Optical studies and dielectric response of [DMA]2MCl4 (M = Zn and Co) and [DMA]2ZnBr4

[DMA]2ZnCl4, [DMA]2CoCl4 and [DMA]2ZnBr4 crystallized in the monoclinic system, in the P21/n, P21/n and P21/c space groups, respectively. The optical properties of [DMA]2MCl4 (M = Zn and Co) and [DMA]2ZnBr4 were studied using ultraviolet-visible (UV-Vis) spectroscopy in the range of 200–800 nm. The Tauc model was used to determine the band gap energy of each hybrid compound. The calculated values of the direct and indirect band gaps (Egd, Egi) for all samples were found to be in the range of 1.91 eV to 4.29 eV for [DMA]2ZnCl4, 4.76 eV to 5.34 eV for [DMA]2ZnBr4 and 1.77 eV to 3.84 eV for [DMA]2CoCl4. The Urbach energy (Eu), extinction coefficient (k) and refractive index (n) of each compound was calculated. On the other hand, the dispersion of (n) is discussed in terms of the single oscillator Wemple–DiDomenico model. The single oscillator energy (E0), the dispersion energy (Ed), and both the real εr and imaginary parts εi of the dielectric permittivity were estimated. The variation of optical conductivity with the incident photon energy has also been studied. We employed impedance spectroscopy to thoroughly investigate the dipolar dynamics in the prepared materials. The evolution of the dielectric loss, as a function of frequency, showed a distribution of relaxation times, which probably could be of a Maxwell–Wagner type interfacial polarization relaxation, possibly attributed to grain boundary effects or blocking at the contacts. In fact, the current work opens an efficient path to high quality organic–inorganic halide perovskites with good optical properties, which makes them suitable for application in nonlinear optoelectronic devices.


Introduction
[N(CH 3 2 MeX 4 (Me ¼ Zn and Co and X ¼ Cl and Br)) are members of the A 2 MeX 4 crystal family, which have been extensively studied as typical materials showing various successive phase transitions when the temperature varies. On the other hand, the A 2 MeX 4 type crystals are interesting because of their many physical properties related to the ferroelectric and commensurate or incommensurate phase transitions. Moreover, most of these materials show many physical properties related to structural phase transitions at low temperatures. Therefore, these fundamental properties make the crystal family suitable for several applications, such as temperature and humidity sensors, and memory effects that manifest themselves as temperature anomalies in their physical properties. [1][2][3] Dimethylammonium tetrachlorozincate [DMA] 2 ZnCl 4 , dimethylammonium tetrachlorocolbatate [DMA] 2 CoCl 4 and dimethylammonium tetrabromozincate [DMA] 2 ZnBr 4 crystals have turned out to be very interesting members belonging to an A 2 MeX 4 that undergoes different phase transitions at and below room temperature. In fact, at room temperature, [DMA] 2 ZnCl 4 crystallizes in the monoclinic system with the P2 1 /n space group. Then, the rened parameters are: a ¼ 13,297Å, b ¼ 8,620Å, c ¼ 11 494Å and b ¼ 89, 8 . 4,5 However, the phase transition temperatures of [DMA] 2 ZnCl 4 have not yet been correctly established. Therefore, an investigation of optical birefringence and piezoelectric coefficients revealed a range of phase transitions occurring at 217 K, 238 K, 250 K, 272 K, 295 K, and 310 K. 6 Therefore, the temperatures of some phase transitions were determined through investigations of specic heat at 151 K, 240 K, 253.9 K, 272.2 K, 298.3 K, and 309.1 K. 7 In addition, heat capacity measurements showed phase transitions at 201 K, 250 K, 272 K, and 310 K. 8 Moreover, the occurrence of phase transitions at 444 K was conrmed by DSC measurements. 9 Monoclinic crystals of [DMA] 2 CoCl 4 are of the space group P2 1 /n. Unit cell dimensions are as follows: a 8.5313Å, b ¼ 11.4382Å, c ¼ 13.3070 A and b ¼ 90.038 . 10 The transition temperatures of [DMA] 2 CoCl 4 are T 1 ¼ 292 K, T 2 ¼ 319 K, T 3 ¼ 365 K, T 4 ¼ 374 K and T 5 ¼ 444. 