and −11.3 cm⁻¹/GPa, respectively, in the range from ambient pressure to 12 GPa (see Fig. 2 ). These values are larger than those found for the R-lines of Cr³⁺ in ruby (−7.35 cm⁻¹/GPa). These results make the R_1,2→Z₅ transitions of the co-doped Cr³⁺,Nd³⁺:GSGG an appropriate candidate as an optical pressure sensor in the near-infrared. Beyond 12 GPa it is not possible to resolve these bands, due to the increase of the linewidth and the overlapping of both peaks with pressure, limiting the use of this garnet at room temperature to this pressure.

 

Fig. 2 Energy positions of the ⁴F_3/2(R_1,2)→⁴I_9/2(Z_1-5) emission lines as a function of pressure at RT.

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On the other hand, and as a general feature, the emission lines from the R₂ Stark level increases their intensities compared to those of the R₁ level with the increase of temperature, with a fluorescence intensity ratio R one order of magnitude larger for the emission lines to the Z₁ ground Stark level than to the Z₅ Stark level. As an example, the emission spectra of the Nd³⁺ at around 8.8 GPa are shown in Fig. 3 for different temperature ranging from 30 to 245 K, in which a large thermal sensitivity S (dR/dT) [5] was found. From a fit to a Boltzmann-type population distribution, R = 5.1 exp(−40.9/T) and a R₂-R₁ energy gap of 28.5 cm⁻¹ is obtained, quite similar to the energy gap of 27 cm⁻¹ experimentally measured, while the maximum sensitivity reaches a value of 0.067 K⁻¹ at 20 K. Thus the co-doped Cr³⁺,Nd³⁺:GSGG can be also an appropriate candidate as an optical low temperature sensor.

 

Fig. 3 Emission spectra associated to the ⁴F_3/2(R_1,2)→⁴I_9/2(Z_1-5) transition as a function of temperature at 8.8 GPa. The fluorescence intensity ratio R of the R_1,2→Z₁ transitions and its sensitivity S to changes of the temperature are given in the 10 to 300 K range.

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In the frame of the crystal-field theory, the energy level positions of a rare-earth ion are associated to the free-ion Hamiltonian, including Coulomb repulsion and spin-orbit coupling and mainly responsible for the red-shift of barycenters of the ^{2S + 1}L_J multiplets, and the crystal-field Hamiltonian, characterizing the interaction of the rare-earth with its ligands, that accounts for the position of the Stark levels in each state [13]. Roughly speaking, the maximum splitting of each ^{2S + 1}L_J multiplet depends linearly on the overall crystal-field strength. In low symmetry sites, it is often convenient to describe the effect of the crystal-field as a deformation or distortion of a main cubic symmetry. Thus for the D₂ Hamiltonian, found in the GSGG garnet for the Nd³⁺ ion, the cubic symmetry component is described by only the real $B_0^4$and $B_0^6$crystal-field parameters ($B_4^4$and$B_4^6$are then obtained by specific cubic ratios), and the non-cubic symmetry component, which accounts for the true D₂ symmetry at the Nd³⁺ sites, and governed by the appearance of other crystal-field components and the deviation from the cubic ratios of rank 4 and rank 6 components [13].

Pressure enhances the Nd³⁺–O^2- interaction and then an increasing of the overall crystal-field is observed, giving rise to an increase of the splitting of each ^{2S + 1}L_J multiplet. In Fig. 2, a different rate of red shifts of all the R_1,2→Z_N transitions are appreciated, which tend to make closer to each other with increasing pressure. Since in cubic symmetry the ⁴F_3/2 state of Nd³⁺ gives no splitting, the non-cubic component of the crystal-field must be directly responsible for the observed splitting of the ⁴F_3/2 multiplet in the R₁ and R₂ lines, which is strongly reduced when increasing pressure from ambient pressure up to 12 GPa. This fact indicates that the $B_q^2$components of the crystal-field are also reduced, and then a tendency towards a cubic character of the site symmetry for Nd³⁺ in the garnet lattice is expected [9].

Except from the strong variation of the Z₅ position, the Z_1,2,3,4 Stark levels of the ⁴I_9/2 ground state show a very low sensitivity to pressure variation, see Fig. 2, and their energy separations remains mainly constant. The energy positions of the Z_N lines are related to all crystal-field parameters, although the ⁴I_9/2 state is especially sensitive to the rank 6 components of crystal-field [13] since a small variation of the cubic$B_0^6$ parameter strongly changes the energy position of all Z_N lines. On the other side, the energy position of the Z₅ Stark level appears to be particularly dependent to the rank 4 cubic part of the crystal-field. In fact, increasing only the cubic $B_0^4$parameter, the Z₅ energy position increases while the Z_1-4 energy positions remains mainly constant, in such a way that increasing a 20% the $B_0^4$parameter (and, with cubic ratio, the$B_4^4$) the observed pressure dependence can be reproduced. In brief, under compression the overall strength of the crystal-field increases, the $B_q^2$parameters (and the R-lines splitting) decreases and the ratios of the crystal-field parameters becomes more cubic, while the influence of the non-cubic D₂ crystal-field decreases. Moreover, increasing the cubic crystal-field of rank 4 results in larger separation of the Z₅ line from the other Z_N lines whereas the variations of the non cubic parameters related to a small orthorhombic distortion parameters have scarce influence.

4 Conclusions

In summary, simultaneous P and T determination has been carried out in a DAC measuring the luminescence spectra of the ⁴F_3/2→⁴I_9/2 transition of Cr³⁺,Nd³⁺-doped GSGG as a function of pressure (up to 12 GPa) and temperature (10-300 K). Two intense and isolated lines corresponding to R₁→Z₅ and R₂→Z₅ centred in the range from 10600 to 10800 cm⁻¹, respectively, are the most sensitive to pressure with coefficients of −11.3 cm⁻¹/GPa and −8.8 cm⁻¹/GPa, respectively, while the relative intensities of the R_1,2→Z₁ transitions show a large dependence with temperature. These facts, together with the advantages of excitation with a conventional Ar⁺ laser or a laser diode and the available near-infrared-extended photomultipliers, make this active garnet as a candidate to be used as a near-infrared P-T sensor in anvil cells at low temperatures and from ambient pressure up to 12 GPa.