Relative magnetoresistance in polycrystalline In–Cu chalcogenides under high pressure up to 50 GPa

This paper is devoted to the investigation of relative magnetoresistance MR in semiconductor polycrystalline materials: CuInAsS3, CuInAsSe3, CuInS2 and CuInSe2 under high pressures up to 50 GPa and at a constant transverse magnetic field. The pressure ranges of significant changes in the behavior of electrical resistance and magnetoresistance were identified for these materials. The features in the properties of CuInSe2, CuInS2 and CuInAsSe3 at these pressures are consistent with the data on the baric structural phase transitions in these materials. In the case of CuInAsS3 and CuInAsSe3 a shift of pressure intervals in which phase transitions can occur is observed that can be explained by an effect of chemical compression due to the changing the atom radii of the chemical elements forming the compounds.


Introduction
Polycrystalline indium and copper chalcogenides from the Cu-In-As-S (Se) and Cu-In-S (Se) systems have a profound scientific and practical interest because these materials can be used in various optical devices such as solar cells, LEDs, etc [1][2][3][4][5][6][7]. For the reliable operation of the devices based on them, it is necessary to investigate the physical properties of these materials in a wide range of external influences such as temperature, pressure, constant and alternating magnetic and electrical fields, etc.
The aim of this work is to study the behaviour of relative magnetoresistance MR of semiconductor polycrystalline materials: CuInAsS 3 , CuInAsSe 3 , CuInS 2 and CuInSe 2 under high pressures up to 50 GPa in a constant transverse magnetic field.

Materials and methods of study
The bulk polycrystalline materials CuInAsS 3 , CuInAsSe 3 , CuInS 2 , CuInSe 2 were synthesized by melting the initial components in a quartz containers. First of all, when all components of synthesized material were placed in ampoule, a constriction that divides ampoule into two parts was made. Then the titanium sponge was placed in the second part of ampoule and the second constriction was made. Ampoule have been evacuated to a residual pressure of 10 −4 Pa and filled with super pure argon to 0.5 × 10 5 Pa. The second constriction was sealed. After that, deoxygenation via annealing with titanium sponge was carried out. And finally, the volume of ampoule with the charge was sealed and placed in a muffle furnace for melting. A more detailed description of the synthesis process is given in [ Figure 1. Powder x-ray diffractions of (a) CuInAsS 3 , CuInS 2 , (b) CuInAsSe 3 and CuInSe 2 . A series of the reflections corresponding to the tetragonal chalcopyrite structure is visible on the diffraction patterns.
The compounds crystallized in the tetragonal chalcopyrite structure. The series of lines of chalcopyrite structure (figure 1) is presented on the diffraction patterns obtained by the x-ray diffractometer Shimadzu XRD 7000 (CuK α radiation). For CuInAsS 3 the dominant orientation is in the 112 direction, the orientation degree is about 65%.
The lattice parameters are a = 5.5227Å, c = 11.1329Å and a = 5.7820Å, c = 11.6217Å for CuInS 2 and CuInSe 2 (refined formula, Cu 0.933 InSe 2 ) respectively. The lattice parameters of CuInAsS 3 (a = 5.5184Å, c = 11.0845Å) and CuInAsSe 3 (a = 5.7967Å, c = 11.5471Å) are close to the lattice parameters of the compounds without arsenic. Arsenic atoms in these compounds can occupy the same tetrahedral sites that are occupied by copper and indium atoms in the structure of CuInSe 2 and CuInS 2 , or As atoms can be placed in the tetrahedral voids in the chalcopyrite structure. The similar values of ionic radii and charges of the corresponding ions are also support this view [8].
The high pressures up to 50 GPa were produced in the high-pressure cell (HPC) with the anvils from the carbonado-type artificial diamonds with good conductivity that make it possible to examine the electrical properties of samples placed into HPC [9]. The studied samples with a diameter of ≈ 0.2 mm and thickness from 10 to 30 µm, were obtained by compression in HPC of the initial powdered materials.
The constant transverse magnetic field was produced by a testaceous electromagnet, the value of magnetic induction B varied from 0 to 1 T. Relative magnetoresistance (MR) was calculated using the following formula: where R(B) is the electrical resistance at fixed magnetic field and fixed pressure, and R 0 is the electrical resistance at the absence of magnetic field at the same pressure.

