Based on the electronic structure of the ferromagnetic Gd 2 In and (Gd0.5 Y0.5) 2 In compounds the high-temperature magnetic part of the electrical resistivity of (Gd 1-x Yx ) 2 Ιn as a function of Y concentration was calculated and analyzed. The main interaction which causes the finite magnetic part of the conductivity was assumed in a form of stochastically distributed in space S—f interaction. The calculated resistivity of (Gd1-xYx)2Ιn alloys qualitatively reproduces the experimental data

Borgieł, Władysław

Deniszczyk, Józef

Acta Physica Polonica A

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Repozytorium Uniwersytetu Śląskiego RE-BUŚ

             Title: Electronic structure and electron transport properties of (GdxYx )2 in compounds  Author: Władysław Borgieł, Józef Deniszczyk  Citation style: Borgieł Władysław, Deniszczyk Józef. (2000). Electronic structure and electron transport properties of (GdxYx )2 in compounds. "Acta Physica Polonica A" (Vol. 97, nr 5 (2000), s. 783-786).  Vol. 97 (2000) 	 A CtA PHYSICA POLONICA A	 No. 5Proceedings of the European Conference "Physics of Magnetism ,99", Poznań 1999ELECTRONIC STRUCTUREAND ELECTRON-TRANSPORT PROPERTIESOF (Gd1-x Υx ) 2 Ιn COMPOUNDSW. BORGIEŁa AND J. DENISZCZYKba'Institute of Physics, Silesian University, Universytecka 4, 40-007 Katowice, Polandblnstitute of Physics and Chemistry of Metals, Silesian UniversityBankowa 12, 40-007 Katowice, PolandBased on the electronic structure of the ferromagnetic Gd 2 In and(Gd0.5 Y0.5) 2 In compounds the high-temperature magnetic part of the elec-trical resistivity of (Gd 1-x Yx ) 2 Ιn as a function of Y concentration was cal-culated and analyzed. The main interaction which causes the finite magneticpart of the conductivity was assumed in a form of stochastically distributedin space S—f interaction. The calculated resistivity of (Gd1-xYx)2Ιn  alloysqualitatively reproduces the experimental data.PACS numbers: 72.10.-d, 72.15.—v, 71.20.Eh, 71.20.—b1. IntroductionThe (Gd1-xYx)2Ιn compounds were widely studied experimentally with theuse of different methods and a variety of magnetic properties was reported forthem (see Ref. [1] and references therein). For samples with around 15% of yt-trium the effective magnetic moment reaches the maximum value and magneticsusceptibility shows the minimum. The resistivity ineasurements at temperaturesbelow 100 K revealed the magnetic transitions for Y concentrations x < 0.15,while the saturation resistivity reaches the maximum at about x = 0.15. In ourearlier paper [2] we have discussed already the most important results of theTB-LMTO [3] band structure calculations of the (Gd1-xYx )2Ιn compounds. Themethod description and the parameters used in the band structure calculationswere also presented there. The calculated properties of (Gd1-xYx )2Ιn confirm theexperimental observations. The density of states (DOS) around the Fermi level(εF ) composed of mainly d-states of Gd and Y atoms displays a similar behavioras that observed by XPS measurements. In the present paper we resume the rel-evance of the resistivity calculations results of band structure investigations andreport the calculations of the saturation electrical resistivity of the (Gd 1-xYx ) 2 Incompounds in the concentration range x = 0.0 ¸ 0.5.(783)784	 W. Βοrgieł, J. Deniszczyk2. Calculations and resultsIn order to calculate the electrical resistivity it is important to know thechanges of the DOS structure (the shape and positions of the peaks) around theεF upon alloying. Figure 1 presents the summed s, p, and d DOS of Gd2In and(Gd0.5Y0.5 ) 2 In. The analysis of the complete DOS has shown that the 4 f-minοrity--band of Gd atoms which lies above the Fermi level does not contribute signifi-cantly to DOS below and at εF. The influence of 4f levels on the electrical trans-port is mainly due to scattering of the conduction electrons on the localized spinsof Gd atoms and to some extent due to the hybridization of minority 4f-bandstates with spd-states which modifies the shape and position of spd-DOS aroundthe 6F. The analysis of Fig. 1 shows that the replacement of Gd with isoelectronicY atoms removes the sharp peak of d-DOS from below the εF, broadens and shiftsthe d-states DOS around the εF to higher energies.To calculate spin disorder resistivity for the compounds it is necessary toknow the structure of the lowest excited states which is not available within theground-state TB—LMTO approach. Therefore we apply the well-known structureElectronic Structure and Εlectron-transpοrt Properties ... 