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Carrier-ion exchange interaction in diluted magnetic semiconductors
Journal of Magnetism North-Holland
and Magnetic
Materials
104-107
(1992) 995-996
Carrier-ion exchange interaction magnetic semiconductors J.P. Lascaray ‘, F. Hamdani ‘, D. Coquillat I’G.E.S. UrziomitC Mmtprllier II, Pluce E. Batuillon, 34095 ” Luhorutoire
dr Physique
des Solides,
Unirwsite’
in diluted
a and A.K. Bhattacharjee Montpellier
h
Cedex 5, Frunce
Puris Sud, Centre d’Orsuy,
91405 Orsuy Cedex, Frunce
We have determined the exchange constants N,,cu (conduction band) and N,,p (valence band) in Cd, oxFe ,Te, Zn, ,Co,Se and Cd, ~, Co, Se. Using these and other available data we discuss the variation of N,,cu and N,,p with the transition-metal ion in d.ifferent host lattices. Manganese-based
diluted
magnetic
semiconductors
(DMS) such a Cd, ,Mn,YTc have been extensively studied during the past fifteen years. Interesting magnetic and magneto-optical properties of these systems arise from the exchange interaction between Mn ions on the one hand, and that between band electrons and Mn ions on the other. The former (d-d exchange) is usually represented by the Heisenberg Hamiltonian and the latter (sp-d exchange) by the Kondo Hamiltoman. The Mn’+ ion (3d’) is well described in terms of the Hund’s rule ground state: L = 0, S = S/2. New materials have been synthesized with iron as the magnctic ion and, more recently, with cobalt. The rcspcctive free-ion ground states “D and 4F arc split by the crystalline electric field and the spin-orbit interaction. Nevertheless, the same spin-only Kondo Hamiltonian proves adequate for explaining the magneto-optical properties of the Fe- and Co-based DMS. In this paper we focus our attention on the sp-d exchange constants N,,cy and N,,/3, for the conduction and valence band edges, respectively, and their variation with the transition-metal ion in different host lattices. We first present our determination of N,~N and and Cd,_,Co,Se, N,,p in Cd, ~I Fc,Te, Zn i .,Co,Se by combining magnetoreflectivity and magnetization measurements. Experiments were carried out at 1.8 K in magnetic fields of up to 5.5 T. In a magnetic field the T, conduction band splits into two components; the splitting is N,,cux(S,), where the average ion spin is related to the magnetization M =gpfiN,,x(S,). It is important to note that g,, = 2, but g,, = 2.29 and (CdFeTe) g,., = 2.3 (CdCoSe) because of the orbital contribution. In a zinc blende DMS, The TX valence band splits into four components, the overall splitting being N,$x(SZ). Thus, the Zeeman splittings of the exciton line plotted against X( Sz> yield straight lines, the slope of each giving the corresponding linear combination of N~)(Yand N,,/3. In the Faraday configuration, the exciton line splits into a strong and a weak component in each polarization, which are well resolved in Mn-based DMS, leading to accurate values of NOcy and N,,p. In CdFeTe and ZnCoSe the excitonic structure is broad 0312~8853/92/$05.00
0 1992 - El-sevier Science
Publishers
