11
W. HEIMBRODT et al. : Optical Effects Due to Antiferromagnetic Spin-Ordering 405 phys. stat. sol. (b) 154, 405 (1989) Subject classification: 78.20; 75.30; S8.15 Sektion Physik der Humboldt-Universitdt zu Berlin, Bereich Halbleiteroptikl) ( a ) and Institut fur Festkorperphysik der Technischen Universitdt Berlin, Berlin ( West)2) (b) Optical Effects Due to Antiferromagnetic Spin-Ordering in (Cd, Mn)S at Highest Mn Coneentrations BY W. HEIMBRODT (a), C. BENECKE (b), 0. GOEDE (a), and H.-E. GUMLICH (b) The antiferromagnetic phase transition in (Cd, Mn)S single crystals and thin films with highest Mn concentrations 0.8 5 ZM,, 5 1 is studied by luminescence emission and excitation measure- ments. Luminescence bands near 1.5 and 1.8 eV are observed in the samples with rocksalt and zincblende/wurtzite structure, respectively, being excited by the corresponding Mn2+ d-d transi- tions. Below the spin-freezing temperature TN(zM~) the Mn2+ d-d excitation bands shift to higher energies nearly proportional to the square of the ordering parameter, due to the different spin- ordering induced energy relaxation in ground and excited states. The exchange interaction para- meters of the excited Mn2+ states are determined in a mean-field approximation. Using a ligand field model the p-d mixing and crystal field parameters for the paramagnetic and antiferro- magnetic phase are obtained. The observed finestructure of the 6Alg-. 4A~g, 4Eg excitation band in MnSRs is ascribed to covalent bonding effects and LO phonon and magnon interaction. The measured luminescence decay parameters increase significantly below T~(ziy~), indicating the energy transfer rates to be influenced by the antiferromagnetic spin ordering. Der antiferromagnetische Phasenubergang in (Cd, Mn)S-Einkristallen und -Dunnschichten mit hochsten Mn-Konzentrationen 0,s ZM~ 5 1 wird durch Lumineszenz-Emissions- und -An- regungsmessungen untersucht. In den Proben mit Steinsalz- bzw. Zinkblende/Wurtzit-Struktur werden Lumineszenzbanden nahe 1,5 bzw. 1,8 eV beobachtet, die durch die entsprechenden Mnz+ d-d-ubergange angeregt werden. Unterhalb der Spin-Einfriertemperatur TN(ZMn) ver- schicben sich die Mn2+ d-d-Anregungsbanden zu hoheren Energien annahernd proportional ziim Quadrat des Ordnungsparameters infolge der durch die Spinordnung induzierten Energierelaxa- tion, die fur den Grundzustand und die angeregten Zustiinde unterschiedlich ist. Die Austausch- wechselwirkungsparameter der angeregten Mn2+-ZustLnde werden in ,,mean-field"-NLherung be- stimmt. Im Rahmen eines Ligandenfeld-Modells werden die p-d-Mischungs- und Kristallfeld- Parameter fur die paramagnetische und die antiferromagnetische Phase erhalten. Die bei MnSRs beobachtete Feinstruktur der 6A1g ---t 4A1g,4Eg-Anregungsbandewird Kovalenzeffekten und einer LO-Phonon- und Magnon-Wechselwirkung zugeschrieben. Das signifikante Anwachsen der ge- messenen Lumineszenz- Abklingparameter unterhalb TN(~~n) zeigt, daB die Energietransferraten durch die antiferromagnetische Spinordnung beeinfluRt werden. 1. Introduction (Cd, Mn) and (Zn, Mn) chalcogenide mixed crystals are the most prominent diluted magnetic ("semimagnetic") semiconductors, which show outstanding magneto-optical properties caused by a strong s, p-d exchange interaction between electron/hole band states and Mn2+ 3d electron states. (For a recent review see, e.g., [l, 21.) These materials are further characterized by an antiferromagnetic correlation between the Mn2+ (S = 512) spins due to a d-p-d superexchange interaction [3, 41. At a Mn con- centration-dependent spin-freezing temperature this interaction leads to a phase tran- 1) Invalidenstr. 110, DDR-1040 Berlin, GDR. 2, Hardenbergstr. 36, D-1000 Berlin( West) 12.

