Alexander Belyaev
email: belyaev@ihps.nnov.ru

Liza Basyrova

Vadim Sysoev

Maxim Lelet

Stanislav Balabanov

Vladimir Kalganov

Vladimir Mikhailovski

Mikhail Baranov

Evgeniia Stepanidenko

Vladimir Vitkin

Olga Dymshits

Pavel Loiko

G G Devyatykh

Microstructure, doping and optical properties of Co 2+ :ZnAl 2 O 4 transparent ceramics for saturable absorbers: Effect of the ZnF 2 sintering additive

Keywords: Transparent ceramics, Hot pressing synthesis, Sintering additive, Gahnite, Cobalt ions, Microstructure, Saturable absorbers of lasers

Transparent cobalt-doped zinc aluminate spinel (gahnite), Co 2+ :ZnAl2O4, ceramics were fabricated by hot pressing of (Zn,Co)Al2O4 / ZnF2 nanopowders at 1520 ºC for 4 hours. A novel approach was suggested for the preparation of (Zn,Co)Al2O4 precursor: the (Zn,Co)Al2O4 powders were synthesized by mixing an alcohol solution of aluminium isopropoxide with a joint aqueous solution of zinc formate (the source of zinc), cobalt nitrate and zinc fluoride (the sintering additive) followed by drying and calcination in air. The study of the thermal behavior of precursors revealed an optimum calcination temperature (700 ºC) preventing the loss of the sintering additive (ZnF2). The effect of the ZnF2 content (3-10 wt%) on the microstructure, the cobalt doping concentration, absorption and luminescence of ceramics was systematically studied. The ceramics exhibit a close-packed microstructure with a mean grain size of 50-70 μm and high in-line transmission (about 84% at ~2 μm). The actual concentration of Co 2+ ions in tetrahedral (Td) sites of gahnite is lower than the Co 2+ doping level and it decreases with the ZnF2 content. We propose a possible mechanism of this variation including both the losses of Co 2+ via evaporation of the intermediate CoF2 phase and a partial location of Co 2+ ions in octahedral (Oh) sites of gahnite due to its partly inverse spinel structure. The developed ceramics are promising for saturable absorbers of erbium lasers.

Introduction

Spinel crystals are complex oxides with a cubic symmetry (sp. gr. Fd3¯m) having a general chemical formula of AB2O4 where A and B are cations with variable valence. Typically, A is a divalent cation, e.g., Mg 2+ , Fe 2+ , Zn 2+ or Mn 2+ and B is a trivalent one, e.g., Al 3+ or Fe 3+ (the so-called 2-3 spinels). A well-known example is MgAl2O4 [START_REF] Ganesh | A review on magnesium aluminate (MgAl2O4) spinel: synthesis, processing and applications[END_REF]. Spinel crystals offer good mechanical and thermal properties and they possess a broad transparency range.

3d transition-metal (TM) ions feature partially filled 3d orbitals which are not shielded. Their spectroscopic properties determined by transitions of 3d electrons are sensitive to the ligand field symmetry and strength. TM ions embedded in tetrahedral (Td) sites in crystals are attractive because of their broadband linear and nonlinear absorption [START_REF] Malyarevich | Saturable absorbers based on tetrahedrally coordinated transition-metal ions in crystals[END_REF]. The latter arises from the fact that the Td local field symmetry results in high transition intensities (several orders of magnitude stronger than those for the octahedral (Oh) field). As a result, crystals doped with TM ions entering into the Td sites are used as saturable absorbers (SAs) of lasers [START_REF] Yumashev | Nonlinear absorption properties of Co 2+ :MgAl2O4 crystal[END_REF][START_REF] Tsai | Co 2+ :ZnS and Co 2+ :ZnSe saturable absorber Q switches[END_REF][START_REF] Yumashev | Excited state absorption and passive Q-switch performance of Co 2+ doped oxide crystals[END_REF].

Spinels and, in particular, MgAl2O4, are attractive for doping with TM ions [START_REF] Izumi | Optical properties of 3d transition-metal-doped MgAl2O4 spinels[END_REF] such as Ni 2+ [START_REF] Kuleshov | Spectroscopy and excited-state absorption of Ni 2+ -doped MgAl2O4[END_REF][START_REF] Saleem | Structural, magnetic and dielectric properties of nano-crystalline spinel NixCu1-xFe2O4[END_REF][START_REF] Yu | A facile approach towards fabrication and ultrabroad band emission properties of nickel ion-doped ZnAl2O4 transparent ceramics[END_REF][START_REF] Wang | Synthesis, characterization and properties of Ni 2+ -doped ZnAl2O4-based spinel-type solid acid catalysts: SO4 2-/Zn1-xNixAl2O4[END_REF], Co 2 + [START_REF] Kuleshov | Absorption and luminescence of tetrahedral Co 2+ ion in MgAl2O4[END_REF], Mn 2+ [START_REF] Song | Heavy Mn 2+ doped MgAl2O4 phosphor for high-efficient near-infrared light-emitting diode and the night-vision application[END_REF][START_REF] Tomita | Luminescence channels of manganese-doped spinel[END_REF][START_REF] Huang | Optical properties and theoretical study of Mn doped ZnAl2O4 nanoparticles with spinel structure[END_REF][START_REF] Ashok | Structural, optical and magnetic properties of Zn1-xMnxFe2O4 (0 ≤ x ≤ 0.5) spinel nano particles for transesterification of used cooking oil[END_REF][START_REF] Song | A thermally stable narrow-band green-emitting phosphor MgAl2O4:Mn 2+ for wide color gamut backlight display application[END_REF], Fe 2+ [START_REF] El-Fadl | Syntheses of new spinels Zn1-xFexAl2O4 nanocrystallines structure: Optical and magnetic characteristics[END_REF][START_REF] Basyrova | Synthesis, structure and spectroscopy of Fe 2+ :MgAl2O4 transparent ceramics[END_REF][START_REF] Osipov | Fabrication and characterization of IR-transparent Fe 2+ doped MgAl2O4 ceramics[END_REF] or Cr 3+ [START_REF] Feofilov | Fluorescence of Cr 3+ ions in MgAl2O4 epitaxial nanosize spinel films on SrTiO3 substrates[END_REF]. For MgAl2O4, one example is doping with divalent cobalt (Co 2+ ) ions replacing the Mg 2+ cations in Td sites and featuring broad absorption at ~1.5 μm [START_REF] Kuleshov | Absorption and luminescence of tetrahedral Co 2+ ion in MgAl2O4[END_REF]. This absorption spectrally matches the emission of eye-safe erbium lasers. As a result, Co:MgAl2O4 based crystalline materials have been recognized as SAs of pulsed erbium lasers [START_REF] Karlsson | Diode-pumped Er-Yb:glass laser passively Q switched by use of Co 2+ :MgAl2O4 as a saturable absorber[END_REF][START_REF] Gorbachenya | Eye-safe 1.55 μm passively Q-switched Er,Yb:GdAl3(BO3)4 diode-pumped laser[END_REF][START_REF] Loiko | Crystallization and nonlinear optical properties of transparent glass-ceramics with Co:Mg(Al,Ga)2O4 nanocrystals for saturable absorbers of lasers at 1.6-1.7 µm[END_REF][START_REF] Vitkin | Passive Q-switching of an Er, Yb:glass laser with Co:Mg(Al,Ga)2O4-based glass-ceramics[END_REF] with applications in range-finding, remote sensing (LIDAR), medicine, etc.

Zinc aluminate (gahnite) ZnAl2O4 is another well-known compound in the spinel crystal family [START_REF] Ferguson | Crystal-field spectra of d 3,7 Ions. V. Tetrahedral Co 2+ in ZnAl2O4 spinel[END_REF]. In the mineral form, its color ranges between green, blue, yellow or brown due to the TM ion impurities. Compared to MgAl2O4, gahnite features better thermal conductivity. E.g., in [START_REF] Van Der Laag | Structural, elastic, thermophysical and dielectric properties of zinc aluminate (ZnAl2O4)[END_REF] for ceramic ZnAl2O4, it was estimated to be ~25 W/mK. ZnAl2O4 exhibits high mechanical strength (Mohs hardness: 8.0), high thermal and chemical stability and wide band gap (~6 eV). Unfortunately, bulk single crystals of ZnAl2O4 cannot be obtained by conventional melt growth methods due to dissociation of zinc aluminate at high temperatures close to the melting point (about 1950 °C, depending on the impurities). As an alternative to single crystals, Co:ZnAl2O4-based transparent glass-ceramics (GCs) [START_REF] Denisov | Linear and nonlinear optical properties of cobalt-doped zinc aluminum glass ceramics[END_REF][START_REF] Alekseeva | Structure evolution and optical properties of Co-doped zinc aluminosilicate glass-ceramics[END_REF] and Co:ZnAl2O4 ceramics [START_REF] Loiko | Synthesis, characterization and absorption saturation of Co:ZnAl2O4 (gahnite) transparent ceramic and glassceramics: A comparative study[END_REF] were proposed.

Polycrystalline transparent ceramics are obtained at temperatures significantly lower than the melting point of corresponding bulk crystals. Their spectroscopic properties resemble those of the crystals. As compared to GCs, they do not contain residual glass phase. The development of cobalt-doped spinel ceramics was manifested by Co:MgAl2O4 ones [START_REF] Goldstein | Development of saturable absorbers for laser passive Q-switching near 1.5 µm based on transparent ceramic Co 2+ :MgAl2O4[END_REF][START_REF] Luo | Fabrication and spectral properties of hotpressed Co:MgAl2O4 transparent ceramics for saturable absorber[END_REF][START_REF] Su | A simple way to prepare Co:MgAl2O4 transparent ceramics for saturable absorber[END_REF][START_REF] Luo | Fabrication and spectroscopic properties of Co:MgAl2O4 transparent ceramics by the HIP post-treatment[END_REF][START_REF] Liu | Fabrication and properties of Co:MgAl2O4 transparent ceramics for a saturable absorber from coprecipitated nanopowder[END_REF][START_REF] Su | A simple way to prepare Co:MgAl2O4 transparent ceramics for saturable absorber[END_REF]. Recently, transparent ZnAl2O4 ceramics were obtained by Goldstein et al. by hot isostatic pressing at 1550 °C using hydrothermally synthesized powders [START_REF] Goldstein | Fabrication of transparent polycrystalline ZnAl2O4 -A new optical bulk ceramic[END_REF]. Since then, several studies dedicated to undoped gahnite ceramics [START_REF] Kim | Transparent ZnAl2O4 ceramics fabricated by spark plasma sintering[END_REF][START_REF] Fu | The microwave dielectric properties of transparent ZnAl2O4 ceramics fabricated by spark plasma sintering[END_REF][START_REF] Yong | Optical properties of transparent ZnAl2O4 ceramics: A new transparent material prepared by spark plasma sintering[END_REF][START_REF] Sokol | On the effects of LiF on the synthesis and reactive sintering of gahnite[END_REF] and only few devoted to Co 2+ -doped ones [START_REF] Loiko | Synthesis, characterization and absorption saturation of Co:ZnAl2O4 (gahnite) transparent ceramic and glassceramics: A comparative study[END_REF] appeared. More recently, Ni 2+ -doped ZnAl2O4 transparent ceramics [START_REF] Yu | A facile approach towards fabrication and ultrabroad band emission properties of nickel ion-doped ZnAl2O4 transparent ceramics[END_REF] were prepared by melting-vaporing procedure using TeO2 and Na2O as melting agents.

