1.
Introduction

The pure mercury chalcogenide HgTe with zinc blende structure belongs to a unique group of materials exhibiting so-called inverted band structure^[1] semimagnetic semiconductor of n-type (A^IIB^VI). The compound Hg_xCd_1?xTe is the most widely used semiconductor with a variable band gap^[2]. In Hg_1?xCd_xTe the Hg atoms are found to vibrate with amplitudes larger than the rest of the atoms for all compositions studied, while a minimum in the amplitudes is reached at x = 0.7 for all constituent atoms and maximum is near x = 0.24^[3]. Analysis of dispersion and attenuation of helicon waves in Hg_xCd_1?xTe (x = 0.16 ÷ 0.22) showed the existance of two groups of electrons which are comparable in magnitude of concentration and different in mobilities up to 30 times^[4]. Moreover Hg_0.76Cd_0.24Te is of interest because the conduction electrons are confined to the lowest spin-polarized Landau level for magnetic fields exceeding 2 kOe^[5]. The magnetoresistance and Hall resistance increase abruptly by several orders of magnitude over a narrow range of field centered on a critical magnetic field for helium temperature. The authors have observed the nonlinear current–voltage characteristic. This behavior is characterized as transition to the insulating ground state in magnetic field for Hg_0.76Cd_0.24Te^[5]. It was suggested that this fact indicates the formation of a Wigner crystal with a domain size of tens of microns. The nature of the metal–insulator transition induced by a magnetic field in a semiconductor Hg_0.8Cd_0.2Te led to a wide discussion in Ref. [6]. The dependencies of resistivity from temperature, magnetic and electric fields can be explained on the basis of a model of overlapping conductivity band and impurity states between which a gap is formed in sufficiently strong magnetic fields and is increased with increasing magnetic field^[6]. The Hall effect, resistivity and p–n-junction characteristics were investigated on high pure and perfect p-type Hg_1?xCd_xTe crystals (x ~ 0.2) versus temperature, doping and methods of annealing^[7].



Implantation by Ag⁺ ions modifies the carrier concentrations due to the introduction of defects in the surface layer that greatly affects the skin effect. A change of the valence N on surface of A^NB^8?N from two to one leads to a change in the structure of these compounds from a zinc blende with a fourfold coordination to a NaCl with a sixfold coordination^[8] and change the structure on the surface, the concentration and the mobility of charge carriers.



The mechanism of the inversion of the conductivity from n- to p-type was offered in Refs. [9, 10] from the defects that introduce shallow levels in the band gap of Hg_1?xCd_xTe. In Ref. [9] it was shown that the mercury vacancy defect increases the band gap in comparison with that of the pure materials due to the weaker p-d coupling, but the acceptor levels in the band gap make the response wavelength become longer for the mercury cadmium telluride with a mercury vacancy defect and the the valence band maximum of the Hg or Cd vacancy defects are a function of the Fermi levels. In Refs. [9, 10] it has been shown that in situ gold impurity acts as an efficient p-type dopant in Hg_0.75Cd_0.25Te.



Characteristics of charge carriers can be investigated by the microwave absorption by using magnetic resonance method. The aim of this work was to study the magnetic and transport properties of the implanted and thermally annealed by silver ions Ag:Hg_0.76Cd_0.24Te monocrystals by magnetic resonance method.

2.
Sample and experimental details

The samples were grown by continuous feeding of the melt. The Hg_0.76Cd_0.24Te crystals have n-type conductivity with carrier concentration of ≈ 10¹⁶ cm^?3. The most commonly used impurities for obtaining p-type Hg_1?xCd_xTe are the first group elements. For this reason the samples were subjected to ion implantation by Ag⁺ ions on ILU-3 accelerator with energy 30 keV, doze 6 × 10¹⁵ cm^?2, doze rate 0.4? 0.5 μA/cm². After implantation the sample was annealed in a sealed quartz tube in a saturated mercury atmosphere at a temperature of 300 °C for 20 days. After these procedures the conductivity was inverted to p-type with carrier concentration of 4 × 10¹⁵ cm^?3. The crystal composition was determined from measurements of the Hall coefficient and spectral distribution of photoconductivity^[11].



The electron spin resonance (ESR) spectra were recorded using Varian E12 in two frequency ranges: X-band (9.36 GHz) and Q-band (34 GHz). Measurements were performed at the temperatures 4.2–20 K and at the magnetic fields varying from 0 to 10⁴ Oe at X-band (9.36 GHz) and to 2 × 10⁴ Oe at Q-band (34 GHz). Temperature dependencies were measured an ER 200 SRC (EMX/plus) spectrometer (Bruker) at the frequency of 9.4 GHz using temperature controller ITS 503S (Oxford instruments) from 5 to 20 K. The samples of 2 × 2 × 2 mm³ were placed in the cavity and the outside magnetic field was applied. The microwave absorption power derivative (dP/dH) was registered in the experiments.