Optical Effects Due to Antiferromagnetic Spin-Ordering in (Cd, Mn)S at Highest Mn Concentrations

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W. HEIMBRODT e t al. : Optical Effects Due to Antiferromagnetic Spin-Ordering 405

phys. stat. sol. (b) 154, 405 (1989)

Subject classification: 78.20; 75.30; S8.15

Sektion Physik der Humboldt-Universitdt zu Berlin, Bereich Halbleiteroptikl) ( a ) and Institut f u r Festkorperphysik der Technischen Universitdt Berlin, Berlin ( West)2) (b )

Optical Effects Due to Antiferromagnetic Spin-Ordering in (Cd, Mn)S at Highest Mn Coneentrations

BY W. HEIMBRODT (a), C. BENECKE (b), 0. GOEDE (a), and H.-E. GUMLICH (b)

The antiferromagnetic phase transition in (Cd, Mn)S single crystals and thin films with highest Mn concentrations 0.8 5 ZM,, 5 1 is studied by luminescence emission and excitation measure- ments. Luminescence bands near 1.5 and 1.8 eV are observed in the samples with rocksalt and zincblende/wurtzite structure, respectively, being excited by the corresponding Mn2+ d-d transi- tions. Below the spin-freezing temperature T N ( z M ~ ) the Mn2+ d-d excitation bands shift to higher energies nearly proportional to the square of the ordering parameter, due to the different spin- ordering induced energy relaxation in ground and excited states. The exchange interaction para- meters of the excited Mn2+ states are determined in a mean-field approximation. Using a ligand field model the p-d mixing and crystal field parameters for the paramagnetic and antiferro- magnetic phase are obtained. The observed finestructure of the 6Alg-. 4 A ~ g , 4Eg excitation band in MnSRs is ascribed t o covalent bonding effects and LO phonon and magnon interaction. The measured luminescence decay parameters increase significantly below T ~ ( z i y ~ ) , indicating the energy transfer rates to be influenced by the antiferromagnetic spin ordering.

Der antiferromagnetische Phasenubergang in (Cd, Mn)S-Einkristallen und -Dunnschichten mit hochsten Mn-Konzentrationen 0,s Z M ~ 5 1 wird durch Lumineszenz-Emissions- und -An- regungsmessungen untersucht. In den Proben mit Steinsalz- bzw. Zinkblende/Wurtzit-Struktur werden Lumineszenzbanden nahe 1,5 bzw. 1,8 eV beobachtet, die durch die entsprechenden Mnz+ d-d-ubergange angeregt werden. Unterhalb der Spin-Einfriertemperatur TN(ZMn) ver- schicben sich die Mn2+ d-d-Anregungsbanden zu hoheren Energien annahernd proportional ziim Quadrat des Ordnungsparameters infolge der durch die Spinordnung induzierten Energierelaxa- tion, die fur den Grundzustand und die angeregten Zustiinde unterschiedlich ist. Die Austausch- wechselwirkungsparameter der angeregten Mn2+-ZustLnde werden in ,,mean-field"-NLherung be- stimmt. I m Rahmen eines Ligandenfeld-Modells werden die p-d-Mischungs- und Kristallfeld- Parameter fur die paramagnetische und die antiferromagnetische Phase erhalten. Die bei MnSRs beobachtete Feinstruktur der 6A1g ---t 4A1g, 4Eg-Anregungsbande wird Kovalenzeffekten und einer LO-Phonon- und Magnon-Wechselwirkung zugeschrieben. Das signifikante Anwachsen der ge- messenen Lumineszenz- Abklingparameter unterhalb T N ( ~ ~ n ) zeigt, daB die Energietransferraten durch die antiferromagnetische Spinordnung beeinfluRt werden.

