In the paper, the properties of magnetic diluted and strong correlated systems of Mn xSi 1–x systems are discussed. The double defects including manganese ion and silicon vacancy are the frame work of the our model introduced for the description of these systems properties. The role of the Jahn-Teller distortions of different symmetry types in MnSi system magnetic-properties formation is discussed. It has been established that the manganese related defect is the center with negative- U properties and Jahn-Teller’s full symmetric vibration mode initiates change of a crystal-field value from intermediate to strong.
Intermetallic compounds based on the elements with incompletely filled 3d- or 4f-shell have attracted attention of researchers on an extent of more than 40 years [
The problem of a manganese ions ground state in
Both systems are crystallized in the cubic lattice type. Symmetry group
Magnetic moment value of the manganese ions in the systems in a wide temperature interval will be the main subject of our investigation. The model of the double defect, formulated early by us [
Two different defect types in semiconductors irrelevant with each to other are discussed as a usual [
In the same times, in the frame of the double defect model, the interstitial and substitution defects are considered as a two limiting cases of double defect. A silicon vacancy
At that when,
・ distance between partners is infinity, then interstitial defect type is realized;
・ distance between partners is an infinitesimal value, then we have substitution type of defect.
The account of silicon vacancy at interstitial defect case is necessary to consider all type of double defects from the common base. This will result to unique parameter―Fermi level position
The intermediate case, when distance between partners is of the order of the lattice period, the only one valence bond saturated exists between partners. Such type of defects has been named by the pairing defects. A plenty of pairing defect different types may exist, depending on overlapping integral of wave functions partners and number of nonequivalent crystallographic positions in a lattice. Only single type of pairing defects is realized in silicon. Moreover, we can see electronic density redistribution between the central ion and ions of the nearest crystal environment as a result of temperature variation or other factors, in particular, a electronic configuration change of everyone components as result of Jahn-Teller distortions in the frame of the model. It is necessary to note, that electronic density redistribution can be realized and without a free carrier generation. The magnetic-moment average value located at manganese ion can be renormalized very strongly as free carriers appear in the system.
The considering of double defect model we intentionally limit to the consideration of single elementary cell, understanding thus, that significant electronic density delocalization take place due to hybridization effects and indemnification of a charge occurs much further, than the first coordination sphere. Here and further for a de-
signation of such defects we shall use the notation for substitution
with respect to its nucleus. Take into account an electro neutrality condition of a crystal as a whole, we can write equation for the neutral charge state of double defect:
where
Now all are ready for proceed to discussion of a manganese ion ground state in intermetallic compound
The crystal lattice in such compound will mainly consist of silicon atoms and is described by point group of symmetry
Mono- and polycrystalline silicon used as a material for solar batteries, is presented up to 15 metal impurities at concentration above than 1012 ions/sm3 and higher [
But, crystal field effects and hybridization between impurity and band states are played a dominant role in the formation of the magnetic-ions electronic structure. Manganese atoms have half-filled 3d-shell and two electrons occupy an outside 4s-shell. An electronic configuration of the Mn0 looks like 3d54s2. Impurity ion 3d-or- bitals are split by tetrahedral-symmetry crystal field on the t2- and e2-orbitals (three- and double-degenerated states). The electronic configuration looks like
In early works directed to research the behavior of manganese ions in silicon [
Fermi level
As very well know, that
In the same time EPR spectra of
The similar situation took place in system GaAs:Mn and was a subject of discussions more than 30 years [
Let’s consider, that in valence bond formation between magnetic ion and surrounding only electrons with bonding energy in free atom less than 35 eV on absolute value are involved. Energy scale is counted from a vacuum level position. In other words, two from four valence bond is saturated in
where
A dynamic type of Jahn-Teller effect takes place for the manganese ions in such system (see EPR spectra). But, we shall have full moment J, located on manganese ion incoming in
Provided that simultaneously with tetragonal distortion it takes place also full symmetric Jahn-Teller distortions of local symmetry (
ganese is equal
As we see, very good consent between calculated and experimentally values of moment J takes place. In other words, the defect
but, transition between configurations take place without change of density of free carriers of a charge.
The defects with an electronic configuration (4b) are responsible for observable EPR spectra. In the same time, DLTS spectra are connected with (4a) configuration of the double defect.
In this case it is easy to coordinate value of activation energy
where
The process of electron capture on the deep level is defined by:
where
Within the framework of the standard approach:
Look discussion in [
In the conclusion we shall note, that full symmetric vibration mode initiates change of a crystal field value from intermediate (a configuration
Crystalline system MnSi, in which both components are approximately having equal concentrations, traditionally attributes to strong correlated systems [
At the same time, small distinction in types of a crystal lattice between magnetic diluted system (group of symmetry
Displacement of atoms of the nearest environment in the opposite direction in lattice B20 in comparison with atoms position in tetrahedral lattice is powerful argument for the existence of the cooperative Jahn-Тeller effect in such system. But, distances between the nearest ions of manganese in Mn0.5Si0.5, which do not form valence bonds with each other, practically coincides with such parameter for metallic g-manganese [
Systematic measurements of the magnetic moment, located on the manganese ions, show presence of several temperature intervals in which magnetic ions demonstrate completely different properties [
Within the framework of double defect model the given transformations can be treated in the following way. The value of the magnetic moment, located on the manganese ions, in a paramagnetic phase (
First-order transition take place at 29.5 K and transition
It is necessary to note, that very intricate case of Jahn-Teller distortions is realized here―trigonal + tetragonal + full symmetrical types of distortions take place simultaneously and we have got a problem with large quantity of independent parameters. As result, numbers of Jahn-Teller’s minima can be equal to 24 [
the spiral structure is connected with a jump between minima of potential energy. As result of applied external magnetic field, the transformation of a local minimum to absolute one is a case of the transition from the spiral structure to ferromagnetic order type in Mn0.5Si0.5. Parameter
Separately it is necessary to focus on the dependence of the phase-transition temperature from hydrostatic pressure value.
As we already discussed above, the first order phase transition, occurring at temperature 29.5 K at normal pressure, is connected with redistribution of electronic density between manganese and surrounding silicon atom. But 3р-orbitals of silicon is more delocalizated in comparison with 3d-orbitals of manganese [
where
But if ratio (10) is corrected, the phase transition temperature has to drop at the hydrostatic-pressure increase. Moreover, there is critical value
Thus, the model of double defect, stated above, сan be successfully applied for the description of the magnetic properties of
We found that the angular momentum (J) of a manganese ion is integer, but not fractional as assumed early.
It is assumed that local level, located in the forbidden band of silicon and connected with recharging of impurity manganese ions, transforms in the band with increase of manganese concentration up to
It has been established that
The favorable difference of our model from the approach of weakly-fluctuated Fermi-liquid one, which was widely used for the description of physical properties of manganese silicide in last years, is the opportunity of definition of original causes of those or other effects.
It is obvious that, it is necessary to perform a number of experimental and theoretical studies with the aim of the specification of our model parameters. First of all, it concerns measurement of inelastic neutrons scattering spectra on the MnSi single-crystalline sample and on amorphous a-MnSi, in which helical magnetic order is absent. It is fruitful to compare EPR spectra of
Useful addition to these experiments would be a comparison of the
The author is indebted to P. A. Alekseev and V. N. Luzukov for helpful discussion and critical reading of the manuscript.