Magnetization and exchange interactions in Zn1−xFexTe diluted magnetic semiconductors

PERGAMON

Solid State Communications 113 (2000) 695–698 www.elsevier.com/locate/ssc

Magnetization and exchange interactions in Zn12xFexTe diluted magnetic semiconductors C. Testelin a,*, J.B. Prost a, M. Menant a, M. Zielinski b, A. Mycielski b a

Groupe de Physique des Solides, Universite´s Paris 6 et 72, place Jussieu, 75251 Paris Cedex 05, France b Institute of Physics, Polish Academy of Sciences, Al. Lotnikow 32/46, 02668 Warsaw, Poland Received 4 November 1999; accepted 6 December 1999 by B. Jusserand

Abstract Magnetization and magnetoreflectivity measurements have been performed in diluted Zn12xFexTe compounds, at T ˆ 1:8 K: The magnetization of Fe 21 ions is quantitatively analyzed in the framework of the crystal field and spin–orbit coupling model and is in excellent agreement with the crystal field and spin–orbit coupling parameters we deduced from previous optical studies (D ˆ 22693 cm21 and l ˆ 2102:2 cm21 ). The six Zeeman-like components of the free exciton spectrum are observed, in Faraday or Voigt configuration. The comparison between the energy splittings and the magnetization data yields the values for the conduction and valence exchange parameters: N0 a ˆ 0:29 ^ 0:09 eV and N0 b ˆ 21:50 ^ 0:17 eV: q 2000 Elsevier Science Ltd. All rights reserved. Keywords: A. Semiconductors; D. Exchange and superexchange; E. Light absorption and reflection

1. Introduction The characteristic feature of diluted magnetic semiconductors (DMS) is a strong exchange interaction between 3d electrons localized on paramagnetic ions (Mn, Fe, …) and band carriers (s or p). This interaction leads to giant Faraday rotations and a large Zeeman splitting of the free exciton. The available data on DMS, show that the s–d exchange is almost independent of the DMS crystal, whereas the p–d exchange varies strongly with both magnetic ion and host lattice. In the past, these effects have been intensively investigated in Mn-based compounds [1] and in some Fe-based materials (Zn12xFexSe [2]; Cd12xFexSe [3,4]; Cd12xFexTe [5]). Contrary to ZnTe:Mn, Co compounds studied before, sp–d exchange interactions in Zn12xFexTe materials were not an object of detailed research, mainly because of difficulties in preparing crystals of good quality for magnetooptical studies: to our knowledge, only Mac et al. [6] have presented some magnetooptical results on Zn12xFexTe. Unfortunately, the iron concentration was too low so that they have detected only two circularly polarized excitonic transitions among the four transitions allowed in the Faraday * Corresponding author.

configuration. This lack of data leads to a large uncertainty on the sp–d exchange integrals N0a and N0b and does not permit to estimate both exchange integrals independently (the authors estimate the p–d exchange integral N0 b ˆ 21:9 ^ 0:45 eV; assuming N0 a ˆ 0:2 eV). The purpose of this paper is to complete the data on the exchange integrals in DMS compounds. We present a study of the magnetization and the exchange phenomena in Zn12xFexTe by means of low temperature magnetoreflectivity in Faraday and Voigt configurations and magnetization experiments.

2. Experimental details Zn12xFexTe crystals were grown by a modified Bridgman method [7]. We selected homogeneous samples whose iron molar fraction was determined by X-ray fluorescence (XRF). We used slides of unoriented ingots which were prepared for optical measurement by polishing and chemical etching. The homogeneity of each investigated sample was controlled by the determination of the exciton energy on different regions of the sample surface and by comparison of XRF concentration measurements with the values evaluated from magnetization curves.

0038-1098/00/$ - see front matter q 2000 Elsevier Science Ltd. All rights reserved. PII: S0038-109 8(99)00566-9

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C. Testelin et al. / Solid State Communications 113 (2000) 695–698

Fig. 1. Magnetization of samples I and II versus magnetic field, at T ˆ 1:8 K: Open and close symbols are experimental data for samples I and II, respectively. Dashed lines: calculated magnetization for Fe content determined by X-ray fluorescence (x ˆ 0:875 and 1.21%). Solid lines: best fits for x ˆ 0:86 and 1.16%, respectively.

