EXCHANGE INTERACTIONS IN ML BASED ON Mn

IC/99/69

United Nations Educational Scientific and Cultural Organization and International Atomic Energy Agency THE ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS

EXCHANGE INTERACTIONS IN ML BASED ON Mn-ALLOYED DMSC: I. THE d-d EXCHANGE INTERACTIONS

K. Afif Laboratoire de Magnetism,?, et Physique des Hautes Energies, Departement de Physique, Faculte des Sciences, Universite Mohamed V, BP 1014, Rabat, Morocco and The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy, A. Benyoussef1 Laboratoire de Magnetisme et Physique des Hautes Energies, Departement de Physique, Faculte des Sciences, Universite Mohamed V, DP 1014, Rabat, Morocco, M. El Metoui Groupe d'Electronique et de Physique du Solide, Faculte des Sciences, BP 2121, Tetouan, Morocco and Departement de Physique, Faculte des Sciences et Techniques, BP 416 Tanger, Morocco and J. Diouri Groupe d'Electronique et de Physique du Solide, Faculte des Sciences, BP 2121, Tetouan, Morocco. MIRAMARE - TRIESTE June 1999

Author for all correspondence.

Abstract From a double theoretical comparison with experiment, we highlight the dimesional effects on magnetic properties resulting for short period structures. In a primary section, we perform spin-glass freezing temperature calculations using generalised scaling analysis, he second section is devoted to Monte Carlo simulations performed to bring out new features in thermodynamically quantities, specific to multilayered structures. An application is realised for Cd1_a.Mn2.Te/CdTe superlattice with m diluted magnetic and n non-magnetic alternated monolayers.

Introduction

The advance in the growth techniques like molecular beam epitaxy has lead to high quality multilayered (ML) structures consisting of alternating semiconductors with different band gap energies. This induced the creation of periodic steps in the potential profile i.e. barriers and wells for the carriers. For sufficiently thin layers, this leads to the well-known quantum well (QW) and superlattice (SL) structures which offer the possibility of tailoring their optical and electronic properties by an appropriated choice of the alternated SC thicknesses, thus the number of monolayers and the number of periods in these heterostructures (HS) [1,2]. However, less investigated is the possibility of tuning the magnetism in these ML's, and studying, for the same crystal structure and well energy gap, different magnetic phases. Adequate candidates are SL based on diluted magnetic semiconductors (DMSC's) (such as CdMnTe) where the DMSC is a semiconducting compound which contains transition elements, such as Mn 2+ (S M n =—), at random location on cation sites. These compounds display important composition-dependent behaviour such as the dependence of the band gap (Eg), lattice parameter (a), effective mass (m*) on the Mn 2+ dilution ratio (x). Furthermore, the magnetic ions endow unique properties to DMSC's and associate SLs. Remarkable features occur in these alloys, like magnetic excitations manifestation, dilution and percolation problems... also, the spin-spin d-d exchange interaction between the magnetic moment of the localised Mn 2+ ions (theme of the present paper) and the spin-spin sp-d exchange interactions between the Mn 2 + ions and the band carriers[3]. Some experimental data related to the existence and the type of spin-glass (SG) phases in short

barriers

superlattices

seems

to

be

quite

opposite.

Our

contribution tries to settle this question, and try to modulate manifestations special to interfacial problem, as thermodynamic quantity modified answers to physical conditions. Theory and model

Being interested by the ML based on DMSC where the Cd-Mn substitution occurs, we perform calculations based on those carried out by Bednarsky et al. (1996) [4], The scaling analysis allows us to study the dependence of the spin-glass freezing temperature (Tf) of these layers on their concentration on Mn ([Mn]=x). A generalised scaling analysis (GSA) to dimension d, which combines the average distance between ions R av with their redefined concentration x -either on the HS (x SL ) or on a given layer (xjj)- is written R^v[Mn] = Rf;

R] is the nearest neighbour distance (a/V2)

(1)

This is the leading equation in GSA calculations, a is the lattice constant. While the d-d exchange interaction between the paramagnetic ions is mostly due to the super-exchange (SE) for nearest neighbours (nn), the longrange interaction becomes dominant for more distant neighbours (mnn) (i.e. for low [Mn]); Bloembergen-Rowland (BR) seems to be the adequate representation of long-range magnetic exchange in these materials. Hence, one conjugates the contribution of both types of interactions, J o = J SE + J B R . So the equation (1), allows us to study the concentration dependence of Tf (Tf (x)) and gives the range of the exchange interaction between Mn ions T f (x)ocJ(R av )S(S + l)

