Electron paramagnetic resonance of Mn2+ in strained-layer semiconductor superlattices

Solid State Communications, vol. %, No. 6,

Pergamon

.405

409,1995

,*tip$gfg$gyy+~ 0038-io!l8/9

s9.50 + .oo

003s1898ooo373-8

ELECTRON

PARAMAGNETIC RESONANCE OF Mn2+ IN STRAINED-LAYER SEMICONDUCTOR SUPERLATTICES

M. Qazzaz, G. Yang, S.H. Kin, L. Montes, H. Luo* and J.K. Furdyna Department

of Physics, University of Notre Dame, Notre Dame, IN 46556, U.S.A. (Received 17 March 1995 by E.E. Men&z)

We report giant crystal field splittings of Mn2+ electron paramagnetic resonance (EPR) lines observed in ZnTe/MnTe and CdTe/MnTe superlattices. The EPR spectra of isolated Mn2+ ions diffused into the ZnTe or the CdTe layers provide a direct and precise measure of both the magnitude and the uniformity of strain produced by lattice mismatch between the superlattice constituents. Keywords: A. magnetic films and multilayers, A. semiconductors, C. crystal structure and symmetry, D. crystal and ligand fields, E. electron paramagnetic resonance.

ELECTRON paramagnetic resonance (EPR) of paramagnetic ions in a crystal lattice is strongly affected by the crystal field, which results in the well-known fine structure observed in EPR spectra at very dilute concentration of such ions [l]. Since the crystal field arises from the precise atomic arrangement of the crystal, it will clearly be a&&d by strain. We note in this connection that semiconductor superlattices are generally under considerable strain, due to the lattice mismatch between materials comprising these structures. This has prompted us to explore the effect which such mismatched-induced strain will have on the EPR fine structure. Investigation of EPR in strained-layer systems - where strains are larger by orders of magnitude than those produced by conventional uniaxial pressure techniques [2-51 affords an opportunity to observe the behavior of EPR in a limit not previously accessible. Conversely, we show that EPR can also serve as a tool for determining the magnitude and sign of strain, as well as its distribution (fluctuation) within the layers of the superlattice. In this letter we report the observation of enormous crystal field splittings in the EPR spectra

* Present address: Department of Physics, State University of New York at Buffalo, Buffalo, NY 14260, U.S.A.

of ZnTe/MnTe and CdTe/MnTe superlattices. These splittings, observed in the spectra of isolated Mn2+ ions which diffused into the ZnTe or CdTe layers from MnTe, are induced by the (tensile or compressive) strain due to the lattice mismatch between MnTe and, respectively, ZnTe or CdTe. In addition to providing a sensitive measure of the magnitude and sign of the strain, we show that such EPR spectra also give direct quantitative information on the strain distribution (fluctuations) within the respective layers. This provides a direct and rather precise measure of the microscopic uniformity of the multilayer structure. A series of ZnTe/MnTe and CdTe/MnTe superlattices were prepared by molecular beam epitaxy (MBE) using a 32 R&D Riber MBE system and elemental sources. All superlattices were grown on the (0 0 1) faces of commercial semi-insulating GaAs substrates, which were kept at 310°C during growth. Before growing ZnTe/MnTe superlattices, a ZnTe buffer (- 2 pm thick) was deposited on the substrate. Before growing CdTe/MnTe superlattices, we deposited a ZnTe buffer (- 1 pm) followed by a CdTe buffer (- 1.5 F). The thicknesses of ail superlattices were in excess of 1 m, i.e., they can be assumed to be fully reh*ed, while the constituent layers (typicaIly 120 A or less) can be taken as pseudomorphic. The individual layer thicknesses were determined quite precisely using reflection high energy electron

405

406

ELECTRON

PARAMAGNETIC

v=9.46GHz T=4.2K (a)

5

1.5

2.5

3.5

4.5

5.5

6.5

Magnetic Field (kG)