and the weak component hard to locate. We, therefore, carried out complementary magnetoreflectivity measurements in the Voigt configuration with the r polarization (E I/ B). The exchange constants, thus dctermined are [1,2]: N(,N = 0.216 eV, N,,p = ~ 1.28 eV and N,,a = 0.231 eV, N,,/3 = ~1.853 in Cd ,_,Fe,Te, cV in Zn , -.,Co,Se. The situation in the DMS wurtzitc is more complicated. The crystalline electric field and spin-orbit interaction split the upper valcncc band into three subbands, giving rise to excitonic transitions labellcd A, B and C. These are mixed by the exchange field. A mean-field analysis based on the full (6 X 6) cffcctive Hamiltonian yields the band splittings. They depend strongly on the orientation of the applied magnetic field with respect to the c-axis of the crystal. N,,a and N,,p can then be derived by fitting the exciton splittings observed in the Faraday and Voigt configurations with B I/ C, by assuming that the crystal-field and spin-orbit parameters are the same as in the host matrix. This approach was followed in ref. [3] for Cd,_,Co.,Sc. Here we present the results of a more direct method. N,,(a ~ /3) is first deduced from the A exciton splitting in the Faraday configuration with B 11C. N,,a is obtained by measuring the conduction band splitting, through the observation of the cxcitonic transitions allowed between a given valence subband and the two conduction band components in the B I C geometry. An example of the magnetoreflectivity spectra is shown in fig. 1. We obtain [4]: N,,cu = 0.258 eV and N,,p = - I.883 eV in Cd, _,Co,Se. Together with our results, a set of available N,,o and N,,/3 values are presented in table 1. Clearly, the overall variation of N,,rw is rather small. However, I N,,p I increases systematically as one passes from Mn to Fe to Co in a given host. We now discuss the variation of the exchange parameters with the transition-metal ion within the framework of ref. [5]. The relatively weak ferromagnetic (positive) value of Nr,cy corresponds to the ordinary “potential” exchange. For an s-like conduction band, it is expected to vary little with the number of electrons in the d shell [6]. Indeed, the experimental
B.V. All rights reserved
996 Table 1 ion-Carrier exchange parameters brackets arc references Parameter feV)
CdMnSe
CdFeSe
CdCoSe
11.31
[I41
[41 0.258 - I .X83
N,P
0.26 I
jV,li,,B
determined
-
I.238
-
0.250 I .450
by magneto-optical
CdMnTe
CdFeTc
[31
[‘)I
[lOI
Dl
[I21
[II
[ISI
0.27’) - 1.873
0.26 - I.31
0.244 - 1.74
0.23 1 - 1.X53
0.22 - 0.88
0.2h ~ 1.28
0.30 ~ 1.27
1 E, + UC,,- E,, I
B //
(1)
c
Et
5T
5T
1.82
1.85
i.88 ENERGY
1.91
1.94
i.97
DMS. Numbers
ZnCoSe
in the usual notation. In general, for a non-S state ion, hybridization yields not only the spin-spin exchange term retained above but also the orbital exchange terms. Howcvcr, the latter are quenched in the case of the Fe and Co ions in tetrahedral symmetry [S]. In the strong crystal-field coupling scheme, the respective ground states 5E and ‘A2 belong to the configurations c3tG and e”t:, whereas the ‘A, ground state of Mn belongs to c’t;. Thus, in all three cases, every t2 orbital is singly occupied. As only t, orbitals hybridize with the valence band at I, eq. (11 ;s expected to be a
A
iron and cobalt
ZnFeSe
values in table 1 show only a small variation. On the other hand, the strong antiferromagnetic (negative) value of N,,p is dominated by “kinetic” cxchangc arising from the hybridization of the d orbitals with the anion p-like valcncc band states. For the S-state on Mn, neglecting direct exchange, it is given by the gcncralized Schrieffer-Wolff formula [7]:
r+ A
for manganese,
ZnMnSe
Nno
1 p+ E,. - E,
experiments
2.00
(eV)
Fig. 1. Magnetoreflectivity spectra of Cd,,,,Co,,,,,,Se at T = 1.X K in the Faraday and Voigt configurations using circular and linear polarizations respectively with B ]]C. The A and B exciton components are indicated.