One of the limiting factors in the work on obtaining this material is the absence of commercially available powders. The existing methods of synthesis of ZnAl2O4 powders have certain difficulties. In particular, in the case of simultaneous precipitation of zinc and aluminium nitrates with ammonia solution [START_REF] Yang | Site Inversion induces thermodynamic stability against coarsening in zinc aluminate spinel[END_REF][START_REF] Yang | Grain boundary strengthening in nanocrystalline zinc aluminate[END_REF], due to formation of complex compounds of zinc with ammonia that are soluble in water, the resulting powder is enriched with aluminium. The same applies to cobalt, which is also coordinated by ammonia, so that it is impossible to control its exact content in the powder. According to literature data, powders synthesized by hydrothermal method [START_REF] Goldstein | Fabrication of transparent polycrystalline ZnAl2O4 -A new optical bulk ceramic[END_REF], decomposition of sulphate salts [START_REF] Kim | Transparent ZnAl2O4 ceramics fabricated by spark plasma sintering[END_REF][START_REF] Fu | The microwave dielectric properties of transparent ZnAl2O4 ceramics fabricated by spark plasma sintering[END_REF], as well as mixing of powders of aluminium and zinc oxides [START_REF] Yong | Optical properties of transparent ZnAl2O4 ceramics: A new transparent material prepared by spark plasma sintering[END_REF][START_REF] Sokol | On the effects of LiF on the synthesis and reactive sintering of gahnite[END_REF] were used to fabricate ceramics. Recently, many works on the synthesis of powders have been published, among which are solgel synthesis [START_REF] Elakkiya | Ce and Fe doped gahnite: Cost effective solar reflective pigment for cool coating applications[END_REF], combustion synthesis [START_REF] Ianoş | Combustion synthesis of ZnAl2O4 powders with tuned surface area[END_REF][START_REF] Ianoş | Combustion synthesis of a blue Co-doped zinc aluminate near-infrared reflective pigment[END_REF][START_REF] Jain | Enhanced near-infrared luminescence in zinc aluminate bestowed by fuel-blended combustion approach[END_REF][START_REF] De | Synthesis and characterization of pigments based on copper-zinc aluminate (CuxZn1-xAl2O4) by combustion[END_REF][START_REF] De | Synthesis and characterization of colourful aluminates based on nickel and zinc[END_REF], hydrothermal synthesis [START_REF] Huang | Optical properties and theoretical study of Mn doped ZnAl2O4 nanoparticles with spinel structure[END_REF].

Recently, we showed that synthesis the ZnAl2O4 powders by hydrolyzing alcohol solutions of aluminium isopropoxide with an aqueous solution of zinc acetate [START_REF] Belyaev | Sol-gel synthesis and characterization of ZnAl2O4 powders for transparent ceramics[END_REF] is promising for producing transparent ceramics. In this work, we optimize the ZnAl2O4 powder synthesis by replacing zinc acetate with zinc formate. Zinc formate easily decomposes [START_REF] Dollimore | The thermal decomposition of zinc and manganous formats[END_REF] to form zinc oxide and a mixture of gases, i.e., CO, CO2, H2 and H2O (↑), without formation of carbon residues in the temperature range of 250-300 °C. Other possible option is zinc nitrate. However, nitrate groups contribute to formation of hard particles, which are very difficult to grind in mills of any type. The transition to nitrate forms of metal sources will be possible using automated techniques for obtaining fine precursor powder, e.g., spray drying. Compared to nitrate sources, formate ones make it possible to obtain softer powders. The obtained powders are sintered to produce transparent ceramics by hot pressing in the presence of zinc fluoride (ZnF2) [START_REF] Belyaev | A new approach to producing transparent ZnAl2O4 ceramics[END_REF] as a sintering additive. Also in this work, we propose to introduce ZnF2 directly into the precursor sol, thus excluding an additional step of introduction of the sintering additive at later stages.

In the present paper, we describe the production of Co:ZnAl2O4 transparent ceramics by hot pressing from powders with different content of cobalt and sintering additive (ZnF2). We also report on the effect of the sintering additive on microstructure, cobalt doping and spectroscopic properties of ceramics.

Experimental

Thermal evolution of precursor powders

The precursors for production of Co-doped ZnAl2O4 powders were prepared by hydrolysis of an alcohol solution of aluminium isopropoxide (Al(OCH(CH3)2)3), joint aqueous solution of zinc formate (Zn(CH2O)2) and cobalt nitrate (Co(NO3)2), as well as aqueous solution of zinc fluoride (ZnF2). The solubility of ZnF2 in water is about 15 g/l (at 20 °C). The molar ratio (zinc + cobalt) / aluminium was 1:2. The procedure for the preparation of reagents and hydrolysis is described in detail in [START_REF] Belyaev | Sol-gel synthesis and characterization of ZnAl2O4 powders for transparent ceramics[END_REF]. The resulting precursor was dried in a vacuum box (at a pressure of 60 kPa) under heating up to 250 °C with a rate of 2 °C/min. The dried precursor was grinded in a planetary ball mill and calcined in air in the temperature range of 300 to 900 °C for 20 min. Zinc aluminate powders doped with 0.02 at.% or 0.10 at.% cobalt, and 3, 6 or 10 wt% zinc fluoride were obtained at the optimum temperature of 700 °C for 20 min.

The study of thermal behavior of the precursor and the choice of the heat-treatment regime were carried out by the thermal gravimetric analysis (TGA) and the differential thermal analysis (DTA) using a synchronous TGA / DTA analyzer (model DTG-60H, Shimadzu) in air at a heating rate of 5 °C/min. The phase composition of powders was identified by X-ray diffraction (XRD) using the LabX XRD-6100, Shimadzu diffractometer.

Zinc fluoride has high vapor pressure (p(ZnF2) = 7 Pa at 775 °С [START_REF] Brunetti | Vapor pressures and sublimation enthalpies of cadmium difluoride and zinc difluoride by the torsion-effusion method[END_REF], 53 Pa at 855 °С [START_REF] Biefeld | The sublimation thermodynamics of zinc (II) fluoride[END_REF]). Calcination of the Co:ZnAl2O4/ZnF2 precursor at high temperatures may lead to a significant loss of the sintering additive. To avoid this, a thermal gravimetric study of decomposition of the precursor was carried out. The TGA / DTA data of the 0.1 at.% Co:ZnAl2O4 / 6 wt% ZnF2 dried precursor are shown in Fig. 1. The mass loss (about 7 wt%) at the temperatures up to 200 °C accompanying an endothermic peak (105 °C) corresponds to the removal of water. A small exothermic peak at ~245 °C may correspond to oxidation of formate groups by atmospheric oxygen and oxidation initiated by NO3 -groups. The significant mass loss of ~25 wt% between 220 °C and 300 °C accompanying an endothermic peak (276 °C) corresponds to decomposition of formate groups. Further mass losses (5 %) starting at above 500 °C correspond to evaporation of the sintering additive of ZnF2 (melting point: 872 °C) and removal of hydroxyl groups. Thus, significant losses comparable to the content of the sintering additive can be explained by the predominant evaporation of ZnF2. An exothermic peak at 850 °C corresponds the crystallization of zinc aluminate. The reason for the appearance of an exothermic peak with a maximum of 585 °C is not entirely understandable. Most likely, it is associated with the formation of intermediate fluorine-containing compounds because an exothermic peak at 585 °C was not observed on the TGA / DTA curve of the precursor without zinc fluoride, according to [START_REF] Belyaev | Sol-gel synthesis and characterization of ZnAl2O4 powders for transparent ceramics[END_REF] and the laboratory protocol. To decrease the unwanted loss of the sintering additive, the powders should be calcined at the lowest possible temperature for the shortest possible time. The use of zinc in the formate form allowed us to decrease the temperature and time of powder calcination, as high temperatures are not required for removal of organic residues.

Fig. 2 shows XRD patterns of powders calcined at the temperatures in the range of 300-900 °C for 20 min. Gahnite crystallization begins at 500 °C, as confirmed by the appearance of weak and broad diffraction peaks. The calcination at 900 °C gives a significant increase in the crystal size and crystallinity of the powder, as indicated by notably narrowed diffraction peaks increased in intensity. The mean size of crystallites in the powders calcined at 700 °C and 900 °C was estimated using the Scherrer's equation [START_REF] Lipson | Interpretation of X-ray powder patterns[END_REF] to be 8 nm and 37 nm, respectively. The crystallization of zinc aluminate at 500 ºC and 700 °C occurs by a solid-phase reaction, and at 900 °C -by dissolving and re-precipitation in the in the ZnAl2O4 / ZnF2 eutectic melt. It should be noted that the XRD patterns of calcined powders do not contain reflexes of ZnF2. The mass loss of the Co:ZnAl2O4 / ZnF2 precursor at above 700 °C observed during the TGA / DTA analysis (Fig. 1) is undesirable, so that the heat treatment of the powders at 700 °C is preferable.

Note that weak reflexes of zinc oxide (ZnO) are present in the XRD pattern of powder calcined at 900 °C. The impurity phase of ZnO may indicate that the crystallization of zinc aluminate has not been completed, but will be completed at hot pressing of ceramics. Note that these powders were not used for the synthesis of ceramics in the present work. If calcination of powders at higher temperatures would be required, the initial batch should be enriched in aluminium if the powder stoichiometry is shifted to zinc.

Fabrication of ceramics

To fabricate transparent ceramics, synthesized powders were hot pressed in a homemade machine at a temperature of 1520 °C for 4 h. The powders were pressed under 50 MPa in a steel mold (diameter: 15 mm) and placed into a graphite mold. The hot pressing included the following stages: (i) heating up to 950 °C with a constant pressure of 3 MPa, (ii) first dwell for 10 min with a constant pressure, (iii) heating up to 1200 °C with a gradual pressure rise up to 40 MPa, (iv) second dwell for 20 min with a constant pressure, (v) heating up to 1520 °C, (vi) final dwell for 4 h, (vii) free cooling. Sintering of ceramics was carried out in a vacuum atmosphere.

The general mechanism of action the sintering additive for liquid-assisted-sintering (ZnF2, in our case) includes (i) its role as a lubricant that promotes sliding of particles during shrinkage, (ii) recrystallization in the melt due to dissolution of small particles and precipitation on large particles and (iii) formation of sintering additive-associated vacancies that facilitate sintering at later stages of the sintering process.

The ceramic disks (thickness: 2 mm, diameter: 15 mm) were polished to laser-grade quality from both sides. They were transparent, Fig. 3, and had a blue coloration due to the cobalt doping. For a fixed Co content in the initial powders, the coloration decreased with increasing the ZnF2 content (see below).

For spectroscopic studies, half of the ceramic disk was additionally annealed at 1400 °C for 30 min in air to eliminate the possible oxygen vacancies.

Characterization of ceramics

The X-ray powder diffraction (XRD) patterns of ceramic samples were recorded using a Shimadzu XRD-6000 diffractometer, Cu Kα radiation (1.54060 Å) with a Ni filter. The lattice constant a for ceramics was determined by Rietveld refinement.

The microstructure of a clean fracture surface of ceramic disks was studied using a scanning electron microscope (SEM, MERLIN, Carl Zeiss). The size distribution of grains was analyzed by manual counting using ImageJ software. The composition of ceramics was studied by Energy Dispersive X-ray (EDX) spectroscopy. For this, we used a similar electron microscope (accelerating voltage: 20 kV, beam current: 2 nA) equipped with an INCA X-Act (Oxford Instruments) microanalyzer. To avoid the unwanted charging of the dielectric ceramic surface, it was coated with a thin (thickness: 10 nm) carbon film prior to SEM studies.

