Effect of Strong Correlations on the Spin-polarized Electronic Energy Bands of the CdMnTe Solid Solution

The influence of strong d-electron correlations on the values of the parameters of the electron energy bands in the solid solution Cd1-xMnxTe (x  0.25) was studied. At the first stage, the spin-resolved electronic energy bands were obtained in the GGA approach. At the second stage, strong correlations were taken into account for the Mn d-electrons by means of the hybrid exchange-correlation function PBE0, and at the third stage, correlations of the Mn and Cd d-electrons were included simultaneously. It was revealed that the material is a semiconductor for both spin channels. Found that for spin-up electrons, after taking into account the strong correlations of the Mn 3d-electrons, the top of the valence band was shifted by – 0.10 eV, and the bottom of the conduction band has increased by 0.02 eV, which resulted in an increase in the band gap, Eg, by 0.12 eV. Strong correlations of the Cd 4d-electrons add to an increase in Eg a value of 0.03 eV. The total increase in Eg for spin-up electrons is equal to 0.15 eV. For the spin-down electrons, the inclusion of strong 3d-electron correlations of Mn led to an increase in the top of the valence band by 0.12 eV, and the bottom of the conduction band has increased by 0.54 eV, resulting in an increase in the band gap by 0.42 eV. Strong correlations of the Cd 4d-electrons add to an increase in Eg a value of 0.02 eV. The total increase in Eg for spin-down states equals 0.44 eV. It was found that for spin-up electrons, the value of Eg of solid solution, without taking into account strong correlations of d-electrons, is 1.32 eV, and the inclusion of 3d-electron correlations of Mn leads to the Eg value of 1.44 eV. And the additional inclusion of 4d-electron correlations of Cd gives the Eg value of 1.47 eV. It was found that for spin-down electrons, the value of Eg of a solid solution, without taking into account the strong correlations of d-electrons, is 1.69 eV, and the inclusion of 3d-electron correlations of Mn leads to the Eg value of 2.11 eV. And the accounting of 4d-electron correlations of Cd has caused only a slight increase in the Eg to 2.13 eV.


INTRODUCTION
Solid solutions of the Cd1-xMnxTe system, which are obtained in the quasi-binary CdTe-MnTe section via the controlled substitution of Mn for Cd, represent a quite broad class of dilute magnetic semiconductors (DMSs) [1][2][3]. The main specific feature of DMSs consists in the fact that, apart from pure semiconductor properties, they also exhibit giant magnetooptical effects and magnetic polarons, which is caused by the high magnetic moments of the atoms with unfilled 3d shells in their compositions [3][4][5]. As a result, DMSs exhibit a strong exchange interaction between their magnetic atoms and between the magnetic atoms and electrons. This exchange interaction can be used in the spintronics which is promising for discovering a new way of data storage media in the chip-producing industries [6]. Spintronics is a branch of science and technology which employs both the charge and the spin of the electron. This, in turn, requires the materials which exhibit both ferromagnetic and semi-conductor properties in order to combine the permanent magnetic storage and the conventional electronics of semiconductors in one device [7]. Namely these properties are characteristic of CdMnTe solid solution.
In this article we present the results of investigation of the electronic structure of zinc blende solid solution Cd1-xMnxTe (x  0.25) that was carried out within the GGA [8] and PBE0 [9] approaches. All the calculations have been done by means of ABINIT code [10,11]. It should be noticed that the self-consistent wave functions and crystalline potential obtained on the basis of ABIN-IT code can be used to calculate the electrical properties of spintronics devices. This can be done in future by using the method proposed in [12,13]. This method is based on the short-range scattering models for electron interaction with a various types of crystal defects and demonstrates much better qualitative and quantitative agreement with experiment compared with commonly used long-range scattering models.

CALCULATION
The electronic structure calculations have been carried out using the PAW [14] method, in which the electron wave function with its full nodal structure where  is the transformation operator, and | ( ) is the all-electron basis function, | ( ) a i   r is the pseudopotential basis function, and | ( ) the projector function, which was calculated using the AtomPAW code [15]. The subscript i denotes the quantum numbers, and the superscript a represents the atomic augmentation sphere index. Substituting (1), (2) to the Kohn-Sham equation we obtain the system of linear equations where  is the band number, k denotes the vector in the first Brillouin zone, and   defines the Hermitian conjugate of  . The exchange-correlation potential was calculated in the form of PBE0 [9], according to which the exchange-correlation energy is written as where PBE E xc corresponds to the PBE exchangecorrelation functional [8], and s  , s  represent the wave function and the electron density of the selected electrons, respectively [10]. The latter are the Mn 3delectrons and Cd 4d-electrons. The mixing coefficient value   0 corresponds to the usual exchangecorrelation functional PBE without strong correlations. In order to take into account the strong correlations in formula (5), the authors recommend the value   0.25.
The crystal symmetry is described by the space group P-43m (number 215) Bravais lattice is cP (primitive cubic). We have generated the PAW functions for the following valence basis states: {4s 2 4p 6 4d 10 5s 2 5p 0 } for Cd, {3s 2 3p 6 3d 5 4s 2 4p 0 } for Mn and {5s 2 5p 4 } for Te. The PAW functions have been evaluated by means of the AtomPAW code [14,15]. The inclusion in the basis of 4s and 4p states of the Cd atom and of 3s and 3p states of the Mn atom slows down the calculation, but increases the precision and eliminates the problem of ghost states which can appear among solutions of the secular equation constructed on a minimal set of functions [16]. The radii of the augmentation spheres are 2.2, 2.1 and 2.4 a.u. for Cd, Mn and Te, respectively.

RESULTS AND DISCUSSION
Let us consider the results obtained in the GGA and PBE0 approaches. In the GGA approach, the strong correlations of 4d (Cd) and 3d (Mn) electrons are not taken into account, whereas in the PBE0 approach they are included in the calculation scheme.
First, we consider the electronic energy band spectrum of a solid solution obtained using the hybrid exchange-correlation functional PBE0. Fig. 1a-b shows energy bands with the spin-up (1a) and spin-down (1b), respectively. We can see that for both values of the spin moment we have a material with a direct optical and fundamental band gap at the point  of the first Brillouin zone. In addition, we note that the Fermi level is inside the band gap.  [17].
In the case of the PBE0 approach, i.e. with strong correlations, the minimum optical and fundamental gaps are equal to 1.47 eV for spin-up, and 2.13 eV for spin-down. Table 1 summarizes the quantitative parameters of the electron energy band spectrum of a solid solution CdMnTe.    Table 1

CONCLUSIONS
In this work, the effect of strong correlations of the Mn and Cd d-electrons on the parameters of the electron energy spectrum of a solid solution CdMnTe has been studied. It is established that the Mn 3d-electrons are localized in the valence band in the energy range from -4.0 to -1.0 eV, provided that the strong correlations of the 3d electrons are neglected.After inclusion of strong correlations of the 3d electrons of the Mn atom, this interval increases and extends from -5.0 to -1.0 eV. Simultaneous inclusion of strong correlations of the Mn and Cd d-electrons almost does not cause a change in this interval, although the main peak of the density of states of the Cd 4d-electrons shifts down by about 0.7 eV, as can be seen from Figs. 2-c and 3-c. Consequently, we can conclude that there is a small overlap between 3d-states of Mn and 4d-states of Cd. It is also worth noting that the Cd 4d-states reveal a little overlap with the states of the conduction band, since the inclusion of their strong correlations almost does not affect the values of the band gaps and the magnetic moment of the elementary cell, as confirmed by the corresponding data presented in Table 1.