X-band measurements were performed with three orientations of the sample relative to the direction of the applied magnetic field. In the first case, the value of angle between the rotation axis and selected axis was 0 degrees, in the second case, the rotation axis was 90 degrees to the selected axis. In the last case the angle between rotation and selected axis was 45 degrees. The Q-band measurements were performed only for one plane.



The magnetization and resistivity magnetic field dependencies were measured at a temperature of 5 K on the multi-functional system for measuring physical properties with superconducting magnet Physical Property Measurement System (PPMS-9).



For the determination the orientation axes of the crystal, one of the samples was irradiated by prolonged X-ray exposure (about 2 hours) in a tube BSV-22 with an iron anticathode, U = 24 kV, I = 2 mA.



The microstructure and elemental composition of Hg_1?xCd_xTe was studied with an EVO 50 XVP scanning electron microscope (SEM) and energy-dispersive X-ray spectroscopy (EDS, Oxford, Inca Energy 350, equipped in a scanning electron microscope).

3.
Experimental results

The X-band angular dependencies Ag:Hg_0.76Cd_0.24Te single crystal spectra as a function of the magnetic field are shown in Fig. 1(a) and as a function of the inverse magnetic field in Fig. 1(b). The Q-band angular dependencies of the microwave absorption from magnetic field are presented in Fig. 1(c). In spectra the resonance line in the field about 13 kOe comes from carbon centered organic free radicals (standard) which is used for matching the data obtained in different frequencies. The magnetization curve is presented in Fig. 2(a). We suppose that the paramagnetic and diamagnetic parts from charge carriers are determining the temperature dependencies of the magnetization. We subtracted the diamagnetic part $M_1=-chi_{
m diam} H$ and paramagnetic part as Langevin function $M_2=A({
m {cth}}(H/alpha)-alpha/H)$ from experimental magnetization data^[12]. After subtracting the contributions of M₁ and M₂ in the residual dependence of magnetization M_osc the oscillations were observed as shown in the inset of Fig. 2. The fitting parameters for magnetization temperature dependencies were the following: χ_diam = 2.37 × 10^?4 emu/mol; A = 0.96 emu/mol; α = 901 Oe (1/α = 1.11 × 10^?3 1/Oe).






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Figure1.
(Color online) The angular dependencies of ESR spectra in Ag:Hg_0.76Cd_0.24Te at the T = 4.2 K in the X-band (9.3 GHz) (a) as the function of magnetic field; (b) versus of the inverse magnetic field. (c) The magnetic resonance spectra in the Q-band (34 GHz).






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Figure2.
(Color online) (a) The dependencies of magnetization versus magnetic field at 5 K. Inset: The residual data after subtracting the diamagnetic contribution of the conduction electrons and the Langevin function of magnetic saturation. (b) The dependence of the resistivity versus magnetic field at 5 K. Solid red line: fitting according to Eq. (1).




The resistivity dependence from the magnetic field is shown in Fig. 2(b). The curved behavior can be fitted by the following equation^{[13, 14]}:

$$R=R_{0}(1+beta H^{2}), $$

(1)

where R₀ = 55 × 10³ Ω·cm is resistivity in a zero magnetic field and β = 1.8 × 10^?11 Oe^?2.

4.
Discussion

In the spectrum of magnetic resonance Ag:Hg_0.76Cd_0.24Te two types of oscillations are observed: low- and high-frequencies at low temperatures (4.2–20 K) and in the magnetic field from 2 × 10³ Oe (see Fig. 1). In accordance with Refs. [13, 14] we fitted the dependence of high-frequency oscillation period using the equation:

$$Delta H = Delta H_0 (1+k H^2), $$

(2)

where H is external magnetic field. This is consistent with the fact that in weak magnetic fields the resistance in the semiconductor is increasing proportionally to the square of the applied magnetic field^[1]. The fitting magnetoresistance coefficients in Eq. (2) are equal k = 4.84 × 10^?7 Oe^?2 and ?H₀ = 55 Oe. The obtained parameters k and ?H₀ are the same: (i) for all directions of the external magnetic field relative to the crystallographic axes of the sample, (ii) for X-band and Q-band data with accuracy up to experimental error and (iii) they perfectly coincide with the oscillation period which was obtained from the PPMS measurements (Fig. 3(a)).






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Figure3.
(Color online) (a) The high-frequency oscillation period dependence from magnetic field that was obtained from ESR and PPMS data. Dotted line: fitting according to Eq. (2). (b) The angular dependence of first minimum location of low-frequency oscillation obtained from ESR (X-band).




The dependence of the first minimum locations of low-frequency oscillations between the magnetic field and the axis of the crystal are presented in Fig. 3(b). Figs. 1(a) and 4(a) show the derivative of microwave absorption power as a function of the inverse applied magnetic field. As can be seen from these figures the oscillation periods ?(1/H) = ?(H^?1) in the investigated inverse magnetic field are changed from 2.8 to 3.23 × 10^?5 Oe^?1.