All spectroscopic studies were performed at room temperature (20 °C). The transmission spectra were measured with a Shimadzu UV 3600 spectrophotometer (0.3-2 μm). The Raman spectra and the luminescence were detected using a confocal Raman microscope (in-Via, Renishaw) equipped using a Leica ×50 objective (N.A. = 0.75). The excitation wavelength λexc was 514 nm (Ar + laser line).

The luminescence decay was studied using a time-resolved confocal fluorescence microscope equipped with a ×100 objective (N.A. = 0.95) (MicroTime 100, PicoQuant). As the excitation source, a picosecond (ps) diode laser emitting at 405 nm was used.

Results and discussion

Microstructure

The structure and the phase purity of ceramics were confirmed by X-ray powder diffraction, Fig. 4. The measured XRD patterns correspond to that of undoped ZnAl2O4 (according to the ICSD (Inorganic Crystal Structure Database) card #9559) [START_REF] Cooley | Equilibrium cation distribution in NiAl2O4, CuAl2O4, and ZnAl2O4 spinels[END_REF]. Co:ZnAl2O4 is cubic (sp. gr. O 7 h -Fd3¯m, #227). The lattice constant a for ceramics was weakly dependent on the ZnF2 content. For ceramic prepared from powders containing 0.1 at.% Co and 10 wt% ZnF2, a = 8.088 Å.

A similar microstructure was observed for all studied ceramics. The example SEM images of a fracture surface of ceramics prepared from powders containing 0.1 at.% Co and 3 / 10 wt.% ZnF2 are shown in Fig. 5(a,b). The ceramics exhibit a close-packed structure with clean grain boundaries and a lack of μm-sized pores. The mean grain size was determined by counting about 100 crystallites for each sample. The measured linear dimensions of grains were multiplied by a shape factor of 1.2 (accounting for slight deviations from the spherical shape). Fig. 6(a) shows the grain size distribution for the series of ceramics prepared from powders doped with 0.02 at.% Co and 3-10 wt% ZnF2. For all samples, a relatively broad range of grain sizes (20-100 μm) was observed revealing a dependence on the position in the ceramic disk: larger grains in the central part and smaller grains at the perimeter of the disk.

The effect of the ZnF2 content on the mean grain size Dgrain is shown in Fig. 6(b). For 0.02 at.% Co doping, with increasing the amount of the sintering aid, first, Dgrain slightly increases (from 55 μm for 3 wt% ZnF2 to 68 μm for 6 wt% ZnF2) and then decreases to 60 μm for 10 wt% ZnF2. A similar tendency is observed for 0.1 at.% Co doping. These values are larger than those observed in an undoped ZnAl2O4 ceramics (Dgrain = 40 μm, using the same shape factor) produced by a similar method with 5 wt% ZnF2 [START_REF] Belyaev | A new approach to producing transparent ZnAl2O4 ceramics[END_REF]. The observed trends for the variation of the grain size may be masked by the relatively broad grain size distribution observed in the studied ceramics; therefore, it is difficult to draw conclusions in this relation.

The composition of ceramics was studied by EDX. The presence of fluorine was detected in all the studied samples. The concentration of F -ions in ceramics slowly increased with the ZnF2 content in the precursor powders. We assume that the F -ions may be diffusely distributed at the grain boundaries or dissolved in the grains. The EDX spectra of ceramics prepared from powders containing 0.1 at.% Co and 3-10 wt% ZnF2 are shown in Fig. 7. The element mapping (Al, Zn, O, Co and F) obtained by the means of EDX is shown in Fig. 8.

Raman spectra

The structure of ceramics was confirmed by Raman spectroscopy, Fig. 9. According to the group-theory analysis, the irreducible representations at the Г point (k = 0) of the Brillouin zone are as following: Г = A1g + Eg + T1g +3T2g + 2A2u + 2Eu + 5T1u + 2T2u [START_REF] White | Interpretation of the vibrational spectra of spinels, Spectrochim[END_REF]. Five modes (A1g, Eg and 3T2g) are Raman-active, five (5T1u) are IR-active and other are acoustic or silent. In the Raman spectra of ceramics, all five modes are observed at 195 cm -1 (T2g), 417 cm -1 (Eg), ~510 cm -1 (T2g), 657 cm -1 (T2g) and ~800 cm -1 (A1g). The spectra are weakly dependent on the starting composition. The two most intense modes are due to the motion of Al and O atoms [START_REF] Lopez-Moreno | Lattice dynamics of ZnAl2O4 and ZnGa2O4 under high pressure[END_REF].

A careful inspection of the Raman spectra did not reveal characteristic vibrations of possible fluoride phases (CoF2 or ZnF2) and ZnO. In particular, for CoF2, these are 68, 246, 366 and 494 cm -1 [START_REF] Macfarlane | Light scattering from phonons in CoF2[END_REF] and for and for ZnF2 -70, 253, 350 and 522 cm -1 [START_REF] Porto | Raman spectra of TiO2, MgF2, ZnF2, FeF2, and MnF2[END_REF]. For ZnO, the characteristic Raman bands are at 99, 333 and 438 cm -1 [START_REF] Cuscó | Temperature dependence of Raman scattering in ZnO[END_REF].

Optical absorption

The in-line transmission (T) spectra of polished ceramic disks are shown in Fig. 10(a). First, let us discuss the transmission at 1.9 μm (out of cobalt absorption bands). Depending on the composition of the precursor, it amounts to T = 83.2%-84.0%, which is close to the theoretical value set by Fresnel losses, T0 = 84.3%, assuming a refractive index n of 1.80 [START_REF] Medenbach | Refractive index and optical dispersion of In2O3, InBO3 and gahnite[END_REF]. High transmission indicates good optical quality of ceramics. For the increased cobalt concentration in the precursor, the transmission slightly decreases. However, we did not observe a direct relation between transmission and the ZnF2 content.

The observed spectral bands are due to absorption of Co 2+ ions in tetrahedral sites in the spinel structure. The Co 2+ ion has the electronic configuration of [Ar]3d 7 . The ground-state is 4 A2( 4 F), so that the spin-allowed transitions occur to quartet states, 4 F and 4 P. However, the transition to the lower-lying excited-state 4 T2( 4 F) is forbidden in an undistorted Td ligand field, so it has a small oscillator strength [START_REF] Kuleshov | Absorption and luminescence of tetrahedral Co 2+ ion in MgAl2O4[END_REF] and it is observed as a weak band at ~2.55 μm. The intense and broad (1.06-1.64 μm) absorption band with local peaks at 1248, 1297, 1428, and 1503 nm corresponds to transitions to the 4 T1( 4 F) state. The second intense band in the visible (0.50-0.68 μm) with local peak at 547, 587 and 620 nm corresponds to transitions to the 4 T1( 4 P) state. The local peaks in both bands are related to the spin-orbit splitting of the quartet states [START_REF] Goldstein | Development of saturable absorbers for laser passive Q-switching near 1.5 µm based on transparent ceramic Co 2+ :MgAl2O4[END_REF]. For example, for the 4 T1( 4 F) state of tetrahedral Co 2+ ions in gahnite, the previously determined energies of the spin-orbit splitted sub-levels of 4 T1( 4 P) at 4.2 K are 6756(Г6), 7072(Г8), 7776(Г7) and 7850(Г8) cm -1 [START_REF] Ferguson | Crystal-field spectra of d 3,7 Ions. V. Tetrahedral Co 2+ in ZnAl2O4 spinel[END_REF], corresponding to the wavelengths in absorption of 1480, 1414, 1286 and 1273 nm, respectively. For the studied ceramics, the positions of sub-levels may slightly vary as compared to the single-crystal.

Besides the spin-allowed transitions, the spectra contain weak bands assigned to transitions to the higher-lying splitted 2 G, 2 P and 2 H doublet excited-states. In particular, the transitions to the 2 E, 2 T1, 2 A1 and 2 T2( 2 G) excited-states (in an increasing energy order) contribute to intense absorption band in the visible. At shorter wavelengths (<0.50 μm), weak structured absorption is due to transition to the 2 T1( 2 P), 2 T2, 2 T1, 2 E and 2 T1( 2 H) excited-states (in an increasing energy order). Here, the assignment is according to the energy levels reported in [START_REF] Ferguson | Crystal-field spectra of d 3,7 Ions. V. Tetrahedral Co 2+ in ZnAl2O4 spinel[END_REF][START_REF] Tanaka | Preparation and optical properties of transparent glass-ceramics containing cobalt (II) ions[END_REF]. More details about the crystal-field of tetrahedral Co 2+ ions in gahnite can be found elsewhere [START_REF] Ardit | Structural relaxation in tetrahedrally coordinated Co 2+ along the gahnite-Co-aluminate spinel solid solution[END_REF]. Weak and broadband absorption at these wavelengths may also originate from Co 2+ ions in octahedral sites [START_REF] Duan | Cation distribution in Co-doped ZnAl2O4 nanoparticles studied by X-ray photoelectron spectroscopy and 27 Al solid-state NMR spectroscopy[END_REF] (see Section 4.4).

A detailed view on visible absorption of an example ceramic sample made of powders doped with 0.1 at.% Co and 3 wt% ZnF2 is given in Fig. 10(b). The bands at 477 nm, ~445 nm and 406 nm are assigned to transitions to the 2 T1( 2 P), 2 T2 and 2 T1( 2 H) states, respectively. Other transitions to the 2 H doublet states are not visible because of their weak intensity. For the as-sintered ceramic, a broad absorption band at ~275 nm is observed overlapping with the UV absorption edge (λUV = 245 nm, optical bandgap Eg: ~5.5 eV). After annealing, the Co 2+ absorption features do not change implying that new Co 2+ sites with Td symmetry are not formed, while the intensity of the UV band increases significantly thus shifting the absorption edge to λUV = 292 nm. In the previously studied undoped ZnAl2O4 ceramics sintered with 5 wt% ZnF2 [START_REF] Belyaev | Sol-gel synthesis and characterization of ZnAl2O4 powders for transparent ceramics[END_REF], no such absorption was detected resulting in Eg = 6.05 eV. In the present work, sintering of ceramics was carried out in a vacuum atmosphere, which may lead to formation of oxygen vacancies. Oxidative annealing contributes to the drain of vacancies (see Section 4.5) with formation of pores of nm and sub-μm size leading to additional light scattering and a red-shift of the UV absorption edge of the material.

The scheme of energy levels of tetrahedral Co 2+ ions can be analyzed within the equivalent Tanabe-Sugano diagram [START_REF] Tanabe | On the absorption spectra of complex ions I[END_REF] for the d 3 complexes in octahedral field, Fig. 11(a). Here, we omit the "g" subscripts because all the states are even (gerade). The Co 2+ absorption in the ZnAl2O4 matrix corresponds to the region of the diagram where the branches corresponding to the 4 P and 2 G states intersect. As a result, the doublet states 2 E and 2 T1( 2 G) are lying below the quartet 4 T1( 4 P) one, as shown in Fig. 11(b) according to the crystal-field splitting from [START_REF] Ferguson | Crystal-field spectra of d 3,7 Ions. V. Tetrahedral Co 2+ in ZnAl2O4 spinel[END_REF]. As compared to Co:MgAl2O4 [START_REF] Deren | The optical spectra of Co 2+ in MgAl2O4 spinel[END_REF], gahnite shows smaller splitting of the 4 T1( 4 F) and 4 T1( 4 P) states.

