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202 New Magnetic Semiconductors on the Base of TlBV I-MeBV I Systems

In the temperature range 80-110 K, where TlNiS2 samples possess activationless hopping conduction (∆˚A=0), the slope of the curve α(T) is equal to 0.13 µV/ K2. At temperatures T> 110 K, when the activation energy of conduction varies monotonically with temperature, the

temperature coe cient for the thermopower is approximately six times larger: B = ∂T∂α = µV/ K2.

Figure 6. Dependence of thermo-e.m.f. on temperature in TlCoS2 .

The extrapolated lowtemperature branch α(T) goes through zero, i.e., A=0 in formula (6). This indicates that, in the temperature range 80-110 K, where the electrical conductivity σ does not depend on T, the experimental values of α satisfy formula (2) for the thermopower of metals. In the temperature range 110-240 K, the thermopower obeys relationship (6). The thermopower is determined primarily by the density of states and, hence, has positive sign in the region of hopping conduction.

Earlier [1], we showed that similar behavior of α(T) is also observed in TlFeSe2 ; i.e., under conditions of hopping conduction, the sign of the thermopower is positive and the temperature dependence α(T) is linear ( α˜T).

It is evident from Figs. 1 and 2 that, at temperatures close to 240 K, the dependences α(T) and σ(T) exhibit a jump; i.e., the thermopower sharply decreases, whereas the conductivity increases by more than three orders of magnitude. In this range of temperatures, the slope of the curve ln σ (1/T) is estimated at ˜ 1.0eV. Such a sharp increase in the conductivity σ at the activation energy ∆E =1.0eV can be associated with the onset of intrinsic conduction. In the case when the current

New Magnetic Semiconductors on the Base of TlBV I-MeBV I Systems 203

is transferred by carriers over states distributed throughout the whole sample, the parameter γ in formula (1) should be of the order of unity. At T≈240 K, the thermopower in TlNiS2 sample, which was estimated from formula (1) at ∆E=1.0eV and γ =1, is more than one order of magnitude higher than the experimentally observed thermopower. In other words, the experimental values of α are not as large as those calculated with the activation energy ∆E obtained from the slope of the curve ln σ(1/T). Possibly, this deference is caused by the fact that, at high temperatures, both holes and electrons are involved in conduction. Of course, in this case, the thermopower α is less tan that calculated from formula (1), which holds for semiconductors with single-type charge carriers.

Figure 7. Temperature dependence of magnetic susceptibility of TlFeSe2 at H=636 kA/m: 1 - H c-axis ; 2 - H||c-axis of crystal.

204 New Magnetic Semiconductors on the Base of TlBV I-MeBV I Systems

Thus, it was demonstrated that, at low temperatures, when hopping conduction dominates, the thermopower of TlNiS2 is proportional to the temperature. As the temperature increases, the charge carriers excited in the allowed band begin to dominate in conduction and the thermopower decreases drastically (by a factor of ˜200) and becomes virtually independent of the temperature. At high temperatures, small values of the thermopower are associated with the ambipolarity of conduction, when the concentrations of holes and electrons involved in conduction are of almost the same order of magnitude. The absence of sign inversion of the thermopower indicates that the concentration of holes in TlNiS2 always exceeds concentration of electrons involved in conduction.

The electric and thermoelectric properties of TlMnSe2 and TlMnS2 were studied. In the temperature range 130÷315K temperature dependence of the conductivity (σ ) of TlMnS2 increases exponentially with increasing temperature, i.e. σ(T) -dependence had the semiconductor nature. It was shown that σ(T) -dependence of TlMnS2 consists of regions with following activation energies: 0.178 and 0.44 eV (Fig. 3).

The temperature dependence of the conductivity of TlMnSe2 had the metallic nature (Fig. 4). Temperature dependence of the thermoelectromotive force (α) in TlMnSe2 was studied. The thermo-e.m.f. sign corresponded to the p-type conductivity of TlMnSe2 in the temperature range 88÷300K (Fig. 4, curve 2). With increasing of temperature from 88 to 300K the value of thermo-e.m.f. in TlMnSe2 was increased from 77 to 200 µ V/K. At T=194 K the anomaly was revealed on the dependence α (T).