1. Introduction (Cd, Mn) and (Zn, Mn) chalcogenide mixed crystals are the most prominent diluted magnetic ("semimagnetic") semiconductors, which show outstanding magneto-optical properties caused by a strong s, p-d exchange interaction between electron/hole band states and Mn2+ 3d electron states. (For a recent review see, e.g., [l, 21.) These materials are further characterized by an antiferromagnetic correlation between the Mn2+ (S = 512) spins due to a d-p-d superexchange interaction [3, 41. A t a Mn con- centration-dependent spin-freezing temperature this interaction leads to a phase tran-

1 ) Invalidenstr. 110, DDR-1040 Berlin, GDR. 2, Hardenbergstr. 36, D-1000 Berlin( West) 12.

406 W. HEIDIBRODT, C. BENECKE, 0. GOEDE, and H.-E. GUMLICH

sitioii from the paramagnetic to a spin-ordered state which can be considered as a spin- glass-like or (disordered) antiferromagnetic phase a t lower and highest Mn concentra- tions, respectively [I, 21.

In the present paper the effects of the spin-ordering on the internal optical Mn2+ d-d transitions are studied on (Cd, Mn)S as an example. These effects are expected to be maximum a t highest Mn concentrations xlfn. Due to the restricted niiscibility region, however, (Cd, Mn)S crystals with the tetrahedrally coordinated wurtzite struc- ture are available only up to about xlIn = 0.45. Therefore, in the present paper (Cd, Mn)S bulk crystals with rocksalt structure are studied which can be grown for xszl, 2 0.8 and have similar exchange-interaction induced properties in spite of their octahedral coordination. In our recent paper [ 5 ] the spin-freezing temperatures of these crystals were determined as a function of XM,, by measurements of the temperature dependence of the Mn2+ EPR linewidth. MnS thin films both with octahedral and tetrahedral coordination prepared by a low-temperature growth technique are also included in the optical investigations of the present paper. The obtained results concern- ing the spin-ordering induced energy relaxation of the various Mn2+ 3d5 states and the changes of the energy transfer rates are relevant to all (Cd, Mn) and (Zn, Mn) chalco- genides.

2. Experimental

The investigated MnS and (Cd, Mn)S (xMn 2 0.8) bulk crystals with RS structure were grown by I, transport technique in a closed evacuated quartz vessel a t temperatures between 950 and 1000 "C, starting with pressed and sintered MnS/CdS powder. The polycrystalline MnS thin films with thicknesses in the range 1 to 2 pm were prepared on glass or quartz substrates by vacuum evaporation of pure MnS powder with an evaporation rate of about 1 nm s-l using a molybdenum heater. Controlled by the substrate temperature T,, MnS thin films with ZB/W ( T , = 50 to 100 "C) and RS structure ( T , = 300 "C) were obtained. The crystallographic structure of the samples was proved by X-ray diffractometry. The Mn concentrations of the (Cd, Mn)S samples were determined by X-ray fluorescence measurements using an electron-beam micro- probe equipment.

The optical measurements were carried out in the range 4 to 300 K using a He cryo- stat with a gas-stream controlled temperature. The emission spectroscopy and decay measurements were performed using an excimer-laser pumped dye laser for excitation. The excitation spectra were obtained by a conventional arrangement consisting of grating monochromator and halogen lamp or, in smaller spectral regions, by tuning the dye laser. The signals were recorded with a cooled S1 multiplier using photon- counting or lock-in techniques.

3. Results and Discussion

3.1 Spin-ordering induced energy relaxation of Mnzf 3135 states

To obtain the maximum energy relaxation of the various Mn2+ 3d5 states caused by the successive spin-ordering below the spin-freezing temperature, the energies of the optical d-d transitions are carefully determined as a function of the temperature by luminescence excitation measurements of MnS with octahedral (RS) or tetrahedral (ZB/W) coordination. The observed luminescence bands are situated in the infrared (1.45 to 1.65 eV) and red region (1.80 to 1.95 eV) for MnSRs and MnSzBlw, respec- tively, and are excited via energy transfer by the d-d transitions from the ground state to the (lowest) excited states of the Mn2+ ions being characteristic of the corre-

Optical Effects Due to Antiferromagnetic Spin-Ordering in (Cd, Mn)S 407

sponding crystal field (see Section 3.2). In the present context the nature of the various luminescence centres and the detailed energetic positions of the emission bands are irrelevant. (See [2] and Section 3.3 for further discussion.)