Cobalt doping

A general chemical formula for spinels is AB2O4 (cubic system, sp. gr. Fd3¯m). Each unit cell contains 32 anions (O 2-) in a face-centered cubic packing. Inside the oxygen lattice, the cations (A 2+ and B 3+ ) have 32 octahedral (Oh) and 64 tetrahedral (Td) available interstitial sites per unit cell. In a normal spinel structure, 1/8 of the Td sites are occupied by divalent cations A 2+ and 1/2 of the Oh sites are occupied by trivalent cations B 3+ . Spinels can demonstrate a certain degree of cation disorder. It is described by an inversion parameter δ which is a fraction of B 3+ cations in the Td sites (or, equivalently, a fraction of A 2+ cations in the Oh sites). As a result, the formula for spinels may be written as IV [A1-δBδ] VI [B2-δAδ]O4. The spinel is normal for δ = 0 and inverse for δ = 1. For δ = 2/3, cations have a completely random distribution over the Td and Oh sites [START_REF] Ardit | Structural relaxation in tetrahedrally coordinated Co 2+ along the gahnite-Co-aluminate spinel solid solution[END_REF].

In the case of gahnite, this formula is IV [Zn1-δAlδ] VI [Al2-δZnδ]O4. Here, the superscripts are the coordination numbers (C.N. = IV and VI for the Td and Oh sites, respectively). The Co 2+ ions in the spinel structure are expected to replace the Zn 2+ ones. In this way, some part of Co 2+ ions may be located in octahedral sites [START_REF] Ardit | Structural relaxation in tetrahedrally coordinated Co 2+ along the gahnite-Co-aluminate spinel solid solution[END_REF][START_REF] Popović | Inverse spinel structure of Codoped gahnite[END_REF]. Because a center of symmetry is present for the Oh site, the intensity of transitions for VI Co 2+ ions will be several orders of magnitude weaker as compared to the IV Co 2+ ones [START_REF] Ferguson | Crystal-field spectra of d 3,7 Ions. V. Tetrahedral Co 2+ in ZnAl2O4 spinel[END_REF]. Thus, the former species will contribute to absorption with much lower intensity.

It is known that Co:ZnAl2O4 exhibits a notable inversion, depending on the size of the crystallites and Co 2+ concentration. With increasing the Co 2+ doping level reaching the stoichiometric composition of cobalt aluminate (CoAl2O4), δ increases [START_REF] Popović | Inverse spinel structure of Codoped gahnite[END_REF]. It was also shown that the inversion parameter decreases with increasing the crystallite size [START_REF] Duan | Cation distribution in Co-doped ZnAl2O4 nanoparticles studied by X-ray photoelectron spectroscopy and 27 Al solid-state NMR spectroscopy[END_REF]. However, the presence of a notable fraction of octahedral Co 2+ ions in bulk gahnite crystals was also claimed [START_REF] Ferguson | Crystal-field spectra of d 3,7 Ions. V. Tetrahedral Co 2+ in ZnAl2O4 spinel[END_REF].

It is known that the lattice constant of Co 2+ -doped ZnAl2O4 is an indication of a degree of inversion. For an undoped ZnAl2O4 ceramics studied for comparison, we have determined a = 8.087 Å which is a typical value for undoped synthetic gahnite [START_REF] O'neill | Crystal structures and cation distributions in simple spinels from powder XRD structural refinements: MgCr2O4, ZnCr2O4, Fe3O4 and the temperature dependence of the cation distribution in ZnAl2O4[END_REF]. The assumption that Co 2+ ions are entering into the spinel structure solely in Td sites should lead to a decrease of a. Indeed, for a C.N. = IV, the ionic radii of Co 2+ and Zn 2+ are 0.58 Å and 0.60 Å, respectively [START_REF] Shannon | Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides[END_REF]. In [START_REF] Popović | Inverse spinel structure of Codoped gahnite[END_REF], it was suggested that the main reason for increasing a is the intersite-cation exchange (quantified by increasing δ parameter), namely, Co 2+ for Al 3+ substitution on the Oh sites. Indeed, the corresponding ionic radii of Co 2+ and Al 3+ for C.N. = VI are 0.745 Å and 0.535 Å [START_REF] Shannon | Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides[END_REF]. Now, let us analyze the broad absorption band due to the 4 A2( 4 F) → 4 T1( 4 F) transition of IV Co 2+ ions, Fig. 12(a). For a fixed concentration of Co 2+ in the precursor, the absorption coefficient (αabs) decreases linearly with increasing the ZnF2 content, e.g., as shown in Fig. 12(b) for the reference wavelength of 1.54 μm. Moreover, even extrapolation of the αabs(ZnF2) dependence to the limit of absent sintering additive gives a lower value of the absorption coefficient than the expected one, αabs0 = σGSA·NCo0. Here, σGSA is the ground-state absorption (GSA) cross-section of Co 2+ ions in Td sites, NCo0 is the Co 2+ concentration assum-ing that all cobalt ions enter into the ceramic grains. For the initial concentrations of 0.02 at.% and 0.1 at.% Co, NCo0 = 0.303×10 19 cm -3 and 1.515×10 19 cm -3 , respectively (as calculated assuming the density of ceramics ρ = 4.61 g/cm 3 ). Previously, for transparent GCs based on Co:ZnAl2O4 nanocrystals, σGSA at 1.54 μm was determined to be 2.0×10 -19 cm 2 [START_REF] Denisov | Linear and nonlinear optical properties of cobalt-doped zinc aluminum glass ceramics[END_REF] and 2.45×10 -19 cm 2 (used in the present work) [START_REF] Goldstein | Development of saturable absorbers for laser passive Q-switching near 1.5 µm based on transparent ceramic Co 2+ :MgAl2O4[END_REF] being lower than that for the Co:MgAl2O4 single-crystal, 3.5×10 -19 cm 2 [START_REF] Yumashev | Nonlinear absorption properties of Co 2+ :MgAl2O4 crystal[END_REF]. A similar analysis can be performed based on the visible absorption band of Co 2+ ions. In particular for ZnAl2O4, it is complicated by the lack of reliable data on the GSA cross-sections for the 4 A2( 4 F) → 4 T1( 4 P) transition.

From the measured absorption coefficient αabs at 1.54 μm, we estimated the actual concentration of Co 2+ ions in Td sites NCo(Td) = αabs/σGSA (Table 1). It decreases linearly with the ZnF2 content and it is about 2 times lower than the NCo0 value. There can exist two reasons for this. One is the presence of a fraction of Co 2+ ion in Oh sites (as described above) that does not contribute to linear absorption at ~1.54 μm. A similar mechanism was proposed previously for Co:ZnAl2O4-based transparent glass-ceramics to explain their non-saturable losses [START_REF] Alekseeva | Structure evolution and optical properties of Co-doped zinc aluminosilicate glass-ceramics[END_REF]. However, as all the studied ceramics are synthesized under the same conditions, this fraction is expected to be nearly independent of the ZnF2 content. Consequently, another reason is a chemical process involving ZnF2 and occurring during sintering of ceramics.

Let us describe the role of ZnF2. We suppose that cobalt (II) fluoride (CoF2) is the key intermediate of the sintering process. CoF2 can be formed both at the stage of precursor synthesis and during the sintering itself (through an interaction of ZnF2 and AlF3 (if it is formed during the evolution of a precursor or during the sintering) with cobalt ions within the green body), according to the following reactions:

Co 2+ + 2F → CoF2↓, ZnF2 + Co 2+ → CoF2 + Zn 2+ , 2AlF3 + 3Co 2+ → 3CoF2 + 2Al 3+ , respectively.
The formed CoF2 is less volatile (~12 Pa at 950 °C [START_REF] Brunetti | Torsion and Knudsen measurements of cobalt and nickel difluorides and their standard sublimation enthalpies[END_REF]) than ZnF2 (~458 Pa at 950 °C, extrapolated from [START_REF] Biefeld | The sublimation thermodynamics of zinc (II) fluoride[END_REF]) and AlF3 (~ 395 Pa at 950 °C [START_REF] Witt | The heat of sublimation of aluminium trifluoride and the heat of formation of aluminium monofluoride[END_REF]), hence, it is removed later (at higher temperatures). Indeed, the melting points of ZnF2 and CoF2 are 872 °C and ~1200 °C, respectively. CoF2 may be removed by evaporation and / or sublimation. The AlF3 vapor pressure is lower than that of ZnF2 but of the same order; therefore, sintered ceramics can be slightly enriched with zinc (see Fig. 2, 900 °C), as AlF3 can also evaporate. The following equations describe the process of regeneration of spinel lattice according to the reverse exchange reactions ((l) and (s) stand for liquid and solid phases, respectively):

CoF2(s) + Zn 2+ → ZnF2↑ + Co 2+ , CoF2(l) + Zn 2+ → ZnF2↑+ Co 2+ . If the rate of these processes is less than the rate of evaporation / sublimation of CoF2, the actual Co 2+ concentration in the ceramics will decrease. Here, CoF2(l) is a melt. The melting point of CoF2 is ~1200 °C and during the hot pressing, cobalt fluoride which has not been evaporated yet, will be completely liquid. In more details, taking into account the thermodynamic approach, similar processes are considered for the MgAl2O4 / LiF system in [START_REF] Esposito | A thermodynamic approach to obtaining transparent spinel (MgAl2O4) by hot pressing[END_REF].

Separately, it is worth noting that there is a possibility of presence of diffusely distributed CoF2 at the grain boundaries as a residue, because fluorine is found in ceramics at the level of the detection limit (Section 4.1). However, this option does not change the model of probable formation of CoF2.

Note that we did not use Co:ZnAl2O4 ceramics fabricated without the sintering aid for the analysis in Fig. 12(b) as they were translucent and it was impossible to quantify the Co 2+ absorption.

To conclude, the reduction in Co 2+ concentration in Td sites with respect to the value obtained when extrapolating the αabs(ZnF2) dependence to the limit of no sintering aid is due to the ZnF2-assisted evaporation of cobalt in the form of CoF2. The residual difference in concentrations (45% for 0.1 at.% Co and 28% for 0.02 at.% Co) is ascribed to the inverse spinel structure (predominantly) and losses of cobalt not related to ZnF2. Indeed, cobalt may also reduce to the metallic form with the zero oxidation state (e.g., due to the reaction with CO gas or graphite). This will however lead to formation of pores and translucent character of ceramics which is not observed in our case. It should be also noted that oxidative annealing would lead to the oxidation of metallic cobalt and the entry of Co 2+ into the spinel lattice, as well as to an increase in the intensity of cobalt absorption bands. However, it is not noted (see Fig. 10(b)). Thus, this mechanism seems to play a minor role.

Luminescence

The luminescence spectra of as-sintered Co:ZnAl2O4 ceramics are shown in Fig. 13(a). The spectra contain an intense band centered at ~645 nm (emission bandwidth: 43 nm) and a weak and broad band centered at ~860 nm both ascribed to Co 2+ ions in Td sites. The spinallowed transitions in emission occur from the 4 T1( 4 P) state to the 4 A2( 4 F) and 4 T2( 4 F) ones, respectively. As mentioned above, the doublet states 2 E and 2 T1( 2 G) in Co:ZnAl2O4 are lying below the 4 T1( 4 P) state while their populations are thermalized at room-temperature. Thus, 2 E( 2 G) is the emitting state.