good approximation
in
for Fc and Co as well. A compara-
experiments in photoemission Cd , , Mn , Se and Cd, 1Fe, Se suggests a smaller value of U,,, in Fe [l 11, leading to an increase of the sum in the square brackets in cq. (I) by about 15%. On the other hand, according to Harrison’s rules we cxpcct a decrease of the p-d hybridization parameter V,,,, due to decreasing d-shell radius. Apparently these two cffects more or less compensate: the scaling factor (2s) ’ by itself can roughly account for the observed increase of / N,$I from Mn to Fe to Co. Howcvcr, further experimental studies, namely, EXAFS for bond lengths and photoemission for energy levels, arc indispcnsablc for a more quantitative evaluation of the model. To conclude, WC have presented sp-d exchange constants in recently synthesized Fc- and Co-based DMS and explained the large variation of N,,p with the transition-metal ion within the Schrieffer-Wolff framework. tivc
analysis
of
References [I] D. Coquillat et al., to be published. [2] F. Hamdani et al., to be published. [3] M. Nawrocki, F. Hamdani, J.P. Lascaray. Z. Golacki and J. Deportes, Solid State Commun. 77 (1991) 1I I. [4] F. Hamdani et al., to he published. [S] A.K. Bhattacharjee. G. Fishman and B. Coqblin. Physica B 117& 118(1983)449. [6] S.11. Liu. Phys. Rev. 121 (1961) 451. [7] J.R. Schrieffer, J. Appl. Phys. 3X flYh7) 1143. [X] J. Blinowski and P. Kacman, Proc. 20th Int. Conf. on the Physics of Semiconductors. ed. E.M. Anastassakis and J.D. Joannopoulos (World Scientific. Singapore, IYYO) p. I X27. [9] A. Twardowski, M. Von Ortenberg, M. Demianiuk and R. Pauthenet, Solid State Commun. 51 (lY84) 849. [IO] A. Twardowski. P. Gold, W.J.M. de Jonge and M. Demianiuk, Solid State Commun. 64 (19X7) 63. [l I] M. Taniguchi. Y. Ueda, 1. Morisada. Y. Murashita and Y. Oka, Phya. Rev. B 41 (1990) 3069. [12] J.A. Gaj, R. Plane1 and G. Fishman. Solid State Commun. 29 (1979) 435. [13] M. Arcisrewska and M. Nawrocki. J. Phys. Chem. Solids. 47 (1986) 30’). [14] D.W. Shih, R.L. Aggarwal, Y. Shapira. S.H. Bloom. V. Bindilatti. R. Kershaw, K. Dwight and A. Wold. Solid State Commun. 67 (1990) 5107. [IS] C. Testelin, C. Rigaux, A. Mycielski, M. Menant and M. Guillot, Solid State Commun., in press.
and Magnetic
Materials
104-107
(1992) 995-996
Carrier-ion exchange interaction magnetic semiconductors J.P. Lascaray ‘, F. Hamdani ‘, D. Coquillat I’G.E.S. UrziomitC Mmtprllier II, Pluce E. Batuillon, 34095 ” Luhorutoire
dr Physique
des Solides,
Unirwsite’
in diluted
a and A.K. Bhattacharjee Montpellier
h
Cedex 5, Frunce
Puris Sud, Centre d’Orsuy,
91405 Orsuy Cedex, Frunce
We have determined the exchange constants N,,cu (conduction band) and N,,p (valence band) in Cd, oxFe ,Te, Zn, ,Co,Se and Cd, ~, Co, Se. Using these and other available data we discuss the variation of N,,cu and N,,p with the transition-metal ion in d.ifferent host lattices. Manganese-based
diluted
magnetic
semiconductors
(DMS) such a Cd, ,Mn,YTc have been extensively studied during the past fifteen years. Interesting magnetic and magneto-optical properties of these systems arise from the exchange interaction between Mn ions on the one hand, and that between band electrons and Mn ions on the other. The former (d-d exchange) is usually represented by the Heisenberg Hamiltonian and the latter (sp-d exchange) by the Kondo Hamiltoman. The Mn’+ ion (3d’) is well described in terms of the Hund’s rule ground state: L = 0, S = S/2. New materials have been synthesized with iron as the magnctic ion and, more recently, with cobalt. The rcspcctive free-ion ground states “D and 4F arc split by the crystalline electric field and the spin-orbit interaction. Nevertheless, the same spin-only Kondo Hamiltonian proves adequate for explaining the magneto-optical properties of the Fe- and Co-based DMS. In this paper we focus our attention on the sp-d exchange constants N,,cy and N,,/3, for the conduction and valence band edges, respectively, and their variation with the transition-metal ion in different host lattices. We first present our determination of N,~N and and Cd,_,Co,Se, N,,p in Cd, ~I Fc,Te, Zn i .,Co,Se by combining magnetoreflectivity and magnetization measurements. Experiments were carried out at 1.8 K in magnetic fields of up to 5.5 T. In a magnetic field the T, conduction band splits into two components; the splitting is N,,cux(S,), where the average ion spin is related to the magnetization M =gpfiN,,x(S,). It is important to note that g,, = 2, but g,, = 2.29 and (CdFeTe) g,., = 2.3 (CdCoSe) because of the orbital contribution. In a zinc blende DMS, The TX valence band splits into four components, the overall splitting being N,$x(SZ). Thus, the Zeeman splittings of the exciton line plotted against X( Sz> yield straight lines, the slope of each giving the corresponding linear combination of N~)(Yand N,,/3. In the Faraday configuration, the exciton line splits into a strong and a weak component in each polarization, which are well resolved in Mn-based DMS, leading to accurate values of NOcy and N,,p. In CdFeTe and ZnCoSe the excitonic structure is broad 0312~8853/92/$05.00
0 1992 - El-sevier Science
Publishers
and the weak component hard to locate. We, therefore, carried out complementary magnetoreflectivity measurements in the Voigt configuration with the r polarization (E I/ B). The exchange constants, thus dctermined are [1,2]: N(,N = 0.216 eV, N,,p = ~ 1.28 eV and N,,a = 0.231 eV, N,,/3 = ~1.853 in Cd ,_,Fe,Te, cV in Zn , -.,Co,Se. The situation in the DMS wurtzitc is more complicated. The crystalline electric field and spin-orbit interaction split the upper valcncc band into three subbands, giving rise to excitonic transitions labellcd A, B and C. These are mixed by the exchange field. A mean-field analysis based on the full (6 X 6) cffcctive Hamiltonian yields the band splittings. They depend strongly on the orientation of the applied magnetic field with respect to the c-axis of the crystal. N,,a and N,,p can then be derived by fitting the exciton splittings observed in the Faraday and Voigt configurations with B I/ C, by assuming that the crystal-field and spin-orbit parameters are the same as in the host matrix. This approach was followed in ref. [3] for Cd,_,Co.,Sc. Here we present the results of a more direct method. N,,(a ~ /3) is first deduced from the A exciton splitting in the Faraday configuration with B 11C. N,,a is obtained by measuring the conduction band splitting, through the observation of the cxcitonic transitions allowed between a given valence subband and the two conduction band components in the B I C geometry. An example of the magnetoreflectivity spectra is shown in fig. 1. We obtain [4]: N,,cu = 0.258 eV and N,,p = - I.883 eV in Cd, _,Co,Se. Together with our results, a set of available N,,o and N,,/3 values are presented in table 1. Clearly, the overall variation of N,,rw is rather small. However, I N,,p I increases systematically as one passes from Mn to Fe to Co in a given host. We now discuss the variation of the exchange parameters with the transition-metal ion within the framework of ref. [5]. The relatively weak ferromagnetic (positive) value of Nr,cy corresponds to the ordinary “potential” exchange. For an s-like conduction band, it is expected to vary little with the number of electrons in the d shell [6]. Indeed, the experimental
B.V. All rights reserved
996 Table 1 ion-Carrier exchange parameters brackets arc references Parameter feV)
CdMnSe
CdFeSe
CdCoSe
11.31
[I41
[41 0.258 - I .X83
N,P
0.26 I
jV,li,,B
determined