I n Fig. l a the low-temperature excitation spectrum is shown for MnSRs. It should be pointed out that thin films, due to their small thickness, remain sufficiently transpa- rent in the absorption peaks and, therefore, yield much better resolved spectra than bull; crystals. In addition to the three well-resolved lowest-energy excitation bands gAlg(6Ss) + 4T1, (4G), -+ 4T2g(4G), -+ 4A1g, 4Eg(4G) also the DA1g(%) -+ 4T2g(4D) transi- tion is observed at low temperatures as a shoulder on a gap-related excitation peak. At higher temperatures, however, this "Alg + 4Tzg(4D) structure cannot be sufficiently resolved due to the decreasing MnSEs gap energy and, therefore, is not further consi- dered in the following. The total excitation spectrum for MriSzBp can be seen, e.g., in [2] (Fig. lob).

With decreasing temperature all excitation peaks shift remarkably to higher ener- gies as demonstrated in Fig. 1 b for the 6Alg(6S) + 4T2g(4G) transition in MnSRs as an example, in contrast to the nearly temperature-independent peak positions in the case of Mn2+ impurities in 11-VI semiconductors. In Fig. 2 the measured temperature de- pendence of the three lowest-energy excitation bands of MnSRs and of the best resolv- able excitation bands of MnSzBIw are shown. The observed, almost step-like increase of the peak energies just below the indicated spin-freezing (NBel) temperature TN = = 152 K (MnSRs) [B, 121 and 90 K (MnSzBlw)3) clearly demonstrates the correlation with the antiferromagnetic spin ordering in these materials.

Similar spin-ordering correlated shifts of the Mn2+ d-d transition energies were found by absorption measurements of MnORs [6]. Also in this case the total shift be- tween T K and T = 0 is maximum for the "Alg + 4T2g(4G) transition as observed for MnSRs (see Fig. 2).

t, 2.3 2.4 2.5 2.6

energy (ev) --+

Fig. 1. Excitation spectra of the infrared emission band for a MnSRs thin film. Eem = 1.45 eV, film thickness d = 1.64 pm. a) Total spectrum at 8 K, b) BAlg -4Tzg(4G) excitation band a t various temperatures (1) T = 8, (2) 120, and (3) 170 K

3) The effect,ive NBel temperature of the MnSzBlw thin films was determined by measurements of the temperature dependence of the Mn2+ EPR linewidth as described in [5].

408 W. HEIMBRODT, C. BENECKE, 0. GOEDE, and H.-E. GUMLICH

Fig. 2. Excitation peak positions as a func- tion of the temperature for MnS thin films with RS ( 0 ) and ZB/W (0) structure. MnSRs: E,, = 1.45 ev, d = 1.54 pm; MnSzs/w: E,, = 1.80 eV, d = 0.96 pm. - Dashed vertical lines indicate the spin-

kl

2.97 $ freezing (Nbel) temperatures

2.54

2.50 For the present purpose the d-p-d superexchange interaction in MnS is sufficiently described by the isotropic Heiseriberg Hamiltonian 3e = = - C J$LSj with only nn and nnn

i. i interactions determined by the para; meters J,, and Jnnn, respectively (Jnn, J,,, < 0). The exchange interac- tion induced energy relaxation 8 ( T ) per Mn2+ ion is then obtained T(K)----+

in a mean-field approximation (MFA),

8 ( T ) = (3ei=1) = -C J l j (S i ) (8;) = j

= - < X i > [Jnn C (8;) + Jnnn C (8j")l * (1) nn nnn

As fluctuation effects are neglected in the MFA one obtains i5 (T >= TN) E 0 and a complete antiferromagnetic spin ordering a t T = 0, corresponding to an f.c.c.-type I1 and f.c.c.-type 111 spin superlattice in the case of RS and ZB/W, respectively [l, 21. For a Mn2+ ion in the ground state (X = 5/2) (1) leads to

6 JnnnS2 for MnSRs (2 a)

(2b) (8 = 5/2) 1 ( 4 J n n - Z J n n n ) s2 for MnSZB/w .