With the increase of the actual Co 2+ concentration in Td sites (cf. Table 1), or, equivalently, with the decrease of the ZnF2 content in the precursor powders, the luminescence intensity gradually increases while no significant change of the spectral shape is observed. No concentration-quenching is observed up to at least 0.050 at.% Co in Td sites (actual).

We have monitored the effect of annealing on the emission properties of ceramics, see Fig. 13(b). After annealing, the intensity of luminescence related to Co 2+ ions in Td sites notably increases while the emission ascribed to defects is suppressed. This is because annealing efficiently removes oxygen vacancies leading to better crystallinity of the material.

Other spectral features are the sharp emission lines at 676-723 nm and a weak and broad emission centered at ~740 nm, Fig. 13(c). Previously, we demonstrated [START_REF] Loiko | Synthesis, characterization and absorption saturation of Co:ZnAl2O4 (gahnite) transparent ceramic and glassceramics: A comparative study[END_REF] that gahn-ite ceramics contains chromium (Cr 3+ ) impurity ions that come with ZnO raw material. The sharp emission lines at 676-723 nm are due to Cr 3+ ions substituting the Al 3+ cations in Oh sites (the so-called N-lines) [START_REF] Chen | Femtosecond laser induced space-selective precipitation of Cr 3+ -doped ZnAl2O4 crystal in glass[END_REF][START_REF] Derkosch | N-lines and chromium-pairs in the luminescence spectra of the spinels ZnAl2O4: Cr 3+ and MgAl2O4:Cr 3+[END_REF]. The broad emission centered at ~740 nm is assigned to the structure defects [START_REF] Jain | Defect induced broadband visible to near-infrared luminescence in ZnAl2O4 nanocrystals[END_REF][START_REF] Jain | Enhanced near-infrared luminescence in zinc aluminate bestowed by fuel-blended combustion approach[END_REF]. In particular, the transitions from the conduction band (CB) or shallow donor defect states (e.g., Al*Znaluminium antisite defects) to deep donor defect states (V*Ooxygen vacancies) may explain this emission.

The luminescence decay was studies for the as-sintered ceramic samples. When exciting the samples at 405 nm and detecting luminescence in the whole visible spectral range, the measured luminescence decay curves exhibited intense "fast" time component (decay time: τfast = 3.0±0.2 ns, being weakly dependent on composition of the starting powders) assigned to emission of defects, and much weaker "slow" component (τslow ~ hundreds of ns) attributed to emission of Co 2+ ions. Indeed, by spectral filtering only the emission band at ~645 nm, see Fig. 13(a), we observed predominantly the latter decay. The luminescence decay curves were well fitted with a single-exponential law, Fig. 14. For ceramics obtained from powders doped with 0.1 at.% Co, the determined decay time τslow decreased in the range 272-222 ns for the ZnF2 content decreasing from 10 to 3 wt% (or, equivalently, with increasing concentration of Co 2+ ions in Td sites). The τslow value has a meaning of the lifetime of the 2 E( 2 G) Co 2+ state. Our observations agree well with the previous studied of Co:ZnAl2O4-based GCs [START_REF] Denisov | Linear and nonlinear optical properties of cobalt-doped zinc aluminum glass ceramics[END_REF][START_REF] Alekseeva | Structure evolution and optical properties of Co-doped zinc aluminosilicate glass-ceramics[END_REF]: it was determined that the lifetime of the 2 E( 2 G) excited-state of Co 2+ ions in Td sites decreases from 200 to 25 ns for increasing the concentration of CoO in the initial glass (0.1-2 wt%).

As a final remark, one may point out the cost effectiveness and simplicity of synthesis of Co 2+ -doped ZnAl2O4 nanopowders and transparent ceramics in the present work. This is in line with the recent studies [START_REF] Khalil | Biosynthesis of iron oxide (Fe2O3) nanoparticles via aqueous extracts of Sageretia thea (Osbeck.) and their pharmacognostic properties[END_REF][START_REF] Matinise | Green synthesis of novel zinc iron oxide (ZnFe2O4) nanocomposite via Moringa Oleifera natural extract for electrochemical applications[END_REF] focusing on similar materials.

Conclusions

We report on fabrication of a series of highly transparent cobalt-doped zinc aluminate spinel (gahnite) ceramics -Co 2+ :ZnAl2O4. For this, we employed a modified approach with the following features: (i) an original way of fabrication of the precursor nanopowders by using zinc formate as a source of zinc and an aqueous solution of zinc fluoride as a sintering additive. The first detail allowed us to reduce the temperature and time of calcination of powders (as formate easily decomposes at 250-300 °C) without carbonization of the powder (formate does not contain C-C bonds). The second detail is the preparation of the precursor using solutions of metal sources together with an aqueous solution of the sintering additive (ZnF2), which eliminates the need for additional steps for its introduction at later stages. Such principles have never been used before for ZnAl2O4 transparent ceramics; (ii) an optimum temperature of powder calcination (700 ºC) determined from thermal studies and reducing losses of the sintering additive (ZnF2), (iii) the particular temperature of hot-pressing (1520 °C) to produce transparent ceramics. With this improved chemical way, we obtained ceram-ics with excellent transparency close to the theoretical limit and suitable microstructure (relatively small grains, clear grain boundaries and the lack of μm-sized pores).

We determined that the concentration of Co 2+ ions in Td sites in the ceramic specimens is lower than the initial concentration in the precursor powders and, furthermore, it decreases with the ZnF2 content. This is ascribed to two main reasons: (i) accommodation of Co 2+ ions in octahedral sites (inversion of spinel structure) and the loss of Co 2+ via evaporation of an intermediate phase of CoF2. A linear variation of the tetrahedral Co 2+ concentration with the ZnF2 content allowed us to control precisely the absorption at around ~1.5 μm (the 4 A2( 4 F) → 4 T1( 4 F) transition of IV Co 2+ ions) without deterioration of optical quality of ceramics. The latter is of practical importance for development of ceramic saturable absorbers for eye-safe erbium lasers. Further efforts should be applied on revealing the effect of octahedral Co 2+ ions on nonlinear properties of Co:ZnAl2O4 ceramics (e.g., via non-saturable losses).

List of figure captions

Fig. 1 .

 1 Fig.1. Thermal evolution of the 0.1 at.% Co:ZnAl2O4 / 6 wt% ZnF2 precursor: thermal gravimetric analysis (TGA) mass loss curve (black) and differential thermal analysis (DTA) curve (blue) measured under heating in air.

Fig. 2 .

 2 Fig. 2. X-ray diffraction (XRD) patterns of the powders doped with 0.1 at.% Co and 6 wt% ZnF2 annealed at 300, 500, 700 and 900 °C. Circles indicate the diffraction peaks of ZnAl2O4, asterisks -ZnO.

Fig. 3 .

 3 Fig. 3. Photographs of transparent ceramics sintered at 1520 °C for 4 h from 0.02 at.% Co (upper raw) and 0.1 at.% Co (lower raw) doped ZnAl2O4 powders with 3, 6 or 10 wt% ZnF2.

Fig. 4 .

 4 Fig. 4. X-ray powder diffraction (XRD) patterns of ceramic samples prepared from powders containing 0.1 at.% Co and 3 / 10 wt% ZnF2, numbers denote the Miller's indices (hkl), red peaksdiffraction peaks for undoped ZnAl2O4 (ICSD card #9559).

Fig. 5 .

 5 Fig. 5. Scanning Electron Microscope (SEM) images of a fracture surface of ceramics produced from powders containing 0.1 at.% Co and (a) 3 wt% ZnF2 and (b) 10 wt% ZnF2.

Fig. 6 .

 6 Fig. 6. (a) Grain size distribution for ceramics produced from powders containing 0.02 at.% Co and 3, 6 or 10 wt% ZnF2; (b) Mean grain size vs. the ZnF2 concentration in the precursor powders.

Fig. 7 .

 7 Fig. 7. EDX spectra for ceramics prepared from powders containing 0.1 at.% Co and 3-10 wt% ZnF2.

Fig. 8 .

 8 Fig. 8. EDX mapping for ceramics prepared from powders containing 0.1 at.% Co and 10 wt% ZnF2: (a) SEM image of the fracture surface, (c-f) the corresponding element maps: (b) Al, (c) O, (d) Zn, (e) F and (f) Co.

Fig. 9 .

 9 Fig. 9. Raman spectra of Co:ZnAl2O4 transparent ceramics (the spectra are shifted for the sake of comparison), λexc = 514 nm.

Fig. 10 .

 10 Fig. 10. In-line transmission spectra of laser-grade polished Co:ZnAl2O4 ceramic disks (thickness: 2 mm): (a) transmission of as-sintered samples; (b) effect of annealing on transmission in the UV and visible of ceramics prepared from powders doped with 0.1 at.% Co and 3 wt% ZnF2. Numbers in (b) indicate the peak wavelengths.

Fig. 11 .

 11 Fig. 11. (a) Tanabe-Sugano diagram of energy levels of d 7 tetrahedral complexes (for C/B = 4.50), vertical dashed line marks the case of Co 2+ :ZnAl2O4; (b) crystal-field splitting of Co 2+ ions in ZnAl2O4 and MgAl2O4 crystals (after [25,65]). Green arrows indicate the observed transitions in emission.

Fig. 12 .

 12 Fig. 12. Analysis of the 4 A2( 4 F) → 4 T1( 4 F) absorption transition of Co 2+ ions in Td sites in Co:ZnAl2O4 ceramics: (a) absorption spectra; (b) variation of absorption coefficient αabs at ~1.54 μm with the ZnF2 concentration in the precursor: dashed linesexpected absorption calculated from the GSA cross-section and the nominal Co 2+ concentration.

Fig. 13 .

 13 Fig. 13. Luminescence of Co:ZnAl2O4 transparent ceramics: (a) spectra of nonannealed samples; (b) effect of annealing on the luminescence spectra of ceramics prepared from powders doped with 0.02 / 0.1 at.% Co and 3 wt% ZnF2; (c) details of impurity and defect emissions for ceramics prepared from powders doped with 0.02 at.% Co and 3 wt% ZnF2, numbers indicate the peak wavelengths. λexc = 514 nm.

Fig. 14 .

 14 Fig. 14. Luminescence decay curves of Co:ZnAl2O4 transparent ceramics prepared from powders doped with 0.1 at.% Co and 3-10 wt% ZnF2 (semi-log plots): circlesexperimental data, solid linestheir single-exponential fits, τslow luminescence lifetime. λexc = 405 nm (ps pulses), λlum ~ 650 nm.

Table 1 .

 1 Concentration of Co 2+ ions in tetrahedral (Td) sites in Co:ZnAl2O4 initial powders and transparent ceramics (determined from the spectroscopic data).

	Material Content of Co Initial powders ZnF2, wt% 3-10 0.02 (0.303×10 19 )	0.10 (1.514×10 19 )
	Ceramics	3	0.011 (0.17×10 19 )	0.050 (0.76×10 19 )
		6	0.010 (0.15×10 19 )	0.052 (0.64×10 19 )
		10	0.007 (0.10×10 19 )	0.037 (0.56×10 18 )

2+

in Td sites, at.% (cm -3 )

Acknowledgements

This study was funded by RFBR (Russian Foundation for Basic Research, Russia) according to the research project No. 18-33-00152 and by Russian Science Foundation (Agreement No. 18-13-00200). The study of thermal evolution of the precursor and its phase purity was carried out on the equipment of the Collective Usage Center "New Materials and Resource-saving Technologies" (Lobachevsky State University of Nizhny Novgorod, Russia). O.D. acknowledges partial financial support from RFBR (Project No. 19-03-00855). EDX studies were performed at Interdisciplinary Resource Center for Nanotechnology of Research Park of Saint-Petersburg University.


M L Cortés

W Rodriguez

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F Nowacki

K Ogata

A Poves

T R Rodríguez

A Schwenk

J Simonis

S R Stroberg

K Yoshida

L Achouri

H Baba

F Browne

D Calvet

F Château

S Chen

N Chiga

A Corsi

A Delbart

J.-M Gheller

A Giganon

A Gillibert

C Hilaire

T Isobe

T Kobayashi

Y Kubota

V Lapoux

H N Liu

T Motobayashi

I Murray

H Otsu

V Panin

N Paul

H Sakurai

M Sasano

D Steppenbeck

L Stuhl

Y L Sun

Y Togano

T Uesaka

K Wimmer

K Yoneda

O Aktas

T Aumann

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F Flavigny

S Franchoo

I Gašpari Ć Aa

R.-B Gerst Ab

J Gibelin

K I Hahn Ac

D Kim

T Koiwai

Y Kondo

P Koseoglou

J Lee Ae

C Lehr

B D Linh

T Lokotko Ae

M Maccormick

K Moschner Ab

T Nakamura

S Y Park Ac

D Rossi

E Sahin Af

D Sohler Ag

P.-A Söderström

S Takeuchi

H Toernqvist

V Vaquero Ah

V Wagner

S Wang

V Werner

X Xu Ae

H Yamada Ad

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M Yasuda

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D F Geesaman

Shell evolution of N = 40 isotones towards 60 Ca: First spectroscopy of 62 Ti

Keywords:

HAL is

Excited states in the N = 40 isotone 62 Ti were populated via the 63 V(p, 2p) 62 Ti reaction at ∼200 MeV/nucleon at the Radioactive Isotope Beam Factory and studied using γ -ray spectroscopy. The energies of the 2 + 1 → 0 + gs and 4 + 1 → 2 + 1 transitions, observed here for the first time, indicate a deformed 62 Ti ground state. These energies are increased compared to the neighboring 64 Cr and 66 Fe isotones, suggesting a small decrease of quadrupole collectivity. The present measurement is well reproduced by large-scale shell-model calculations based on effective interactions, while ab initio and beyond mean-field calculations do not yet reproduce our findings. The shell-model calculations for 62 Ti show a dominant configuration with four neutrons excited across the N = 40 gap. Likewise, they indicate that the N = 40 island of inversion extends down to Z = 20, disfavoring a possible doubly magic character of the elusive 60 Ca.

© 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP 3 .

Our understanding of atomic nuclei largely derives from the concept of nuclear shell structure. Within this picture, the arrangement of nucleons inside the nucleus can be explained by the filling of discrete energy levels. Sizable gaps between these orbits disfavor the population of the higher-energy levels, and are interpreted as closed shells, which give rise to magic numbers. Such shell closures can be evidenced by a relatively high-lying first excited 2 + state, a relatively small electric quadrupole transition probability to the ground state, B(E2)↓, and a steep decrease of the separation energy. Experimental evidence collected in the last decades, particularly since the advent of radioactive ion beams, has shown that shell structure undergoes significant changes for isotopes far from stability [1]. Examples of these changes are the appearance of new magic neutron numbers at N = 32, 34 in the Ca isotopes and neighboring isotopic chains [2][3][4][5][6][7][8][9], and at N = 16 for O isotopes [10][11][12], as well as the disappearance of the shell closure at N = 8 [13][14][15][16], N = 20 [17,18] and N = 28 [19,20] in various neutron-rich isotopes.

Given that N = 40, which corresponds to the filling of the neutron pf shells, is a harmonic oscillator magic number, the study of the structure of N = 40 isotones can provide insight into the mechanisms governing shell evolution. Indeed the characteristics of this isotonic chain vary with the number of protons. For 68 Ni ( Z = 28), a high E(2 + 1 ) energy and a low B(E2)↓ have been observed [21]. However, due to the parity change between the pf shell and the g 9/2 orbit, the 2 + 1 state involves at least two neutrons across N = 40. Such a neutron-dominated excitation could result in a large E(2 + 1 ) energy and low B(E2)↓ value without a large shell gap [22]. For the neutron-rich Fe ( Z = 26) and Cr ( Z = 24) isotopes, a monotonous decrease of the E(2 + 1 ) when approaching N = 40 and beyond has been observed [23][24][25][26]. This decrease indicates a rapid development of collectivity when removing protons from the f 7/2 shell. In contrast, the measurement of the E(2 + 1 ) of 58,60 Ti ( Z = 22) only showed a moderate decrease towards N = 40 [27,28]. The very exotic 60 Ca ( Z = 20), where the Ca isotopic chain meets the N = 40 isotones, is a key nucleus for shell evolution [START_REF]Perspectives in Nuclear Physics[END_REF][START_REF]Reaching for the Horizon[END_REF], but difficult to reach experimentally. Only recently its existence has been established [START_REF] Tarasov | [END_REF], supporting theoretical predictions for a bound 70 Ca. However, the heaviest Ca isotope with known spectroscopic information is 54 Ca [4].

Theoretical calculations in the shell-model framework [32] concluded that the development of collectivity in N = 40 nuclei is due to quadrupole correlations that give rise to deformed ground states, dominated by intruder neutron orbits beyond the pf shell.

This leads to an island of inversion below 68 Ni, similar to the one formed around 32 Mg [32]. These calculations predict an increase in the E(2 + 1 ) energy of the more exotic N = 40 isotones 62 Ti and 60 Ca, while conserving the intruder character in the ground state.

On the other hand, symmetry conserving configuration mixing calculations with the Gogny interaction predict a conservation of the N = 40 gap [33]. These results agree with calculations performed using the five-dimension collective Hamiltonian, which suggest an energy gap of about 4 MeV at N = 40, predicting spherical 62 Ti and 60 Ca [34,35]. It is noted that the beyond-mean-field and the shell model calculations provide similar results for 64 Cr and 66 Fe, while they substantially diverge for 60 Ca and 62 Ti. Therefore, spectroscopy of 62 Ti offers a crucial test between the two different pictures. In addition, the properties of Ca isotopes have been extensively studied with coupled-cluster theory [36] and valenceshell interactions [3,37], in both cases using two-nucleon (NN) and three-nucleon (3N) interactions from chiral effective field theory. Such calculations agree well with experimental energy levels and binding energies up to 54 Ca, and predict the drip line to be located around 60 Ca. This is in contrast to density functional theories based on the mean field approach which predict, depending on the selected interaction, Ca isotopes to be bound up to A = 68 -76.

Beyond N = 40, coupled-cluster theory suggests the existence of two-neutron halos and Efimov states in 62 Ca [38].

Clearly, spectroscopic information on exotic isotopes around 60 Ca is necessary to deepen our understanding of the nuclear structure at N = 40 and to benchmark the theoretical predictions towards the neutron drip line. In the present work, the first spectroscopy of 62 Ti is presented. This isotope represents the closest nucleus to 60 Ca for which spectroscopic studies can be performed at existing radioactive beam facilities.

The experiment was carried out at the Radioactive Isotope Beam Factory, operated by the RIKEN Nishina Center and the Center for Nuclear Study of the University of Tokyo. A primary beam of 70 Zn with an energy of 345 MeV/nucleon and an average intensity of 240 pnA was fragmented on a 3-mm thick Be target to produce a cocktail of secondary beams which included 63 V. The fragments of interest were selected with the Bρ -E -Bρ technique using two wedge-shaped aluminium degraders situated at the dispersive focal planes of BigRIPS [39]. Event-by-event identification was performed by an energy loss measurement in an ionization chamber, position and angle measurements in parallel plate avalanche counters at different focal planes, and the time-of-flight measured between two plastic scintillators. The 63 V isotopes were delivered to the focus area in front of the SAMURAI dipole magnet [40], with an average intensity of 3 pps and an average energy of 239 MeV/nucleon. At this location the MINOS device [41], composed of a 151.3(13) mm long liquid hydrogen target surrounded by a Time Projection Chamber (TPC), was placed. The efficiency of MINOS to detect at least one proton was measured as 93(4)% and the resolution for the vertex reconstruction was estimated to be better than 2 mm (σ ) [42]. Following proton knockout reactions in the liquid hydrogen target, the 62 Ti fragments had an average energy of 154 MeV/nucleon and were identified using the SAMU-RAI dipole magnet and associated detectors [40]. Fig. 1 shows the particle identification obtained with SAMURAI when selecting 63 V as incoming beam. A total of 1880 events corresponding to the 63 V(p, 2p) 62 Ti reaction was reconstructed. The transmission of the unreacted 63 V beam along the beam line was measured to be 50.9 (11)% and the inclusive (p, 2p) cross section was determined to be 4.0(1) mb.

MINOS was surrounded by the high-efficiency γ -ray detector array DALI2 + , composed of 226 NaI(Tl) detectors covering angles between ∼15 • and ∼118 • with respect to the center of the target [43,44]. The array was energy calibrated using standard 60 Co, 88 Y, 133 Ba, and 137 Cs sources. The full-energy-peak efficiency of the array was determined using a detailed GEANT4 [45] simulation and was found to be 30% at 1 MeV with an energy resolution of 11% for a source moving at 0.6c. Doppler corrected γ -ray spectra were obtained using the reaction vertex and the velocity of the fragment reconstructed with MINOS. Peak-to-total ratio and detection efficiency improved by adding-up the energies of γ -rays deposited in detectors up to 10 cm apart. To avoid the reconstruction of add-back events from the large atomic background, γ -rays with energies below 100 keV were not taken into account in the analysis. The Doppler corrected spectrum obtained for the 63 V(p, 2p) 62 Ti reaction is displayed in Fig. 2a). Two peaks are clearly visible and the γγ coincidence analysis demonstrates their coincidence (Fig. 2b). Using a 2-dimensional χ 2 minimization, the energies of the transitions were deduced to be 683 (10) keV and 823 (20) keV. In this minimization procedure, the simulated response of DALI2 + to transitions of different energies were fitted in steps of 5 keV to the experimental data and the χ 2 value was obtained for each combination of energies. The simulation included the experimental resolution of each crystal and a double exponential background was assumed for the fit. The parameters of these exponential functions were chosen based on a consistent analysis of the spectra of proton knockout reactions producing 50 Ar and 60 Ti. The errors on the Fig. 2. a) Doppler corrected γ -ray spectrum of 62 Ti obtained from proton knockout from 63 V. The spectrum was fitted by the convolution of the simulated response of DALI2 + to the observed transitions and a double exponential background. Two additional transitions are included to improve the fit (see text for details). b) Coincidence spectrum obtained when applying the gate indicated by the blue area. transition energies include the statistical error from the fit, as well as the systematic error arising from the calibration of the γ -ray detectors and the possible lifetime of the states. Given that global systematic fits [46] suggest a lifetime of the 2 + 1 state below 30 ps, an uncertainty of 15 ± 15 ps was considered for the decay of the 2 + 1 , while the 4 + 1 was considered short lived. The best total fit as well as the individual response functions of DALI2 + are shown in Fig. 2. The relative intensities of the peaks suggest the tentative assignment of the 683 (10) keV and the 823 (20) keV peaks to the 2

+ 1 → 0 + gs and 4 + 1 → 2 + 1 transitions, respectively.
A structure in the γ -ray spectrum above the estimated background was observed between 1000 and 1500 keV. Two additional transitions at energies of 1222 (37) keV and 1328 (45) keV, were used to reproduce this structure. The significance levels of these peaks are 2σ and 3σ , respectively. The inclusion of more transitions did not provide any further improvement on the χ 2 of the fit. A structure at 320 keV was observed with a significance level of 1σ . The existence of this peak could not be firmly established, therefore it was not considered, and its possible contribution to the partial cross section was assumed to be within the error bars of the analysis. These possible transitions indicate the presence of different states being populated in the reaction, but the limited resolution of DALI2 + and the low statistics did not allow to identify them nor to perform a coincidence analysis. The existence of such transitions, which potentially feed the 2 + 1 or 4 + 1 states, implies a fragmented spectroscopic strength.