Lowtemperature branch of α(T) - dependence in TlMnSe2 had linear character with extapolation to T=0 according to metallic formula for thermo-e.m.f. (2).

Temperature dependences of the conductivity and thermo-e.m.f. of TlCoS2 have been investigated in wide range of temperatures (Fig. 5 and 6). It was established, that TlCoS2 characterized by p-type of conductivity in 77÷225K temperature interval and at 225K inversion of thermo -e.m.f. sign takes place. It was shown, that TlCoS2 is ferromagnetic compound, and TlCoSe2 is ferrimagnetic.

Investigation of the temperature dependence of electrical conductivity and Hall coe cient of TlFeTe2 shows a band gap in TlFeTe2 of a size of 0.42 eV. It was shown that scattering of current carriers on acoustic vibrations of lattice takes place at high temperatures (µ ˜T −3/2 ). Temperature behavior of thermopower. in TlFeTe2 is studied. The concentration (np=6.67.1017 cm−3 ) and e ective mass of hole (mp=0.074m0) are calculated for TlFeTe2 .

Figure 8. Dependence of magnetic susceptibility of TlFeSe2 on magnetic field at T=4.2K: 1 - H||c-axis; 2 - H c-axis

By study of the temperature dependence of electrical conductivity of TlFeSe2, the width of the band gap in TlFeSe2 was established to be 0.68 eV.

Magnetic susceptibility of TlFeSe2 single crystals was investigated within 4.2-295 K temperature range.

Fig. 7 shows temperature dependence of magnetic susceptibility of TlFeSe2 single crystal (χ) at magnetic field H=636kA/m when H c - axis of crystal (curve 1) and H||c (curve 2). From these curves di erence in χ values at H c and H||c and change of temperature behavior of χ are observed.

Dependence of χ on H at T=4.2 K for TlFeSe2 is illustrated by Fig. 8. It is seen from Fig. 8 that with increasing of H, values of χ are decreased.

Obtained regularities of temperature and field dependences of magnetic susceptibility of TlFeSe2 single crystal show that the magnetic properties of this crystal are common for antiferromagnetics [11].

References

[1]S.N. Mustafaeva, E.M. Kerimova and A.I. Dzhabbarly, Fiz. Tverd. Tela, 42 (12), 2132 (2000).

[2]E.M. Kerimova, F.M. Seidov, S.N. Mustafaeva and S.S. Abdinbekov. Neorg. Mater. 35 (2), 157 (1999).

[3]F.M. Seidov, E.M. Kerimova, S.N. Mustafaeva, et al., Fizika, 6 (1), 47 (2000)

[4]E.M.Kerimova, S.N.Mustafaeva, F.M.Seidov. Abstracts of 6th International SchoolConference ” Phase diagrams in Material Science ”. Kiev. Ukraine. 14th -20th October. 2001.

206 New Magnetic Semiconductors on the Base of TlBV I-MeBV I Systems

[5]M.A.Aljanov, E.M.Kerimova, M.D.Nadjafzade. Fiz. Tverd. Tela, 32(8), 1449 (1990).

[6]M.A.Aljanov, E.M.Kerimova, M.D.Nadjafzade. Abstracts of XIV th IUPAC Conference on Chemical Thermodynamics. Osaka. Japan. 25-30 August. 1996.

[7]E.M. Kerimova, R.Z. Sadikhov and R.K. Veliev. Neorg. Mater. 37(2), 180 (2001).

[8]N.F. Mott and E.A. Davis Electronic Processes in Non-crystalline Materials.(Clarendon Press, Oxford, 1971; Mir, Moscow 1974).

[9]V.Augelli, C.Manfredotti, R.Murri, et al. Nuovo Cimento, 38 (2), 327 (1977).

[10]B.I. Shklovskii and A.A. Efros, Electronic Properties of Doped Semiconductors, Nauka, Moscow, 1979; Springer, New York, 1984.

[11]N. D. Mermin, H.Wagner. Phys. Rev. Lett. 17, 1133-1136 (1996).