8,(0) =

At sufficiently low excitation densities an excited (single) Mn2+ ion can be assumed to be situated in an unchanged mean spin-field of the neighbouring Mn2+ ions. For the

Optical Effects Due to Antiferromagnetic Spin-Ordering in (Cd, Mn)S 409

spin-ordering induced energy relaxation gex(0) of such an excited Mn2+ ion in one of the lowest-energy (quartet) states (S' = 3/2) one gets then

6 J2,SS' for MnSRs (3a)

(3 b) (S = 5/2, 8' = 312) I (4JEt - 2 J Z J 8s' for MnSzBlw,

i%X(O) =

where J::, J:&, denote the various exchange interaction parameters between the con- sidered excited Mn2+ ion and an nn or nnn Mn2+ ion in the ground state.

The measured total spin-ordering induced shift of the various excitation peaks,

A W ) = (&X - E*)T=O - (Eex - E g ) T N >

AE(O) = %ex(()) - gg(0)

is then given by

(4) (see also [8]). Using (Z) , (3), and (4) now the exchange interaction parameters for the excited Mn2+ states can be obtained by fitting the experimental AE(0) values after Fig. 2 (see Table 1). For the Mn*+ ground state the known exchange interaction par- ameters of MnSRs (Jnnn/k = -12.5 K) and MnSzB/w (Jnn/k = -12.4 K, IJnnnI < IJnnl) are employed (see [2] for references). As can be seen in Table 1, the J::,, values of the 4T1g(4G) and 4A1g(4G) Mn2+ states in MnSRs are nearly the same as for the 6Alg ground state. The corresponding observed spin-ordering induced peak shifts, therefore, mainly result from the difference between the spin quantum numbers S and S' of ground and excited states, respectively. In the case of the excited states 4T2g(4G) in MnSRs and 4T2(4D) in MnSzsp the exchange interaction nearly vanishes, and AE(0) approxima- tely represents the whole spin-ordering induced energy relaxation of a Mn2+ ion in the ground state gg(0) = -40.4 (MnSRs) and -26.7 mev (MnSzBlw), respectively. For the 4T2(4G) state in MnSZB/w even a positive J t t value results indicating a ferro- magnetic spin ~oupl ing .~)

It should be pointed out that the obtained JeX values describe the superexchange interaction for an excited Mn2+ state with the neighbouring ions in the equilibrium positions of the ground state as the excitation transitions are sufficiently rapid. The following relaxation of the neighbouring ions into new equilibrium positions possibly

Table 1

Exchange interaction parameters J,,, JEn of excited Mn2+ 3d5 states in octahedrally and tetrahedrally coordinated MnS

ex

*) J Z values obtained under the assumption I J&,l Q I Jitp,I, which is fulfilled for the gA,(6S) ground state and can be expected to be true also for the excited states in MnS having zincblende or wurtzite structure.

4) The spin flip into the energetically favoured ferromagnetic orientation can be assumed to occur slowly compared to the excitation transition.

410 W. HEIMBRODT, C. BENECKE, 0. GOEDE, and H.-E. GUMLICH

leads to changes of the Jex values. Therefore, the expected peak shift of the lumines- cence band 4T1 + 6Al may differ from the corresponding excitation peak shift. Spin- ordering related luminescence peak shifts of the same order of magnitude are found for (Cd, Mn)Te and (Zn, Mn)Te mixed crystals at high Mn concentrations XM1, e 0.7 [8].

In the framework of a virtual-crystal approximation a linear xIfn dependence of the total spin-ordering induced excitation peak shift is expected,

AE(O, X3rIn) = XMn AE(O) 7 ( 5 )

where AE(0) is given by (2) to (4). As shown in [5] the decrease of the spin-freezing temperature can be approximated by T&Mln) = &,TN(l) . Equation (5) is suffi- ciently confirmed by the measured excitation peak shifts for the (Cd, Mn)SRs crys- tals with z&fn = 0.8 yielding AE(0, ZM,, = 0.8) = (0.7 t o 0.8) AE(0, MnSKs).

The temperature dependence of the spin-ordering induced excitation peak shifts is now discussed for MnSRs as an example. According to ( 1 ) 8 ( T ) can be evaluated using the MFA expression for the spin expectation values (see [7]). In the special case of f.c.c.-type I1 spin ordering it holds

Here

denotes the Brillouin function. For the central Mn2+ ion 1 in the ground state (8, = = S = 512) it is (X",), = -(~!3:&~ = Sm(T) > 0, where m(T) is the spin-ordering parameter. After (6) rn( T ) is implicitly given by the self-consistency condition

where the MFA expression kT, = 4 \Jnnnl X(S + 1) is used. According to (1) it follows then

8',(T) = 6JnnnS2m2(T). (8)

For the central Mn2+ ion 1 in an excited (quartet) state (8, = 8' = 312) one obtains after (l), (6), using again (#inn) = --Xm(T),

gex(T) == 6J%nSm(T) (&>ex > (9)

where

Aa demonstrated in Fig. 3 the measured temperature dependence of the peak shifts for the lowest-energy excitation bands in MnSRs can well be represented by the cal- culated curves A\E(!Z') = Q,,(T) - $,(T) using (8), (9), and the Jex vahes given in Table 1.

Optical Effects Due t o Antiferromagnetic Spin-Ordering in (Cd, Mn)S 41 1

Fig. 3. Spin-ordering induced excitation peak shift, A&', as a function of the temperature below TN = 152 K for the various excitation transitions 6Alg - 4T2g (o), 4Tlg (U), and 4Alg (0) of MnSRs (after Fig. 2). Solid curves calculated after (S), (10)

3.2 Ligand-field model for Mnz+ in the paramagnetic and antiferromagnetic phase

The observed spin-ordering induced shifts of the Mn2+ d-d excitation bands can also be discussed in the framework of a ligand-field model taking into account the co- valent mixing between the Mn2+ d-states and the anion p-states which is fundamental for the superexchange interaction. In this way information can be expected on model parameter changes due to the antiferromagnetic phase transit.ion. Furthermore, the role of the symmetry reduction caused by spin-ordering can adequately be discussed. The applied model being first proposed by Koide and Pryce is extensively reviewed in [9]. The model contains two Racah parameters B and C5) describing the electron- electron interaction in the free Mn2+ 3d5 ion and one crystal-field parameter Dq in the case of cubic symmetry (0, or Td). The covalent bonding is accounted for in the simplest approximation by only two additional scaling parameters N e and Nt which

T a b l e 2

Ligand-field model for Mn2+ in MnSRs

antiferromagnetic paramagnetic phase phase

(8 K) (TN)

excit,ed state energies E(4T1g) 2.063 eV 2.044 eV of Mn2+ (exper.) E(4T2g) 2.459 eV 2.420 eV

E(4Alg) 2.759 eV 2.744 eV E(4Alg) - E(4Es) 22 meV - 2 meV (calc.)

parameters of the ligand-field model

B 57.4 meV G 491 meV Dq Ne 0.915 0.952 Nt 0.991 0.954

127 meV 101 meV

E("Alg("S)) = 0, free Mn2+ ion: E(4G) = 3.328 eV

s, As shown in [9] terms containing the Racah parameter A can be neglected or included into a n effective Dq value.

W. HEIMBRODT, C. BENECXE, 0. GOEDE, and H.-E. GUMLXCH

Fig. 4. Finestructure of the 6Alg - 4Alg, 4Eg excitation band for MnSRs a t T = = 8 K. (a) Thin film, measured by halo- gen lamp (d = 1.54 pm), (b) bulk crystal, measured by dye laser (uncorrected). Solid marks indicate the uth LO phonon satellite of the 6Alg - 4E, band

characterize the mixing between the e- and t-symmetric one-electron d-states of a Mn2+ ion and the p-states of the anion ligands.6)

The fitting of the model parameters is carried out for MnSRs as an exam- ple using the experimental data from Table 2 and the secular determinants given in [9]. In addition to the three excitation peak positions discussed until now also the observed finestruc- ture of the 6A1g. + 4A1,, 4Eg excitation band is taken into consideration. As shown in Fig. 4 a t Sufficiently low tem- peratures an energy splitting of the

4A1g and 4Eg states due to covalency effects is found. In agreement with [lo] the main peak is interpreted as 6Alg+ 4AlB zero-phonon line. The equidistant structures a t the low- er-energy side are attributed to zero-phonon line and LO phonon satellites of the 6Alg + --+ 4E, transition as indicated in Fig. 4. The energetic distance of 41 & 1 ineV is in good agreement with the value hwLo = 40.9 meV obtained in [ll] by far-infrared reflectivity measurements. A further series of structures indicated by the dashed marks in Fig. 4 is shifted by ho' = 16 & 1 meV and may be caused by a simultaneous emission of one magnon or acoustic phonon. Assuming a Poisson distribution of the two 4Eg series, a consistent decomposition of the total 6Al, -+ 4A1,, 4E, excitation band is possible leading to a Huang-Rhys factor S - 2 . The first moment of the 6A1, --+ 4Eg band is situated a t higher energies with respect to the zero-phonon line by ShwLo + + +hw', whereas the first moment of the 6Alg + 4Alg band nearly coincides with the corresponding zero-phonon line as in this case obviously the electron-phonon coupling is small. The energetic difference between the first moments of these two bands ob- tained a t 8 K is given in Table 2 .

Unfortunately, there are no generally accepted B and C values for the free Mn2+ ion because already the corresponding (four) quartet levels cannot be sufficiently represented by only two Racah parameters (see [9]). Therefore, in the present fitting procedure the relation to the free Mn2+ ion is established only by including the lowest excited free-ion 4G state which dominantly contributes to the considered Mn2+ states in MnSEs. Using now the four MnSRs energies measured in the spin-ordered phase and the free-ion E(4G) value the five fitting parameters B, C, Dq, N,, and Nt were

6, The free Mn2+ ion d-states are replaced by suitable linear combination of Mn2+ d- and anion p-states with the relative weights Ne,t and (1 - Ne,t)*lz, respectively.

Optical Effects Due to Antiferromagnetic Spin-Ordering in (Cd, Mn)S 413

obtained as given in Table 2. The resulting B and C values and, especially, the C I B ratio are consistent with the literature values [9]. Taking the same B and C a fitting of the three excitation peak energies a t T N yields Dq, N,, and N, for the paramagnetic phase.

As can be seen in Table2 a considerable difference between the d-p mixing par- ameters results for the two phases. Whereas in the paramagnetic phase nearly equal mixing occurs for the e- and t-symmetric Mn2+ d-states, in the spin-ordered phase the d-p mixing with the e-symmetric d-states dominates which is favoured by symmetry arguments. The effective (cubic) crystal-field parameter Dq is found to increase as a result of the spin-ordering. A possible axial-symmetric crystal field in the antiferro- magnetic state is obviously negligible as no splitting of the 4T1g and 4Tzg states is detect- able even a t lowest temperatures. As shown in Table 2, for the paramagnetic phase a nearly vanishing 4Alg - 4Eg splitting is calculated as N , = Nt. Experimentally a t T 2 T, no finestructure of the 6A1g -+ 4A1g, 4Eg excitation band could be resolved. Therefore, the 4Alg4E, splitting observed a t low temperatures can be concluded to be caused essentially by the spin-ordering which leads to a sufficient difference between N , and N t . It should be mentioned finally that the suggested energetic order of the 4Alg and 4Eg states is confirmed by the present model, as for the opposite assignment a fitting inside the range of physically reasonable parameters is impossible.

3.3 Spin-ordering effects on energy transfer

As already mentioned in Section 3.1 the observed emission bands of all investigated samples are excited by radiationless resonance energy transfer between the Mn2+ ions and cannot be ascribed to the 4T1(g) -+ 6Al(g) transition in Mn2+ ions in an unper- turbed environment (see [2] and references therein). As an example in Fig. 5 the IR emission band of (Cd, Mn)SRs crystals is shown which practically has a M h concentra- tion independent peak position. The quantum efficiency and decay properties of the luminescence bands are essentially determined by the capture of the mobile excitation energy by centres of radiationless transitions and, therefore, by the energy transfer rate between the Mn2+ ions [2]. At the present highest Mn concentrations xMn 0.8 the Dexter exchange interaction mechanism should dominate which can be

expected to be influenced by spin-ordering processes in the Mn sublattice.