11 At 291 K, [DMA] 2 ZnBr 4 crystallizes in the monoclinic system with the P2 1 /c space group and its unit cell parameters are a ¼ 8.706 (6)Å, b ¼ 11.956 (64)Å, c ¼ 16.289 (95)Å, b ¼ 121.84 , and Z ¼ 4. The [DMA] 2 ZnBr 4 crystal undergoes four phase transitions at T 1 ¼ 281 K, T 2 ¼ 340 K, T 3 ¼ 377 K, and T 4 ¼ 408 K. 12 Theoretical and experimental studies of different crystals with dialkylammonium cation showed that the change of the hydrogen bond network considerably inuences the lattice dynamics and manifests itself in an essential transformation of the crystalline structure. Therefore, due to the availability of H bonds, the above compounds are expected to be proton conductors. As a consequence, they are important because of the proton transport mechanisms in biophysical processes and their employment in numerous electrochemical devices, such as batteries, fuel cells, chemical sensors, electrochromic devices, and super capacitors. 13 During the past years, optical studies have been performed on organic-inorganic nanocomposites. These studies have evolved towards different objectives, such as the development of materials with specic optical properties based on the properties of organic and inorganic chromophores. In fact, because of their several advantages for designing materials for optical applications (versatile and relatively facile chemistry, materials having good mechanical integrity and excellent optical quality), numerous hybrid organic-inorganic materials have been developed in the past few years. The chemical industry has tended to frequently use organometallic complexes because they use a minimum of energy by participating in chemical reactions in the transformation of natural elements. It should also be noted that organometallic complexes are known for their interesting luminescence properties, which have recently played an important role, particularly as phosphorescent components for light-emitting diodes OLEDs "Organic Light-Emitting Diodes". 14 In fact, the most striking examples of functional hybrids exhibit emission properties (solid-state dye laser, rare-earth doped materials), absorption properties (photochromic), and non linear optical (NLO) properties. [15][16][17] The growth of research in nonlinear optics (NLO) is mainly related to the rapid technological advancements that have occurred in several related elds, such as ultra-fast phenomena, optical communication and optical storage devices. On the other hand, nonlinear optical crystals, which have high optical band gap, ultrafast response times and low dielectric constant, are in great demand in the optical storage devices, color display units and optical communication systems, etc.18 Moreover, compared to organic molecules, organometallic compounds showed strong absorptions in UV/V regions due to metal-toligand and ligand-to-metal charge transfer. 19 On the other hand, all the properties combine to make them as a suitable candidate for multifunctional material development. 20 In fact, several studies were performed on [TMA] 2 MeX 4 compounds due to their variety of phase transitions. The obtained results indicate that the tetramethylammonium and the tetrachlorozincate [TMA] 2 ZnCl 4 crystal is suitable for optoelectronic applications around room temperature. Below 296 K, this crystal can directly store the optical data and information. Moreover, the [TMA] 2 -ZnCl 4 crystal is conveniently transparent in the visible light region with low absorption coefficient in this region, which makes it suitable for anti-reection layers of solar. 21 However, the previous optical studies on the use of organic-inorganic hybrid materials in optoelectronic or optical application have received little attention. In fact, to use materials in the eld of optoelectronics, it is necessary to know their optical constants. Additionally, optical measurements can give us a lot of information about the composition and the quality of the materials.
In fact, in the present paper, we have investigated the optical properties of [DMA] 2 MCl 4 (M ¼ Zn, Co) and [DMA] 2 ZnBr 4 compounds. The results of the optical absorption were performed at room temperature. The main aim is to determine some important optical parameters, such as the bandgap energy (E g ), the Urbach energy (E u ), the refractive index (n), the oscillator energy (E 0 ), the dispersion energy (E d ), the real and imaginary parts of the complex dielectric function (3) and the optical conductivity s opt . We have also made an analysis of optical properties correlated with dielectric properties of [DMA] 2 MCl 4 (M ¼ Zn, Co) and [DMA] 2 ZnBr 4 single crystals. These results were analyzed and discussed in the light of published data of some A 2 MX 4 crystals.

Experiment
[DMA] 2 MCl 4 (M ¼ Zn, Co) crystals are prepared by dissolving stoichiometric amounts of water starting materials N(CH 3 ) 2 H 2 Cl and MCl 2 (M ¼ Zn, Co) in water, in a molar ratio of (2 : 1) according to the reaction scheme:

Apparatus
The X-ray diffraction (XRD) pattern of powder was recorded at room temperature using a Philips PW 1710 diffractometer operating with copper radiation (lK a ¼ 1.5406Å) in a range of Bragg's angle (5 # 2q # 80 ) in each compound. Then, the unit cell parameters were rened with the Celref 3 soware 22 by the least square method from the powder data.
Therefore, in order to study the optical properties of [DMA] 2 MCl 4 (M ¼ Zn, Co) and [DMA] 2 ZnBr 4 compounds, the UV-Vis spectra were obtained by a UV-VIS spectrophotometer (Shimadzu UV-3101PC) using a source emitting wavelength radiations varying between 200 and 800 nm on a pellet of each compound. For the optical measurements, we used crystal powder pellets of 8 mm diameter and 0.8 mm thick.
The dielectric measurements were carried out on a pellet of 8 mm diameter and 1.1 mm thick obtained by means of a press of 3 tons per cm 2 from a nely ground powder, using a SOLARTRON SI 1260 impedance bridge, which operates in the frequency range of 10 À1 to 10 7 Hz. Then, the temperature is regulated using a precise regulator tted with a thermocouple placed near the sample.

X-ray diffraction study
The powder X-ray diffraction pattern of [DMA] 2 MCl 4 (M ¼ Zn, Co) and [DMA] 2 ZnBr 4 , recorded at room temperature is shown in Fig. 1. In fact, all the peaks of [DMA] 2 ZnCl 4 are indexed in the monoclinic system with the P2 1 /n space group while the unit cell parameters rened by the least square method are: a ¼ 13.201Å, b ¼ 8.604Å, c ¼ 11.552Å and b ¼ 89. 34 . These values are in good agreement with those found in the literature. 4,5 The [DMA] 2 CoCl 4 compound at 300 K belongs to a mono-clinic system, P2 1 /n space group, with the following unit cell dimensions: Then, compared to the standard value, the obtained diffraction peak positions are found to be in agreement with those of the corresponding literature, conrming the phase and purity of the compound. 10 Moreover, all the reection peaks corresponding to 2q values of [DMA] 2 ZnBr 4 are indexed monoclinic system with the P2 1 /n space group. The obtained lattice parameters are a ¼ 8.    25 The peak around 692 nm in [DMA] 2 ZnCl 4 spectrum can be assigned to -NHspecies. Fig. 2(b) shows the experimental UV-Vis absorption spectrum of [DMA] 2 CoCl 4 at room temperature. As previously seen, there are eight distinct absorption peaks. The spectrum shows three absorption bands in the UV region centered at 376 nm, 304 nm and 258 nm, corresponding to the low energy tail of the band, corresponding to ligand-to-metal charge transfer (3p Cl ! 3d Co). 26 Additionally, the absorption spectrum exhibits ve peaks in the visible domain, located at 635 nm, 579 nm, 534 nm, 448 nm and 405 nm, probably assigned to internal electron transitions of the 3 d 7 conguration of a Co 2+ ion in [CoCl 4 ] 2À . [27][28][29] The observed band positions are very similar to those found in other materials containing organic-inorganic hybrid compound previously reported in the literature. 26,[30][31][32] As expected from some literature data, the corresponding transitions from the initial 4 A 2 ( 4 F) state into the excited states are grouped in Table 1. 30,32 It is also interesting to note that with respect to the mutual position of the bands, the [DMA] 2 CoCl 4 spectrum is very close to the [TMA]CoCl 4 spectrum. 27 In the UV region, one can observe that the absorbance values of the Brbased compound are higher than those of the Cl-based compounds. Moreover, from absorption spectra, the crystals absorb UV radiation, which may be used as an effective UV shelter. 33

Direct and indirect optical band gap and Urbach energy
The band gap energy is determined using the Tauc relation: 34 with a the optical absorbance, hn the photon energy, B a constant, then E g the optical band gap, n ¼ 1 2 or 2 for direct and indirect allowed transition, respectively.