Fig. 1. EPR spectra of a very dilute Mn*+ concentration in ZnTe for H I][0 0 I]: (a) observed in unstrained bulk ZnTe : Mn; (b) observed in ZnTe/MnTe superlattice (16 ml/30 ml, 201 periods); (c) calculated using D, = -503 G in equation (1) and AD = 0.070,in equation (3). diffraction @HEED) oscillations. The EPR measurements were carried out using an X-band (946GHz) Bruker ECS-106 EPR spectrometer, with samplecooling capability down to 4.2K, and a goniometer for precise sample orientation with respect to the applied magnetic field. As a point of reference, we briefly discuss the wellknown EPR spectrum of an isolated Mn*’ atom in an unstrained II-VI host. The spectrum consists of six hype&e-split lines separated from each other by about 60 G. Each hyperfme line is split into five line structure lines by the crystal field, the fine structure splitting depending on the crystal host, and on the angle between the applied magnetic field H and the crystal axes [6J. In ZnTe and CdTe the crystal field splittings of Mn*+ are comparable to the hyperhne structure splittings, leading to relatively complex spectra. The complete spectrum, consisting of thirty lines - six hypehe groups consisting of five fine structure lines each - typically spans about 300 Gauss. We illustrate this in Fig. l(a) by an EPR spectrum of Mn*+ observed on a bulk ZnTe: Mn specimen for H 11[O0 11, the orientation for which the fine structure splitting is largest.

RESONANCE

OF Mn*+

Vol. 96, No. 6

In contrast with this, in Fig. l(b) we show the EPR spectrum observed for a representative ZnTe/MnTe superlattice (201 periods, 16 monolayers (ml) ZnTe by 30ml MnTe), with the external field H parallel to the growth (i.e. [00 11, or z) direction [7j. This spectrum exhibits characteristically different features, consisting of five groups spread over a range of over 4000 G. These five groups actually correspond to the five fine structure lines, each possessing six hype&e lines. It can also be seen that the six hyperfine lines associated with the central group are well resolved, while in the other four groups they are significantly broadened. Such features are the result of an extraordinarily large fine structure splitting induced by the strain existing in the superlattice layers, as well as the inhomogeneous broadening of EPR lines caused by the fluctuation of this strain. For convenience, we label the five fine structure groups Pt, P2, P3,P4 and Ps,ranging from the lowfield (left) side to the high-field (right) side of the spectrum. As will be seen below, the relative positions of the center of each group provide a quantitative measure of the strain. The behavior observed in two other ZnTe/MnTe superlattices with larger ZnTe : MnTe layer-thickness ratios (16 ml : 20 ml and 18 ml : 20 ml) is qualitatively the same as in Fig. l(b), with the positions of groups PI-P5 being closer together due to the smaller strain in the ZnTe layers of those specimens. To discuss the observed behavior, we start with the spin Hamiltonian for describing the spin multiplet of the ground state for an isolated Mn*+ ion in a strained zinc blende host crystal, given by [l]

-js(s+

1)(3S2+3S-

+ D,[Sf-$(S+

l)].

l)] (1)

The tist term in the Hamiltonian is the Zeeman term. The second is the hypetie structure (hfs term, which results from the magnetic dipolar interaction of the electron spin and the nuclear spin of the Mn*+ ion. Its only effect is to split the spectrum into six evenly spaced lines. Since the effect of strain on hfi is insign&ant compared to strain effects on the fine structure, we will not consider it in further analysis (except to recognize that each fine structure line is in actuality a sextet). The third term describes the zero-magnetic-field splitting without strain (i.e. a is the zero-field flne structure splitting parameter for the unstrained semiconductor). The last term arises from the strain-induced axial component of the crystal field, D, being a strain-induced axial-symmetry

Vol. 96, No. 6

ELECTRON

PARAMAGNETIC

RESONANCE

407

OF Mn2+

parameter. For a specitic strained layer of a superlattice grown along the [0 0 l] direction, D, is given by the following relation [8]:

where G1, is the spin-lattice coefficient describing the energy shift of spin levels per unit strain, Cii and C12 are the elastic constants, ax. is the common in-plane lattice constant of the superlattice, and a, is the unstrained lattice constant of the material comprising the strained layer under consideration. By solving the secular equation associated with equation (l), one can find the spin levels, and thus the resonance field positions. For the [0 0 l] growth direction the strain-induced crystal symmetry is tetragonal with the z-axis being the symmetry axis. It should be noted that for the magnetic field H parallel to the growth direction, both the Zeeman and the strain terms in the Hamiltonian are already diagonal. Since in our case a < D,, H, we can then ignore the off-diagonal elements (which are of the magnitude of a). This yields the five resonance fields for the five fine structure lines as follows: H(-;

+-$)=Ho+4Do+2a,

H(-;

-+-i)=H,,+2D,-$a,

H(+$)=Ho, H(i

(3)

+$)=H,-2D,+;a,

H( $+$)=Ho-4D,-2a,

where Ho = hv/g/3, and v is the microwave frequency. The spectrum thus provides a direct determination of the strain-induced axial symmetry parameter D,. Taking H,, as the center of the observed P3 sextet, and a = 32 G for ZnTe [5], the best fit for the resonance positions shown in Fig. l(b) yields D, = -( 503 f 5) G. For comparison, D, can also be evaluated from equation (2). The superlattice in-plane lattice constant uXYfor the same ZnTe/MnTe sample as that used in Fig. l(b) has been determined by neutron scattering [9] to be 6.230 f 0.005A; the lattice constant of the unstrained ZnTe (a,) is 6.102 A; the spin-lattice coefficient G, 1 for Mn2+ in ZnTe obtained from uniaxial stress experiments is (8.56 kO.32) x 103G [5]; and the elastic constants for ZnTe are Ci 1 = 7.13 x 10” dyne cme2 and Cl2 =4.07x 10” dynecme2 [lo]. From these parameters, the calculated value of D, is -576 f 31 G, in rather satisfactory agreement with the EPR result. Taking D, = -503 G, u = 32 G, we show in Fig. 2(a) the calculated field dependence of the spin

0.0

2.0

4.0

6.0

Magnetic Field (kG)

Fig. 2. Schematic illustration of the effect of strain on fine structure splitting of the ground state of Mn2+, calculated (a) for D, = -503 G, and (b) for D, = +503 G. The sequence of bars below each energy diagram represents resonance positions for microwave frequency of 9.46GHz and (qualitatively) the intensity progression of respective fine structure lines. For clarity, the hyperfine structure is not shown. levels for the magnetic field parallel to the growth direction. (For the sake of clarity, hyper8ne splitting is not shown in the figure.) At zero magnetic field, the six-fold degenerate ground state of Mn2+ is split into three doublets by strain, with separations of 40, + 2u (between f $ and f 4) and 20, - 2 a (between f i and &i). In the presence of a magnetic field, all degeneracies are lifted for this orientation. Figure 2(a) also shows (by arrows) the calculated resonance fields at which the five fine structure absorption lines occur for g = 2.0106, a = 32G 151, D, = -503G, and a microwave frequency of 9.46GHz. Figure 2(b) shows that the resonance fields would be the same for D, = +503 G (compressive) as for D, = -503 G (tensile strain). The objective of this communication has been to demonstrate the rather dramatic dependence of the EPR fme structure on strain. The parameter connecting strain and EPR is D,, which can be determined with great precision (‘t l%, and probably better with additional curve-fitting refinements). It can thus be

408

ELECTRON

PARAMAGNETIC

useful as a measure of the magnitude of strain in layers containing dilute amounts of Mn2+. We note, however, that the function relating strain and D, [equation (2)J contains a number of parameters (C, 1, Ci2, Gil). While the elastic constants C,, and Cl2 are known to an accuracy of about l%, the spin-lattice coefficient Gi 1 has an error of f 4%, and this then limits the accuracy of strain as measured by D, to also about f4%. Conversely, however, if strain is determined independently (e.g., by X-ray diffraction) with higher precision, the enormous EPR fine structure shift may directly be applied to improve the accuracy of Gr,. While the EPR line positions [see equation (3)] indicate the magnitude of the strain through D,, the resolution of the hfs lines within each group Pi provides a quantitative measure of strain jluctuations. That is, in the presence of some strain distribution (either along the growth direction or laterally across the layers), there will automatically follow a distribution of resonance fields for each strain-shifted fine structure line (i.e., an “inhomogeneous” broadening) [l 1, 121. This is particularly easy to see for the high-symmetry configuration H]][OO l] where [see equation (3)], for the same strain fluctuation, the inhomogeneous broadening for branches PI and Ps is twice as large as for P2 and Pd. To simulate such broadening associated with strain fluctuation, we assume that the strain-induced fine structure splitting parameter D has a Gaussian distribution around its average value D,:

CD -Dcd2 ,1 AD2

where P(D) is the probability for a specific value of D, and AD is the half width which can be fit to the experimental EPR linewidths. When H is parallel to the growth direction, the inhomogeneously broadened linewidth can thus be obtained by using the Gaussian distribution of D given by equation (4) directly in equation (3). It is easy to see that the linewidths due to strain fluctuation are 4AD for PI and P5, 2AD for P2 and P4, and 0 for the P3 branch. The spectrum shown in Fig. l(c) has been calculated using the already established value of D, = -503G, literature values of a = 32G and A = 6OG for fine and hyperfine splitting constants for Mn2+ in ZnTe [5], a strain distribution parameter AD = 0.070, [see equation (411, and an intrinsic linewidth of 23 G taken from the measured width of the individual lines in the central sextet P3. As can be seen, excellent agreement is found between the calculated spectrum and the experimental spectrum. It is

RESONANCE

OF Mn2+

Vol. 96, No. 6

-v=9.46GHz T=4.2K

CdTehlnTe (a) 15mV45ml (b) 15ml/20ml

/

Magnetic Field (kG) Fig. 3. EPR spectra for three CdTe/MnTe superlatticesintheH][[OOl] orientation, in sequence from the most highly strained (top) to the least strained CdTe layers (bottom) (see thicknesses of CdTe and MnTe layers shown in the figure). Sample (a) consisted of 150 periods, samples (b) and (c) of 100 periods each. important to note that only two adjustable parameters (apart from the measured intrinsic linewidth) were used in calculating this spectrum: D, and AD. So far we have concentrated on the magnitude of D,. Measurement of the relative intensity of the branches PI . . . Ps at low temperatures also provides a way for the determination of the sign of Do, as can be seen by considering Fig. 2. Since the relative populations of the various levels differ at low temperatures [13], the intensities of the absorption lines will be strongest for those lines whose initial states lie lower in energy. Thus, for D, < 0, the - $ level will be more populated at low temperatures than the + f level, etc. As qualitatively illustrated in Fig. 2(a) by the vertical bars, we then expect that the low-field fine structure groups (PI and P2) will be stronger in intensity than the fine structure groups occurring at high fields (P4 and Ps). Close inspection of Fig. 1 reveals just that for our ZnTe/MnTe sample. We have also carried out EPR measurements on three CdTe/MnTe superlattices with various relative

Vol. 96, No. 6

ELECTRON

PARAMAGNETIC

thicknesses of the CdTe and MnTe layers. These results are shown in Fig. 3, in sequence of decreasing strain in the CdTe layers, as inferred from the relative CdTe-to-MnTe layer thicknesses (shown in the figure in monolayers). As expected, the line structure splitting decreases as the strain in CdTe decreases, and the resulting values of D, obtained from the splittings are shown in the figure for each sample. A close inspection of Fig. 3 also reveals that, in contrast to Fig. 1, now the high-field branches P4 and P5 are stronger at low temperature than the low-field branches PI and P2. This indicates that D, is positive since - as can be seen in Fig. 2(b) - for D, > 0 the stronger transitions - i -+ - $ would occur at the highest field, + f --+ + 5 at the lowest, etc. Note the degree of resolution in spectrum (a), in which the hfi is nearly resolved even for Ps. This indicates a remarkable uniformity of strain throughout the sample. We now briefly return to the assumption, stated at the outset, that the resonance observed is due to Mn2+ ions present (in very dilute amo~ts) in the nonmagnetic layers (CdTe or ZnTe) of the superlattices, having entered these layers by diffusion from MnTe. This assumption, made a priori, is reasonable, since EPR in systems with high concentrations of Mn (including the antiferromagnetic MnTe) is broadened to oblivion 1141.We remark now that this ass~p~on is fully verified a posteriori both by the progression of the fine structure splitting, which increases with increasing strain in the non-magnetic layers, and by the respective signs of D, observed for ZnTe and CdTe. Acknowledgement

NSF/MRG

- This work was supported by the Grant DMR92-21390.

RESONANCE

OF Mn2+

409

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2. 3. 4. 5. 6. 7.

8.

W. Low, Paramagnetic resonance in solids, Chapter 2, in Solid State Physics, Supplement 2 (Edited by F. Seitz & D. Tube). (Academic Press, New York (1967). E. Feher, Phys. Rev. 136,Al45 (1964). D. Boulanger & R. Parrot, Phys. Status Solidi (b) 140, K79 (1987). R. Parrot, C. Blanchard & D. Boulanger, Phys. Lett. AM, 109 (1971). M.T. Causa, M. Tovar, S.B. Oseroff, R, Calvo & W. C&at, Phys. Lett. A77,473 (1980). L.M. Matanese & C. Kikuchi, J. Phys. Chem. Solids 1, 117 (1956). In this letter we will restrict ourselves to the H 11[OOI] geometry, which illustrates all the essential points of EPR in strained superlattices in a clear and direct fashion. EPR as a function angle between H and the crystal axes is considerably more complex, and must be left to a more detailed presentation. G. Yang, Electron Paramagnetic Resonance in II-VI ~~~nductor Heterost~ct~~, PhD. Thesis, University of Notre Dame (1993) (unpublished). T.M. Giebultowicz, Private communication. D.A. Berlincourt, H. Jaffe & L.R. Shiozawa, Phys. Rev. 129, 1009 (1963). A.M. Stoneham, Rev. Mod. Phys. 41,82 (1969). R. Parrot & G. Tronche, Phys. Status So~idi (b)

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