The luminescence decay was measured over several decades and found to be not exactly exponential. In Fig. 6 the obtained decay parameters reff, being defined as decay times to one tenth of the initial in- tensity, are given as a function of the tem-

'' ' 1.; ' 7:4 1:5 I 7.; ' 7.'7 I 7.8 ' energy (eVI

Fig. 5. IR emission band of (Cd, Mn)S bulk crystals with rocksalt structure at T = 4 K for various Mn concentrations (a) XMn = 0.8 and (b) 1

W. HEIMBRODT, C. BENECAE, 0. GOEDE, and H.-E. GUNLICE

Y 1 Fig. 6. Effective luminescence decay time, r e f f , as a function of temperature for a) (Cd, Mn)S bulk crystals with RS structure for various Mn concentrations X Q I ~ ; E,, = = 1.6 eV. b) MnS thin films with RS and ZB/W structure; MnSRs: ..8,, = 1.45 eV, d = 1.87 pm; M n S z B p : E,, = 1.80 eV, d = 1.68 pm

TIKI-

perature for samples with various Mn concentrations and crystallographic structures, respectively. A significant increase of teff is found below the corresponding N6el temperature T,, indicating a correlation to the anti- ferromagnetic spin-ordering. Obvious- ly, the energy transfer rate between neighbouring Mn2+ ions in the spin- ordered phase is smaller than in the paramagnetic phase.

The temperature dependence of this energy transfer rate usually is ascribed to a varia- tion of the overlap integral between the 6Al(g) - 4T1(g) emission and absorption band. The different spin-ordering induced relaxations of the 6A1(g) ground and 4Tl(g) excited Mn2+ states could lead to an increase of the Franck-Conclon shift and, therefore, to the observed decrease of the energy transfer rate a t lower temperatures. This implies, however, the 4TI(g) + 6A1(g) emission band to have a smaller spin-ordering induced shift than the + 4T1(g) excitation band. Unfortunately, this cannot be proved experimentally as in the present case of highest Mn concentrations this emission band is not observable.

Also the difference between the d-p mixing in the paramagnetic and antiferro- magnetic phases may contribute to the observed variation of the energy transfer rate. The total effect of the covalent d-p mixing for MnSRs can simply be obtained from the energetic distance between the 4G level of the free Mn2+ ion and the 4Alg level in the crystal which is proportional to (1 - N:N:) (see [9]). As after Table 2

E(4G) - E ( 4 A 1 g ) l ~ N > W4G) - E(4Alg)lsK

i t follows NEN:18~ > N$iV:ITN, indicating the total cl-p mixing to be smaller in the spin-ordered than in the paramagnetic phase. The energy transfer rate between neigh- bouring Mn2+ ions can be expected to decrease with decreasing d-p mixing and, therefore, should be reduced with successive spin-ordering. As t,he usual, electron- phonon interaction induced part of the temperature dependence of t,ff can hardly be separated, a quantitative discussion would be difficult.

Optical Effects Due to Antiferromagnetic Spin-Ordering in (Cd, Mn)S 415

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[5] 0. GOEDE, D. BACKS, W. HEIMBRODT, and M. KANIS, phys. stat. sol. (b) 151, 311 (1989). [6] M. S. SEEHRA and R. D. GROVES, J. Phys. C 16, L411 (1983). [7] W. NOLTINC, Quantentheorie des Magnetismus, B. G. Teubner, Stuttgart 1986. [S] E. MULLER and W. GEBHARDT, phys. stat. sol. (b) 137, 259 (1986). [9] D. CURIE, C. BARTHOU, and B. CANNY, J. chem. Phys. 61, 3048 (1974).

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[lo] H. KOMURA, J. Phys. SOC. Japan 26, 1446 (1969). [ l l ] E. JAHNE, 0. GOEDE, and V. WEINHOLD, phys. stat. sol. (b) 146, K157 (1988). [12] W. KLEEMANN and F. J. SCHAFER, Solid State Commun. 6!1, 95 (1988).

(Received May 5, 1989)