Exclusive cross sections to populate the (2 + 1 ) and (4 + 1 ) states, from which additional feeding should be subtracted, were calculated based on the fitted γ -ray intensities, the total transmission of the isotopes and the efficiency of MINOS. Cross sections of 1.5(3) mb and 0.8(1) mb were obtained for the (2 + 1 ) state and the (4 + 1 ) state, respectively. The cross sections measured for the possible transitions at 1222 (37) keV and 1328 (45) keV were determined to be 0.2(1) mb and 0.3(1) mb, respectively. As no firm statement can be made regarding these transitions, we limit the interpretation to their possible direct feeding to the 2 + 1 state. For this, the average value between 100% feeding and no feeding was considered and the error increased to cover both possibilities, giving a exclusive cross section of 1.3(4) mb for the (2 + 1 ) state. The evolution of measured E(2 + 1 ) and E(4 + 1 ) energies for the N = 40 isotones between Ti and Ge [47] is presented in Fig. 3.

The E(2 + 1 ) and E(4 + 1 ) reported in this Letter for 62 Ti have a similar value than the ones measured for 66 Fe, higher than those of 64 Cr. It is pointed out that 64 Cr, with a E(2 + 1 ) of 420 keV, has the largest quadrupole deformation observed in the region [26,48]. Our results show the first increase of E(2 + 1 ) along the N = 40 isotones towards 60 Ca. This increase establishes a parabolic trend and suggests a decrease in quadrupole collectivity. This, in turn, could be interpreted as a sign of a significant N = 40 shell gap, and gives the possibility of a doubly magic character for 60 Ca.

Large Scale Shell Model (LSSM) calculations, shown by the black lines in Fig. 3, were carried out with the LNPS interaction [32] using a 48 Ca core and a valence space which included the full pf shell for protons and the 0 f 5/2 , 1p 3/2 , 1p 1/2 , 0g 9/2 , and 1d 5/2 orbits for neutrons. This interaction has already successfully reproduced the E(2 + 1 ) of the heavier N = 40 isotones [32]. The LSSM calculations reproduce very accurately the data for both the E(2 + 1 ) and E(4 + 1 ) of the N = 40 isotones including our values for 62 Ti. This agreement strengthens the tentative spin and parity assignment for these states. As shown in Ref. [32], the calculations predict a reduction of the 0 f 5/2 -0g 9/2 gap when going from 68 Ni to 60 Ca, as well as the closeness of the quadrupole partner orbits 0g 9/2 and 1d 5/2 . Due to this proximity, quadrupole correlations produce a gain in energy that largely overcomes the cost of exciting neutrons across the N = 40 gap, thereby favoring manyparticle-many-hole configurations. This situation resembles the behavior at N = 20 and suggests an island of inversion for N = 40 isotones below 68 Ni. For 62 Ti, a gap of about 1 MeV is predicted, with a resulting wave function dominated 4p-4h excitations (63%) and significant 6p-6h component (22%) [32]. Furthermore, a ground-state deformation parameter β = 0.28 for 62 Ti is obtained. The agreement with the measured energies of the N = 40 isotones, including 62 Ti, indicates that the island of inversion in this region extends down to 60 Ca. It is particularly remarkable that although the E(2 + 1 ) for 60 Ca is predicted to be 1.35 MeV, which represents an increase with respect to the neighboring isotones, a 4p-4h configuration dominance (59%) prevails [32]. Symmetry conserving configuration mixing (SCCM) calculations using the Gogny D1S effective interaction [49,50] were performed for 62 Ti, 64 Cr, and 66 Fe, and are indicated by the blue lines in Fig. 3. For the calculations, each individual nuclear state was defined as the linear combination of multiple intrinsic many-body states with different quadrupole (axial and triaxial) shapes [51,33]. Cranked or octupole deformed states were not included, therefore, a systematic stretching of the levels with respect to the experimental values is expected [52,53]. The E(2 + 1 ) predicted for 64 Cr and 66 Fe lie very close to the LSSM predictions, and are in fair agreement with the experimental data. However, when going to 62 Ti, a more abrupt increase of the E(2 + 1 ) is obtained. For the E(4 + 1 ) energies, the calculations overestimate the experimental values by about 500 keV, although the minimum value for 64 Cr is maintained. It is noted that for 64 Cr and 66 Fe, where the deformation is well described by the model, the inclusion of cranking would further improve the agreement with the experimental data. Within this model, the energy gap at N = 40 is conserved, leading to a ground state of 62 Ti highly mixed with the spherical configuration. This is also the case for 60 Ca, which is predicted as a doubly magic nucleus with an E(2 + 1 ) of 4.73 MeV [53]. It is noted that although this calculation yields a spherical ground state for 62 Ti, the 2 + 1 and 4 + 1 states belong to a deformed band starting at the 0 + 2 state. This band can correspond to the predictions of the LSSM calculations and indicate that the SCCM calculations overestimate the N = 40 gap in this region.

Ab initio valence-space in-medium similarity renormalization group (VS-IMSRG) [54][55][56][57][58] calculations were also performed for 62 Ti, 64 Cr, and 66 Fe, as shown by the red lines in Fig. 3. The chiral NN+3N interaction labeled 1.8/2.0 (EM) in Refs. [59,60] was used, which is based on the NN potential from Ref. [61] and 3N forces fitted to light systems up to 4 He only. With this NN+3N interaction, ground-state energies up to Sn [58,59,62,63] are generally well reproduced. As the VS-IMSRG captures 3N forces between valence nucleons via an ensemble normal ordering [57], a separate valence-space interaction is decoupled for each nucleus of interest. Here, the same model space as the LNPS Hamiltonian is considered (adding the 2s 1/2 neutron orbital for 62 Ti). Using the Magnus formulation of the IMSRG [64], operators at the two-body level are truncated in the so-called IMSRG(2) approximation. The VS-IMSRG interaction is diagonalized with the code ANTOINE [65], including, for the first time in the VS-IMSRG, both intruder quadrupole partners, such as 0g 9/2 -1d 5/2 [66]. The VS-IMSRG overestimates the E(2 + 1 ) and E(4 + 1 ) excitation energies in 62 Ti, 64 Cr, and 66 Fe, predicting all states as spherical. Cross-shell excitations to the 0g 9/2 -1d 5/2 orbits stay at the 1p-1h level because of the substantial N = 40 shell gap, 3.7 MeV in 62 Ti. Within this model, a E(2 + 1 ) of around 7 MeV is predicted for 60 Ca, an overestimation which is also observed at other shell closures with the VS-IMSRG [59,63,67]. This limitation has been related to the IMSRG(2) truncation [66], which may not fully capture correlations associated with cross-shell excitations. Preliminary comparisons with coupled-cluster theory indicate that keeping operators at the three-body level will improve the results. Also, choosing a deformed reference state, instead of spherical as in the present work, may capture quadrupole correlations more efficiently [68,69]. Single-particle theoretical cross sections were computed in the DWIA framework [70]. The single-particle wave functions and the nuclear density were obtained by the Bohr-Mottelson singleparticle potential [71]. The optical potentials for the distorted waves in the initial and final channels were constructed by the microscopic folding model [72] with the Melbourne G-matrix interaction [73] and with the calculated nuclear density. The spinorbit part of each distorting potential was disregarded. As for the transition interaction, the Franey-Love effective proton-proton interaction was adopted [74]. Cross sections at different beam energies, from 240 MeV/nucleon at the entrance of the target to 154 MeV/nucleon at the exit, were calculated and weighted according to the energy loss in the target. Theoretical cross sections (σ theo ) were obtained by weighting the single particle cross sections by the calculated spectroscopic factors.

The spin and parity of the ground state of 63 V are not known experimentally. The LSSM calculation suggests it to be 3/2 -, although states with spin and parity of 5/2 -and 7/2 -appear very close in energy, suggesting the presence of isomeric states. No ex-

Table 1

Experimentally deduced excitation energies and cross sections for 62 Ti following the 63 V(p, 2p) 62 Ti reaction, and comparison with theoretical cross sections obtained with the LSSM calculation. The spectroscopic factors and corresponding cross sections are shown for the three possible values of the spin and parity of the ground state of 63 V. The experimental ground-state cross section was calculated by subtracting the cross sections of the measured transitions from the inclusive cross section. perimental evidence of such states has been reported so far and available data are consistent with a 3/2 -assignment [75]. Results of the calculations for the three cases are shown in Table 1, and displayed in Fig. 4, together with the experimental results. It can be seen that neither the absolute value or the general trend shown by the data are reproduced by the calculation in any scenario. The calculation for the ground state of J π = 3/2 -resembles better the experimental data in terms of the number of states that are populated, while for the cases of J π = 5/2 -and J π = 7/2 - a considerable population of the 6 + 1 state would be expected. In particular for the case of J π = 7/2 -a population of the 6 + 1 state higher than the one of the 2 + 1 state would be expected, at odds with the experimental result. It is noted that the calculated spectroscopic factors add up to less than half of the total strength in the three cases. Therefore, population of higher lying states is expected by the calculations. Such a scenario would lead to unobserved transitions feeding the 4 + 1 or the 2 + 1 states directly, which can account for the excess of the measured cross section in comparison with the calculations. Although not in good agreement, the low measured and calculated partial cross sections, as well as the apparent fragmentation of the spectroscopic strength, are consistent with the collective nature of the 62 Ti ground state discussed in this work. However, the large error bars prevent a firmer conclusion.

E (keV) σ exp (mb) E (keV) J π l j σ s.p (mb) J π = 3/2 - J π = 5/2 - J π = 7/2 - C 2 S σ theo (mb) C 2 S σ theo (mb) C 2 S σ theo (mb) 0 1 . 4 ( 4 ) 0 0 + 1 p 3/
In summary, first spectroscopy of 62 Ti was obtained by means of the 63 V(p, 2p) 62 Ti reaction at ∼200 MeV/nucleon. Transitions at 683 (10) keV and 823 (20) keV were assigned to the decay of the 2 + 1 and 4 + 1 states at 683 (10) keV and 1506 (22) keV, respectively. Our result shows for the first time an increase of the E(2 + 1 ) for N = 40 isotones towards 60 Ca. LSSM calculations were in good agreement with the experimental findings. The calculations suggest that although the collectivity decreases approaching 60 Ca, with an ensuing increase of E(2 + 1 ), quadrupole correlation contributions remain and lead to the extension of the N = 40 island of inversion down to 60 Ca. SCCM calculations overestimate the measured E(2 + 1 ) and E(4 + 1 ) of 62 Ti, predicting a doubly magic character of 60 Ca and a weakly deformed ground state in 62 Ti, at variance with the LSSM calculations. For these calculations the N = 40 spherical gap is too large to produce the inversion between the quasi-spherical and deformed 0 + states. VS-IMSRG calculations, which provide a good description of excited states in Ca isotopes, largely overestimate the E(2 + 1 ) and E(4 + 1 ) energies of 62 Ti, even after the inclusion of the neutron 0g 9/2 , 1d 5/2 and 2s 1/2 orbitals. The spectroscopic information presented in this Letter offers an important benchmark for our understanding of nuclear structure approaching 60 Ca and the location of the neutron drip line.