-
I.238
-
0.250 I .450
by magneto-optical
CdMnTe
CdFeTc
[31
[‘)I
[lOI
Dl
[I21
[II
[ISI
0.27’) - 1.873
0.26 - I.31
0.244 - 1.74
0.23 1 - 1.X53
0.22 - 0.88
0.2h ~ 1.28
0.30 ~ 1.27
1 E, + UC,,- E,, I
B //
(1)
c
Et
5T
5T
1.82
1.85
i.88 ENERGY
1.91
1.94
i.97
DMS. Numbers
ZnCoSe
in the usual notation. In general, for a non-S state ion, hybridization yields not only the spin-spin exchange term retained above but also the orbital exchange terms. Howcvcr, the latter are quenched in the case of the Fe and Co ions in tetrahedral symmetry [S]. In the strong crystal-field coupling scheme, the respective ground states 5E and ‘A2 belong to the configurations c3tG and e”t:, whereas the ‘A, ground state of Mn belongs to c’t;. Thus, in all three cases, every t2 orbital is singly occupied. As only t, orbitals hybridize with the valence band at I, eq. (11 ;s expected to be a
A
iron and cobalt
ZnFeSe
values in table 1 show only a small variation. On the other hand, the strong antiferromagnetic (negative) value of N,,p is dominated by “kinetic” cxchangc arising from the hybridization of the d orbitals with the anion p-like valcncc band states. For the S-state on Mn, neglecting direct exchange, it is given by the gcncralized Schrieffer-Wolff formula [7]:
r+ A
for manganese,
ZnMnSe
Nno
1 p+ E,. - E,
experiments
2.00
(eV)
Fig. 1. Magnetoreflectivity spectra of Cd,,,,Co,,,,,,Se at T = 1.X K in the Faraday and Voigt configurations using circular and linear polarizations respectively with B ]]C. The A and B exciton components are indicated.
good approximation
in
for Fc and Co as well. A compara-
experiments in photoemission Cd , , Mn , Se and Cd, 1Fe, Se suggests a smaller value of U,,, in Fe [l 11, leading to an increase of the sum in the square brackets in cq. (I) by about 15%. On the other hand, according to Harrison’s rules we cxpcct a decrease of the p-d hybridization parameter V,,,, due to decreasing d-shell radius. Apparently these two cffects more or less compensate: the scaling factor (2s) ’ by itself can roughly account for the observed increase of / N,$I from Mn to Fe to Co. Howcvcr, further experimental studies, namely, EXAFS for bond lengths and photoemission for energy levels, arc indispcnsablc for a more quantitative evaluation of the model. To conclude, WC have presented sp-d exchange constants in recently synthesized Fc- and Co-based DMS and explained the large variation of N,,p with the transition-metal ion within the Schrieffer-Wolff framework. tivc
analysis
of
References [I] D. Coquillat et al., to be published. [2] F. Hamdani et al., to be published. [3] M. Nawrocki, F. Hamdani, J.P. Lascaray. Z. Golacki and J. Deportes, Solid State Commun. 77 (1991) 1I I. [4] F. Hamdani et al., to he published. [S] A.K. Bhattacharjee. G. Fishman and B. Coqblin. Physica B 117& 118(1983)449. [6] S.11. Liu. Phys. Rev. 121 (1961) 451. [7] J.R. Schrieffer, J. Appl. Phys. 3X flYh7) 1143. [X] J. Blinowski and P. Kacman, Proc. 20th Int. Conf. on the Physics of Semiconductors. ed. E.M. Anastassakis and J.D. Joannopoulos (World Scientific. Singapore, IYYO) p. I X27. [9] A. Twardowski, M. Von Ortenberg, M. Demianiuk and R. Pauthenet, Solid State Commun. 51 (lY84) 849. [IO] A. Twardowski. P. Gold, W.J.M. de Jonge and M. Demianiuk, Solid State Commun. 64 (19X7) 63. [l I] M. Taniguchi. Y. Ueda, 1. Morisada. Y. Murashita and Y. Oka, Phya. Rev. B 41 (1990) 3069. [12] J.A. Gaj, R. Plane1 and G. Fishman. Solid State Commun. 29 (1979) 435. [13] M. Arcisrewska and M. Nawrocki. J. Phys. Chem. Solids. 47 (1986) 30’). [14] D.W. Shih, R.L. Aggarwal, Y. Shapira. S.H. Bloom. V. Bindilatti. R. Kershaw, K. Dwight and A. Wold. Solid State Commun. 67 (1990) 5107. [IS] C. Testelin, C. Rigaux, A. Mycielski, M. Menant and M. Guillot, Solid State Commun., in press.