785of scattering levels for the Gd alloys at high temperatures [4-6]. In the case of(Gd1—xY)2Ιn alloys we assume that for the static electrical resistivity (only thespin disorder resistivity part is discussed) two kinds of scattering mechanism arecrucial. The first one comes from Gd atoms in the lattice. The Gd high spins (7/2,Hund's rule) cause the scattering mainly via s— f interactions represented by thesecond term of Hamiltonian in Eq. (1). The second mechanism is the scatteringdue to the impurity Y atoms which have the atomic levels slightly shifted whencompared with host Gd2In levels. Assuming the completely disordered distributionof Y atoms and the case of high temperature we can apply the formalism ofcoherent potential approximation (CPA) to obtain the quasiparticle structure andDC electrical resistivity. Within the considered model, only one band undergoesthe scattering. The many-body alloy Hamiltonian takes the formwhere si and Si stand for the conducting electron and Gd-4f spins, respectively.Classical stochastic variable j takes the values 1 or 0, when the lattice site Ri isoccupied by Gd or Y atoms, respectively. The hopping integral tij also dependson substitutional disorder and following Shiba [7] we assumed that ti satisfies therelation tGd,Y = (tGd,Gd • tΥ,Y) 1/2 • Using the approach proposed by Rangete etal. [4] the complicated many-body problem involved in (1) was projected onto thesimpler one-body problem. The resulting Hamiltonian iswhere the stochastic variable Εi at the site Ri takes the values VGd — gS/(2S +1),VGd + g(S + 1)/(2S + 1), and Vy with the probabilities (1 — x)S/(2S + 1),(1 — x)(S + 1)/(2S + 1), and x, respectively [8]. For the one-body alloy Hamil-tonian (2) the CPA procedure was applied. Having the projected spd TB—LMTODOS lying closely to the Fermi level EF we have approximated the model DOSin that region by the triangle DOS shapes. Slightly different band-widths and thepositions of the band centers of gravity (VGd, VY) for Gd 2In and (Gd0.5y0.5)2Inconducting electrons were assumed. According to the TB—LMTO results the aver-age number of the electrons responsible for the electric transport is about one half.Using the realistic value for the s— f coupling constant g we have calculated the sat-uration spin disorder resistivity as a function of Y concentration. Figure 2 presentsthe results of calculations together with the available experimental data [1].The calculated resistivity agrees with the experimental one satisfactorily eventhough we have not fitted the values of the model parameters in order to achievethe best agreement. From the TB—LMTO calculations the positions of the effectiveatomic levels VGd, Vy, and widths of the electronic bands λ Gd , λY located veryclosely to the Fermi level were estimated. The exchange coupling constant g wastaken positive with the realistic for the Gd-compounds value of magnitude. Thedetailed values are listed in the description of Fig. 2. From the results (Fig. 2) it ispossible to recognize the mechanism of the scattering. For the high concentration ofthe Gd atoms (x « 1) the scattering on the different atomic levels is rather small.When the concentration x increases the scattering on atomic Gd spins becomes less786	 W. Borgieł' J. Deniszczykimportant and at the same time drastically increases the resistivity part due to theatomic scattering. There is the value of concentration x for which the resistivityreaches the maximum. Simultaneously with decreasing number of Gd atoms thesystem becomes uniform again and the effect of the atomic scattering becomesless important. In order to get much better agreement between calculated andmeasured resistivities one should use the model in which the influence of chemicaldisorder on the band structure closely to the Fermi level is more accurately takeninto account (e.g. KKR—CPA approach of Banhart et al. [9]).AcknowledgmentsThis work was supported in part by the the Committee for Scientific Research(Poland) under contract No. 2 Ρ03B 129 14.References[1] J. Szade, J. Magn. Magn. Mater. 170, 228 (1997).[2] J. Deniszczyk, W. Borgieł, Mol. Phys. Rep., in press.[3] O.K. Andersen, O. Jepsen, Phys. Rev. Lett. 53, 2571 (1984).[4] A. Rangete, A. Yanase, J. Kubler, Solid State Commun. 12, 171 (1973).[5] W. Nolting, T. Dambeck, G. Borstel, Z. Phys. Β 94, 409 (1994).[6] M. Takahashi, K. Mitsui, Phys. Rev Β 54, 11298 (1996); 56, 7389 (1997).[7] H. Shiba, Progr. Theor. Phys. 46, 77 (197I).[8] W. Borgieł, J. Magn. Magn. Mater. 40, 48 (1983).[9] J. Banhart, H. Ebert, P. Weinberger, J. Vοilander, Phys. Rev Β 50, 2104 (1994).

Electronic structure and electron transport properties of (GdxYx )2 in compounds

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Electronic structure and electron transport properties of (GdxYx )2 in compounds

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