The dependence of (ahn) 2 and (ahn) 1/2 on the photon energy is shown in Fig. 3 compounds, respectively. Then, the obtained intersection of the straight line, which is divided by the slope, is equal to the energy band gap of optical transitions. 35 On the other hand, the optical edge or gap was inferred by linear    extrapolation of the absorbance from the high slope region obtained from the spectra. It can also be noted that if erroneously the band gap energy is related directly to the absorption peaks, which appear in as-collected UV-Vis spectra, it can lead to overestimate its value with smaller discrepancies. In fact, the values of the band gap energy (E g ) of the samples at room temperature are listed in Table 2. These results are similar to those obtained for other similar hybrid materials 36-40 (Table 3). Therefore, in order to obtain information on the disorder in a material, an Urbach tail analysis was also performed. In this context, Urbach's rule describes the broadening of the absorption edge and the formation of a band tail. Thus, Urbach tail energy (E u ) is introduced to describe the width of the tails due to localized states in the absorption edge. 41 We can access the value of E u from the following equation: where a 0 is a constant, E u represents the Urbach energy (eV) and hn is the photon energy (eV). As seen in Fig. 6(a and b), the tail cannot accurately t a single slope in the Ln(a) vs. photon energy plot. As seen from Table 2, each of the investigated [DMA] 2 MeX 4 is characterized by its value E u . These values were similar to the band tails found in the literature (Table 3). 21,37,39,40 It is clear that the energy E u is higher for the Cl-based compound compared to the Br-based compounds. The large value may be because of the high degree of defect in the cell. 42 Thus, the rate of recombination in perovskite compounds increased as E u went up because of the rise of the density of the localized states lying deeply between the band gaps.

Optical constants
4.4.1. Extinction coefficient. When optical energy interacts with the matter, it disperses and consequently losses occur, which are described by the extinction coefficient. Then, the absorption coefficient a is related to the extinction coefficient k by: where k represents the imaginary part of the complex refractive index (N ¼ n + ik) and l is the wavelength of the incident photons, which is responsible for the attenuation of the electromagnetic wave in the medium.    each compound. On the other hand, for the compound dimethylammonium tetrachlorocobaltate, the extinction coefficient k shows several peaks and reaches a maximum in the visible region due to the dark blue color of the crystal. However, the two compounds [DMA] 2 ZnCl 4 and [DMA] 2 ZnBr 4 transmit almost most of the incident radiation due to their total transparency in the visible area. In fact, when the crystals exhibit a wide transmission range in the visible domain, they can be used for nonlinear optical applications and antireection layers of solar thermal devices. 21 The Br-based compound showed k-values lower than the Clbased compounds in the visible light spectrum. Therefore, these adequate results justify the use of this material in photovoltaic devices. 43 4.4.2. Refractive index. The refractive index, which is the result of complex phenomena of interaction between elds and atoms of the matter, can be expressed by: where R is the reectance of the surface and k is the extinction coefficient. Then, the variation of the (n) index, as a function of the wavelength, can be described by two models; the Cauchy and the Wemple-DiDomenico models. The Cauchy's formula of the refractive (n) index, as a function of the wavelength l, is: 44,45 where (n 0 , A et B) correspond to the Cauchy's constants and l is the wavelength of the incident photons.