LOCALIZED MAGNETIC POLARITONS IN THE MAGNETIC SUPERLATTICE WITH MAGNETIC IMPURITY

R.T. Tagiyeva

Department of Physics, Faculty of Sciences,

Ankara University, 06100 Tandogan, Ankara,

Turkey and

Institute of Physics Azerbaijan National Academy

of Sciences, Baku-370143, Azerbaijan

Abstract The magnetic polaritons localized at the magnetic impurity layer in magnetic superlattice composed of the alternating ferromagnetic and nonmagnetic layers are investigated in the framework of the electromagnetic wave theory in the Voigt geometry. The general dispersion relation for localized magnetic polaritons is derived in the long-wavelength limit.The dispersion curves and frequency region of the exsistence of the localized magnetic polaritons for di erent parameters of the superlattices and magnetic impurities are calculated numerically and analysed.

Keywords: Magnetic polariton, magnetic superlattice, magnetic impurity.

The propertices of the magnetic polaritons in the magnetic multilayer systems consisting of two and more alternating magnetic or magnetic /nonmagnetic components have attracted considerable attention during the past two decades. Magnetic polaritons, coupled electromagnetic and spin wave modes, although discussed by many authors in di erent ferro and antiferromagnetic arrangements, are a topic of continuing interest. Bulk and surface spin waves and magnetic polaritons in magnetic films and superlattices have been studied in the literature [1], [2], [3],[4][5], [6],[7],[9],[10],[11]. Magnetic polaritons propagating in fi- nite ferromagnetic/non-magnetic superlattice were considered in [8].The magnetic polariton modes in metamagnet thin film and in the antiferromagnetic films, whose thickness is much larger than the interatomic distances are investigated in [12],[13],[14]. Spectrum of the magnetic polaritons localized at the junction between magnetic superlattice and magnetic material were discussed recently in [15], [16]. The aim of this

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paper to extend our previous works [17], [18] on subject, considering the propagation of the localized magnetic polaritons in ferromagnetic/nonmagnetic superlattice with impurity layer. In such systems one finds both surface polaritons, in which excitation is localized near the surface, and guided modes, where excitation has a standing- wave-like character. In this case the impurity region works as waveguide, because of the magnetic polaritons propagate freely over the defect layer and damp in the perpendicular direction on either side of this region.

We consider a geometry in which the film ineterfaces are perpendicular

to the x- axis, whereas the magnetization M0 and the external magnetic

0 are applied in the z- direction. The surface polaritons propagate field H

along the y-axis, parallel to the surface of the impurity layer (Voigt geometry) and perpendicular to the magnetic moments and to the applied external magnetic field. The impurity layer occupy the region 0¡x¡d, d being its thickness.The superlattice consists of alternating ferromagnetic films of thickness d1and nonmagnetic films of thickness d2. The elementary unit of SL have length L=d1+d2. Here we neglect the dielectric properties of the magnetic material and ignore the exchange interaction.

We begin our discussion with the determination of the dynamic response of the classic ferromagnet. In the long-wavelength limit nonvanishing components of the frequency-dependent magnetic permeability tensors is given by

where γ is the gyromagnetic ratio and µ is the high frequency (ω Ω0) permeability, caused by the magnetic dipolar excitations other than the spin wave excitations (i.e. optical magnons).

In order to find the polariton spectra, we use the Maxwell’s curl equations in the magnetic film. After eliminating the electrical field variable

E, we obtain the following wave equation:

respectively and can be written in the form h,m exp(ik r ), where

k2=k2y+k2z- two-dimensional wave vector (our system is translationally invariant in the y and z directions). In the Voigt configuration kz=0 and k = ky = k.

The general solution of the equation 4 can be written in the form:

Figure 2. Same as in fig.1, but now for SL(Ni/non) with impurity Gd.

The presence of the impurity layer leads to appearance of localized magnetic polaritons. In order to have a bounded excitation , we require that the transverse component of the wavevector is imaginary or complex for superlattice. Only in this case we may find surface magnetic polaritons in the frequency gaps between the bulk bands.

From the condition of solvability of the equation 14 we can obtain the following expression: