Resonant Raman scattering on low energy excited states of Fe2+ in Cd1−xFexSe

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Journal of Crystal Growth 101 (1990) 940—943 North-Holland

RESONANT RAMAN SCATTERING ON LOW ENERGY EXCITED STATES OF Fe2~IN Cd 1_~Fe~Se D. SCALBERT, J.A. GAJ and A. MYCIELSKI * * Groupe de Physique des Solides * F-75251 Paris Cedex 05, France

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*

*

A. MAUGER, J. CERNOGORA, C. BENOIT

A LA GUILLAUME

de I’Ecole Normale Supérieure, Tour 23, Université Paris VII, 2 Place Jussieu,

2 ± in Cd The spectrum of low energy excited states of Fe 5 ~Fe~Se has been studied through Raman scattering. (1) The energy position of the first two excited states of symmetry A2 and E have been determined as a function of the applied magnetic field i c and c up to 6 T; they are in very good agreement with a crystal field model. (2) Strong resonant effects on free and bound exciton states have been observed and explained. (3) Above the free exciton level, a cascade process involving mainly n(A1 —. A2) excitations is studied. Backscattering on a face I c strongly favours crossed linear polarizations at each step of the cascade; a longitudinal magnetic field causes an 2* analog ions.of Hanle effect. Analysis of the data gives access to the polariton lifetime and its probability of inelastic scattering on Fe

1. Introduction In this paper we consider the Fe2 ± ion, substituting Cd2~in Cd 2~ ion energy Fe crystal field levels are treated in the1~Fe~Se. conventional model [1]; the most interesting to us will be the ground state A 1 and the first of excited state T2 which splits under the influence the axial cornponent of the crystal field into a singlet A 2 and a doublet E; they are closely linked to Van Vieck paramagnetism. Previous Raman scattering measurements in Cd1 ±Fe~Se [2,3] have determined the positions of the two lowest-lying excited states A2 and E, relative to the ground state A1 the latter values are 13 cm~ and ~E2 17.6 cm’ respectively [3]. =

=

tions in a magnetic field up to 6 T. Fig. 1 shows the results of field I c or c, they are compared to the calculations of Mauger [4]. Excellent agreement is found, from which the best parameters of the model are obtained [5]: the spin—orbit parameter A 95.17 cm’ and the axial field parameter 1 (crystal field splitting lODq 2620 v 44.47 cm cm~’from ref. [1]). =

=

3. Resonance effects Let us write down a typical resonant Raman matrix element: Rik / 0 k ~4~i X I He X —

\~i X(4

~°

2~spectrum in a magnetic field 2. Fe Raman scattering experiments were performed on an x 0.001 sample using off-resonant condi=

*

* *

* * *

Permanent address: Institute of Experimental Physics, University of Warsaw, Hoza 69, 00-681 Warsaw, Poland. Permanent address: Institute of Physics, Polish Academy of Sciences, Al. Lotmkow 32/46, 02-668 Warsaw, Poland. Unite Associée au Centre National de Ia Recherche Scientifique.

0022-0248/90/503.50 © 1990

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~‘i

ii/\

p’ l~O)/(~j~12), where i and k run over the polarization states of the incident and scattered light respectively, characterized by corresponding components of the momentum operator p. 10) represents electronic vacuum and IX) excitonic states; ~ and 4~.denote the ground and the excited state of the ion, respectively, and ~ and z~energy denominators. 2 H —(aS ±/35 ) S is the exciton—ion exchange e e interaction Hamiltonian, where Se, Sh and S denote spin operators of the electron, hole and Fe2~ 1Xf

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Elsevier Science Publishers B.V. (North-Holland)

D. Scalbert el a!.

2 ± in Cd

low energy excitedstales of Fe

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E 25 I—

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1 — ~Fe~Se

~2S

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~2~

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610a

~

10b I

0

2

I

4 B(T)

I

0

6

I

I

I

4

2

6

B(T)

Fig. 1. Energy of excitations A 1 -. A2 and A1 —. E in Cd1 ~Fe~Se for x 0.001 as a function of magnetic field; (a) for B Ic and (b) for B c. The points are experimental and the lines theoretical; the splitting of E state is well observed.

ion respectively, a and $ denoting corresponding exchange constants. trix element factorizesNote into:that the exchange maIS I 4> 3Sh Xc>. aSe ±/ Since (4>2 1> and <4>2 I 4>~>vanish [4], the A 1 —s A2 process involves a factor —

<4>

=

(X~I aS

+

$S~I~),

which allows resonance on A and B excitons. On the other hand, since <4>~~ I SZ I 4>~> 0, the corresponding factor for the A1 E process will be =