In fact, Cauchy suggests that the refractive index depends primarily on the material and the wavelength. The dependence of the refractive index on the l (nm) wavelength for [DMA] 2 -ZnCl 4 , [DMA] 2 ZnBr 4 and [DMA] 2 CoCl 4 is also shown in Fig. 8(ac), respectively. The increase of the refractive index is due to the increase of the reectance. The values of n 0 , A and B are grouped in Table 4. These estimated values are close to the ones reported by. 41,46 It is clear that n 0 is very large for the compound [DMA] 2 ZnBr 4 compared to the [DMA] 2 ZnCl 4 and [DMA] 2 CoCl 4 compounds. We also notice that for the Cl-based compounds, n is almost constant, that is to say that the variation of n depends very little on l (A and B are very weak); however, in the compound [DMA] 2 ZnBr 4 , n is very sensitive to the variation of the wavelength (A and B are greater than for the other two compounds).
The concept of the single oscillator suggested by Wemple-DiDomenico describes the evolution of the refractive n index by the following equation: 47-49 where E 0 is the single-oscillator energy and E d the dispersion energy. In fact, E 0 corresponds to the energetic distance between the valence and conduction bands and hn is the photon energy (eV   Fig. 9 (a-c) Plots of (n 2 À 1) À1 versus (hn) 2  (n 2 À 1) À1 versus (hn) 2 as illustrated in Fig. 9(a-c), respectively. Then, the values obtained for the oscillating parameters are gathered in Table 5. Therefore, the previous equation can be written as follows: where l 0 is the average oscillator wavelength, S 0 corresponds to the oscillator length strength and l is the wavelength of the incident light. Therefore, in order to determine the values of the long wavelength refractive (n N ), index average oscillator wavelength l 0 and the average oscillator strength (S 0 ) for the samples, we can use the following relationship: and The plot of (n 2 À 1) À1 , as a function of (1/l 2 ), gives a linear part ( Fig. 10(a-c) Table 5 shows the values of n N , l 0 and S 0 .
On the other hand, for the development of optical applications of the optical material under study, determining the moments of the spectrum is very necessary. Therefore, the M À1 and M À3 moments can be determined by the following equations: And, The  Table 6. Then, the obtained M À1 and M À3 are slightly elevated for the compound [DMA] 2 ZnBr 4 . These moments determine the average bond strength. Eqn (11) and (12) indicates a single-oscillator approximation to the dielectric response of these materials. The optical moments are related to the macroscopic quantities, like the effective dielectric constant, the effective number of valence electrons in the investigated material. 50 4.4.3. Dielectric constant. Several theoretical models have been developed to study the dielectric constants for material applications in optoelectronic devices, which characterize the optical properties of a solid material. In fact, the real part (3 r ) of the dielectric constant shows how much it will slow down the speed of light in the material, whereas the imaginary part (3 i ) represents the absorption of the associated radiation by free carriers. The complex dielectric constant 3 is related to the refractive index (n) and the extinction coefficient (k) as: 49 Additionally, studies of the real and imaginary parts of the dielectric constant give us the information about the loss factor, which is the ratio of the imaginary part to the real part of the dielectric constant. Then, the variation of the real and imaginary part of the dielectric constant with the incident photon energy for the [DMA] 2 ZnCl 4 , [DMA] 2 ZnBr 4 , [DMA] 2 CoCl 4 sample were determined and shown in Fig. 11 and 12.
On the other hand, the extinction coefficient has a negligible contribution (in the order of 10 À6 ) whereas the refractive index has a comparatively very high value. An increase of the real part was observed with the increase of the photon energy. Consequently, the real part of the dielectric constant depends only on the refractive index by eqn (7). For the [DMA] 2 ZnBr 4 compound, the calculated real dielectric constant values are very high  at the particular interest of the visible region. The imaginary part of the dielectric constant depends on the extinction coefficient by eqn (8). As can be seen from Fig. 12, different shapes of the curves for the imaginary part of the dielectric constant have been observed. Therefore, the imaginary part conrms the free carrier contribution to the absorption. We notice that the imaginary part of the complex permittivity (in the order of 10 À6 ) is very low compared to the real part.
4.4.4. Optical conductivity. Optical conductivity is a significant tool for studying the electronic states in materials. In general, if an external electric eld is applied, a redistribution of charges occurs and currents are induced. Fig. 13 shows the variation of optical conductivity with the incident photon energy. Optical conductivity was determined using the relation: 51,52 where c is the velocity of light and a is the absorption coefficient.