Magnetization measurements were carried out in fields up to 5 T, using a SQUID magnetometer, at T ˆ 1:8 K: Experimental data are presented in Fig. 1 for two compounds with Fe content xˆ 0:875 ^ 0:05% (sample I) and xˆ 1:21 ^ 0:09% (sample II), after subtracting the diamagnetic contribution of the lattice (xd ˆ 23:0 × 1027 emu=g [8]). Magnetoreflectivity has been performed at near normal incidence up to 7 T and T ˆ 1:8 K: Faraday (magnetic field B parallel to the light wave vector k) and Voigt (B perpendicular to k) configurations have been investigated in order to observe the two allowed excitonic transitions in both circular polarizations (s 1, s 2) and in the p polarization. Magnetoreflectivity spectra are presented in Fig. 2 for a sample with Fe content xˆ 0:58% at zero magnetic field and at B ˆ 7 T for the three distinct polarizations.

Fig. 2. Reflectivity spectra for Zn12xFexTe …x ˆ 0:58%† at T ˆ 1:8 K: (a) in zero magnetic field; (b) in Faraday (s 1, s 2 polarization) and Voigt (p polarization) configurations at B ˆ 7 T:

tion from the singlet G 1 ground state to G 5T has been observed at 2486 cm 21 for Zn12xFexTe [12]. Furthermore, the G 1 ! G 4 transition has been seen by Raman spectroscopy at 18.2 cm 21 [13]. Using these experimental values and the model developed in Ref. [9], we determine the crystal field (D ˆ 22693 cm 21 ) and spin–orbit coupling (l ˆ 2102:2 cm21 ) parameters. We have then analyzed the magnetization data according to the model developed in Ref. [11] for Fe compounds with the zinc blende structure. The magnetization per unit mass of isolated Fe 21 ions, taking into account antiferromagnetic nearest-neighbour interactions, is described by: NA x…1 2 x†12 kLz 1 2Sz l m…x†

3. Magnetization

M ˆ mB

The magnetic properties of Zn12xFexTe are governed by the 3d 6 electronic configuration of Fe 21 ions which possess both orbital and spin angular momentum …L ˆ 2; S ˆ 2†: The optical spectra of Fe 21 ion in cubic crystal were previously investigated [9–11]. In a tetrahedral symmetry, the 5D configuration of the free Fe 21 ion is split by the crystal field into an orbital doublet 5E and a triplet 5T2 (separated by D) lying at higher energy. Furthermore, the spin–orbit interaction splits the 5E ground state into five nearly equidistant levels (G 1, G 4, G 3, G 5, G 2) separated by about 6l 2 =D with l being the spin–orbit parameter. The 5T2 level is split into six levels, with G 5T the lowest energy level. The ground state G 1 is a magnetically inactive singlet resulting in a Van Vleck-type paramagnetism. The optical transi-

where mB is the Bohr magneton, NA the Avogadro number, m(x) the molar mass of Zn12xFexTe, kLz 1 2Sz l the z-component of the magnetic moment …B k z† for an isolated ion, at T ˆ 1:8 K; defined in Ref. [11]. Due to the low Fe concentration, we neglect the contribution of iron clusters. Using D ˆ 22693 cm21 and l ˆ 2102:2 cm21 ; we have calculated the z-component of the magnetic momentum kLz 1 2Sz l versus H. Magnetization curves are fitted to the experimental data for samples I and II by adjusting only the Fe concentration. The best fits, reported in Fig. 1, correspond to xˆ 0:86 and 1.16% for samples I and II, respectively. An excellent agreement is found with iron contents obtained from XRF analysis.

…emu=g†

…1†

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Fig. 3. Energy of the exciton line as a function of the Fe content at T ˆ 1:8 K: The line corresponds to a least-square fit to the data.