—

We have 2observed analogous incascade + ion excitations sampleseffects with involving Fe 0.018, provided the excitation phox 0.006 and ton energy was chosen a few tens of cm’ above the free exciton A energy. We report the data for x 0.006 at 1.8 K. A spectrum obtained in back=

=

scattering on a face II c is shown in fig. 2: a repetitive element consisting of two lines, a stronger and a weaker one, the latter at a higher energy, is easy to distinguish. The inset, representing energies of both elements as a function of the repetition order n, justifies this assignment,

J,~=(X,jaSe~±/3S~jXt>(orJ,~);

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hence, resonance occurs only on B excitons in agreement with previous work [3]. Let us remark that J~ —J~where ~ and i~ denote exciton states )~ ~>and j ~ ~>in obvious notation.

~1) I—

=

—

—

0 LI

This will be important in point (2) in section 4. >I(0

z

4. Raman cascade (1) Multiphonon Raman scattering in semiconductors excited above the energy gap has been known since the seventies. This phenomenon is coimnonly explained in terms of a cascade [6], where an exciton is created with sufficient kinetic energy and subsequently undergoes a series of inelastic scatterings on optical phonons before reaching the bottom of its band.

F— W

z

10

20

30

40

50

60

70

80

80

RAMAN SHIFT ( cm~

Fig. 2. Cascade Raman spectrum (Stokes shift) of Cd1~Fe~Se for x =0.006 at 1.8 K. Excitation wavenumber: 14860 cm Incident and scattered light propagate perpendicular to the c axis. FE indicates the luminescence of free exciton, near 14785 cm’. The inset shows Raman line energies as a function of repetition order (see text).

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D. Scalbert et a!.

/ RRS on low energy excited states of Fe2 ± in Cd1

showing that we observed Raman lines at energies nLXE1 and (n 1)LIE1 + LIE2, where n 1,..., 6, 12.8 and LIE2 17.6 cm~. We performed an additional check of this assignment, measuring the cascade spectra as a function of magnetic field. The results are shown in fig. 3. For the stronger lines (n LIE1), the Raman shift energy divided by the repetition order forms a single curve for B I c and B II c, justifying the assignment. Note also the agreement with fig. 1. Besides the primary cascade we observed its one- and two-LO phonon replicas. Since in case of 2 phonon transitions k-dependent selection rules are attenuated to k-space the strongly two-phonon replica due of the originalintegration, cascade is of special interest, being a measure of the density of occupied exciton states. For excitation energy 14850 cm1, we observe a ratio ~ 0.25, where I~is the intensity of the n th replica. This ratio is in fact equal to the ratio of the total lifetime T of cascade exciton states to the time TFe —

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~Fez, Se

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o~

~ IL—20

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1

-

XY

~ ‘W~~XX

10

20

30 40 50 RAMAN SHIFT ( cn~

60

70

Fig. 4. Cascade spectrum for a backscattersng on a face I1.c with linear polarizations. Excitation wavenumber: 14845 cm xx and XY represents respectively parallel and crossed configurations. The inset shows the rate of linear polarization for n = 1, 2, 3 as a function of magnetic field B

=

characterizing diffusion of the exciton on 2~ions. Weinelastic obtain thus: T/TFe 0.25. Fe (2) Very peculiar polarization effects are observed in a backscattering geometry on a face perpendicular to the c axis. Using circular polanzations, the same polarization is predominantly re-emitted. The polarization of each line of the =

20

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E

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cc

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MAGNETIC FIELD

(

)

Fig. 3. Stokes shifts of Raman lines correspondmg to dsfferent A 1 —. A2 replicas (divided by repetition order) plotted versus magnetic field: (0) BIc; (*) Blic; ( ) theory [4].

cascade with respect to that of the previous one, P~+ 1/Pa, is close to 1. That means that the polarization 7~of theis cascade states is(spin) longerrelaxation than theirtime lifetime r. It easy to show that P 1/T 9÷1/Pa 7/(T2 + r); we obtain 4. A very different picture is obtained when Raman scattering is analyzed in terms of linear polarizations. Fig. 4 shows that linear polarization of the exciting light is conserved for cascade lines of pair order. For impair replicas, the polarization is perpendicular to that of the excitation light. To our knowledge no Raman cascade of such properties has been observed before. Attempting to describe a Raman cascade, we face a complicated situation due to the polariton character of the cascade states, involving in principIe k-dependent selection rules and multiple integration over k-space. In what follows we shall restrict ourselves to a simplified picture involving creation, scattering and recombination of simple excitonic states averaged over all possible k values. The remark at the end of section 3 gives the solution: the sign reversal of J~with the angular momentum of the exciton state induces a sign =

=

reversal of the Raman matrix element between Z + + Z and Z Z processes, Z + Z being —

—

—

D. Scalbert et a!.

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2 ± in Cd, — ,~Fe~ Se

RRS on low energy excited states of Fe

forbidden. An obvious consequence is that the ZxxZ process is forbidden and ZxyZ allowed. So, at each step in the cascade, crossed linear polanzation is emitted. This is related to the symmetry of the (A 1 A2) excitation left in the crystal, characteristic of a rotation and not of a vibration. It is interesting that inspecting a table of Raman tensors in crystals collected by Loudon [7], we do not find such a case.

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The sign reversal of the polarization with increasing field, which is clearly observed for n = 3, is a specific feature of n> 1 replicas in a cascade [10].

—*

(3) With a longitudinal field, the (see rate of linear polarization of themagnetic replicas decreases inset of fig. 4) and even reverses its sign for replica n = 3. Unlike the linear polarization, the circular one is not appreciably affected by a magnetic field of the same order. This effect, analogous to the Hanle effect influence of a transverse magnetic field on a circularly polarized emission has been reported for a first order resonant Raman effect under the name of resonant Faraday effect by Nawrocki et al. [8]. It involves a rotation of the polarization plane corresponding to the phase dif—

—

ference between the two circular polarizations (which are the eigenstates). The analysis developed in refs. [8,91 can be easily generalized following the procedure for the Hanle effect and leads to the determination of the field for which wT = 1, where hc~iis the splitting of the exciton induced by 1)1,states the polarization the field In and T= to (T~ lifetime. order get +anT~ absolute time-scale, we determine w from magnetoreflectivity measurements in the Faraday configuration for B II C: (2iw) = 33 cm’ for 1 T. These results allowed us to determine a value of T = 0.2 ps. Knowing r/T 2

(point (2)) and TFe/T (point (1)), we can now determine = 0.25 ps,values ~‘2 = 1 of psall andthose TFC =three 1 ps parameters: for h(~)exc 14850 cm~. The small value of T~ may in fact result from projection effects in inelastic events on Fe2 rather than from true spin relaxation in quasi-elastic collisions. This effect may result in a modification of r and TFe values, which, however, is not significant in view of the large experimental error of T. +

5. Conclusions With the help of resonant Raman scattering, we have analyzed of lowthe energy excited 2~the in properties CdFeSe, under action of a states of Fe magnetic field. A favorable situation was found for the study of a Raman cascade involving preferential scattering in crossed linear polarization in backscattering parallel to the c axis. The application of a longitudinal magnetic field results in an analogue of the Hanle effect, known as resonant Faraday rotation. It allows one to study the dynamics of the scattering process; we were able to determine the lifetime of the exciton states involved in the cascade, as well as the transverse spin relaxation time T 2 and the inelastic scattering time TFe.

References [1J J.P. Mahoney, C.C. Lin, W.H. Brumage and F. Dorman, Chem. Phys. E.D. 53 (1970) 4286, and references [21J.D.A. Heiman, Isaacs, P. Becla, A. Petrou,therein. K. Smith, J. Marsella, K. Dwight and A. Wold, in: Proc. 19th Intern. Conf. on Semiconductor Physics, Warsaw, 1988, Ed. W. Zawadzki (Inst. Phys., Warsaw, 1988), p. 1539. [3] Guillaume D. Scalbert,and J. Cernogora, A. Solid Mauger, Benoit a 69 Ia A. Mycielski, StateC. Cominun. (1989) 453. [4] A. Mauger, to be published. 1 [5] were Limited variations of z~E1which between 13 cm a observed, for reasons are 12.6 not and understood; value Solid of 12.8 cm1 gives a better overall [6] mean R. Zeyher, State Comniiun. 16 (1975) 49. fit. [7] R.A. Loudon, Advan. Phys. 13 (1964) 423. [8] M. Nawrocki, R. Planel and C. Benoit a la Guillaume, Phys. Rev. Letters 36 (1976) 1343. 191 G.L. Bir and G.E. Pikus, Zh. Eksperim. Teor. Fiz. 64 (1973) 2210 [Soviet Phys.-JETP 37 (1973) 1116). [101 M.I. Dyakonov and V. Perel, in: Optical Orientation, Eds. F. Meier and B.P. Zakharchenya (North-Holland, Amsterdam, 1984) pp. 40—44.