The increased optical conductivity is due to the high absorbance of the sample in that region. The optical conductance and The maximum value of conductivity for the compound [DMA] 2 ZnBr 4 (4 Â 10 10 s À1 ) is greater than that of the two compounds [DMA] 2 ZnCl 4 (5.5 Â 10 9 s À1 ) and [DMA] 2 CoCl 4 (1.5 Â 10 10 s À1 ). Besides that, these high values of the optical conductivity of [DMA] 2 ZnBr 4 pointed out to the superiority of the material for such photovoltaic applications. 53

Dielectric relaxation
The dielectric properties are correlated with the electro-optic properties of the prepared crystals. Therefore, the dielectric relaxation studies are important to provide the conduction processes (T g d ¼ 3 00 /3 0 [ 10), since it enables to determine the origin of the dielectric losses. 54 Then, in order to obtain more information about [DMA] 2 ZnBr 4 , [DMA] 2 CoCl 4 and [DMA] 2 -ZnCl 4 dynamic compounds, we measured the impedance spectra of the sample at room temperature from which we derived the frequency-dependent dielectric constant (3 0 ) and the loss tangent (T g (d)) in the frequency range of 10 À1 to 10 7 Hz.
The frequency dependence of the dielectric constant is depicted in Fig. 14. It is clearly that 3 0 shows dispersions at low frequencies and gets almost saturated at higher frequencies.
Such dispersions in both components of the complex dielectric constant are referred to as low frequency dielectric dispersion (LEDD) and are associated with the space charge accumulation effect and/or conducting ion motion. The observed sharp decrease of 3 0 as frequency increases is mainly due to the space charges contributing to the high permittivity in the materials. The magnitude of the dielectric constant depends on the degree of polarization and the charge displacement in crystal. It can be observed that 3 0 approaches a limiting constant value ð3 0 N Þ; at high frequencies, which can be attributed to the absence of space charge polarization near the grain boundary interface. Moreover, with the increase of frequency, 3 0 becomes almost parallel. In fact, the most striking feature is that there are no    55 The analysis of Fig. 15 describing T g (d) revealed one relaxation peak for each hybrid. This peak is noticed at the frequencies of 10 2 , 7 Â 10 3 and 10 4 Hz for [DMA] 2 ZnBr 4 , [DMA] 2 CoCl 4 and [DMA] 2 ZnCl 4 , respectively. Considering the low frequency and the broad peak feature, this relaxation process could be a Maxwell-Wagner type interfacial polarization relaxation, possibly attributed to grain boundary effects or blocking at the contacts. From the graph, it is clear that the for [DMA] 2 ZnBr 4 , [DMA] 2 CoCl 4 and [DMA] 2 ZnCl 4, the crystals exhibit very low dielectric loss at high frequencies, which can be a potential candidate for nonlinear optics NLO applications. 56

Conclusions
In the present study, the powder XRD study of [ It can be observed that the band gap of all the samples lie in the range of semiconductors. Then, the observed variation in optical parameters, such as the refractive index (n), the extinction coefficient (k), the optical conductivity (s opt ), and the dielectric constants (3*) have been evaluated and show sufficient agreement with the values reported for some A 2 BX 4 family single crystals. The refractive index values have been tted to the single oscillator Wemple-DiDomenico (WDD) model. The single oscillator energy (E 0 ), the dispersion energy (E d ), the static refractive index n 0 , the moments of the optical dispersion spectra M À1 and M À3 , the static refractive index n N and the oscillator strength S 0 were estimated at room temperature, which showed sufficient agreement with the values reported for the A 2 BX 4 family. On the other hand, the electrical properties of the high dielectric constant at low frequencies, suggest that [DMA] 2 ZnBr 4 could be used in the energy devices. In fact, the low dielectric constant and the low dielectric loss at high frequencies, suggest that the [DMA] 2 ZnCl 4 , [DMA] 2 ZnBr 4 and [DMA] 2 CoCl 4 crystalline compounds could be used in nonlinear optoelectronic devices.

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