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Figure4.
(Color online) (a) Temperature evolution of the oscillations in Ag:Hg_0.76Cd_0.24Te. (b) Dependence of the oscillation amplitude versus temperature near 4 kOe.




The carrier concentration n_s has been determined at the magnetic field ~4000 Oe using the equation from^[15]:

$$n_{ m s} = frac{e}{pi hbar Delta (H^{-1})} = 1.6 div 1.8 times 10^{11},, { m cm}^{-2}.$$

(3)

For further detailed study of low-frequency oscillations, the additional measurements in a larger field range are needed using other equipment (for example W-band 94 GHz). This comes from fact that the period of the oscillations exceeds the range of used magnetic fields in our experiment.



The temperature dependence of high-frequency oscillation amplitude for Ag:Hg_0.76Cd_0.24Te in the temperature range from 6 to 12 K in X-band is presented in Fig. 4(a). The temperature dependence of the oscillation amplitude near H = 4 kOe is given in Fig. 4(b) and it can be fitted by the expression^[16]:

$$A(T)/A(T_0) = frac{Tsinh(Delta_tau T_0)}{T_0 sinh(Delta_tau T)},$$

(4)

where T₀ = 6 K is relative temperature for normalization. The obtained experimental data is very well fitted by Eq. (4) with ?_τ = 0.38 ± 0.01 K^–1 (Fig. 4(b)). The effective mass can be calculated according to^[16]:

$$m^* = frac{Delta e h H}{2pi^2k_{ m B}} = gamma m_{ m e},$$

(5)

where k_B is Boltzmann constant, h is Planck's constant, H is external magnetic field. We have obtained γ = 0.065 ± 0.002 or 1/γ ≈ 15.4 that is consistent with hole nature of charge carriers in the sample that was obtained from Hall measurement.



We believe that high oscillation was connected with charges localized in the surface layer. One of the possible reason for formation of the surface layer may be uncontrolled evaporation of the mercury atom from the surface of the sample since the samples were stored at room temperature for a long period of time. This suggested that the behavior of the charge carriers in the surface layer of the sample can be similar to the behavior of charge carriers in 2D-gas as was described in the study^[16].



After removal of the surface layer, one of the single crystals Ag:Hg_0.76Cd_0.24Te was placed into the resonator of the spectrometer at helium temperature. In this case the oscillations of the microwave absorption were not observed. This suggests that the oscillations of the microwave absorption in Ag:Hg_0.76Cd_0.24Te can be attributed to charge carriers in the surface layer.



We have performed the experimental study of the elements distribution by SEM method in the surface. The analysis showed that the impurity silver ions are uniformly distributed in the sample after 20 days of annealing, and the formation of a thin layer on the surface is due to evaporation of mercury ions due to prolonged storage in air. The microstructure and elemental composition was studied in the surface of monocrystal Hg_1?xCd_xTe, where it determined the ratio of chemical elements as Hg : Cd = 0.625 : 0.375.



Interestingly, the high-frequency oscillations were not observed in the magnetic resonance spectrum after X-ray irradiation of the sample (see Figs. 5(a) and 5(b). X-ray irradiation probably changes the concentration of defects in the crystal.






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Figure5.
(Color online) (a) The view of spectra before and after X-ray irradiation. (b) The angular dependence spectra after X-ray irradiation (the angles shown here are relative).




We believe that the oscillations of the microwave power derivative correspond to the transverse magnetoresistance ?ρ/ρ and magnetization ?M/M^[1], because the microwave field induces the alternating current on the surface of the sample. As the magnetic field increases, the Landau levels (slitted by the Zeeman energy) cross the Fermi levels. These results of the order parameters of the oscillatory behavior in the magnetic field for Ag:Hg_0.76Cd_0.24Te are similar to the de Haas-van Alphen effect from the influence of the imperfect nesting vector^[17].

5.
Conclusions

We investigated the single crystals Ag:Hg_0.76Cd_0.24Te by magnetic resonance methods, magnetization and resistivity. The low- and high-frequencies oscillations in magnetic resonance spectrum were observed from 4.2 up 20 K in magnetic field beginning from 2 kOe. The period of high-frequency oscillation and resistivity depend on the square of the magnetic field. This period is the same for X- and Q-bands ESR measurements and magnetization data. The magnetization includes three parts: the paramagnetic, diamagnetic and the similar to de Haas–van Alphen oscillations. The concentration of the charge carriers on the single crystal surface isn_S = 1.6 ÷ 1.8 × 10¹¹ cm^?2, their effective mass is equal to 0.065m_e. We assume that low-frequency oscillations are caused by the charge carriers with a strongly anisotropic Fermi surface, that follows from the angular dependence of the first minimum location of the low-frequency oscillations versus magnetic field. After X-ray irradiation high-frequency oscillations were not registered.

Acknowledgement

We thank N. M. Lyadov for the SEM measurements. The magnetic measurements were carried out at the Federal Center of Shared Facilities of Kazan Federal University.