4. Magnetoreflectivity In the absence of applied magnetic field, the reflectivity spectrum exhibits a strong structure, corresponding to the free exciton ground state (Fig. 2a). The exciton line energy Eex was measured at T ˆ 1:8 K on 12 samples, whose the iron concentration x was determined by XRF or from magnetization. Eex(x) is described by a linear relation in the investigated composition range (0–1.2%) (see Fig. 3). From a least-square fit of the data, we obtain: Eex …x† ˆ …2379 ^ 0:5† 1 …1200 ^ 40†x

…meV†

…2†

In the presence of an external magnetic field, the conduction and valence bands undergo a large exchange induced splitting, which affects the free exciton spectroscopy. The exciton spectrum splits into four Zeeman-like components in the Faraday configuration and into two components in the Voigt configuration. Magnetoreflectivity spectra for s 1, s 2 and p are reported in Fig.2b for an alloy of concentration

xˆ 0:58%; in a magnetic field H ˆ 7 T: Two reflectivity lines (marked by an arrow) are observed in each polarization (s 1, s 2 and p). The energy of the six excitonic components versus magnetic field is reported in Fig. 4. The linear and the weak circular components are resolved above 4.5 and 5.5 T, respectively. We have analyzed the data in the framework of the conventional exchange model, assuming a Heisenberg form for the s–d and p–d exchange interactions [14]. The exchange contributions to G 6 and G 8 energies are: E Gexch ˆ N0 ax…1 2 x†12 kSZ lms 6 EGexch ˆ N0 8

b x…1 2 x†12 kSZ lMJ 3

…ms ˆ ^1=2† …MJ ^ 3=2; ^1=2†

…3†

where kSZ l is the thermal average of Fe 21 ion spin along the magnetic field axe, N0 the number of unit cells per unit volume, a and b are the exchange integrals for conduction and valence bands, respectively.

Fig. 4. Energy of the six Zeeman-like components as a function of the magnetic field up to 7 T, at T ˆ 1:8 K and x ˆ 0:58%; closed circles, open circles and crosses are for the s 2, s 1 and p polarizations, respectively.

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The exchange integrals are then obtained: N0 a ˆ 0:29 ^ 0:09 eV

Fig. 5. Zeeman splitting DE1, DE2, DEp versus magnetization for three samples: x ˆ 0:54% (closed circles), x ˆ 0:58% (open circles) and x ˆ 0:86% (closed squares). Solid lines are the least-square fits to the data.

N0 b ˆ 21:50 ^ 0:17 eV

To conclude, using homogeneous Zn12xFexTe crystals with good optical properties, we have been able to observe the six allowed excitonic transitions and to analyze quantitatively the magnetization of this compound, at low temperature. It was then possible to determine the value of the two exchange integrals, with a good accurancy, contrary to Ref. [6]. N0 a shows a ferromagnetic s–d exchange interaction and is in the range 0.2–0.3 eV, as commonly observed for other II–VI DMS. The p–d exchange interaction is antiferromagnetic and the value of N0 b for Zn12xFexTe lies between the results obtained for ZnMnTe (21.05 eV) and ZnCoTe (23.03 eV), in agreement with the chemical tendency already found in other DMS [15].

Acknowledgements The splittings DE1 and DE2 of the strong and weak transitions allowed for s polarization and the splitting DEp associated to the p-polarization are: DE1 ˆ E3=2!1=2 2 E23=2!21=2 ˆ N0 …a 2 b†x…1 2 x†12 kSZ l   b DE2 ˆ E1=2!21=2 2 E21=2!1=2 ˆ 2N0 a 1 x…1 2 x†12 kSZ l 3   b DEp ˆ E1=2!1=2 2 E21=2!21=2 ˆ N0 a 2 x…1 2 x†12 kSZ l 3 …4† Within the crystal field model developed in Ref. [11], we have estimated the ratio of the magnetic momentum kLZ 1 2SZ l to the spin component kSZ l for D ˆ 22693 cm21 and l ˆ 2102:2 cm21 : We found kLZ 1 2SZ l=kSZ l ˆ 2:275 ^ 0:005 independently of the magnetic field value, at T ˆ 1:8 K; implying the proportionality of the splittings (4) to the magnetization (1). The experimental verification of the proportionality between the Zeeman splitting DE1 ; DE2 ; DEp ; and the macroscopic magnetization M measured on the same samples, is presented in Fig. 5 for samples of different iron content (x ˆ 0:54; 0.58 and 0.86%). Least-square fits of DE1, DE2 and DEp lead to: N0 …a 2 b† ˆ 1:76 ^ 0:1 eV   b N0 a 1 ˆ 20:26 ^ 0:16 eV 3   b N0 a 2 ˆ 0:86 ^ 0:11 eV 3

One of the authors, Marcin Zielinski, would like to thank Socie´te´ de Secours des Amis des Sciences for the financial support during part of this work.

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