Fig. 1 .

 1 Fig.1. Particle identification plot for the outgoing fragments measured with the SAMURAI dipole magnet and related detectors. Incoming 63 V isotopes were selected with BigRIPS.62 Ti isotopes are indicated by the ellipse.

Fig. 3 .

 3 Fig. 3. Systematics of E(2 + 1 ) (filled symbols) and E(4 + 1 ) (open symbols) for eveneven N = 40 isotones. The circles represent the present measurement. The black, blue, and red lines represent LSSM, SCCM, and VS-IMSRG calculations, respectively (see text for details).

Fig. 4 .

 4 Fig. 4. Partial proton removal cross sections for the 63 V(p, 2p) 62 Ti reaction. Panel a) shows the experimental results. Panels b) to d) show LSSM calculations using the LNPS interaction assuming the ground state of 63 V as 3/2 -, 5/2 -and 7/2 -, respectively.

We thank the RIKEN Nishina Center accelerator staff and the Bi-gRIPS team for the stable operation of the high-intensity Zn beam and for the preparation of the secondary beam setting. K.O. acknowledges the support by Grant-in-Aid for Scientific Research of the Japan Society for the Promotion of Science (JSPS) JP16K05352. A.P. is supported in part by the Ministerio de Ciencia, Innovación y Universidades (Spain), Severo Ochoa Programme SEV-2016-0597 and grant PGC-2018-94583. F.B. is supported by the RIKEN Special Postdoctoral Researcher Program. L.X.C. and B.D.L. would like to thank the Vietnam Ministry of Science and Technology (MOST) for its support through the Physics Development Program Grant No. ÐTÐLCN.25/18. I.G. has been supported by HIC for FAIR and Croatian Science Foundation under projects no. 1257 and 7194. D. So. was supported by the the European Regional Development Fund contract No. GINOP-2.3.3-15-2016-00034 and the National Research, Development and Innovation Fund of Hungary via Project No. K128947. V.V. acknowledges support from the Spanish Ministerio de Economía y Competitividad under Contract No. FPA2017-84756-C4-2-P. K.I.H., D.K. and S.Y.P. acknowledge the support from the National Research Foundation of Korea grant No. 2018R1A5A1025563 and 2019M7A1A1033186. The development of MINOS was supported by the European Research Council through the ERC Grant No. MINOS-258567. This work was also supported by the JSPS KAKENHI Grant No. 18K03639, MEXT as "Priority issue on post-K computer" (Elucidation of the fundamental laws and evolution of the universe), the Joint Institute for Computational Fundamental Science (JICFuS), the CNS-RIKEN joint project for large-scale nuclear structure calculations, Natural Sciences and Engineering Research Council (NSERC) of Canada, the Deutsche Forschungsgemeinschaft -Projektnummer 279384907 -SFB 1245, the PRISMA Cluster of Excellence, and the BMBF under Contracts No. 05P18RDFN1 and 05P19RDFN1. TRIUMF receives funding via a contribution through the National Research Council Canada. Computations were performed at the Jülich Supercomputing Center (JURECA).


Pavel Loiko

Esrom Kifle

Lauren Guillemot

Jean-Louis Doualan

Florent Starecki

Alain Braud

Magdalena Aguiló

Francesc Díaz

Valentin Petrov

Xavier Mateos

Patrice Camy
email: patrice.camy@ensicaen.fr

Watt-Level Thulium Laser Operating on the 3 H 4 → 3 H 5 Transition with ~70% Slope Efficiency

A Thulium laser operating on the 3 H 4 → 3 H 5 transition in high-phonon-energy KLu(WO 4 ) 2 generates 1.12 W at 2.22&2.29 μm with a record-high slope efficiency of 69.2% representing a twofor-one pump process through efficient energy-transfer upconversion.

Introduction

Coherent light sources operating at 2.3 μm (short-wave infrared, SWIR) are of practical importance for gas sensing, optical metrology of combustion processes and non-invasive glucose blood measurements. One possibility for obtaining such emission is the 3 H 4 → 3 H 5 electronic transition of the Tm 3+ ion in glasses and crystals [START_REF] Soulard | 2.3 μm Tm 3+ :YLF mode-locked laser[END_REF]. The interest to this transition was promoted by the recent demonstration of mode-locked 2.3 μm Tm lasers [START_REF] Canbaz | Kerr-lens mode-locked 2.3-μm Tm 3+ :YLF laser as a source of femtosecond pulses in the midinfrared[END_REF][START_REF] Loiko | Efficient Tm:LiYF 4 lasers at ~2.3 μm: Effect of energy-transfer upconversion[END_REF]. At a glance, the 3 H 4 → 3 H 5 laser scheme is inefficient because of the self-quenching of the upper laser level ( 3 H 4 ) by cross-relaxation (CR) and non-radiative (NR) relaxation in high-phonon-energy materials. Recently, we have shown that the slope efficiency of 2.3 μm Tm lasers may exceed the Stokes limit owing to the energy-transfer upconversion (ETU) [START_REF] Guillemot | Close look on cubic Tm:KY 3 F 10 crystal for highly efficient lasing on the 3 H 4 → 3 H 5 transition[END_REF].

In the present work, we demonstrate the first Tm laser operating on the 3 H 4 → 3 H 5 transition based on a highphonon-energy host material and study the effect of Tm doping level on its performance.

Spectroscopy

As a gain material, we selected the monoclinic Tm:KLu(WO 4 ) 2 crystal. It features a maximum phonon frequency hν ph of ~907 cm -1 . The stimulated-emission (SE) cross-section, σ SE , for the 3 H 4 → 3 H 5 transition was determined using the Füchtbauer-Ladenburg formula for the principal light polarizations of this optically biaxial crystal, E || N p , N m and N g , Fig. 1(a). The maximum σ SE is 1.78×10 -20 cm 2 at 2289 nm and the corresponding emission bandwidth (FWHM) is 32.1 nm for E || N m . The scheme of the Stark splitting of the upper and lower multiplets is shown in Fig. 1(b).

The dependence of the luminescence lifetime of the upper laser level ( 3 H 4 ) on the Tm doping level was analyzed yielding the intrinsic lifetime τ 30 = 0.24 ms and the concentration-independent CR parameter C CR = 2.70×10 -37 cm 6 s -1 .

Laser Operation

For the laser experiments, we used three uncoated N g -cut Tm:KLu(WO 4 ) 2 crystals doped with 0.5, 1.5 or 3.0 at.% Tm. As a pump source, we employed a Ti:Sapphire laser tuned to 793.8 nm (pump polarization: E P || N p ). The pumping was in quasi-CW regime (duty cycle: 1:2). A simple near-hemispherical cavity was constructed by a flat pump mirror coated for high transmission (HT) at ~0.79 μm and for high reflection (HR) at 2.12-2.50 μm, and a set of concave output couplers (OCs) with a radius of curvature of -100 mm and a transmission T OC of 0.1%, 0.7%, 1.3% or 4.0% at 2.18-2.35 μm. To suppress the unwanted 3 F 4 → 3 H 6 transition, the OCs had HT (T > 90%) at 1.80-1.98 μm. The pump spot diameter in the focus was 65±10 μm. For the 3 at.% Tm doped laser crystal, the pump absorption (double-pass) under lasing conditions reached 86.1% -79.4%, depending on the OC (including Fresnel losses at the uncoated crystal surfaces).

The 3 at.% Tm doped crystal generated a maximum peak output power of 1.12 W at ~2.22 and 2.29 µm with a slope efficiency η of 69.2% (vs. the absorbed pump power), Fig. 2(a). The laser threshold was at 0.45 W and the optical-to-optical efficiency, calculated vs. the pump power incident on the crystal reached 44.4% (T OC = 1.3%). The laser emission was linearly polarized (E || N m ). The emission spectra were dependent both on the output coupling and the pump power, Fig. 2(b). All the observed laser lines were assigned according to the crystal-field splitting of the 3 H 4 and 3 H 5 multiplets, Fig. 1(b). The beam profile, Fig. 2(c), was slightly multimode with the measured M 2

x,y factors were 2.2±0.1 and 2.6±0.1, respectively. The performance of the Tm laser gradually improved with increasing the Tm doping from 0.5 to 3.0 at.%, Fig. 3(a). The pump quantum efficiency η q (the number of excitations to the upper laser level, 3 H 4 , per number of absorbed pump photons) was calculated according to the model from [START_REF] Guillemot | Close look on cubic Tm:KY 3 F 10 crystal for highly efficient lasing on the 3 H 4 → 3 H 5 transition[END_REF] using the passive losses L determined from the Findlay-Clay analysis, Fig. 3(b). For the 3 at.% Tm doped crystal, η q reached 1.7±0.2 well above the laser threshold representing an almost "two-for-one" pump process which is assigned to efficient ETU, 3 F 4 + 3 F 4 → 3 H 6 + 3 H 4 , refilling the upper laser level manifold, Fig. 3(с). The rate-equation modeling of the laser performance supported this conclusion.

Conclusions

To conclude, we report on a watt-level Tm:KLu(WO 4 ) 2 laser operating on the 3 H 4 → 3 H 5 transition with a record-high slope efficiency of ~70% well exceeding the Stokes limit. This, together with the broadband emission properties of this crystal at ~2.3 μm (emission bandwidth: >30 nm) highlight its potential for femtosecond mode-locked SWIR lasers.

Fig. 1 .

 1 Fig. 1. Spectroscopy of the 3 H 4 → 3 H 5 laser transition of Tm 3+ in KLu(WO 4 ) 2 crystal: (a) stimulated-emission cross-sections, σ SE , for light polarizations E || N p , N m , N g , the vertical dashes indicate the wavelengths of purely electronic transitions; (b) Crystal-field splitting of the 3 H 4 and 3 H 5 multiplets and the assignment of the observed laser lines.

Fig. 2 .

 2 Fig. 2. Thulium KLu(WO 4 ) 2 laser operating on the 3 H 4 → 3 H 5 transition: (a) input-output dependences, ηslope efficiency; (b) typical laser emission spectra for T OC = 1.3%; (c) 1D intensity profiles in the horizontal (x, || N m ) and vertical (y, || N p ) directions (T OC = 1.3%, P abs = 0.8 W), inset -2D mode profile in the far-field. The laser polarization is E || N m .

Fig. 3 .

 3 Fig. 3. Effect of the Tm doping level on the laser operation on the 3 H 4 → 3 H 5 transition: (a) input-output dependences, ηslope efficiency, T OC = 1.3%; (b) Findlay-Clay analysis of the roundtrip intracavity losses, L; (b) calculated pump quantum efficiency, T OC = 1.3%.