Results and discussion
The electrical resistance of CuInSe 2 and CuInS 2 shown in figure 2. The resistance of these materials decreases by 1.5-2 orders of magnitude when the pressure is raised from the atmospheric to 50 GPa. As shown in figure  The structural changes at pressures up to 29 GPa and at further decrease to atmospheric pressure were studied via x-ray diffraction using a chamber with diamond anvils and synchrotron radiation. The authors of [10,11] showed that the effect of high pressures on CuInS 2 and CuInSe 2 results in the transition of the chalcopyrite structure to the cubic NaCl type structure at the pressures of 9.5 GPa and 7.6 GPa, respectively. At 39.2 GPa the authors [11] observed a subsequent structural phase transition in CuInSe 2 . The new phase was identified as an orthorhombic distortion of the NaCl structure, and it remained stable to the maximum pressure of 53.2 GPa reached in [11]. The structural changes in the opinion of authors [10] are irreversible, and phases formed after removing the pressure differ from the initial ones. The phase restored for CuInSe 2 after removing the high pressure was sphalerite-type cubic and it was amorphous for CuInS 2 .
The features near 9 GPa and 27-35 GPa on the pressure dependence of the resistance of CuInS 2 can be associated with the structural transitions from a hexagonal chalcopyrite structure to a cubic NaCl type structure and with the beginning of amorphization respectively. In the case of CuInSe 2 the first transition occurs at 7.6 GPa [10], which is confirmed by the previous studies of thermo-EMF [12]. The features on the pressure dependence in the resistance of CuInSe 2 into the interval 30-40 GPa can be associated with the second structural phase transition at ≈ 39 GPa.
Our previous studies [12]   . It is assumed that the magnetoresistance is more sensitive to structural phase transitions and features in the behaviour of MR(P ) are beginning to show at lower pressures (for example, for CuInSe 2 ) that the phase transition pressure. As mentioned before, at addition of As in the compounds from the systems of Cu-In-S and Cu-In-Se the arsenic atoms can occupy the same tetrahedral sites that are occupied by copper and indium atoms in the structure of CuInSe 2 and CuInS 2 , or As atoms can be placed in the tetrahedral voids in the chalcopyrite structure [8]. Taking this into account, in the compounds of CuInAsS 3 and CuInAsSe 3 , can be expected the similar magnetoresistance behaviour and the corresponding structural transitions as in CuInS 2 and CuInSe 2 . Figure 4 shows the pressure dependence of electric resistance of CuInAsS 3 and CuInAsSe 3 at 300 and 78 K. As can be seen from the figure 4 the electric resistance decreases with temperature increase that is typical for the semiconductors, and the electric resistance decreases with pressure increasing, and lg R(P ) is almost linear dependence for CuInAsS 3 .
During the measurements of electrical properties under pressure, the relaxation of resistance was observed. Such behaviour of the electrical resistance under pressure can be associated with relaxation processes connected with the change in crystal lattice, characteristics of the charge carriers, etc. In some cases, variation of relaxation time at pressure change can indicate the presence of phase transitions. Usually, in the region of possible baric phase transition the relaxation time increases. For the characterization of electro-resistance relaxation under pressure, the relative resistance was estimated as where R(t 0 )-the electrical resistance of the sample immediately after the pressure fixing, and applying of the constant voltage to the cell, R(t rel )-electrical resistance in the relaxed condition after some time interval t rel at fixed pressure. For studied materials time interval t rel varies from 150 to 200 seconds at room temperature and from 20 to 50 seconds at 78 K. The relative change in the electrical resistance at T = 300 K demonstrates the features in the behaviour at pressure increase in the follow intervals: 38-44 GPa for CuInAsS 3 and 32-42 GPa for CuInAsSe 3 ( figure  5). When temperature is down to 78 K (at ambient pressure this temperature corresponds  to the interval with impurity conductivity in CuInAsSe 3 [6]) the beginning of the pressure interval corresponding to the features in the behavior of the relative electrical resistance of the CuInAsSe 3 , shifts toward lower pressures. This can indicate that precisely the impurity centers (the number of which are rising in the process of structural change with pressure increase) play a major role in the formation of the behavior of the investigated electrical parameters. The features observed in the behaviour of the electrical characteristics of the CuInAsS 3 and CuInAsSe 3 , in particular, the negative magnetoresistance (figure 6) can be manifestations of the supposed structural transitions like in CuInSe 2 and CuInS 2 (these materials have the chalcopyrite structure and the lattice parameters close to the materials under consideration at atmospheric pressure [8]). These transitions are accompanied by decrease in the width of the energy gap, changes in the impurity band structure in the magnetic field, defect states, and changes in the concentration and mobility of carriers with gradual pressure growth. The confirmations of this assumption are preliminary results of the crystal structure studies for CuInAsSe 3 at high pressure using synchrotron radiation [13]. The results of the study indicate the existence of two phase transitions: from the tetragonal to cubic structure (≈ 8-10 GPa) and from the cubic to orthorhombic structure (≈ 36-38 GPa). Figure 6 shows the typical MR dependences upon magnetic field for CuInAsS 3 and CuInAsSe 3 . In addition, the features (extrema) in the behavior of MR(P ) are observed in the follow pressure intervals: 17-24 and ≈ 40 GPa for CuInAsS 3 ; 17-24 and ≈ 36 GPa for CuInAsSe 3 respectively.
Thus, considering this research and previous studies [8,[10][11][12][13][14][15][16] the features on the baric dependences of the electrical characteristics of materials under study, can be connected with the structural phase transitions at pressures ≈ 9 and 27-35 GPa for CuInS 2 ; 30-35 GPa for CuInSe 2 ; and with supposed structural phase transitions at 38-40 GPa for CuInAsS 3 and 36-38 GPa for CuInAsSe 3 . These pressure ranges correlate with the previous estimated baric intervals, in which significant changes in the behaviour of electrical properties, measured under alternative current (such as impedance etc), are observed [14][15][16]. The shifts of intervals of possible structural transitions to the higher pressure (36-40 GPa) for CuInAsS 3 and CuInAsSe 3 compared with the materials without As, can be explained by an effect of chemical compression due to the changing the atom radii of the chemical elements forming the compounds.

Conclusion
Analysis of the pressure dependences of the electrical properties for the polycrystalline CuInAsS 3 , CuInAsSe 3 , CuInS 2 , CuInSe 2 at high pressures up to 50 GPa allowed to establish the pressure ranges of the significant changes in the behaviour of electrical resistance and relative magnetoresistance. Observed features of the studied properties relate to the pressure-induced structural transitions.