(2a)

Tr(x)i-2Xl + 2a I )J

(9a)

2 yl/2

T)

(9b)

Beside, if we suppose no transverse exchange interaction (JOT - 0 ): Tfi(x)is just J(Ravi), where 1 labels the external or the inner layer (I or M). Otherwise (j JQTI > 0 ), we introduce the ansatz R

— av ~

PT?

avT

-i-H /i — P ^ i avIV /

c is a random positive value less than 1.

C\ A\ \^"y

By defining xT (by considering the sites on the NM part as no satisfied candidates during dilution) we also define Ravi xj l - (n + m)/xm

(1 la) 01b)

Keeping n or m finite, we can reproduce physical cases e.g. i) the magnetic coupling between M compounds is enhanced when m is increased. However, if we let ai fixed, xsati becomes small that interfaces ordered first and fast; ii) the SL acquire a bulk behaviour, when n is quite small and aY = 1/ (m - 2); iii) however when n is huge, xx * 0, the M-compounds are de-coupled and a quasi-2D behaviour seems to be installed; iv) another interesting general feature is established when we modify slightly the value of oii from one compound to its adjacent one. Even if there is no real connection between e and a we can construct a relation such as a : = 8a o + a s ( l - s )

(12)

where aT = a o is the bulk feature and aT - a s i s the 2d behaviour. So we can reproduce several situations (0 < e :< l) by executing p random values of s (X.C. Koonm and D.C. Meredith [9], p208): i) first situation: e = 0as(R av - R a v T ) : near zero transverse interaction or 2d problem to describe the interface effect we postulate, as an additional hypothesis J T «J 0 and suppose Xj = x, i.e. oti is greater or lesser than a 0 ; ii) second situation: B = 1 as (Rav = R a vx) or ( x SL

= x

i ) o r (3d problem)

we suppose Ji < Jo and x t « x , i.e. ay is close to ao (e.g. when the weakness of JT is screened by a great value of Jo. Hi) third situation: (0 < s < l) as R is a mixture of RaV i and RavT; JT x). The primary ones are always overestimated (see figure 3). However, GSA calculation is more precise for dilutions lower than 0.15. Using the Monte Carlo simulation technique and the hypothesis from the 3rd situation to characterise the interface effects (see figure 4), and considering oti in the range of 0.9ao and l.la 0 (the grey central zone), and JT< 0.9J0 we get correct temperatures values. However, in the same conditions, we can reproduce as in figures 5 and 6 a good representation of the %(T) answer for the multilayered structure specially in SG phase. These figures show that extra dilution may not be the only way to explain the enhancement seen for interfaces. In the opposite low case for oti, weaker Ji produces a similar feature for low temperature. Another new interesting observation deduced from figure 4, is the possibility for an interface to order antiferromagnetically before the bulk inner part, when ai is great than l.lcto. The magnetisation M(T) results not reported in this paper, are an indicator of the nature of the order reached. The cusp in the M(T) curve below which the temperature dependence isn't weak, indicates a P-SG transition [13]. While the dilution's magnetisation dependence is however, an indicator of percolation. The cusp in magnetisation M(x) is situated around 0.15 as expected (figure 7).

12

Conclusion We have put in evidence the strong effects of the interface in magnetic properties of the heterostructures. Using GSA and MCS, we showed that, beside extra dilution at the interface, weakness of interfacial exchange interaction is responsible of the enhancement of magnetic quantities. It is important to remember that the simulations were performed under the constraints of the available computers. So, the results should be taken carefully otherwise. However, they may be considered as correct with regard to the obtained qualitative similitude with experimental data.

Acknowledgement One of us (K. Afif) wishes to thank the ASICTP-Trieste for hospitality and financial support. Simulations have been partly realised thanks to computing facilities available to 1CTP visitors.

13

References [1]J. Diouri, K. Afif, Phys.Start.Sol. B 193, 85 (1996). [2]K. Afif, J. Diouri, Phys.Stat.Sol. B195, 475 (1996). [3]K. Afif, A. Benyoussef, J. Diouri, M. EL Metoui Phys.Stat.Sol. submitted. [4]H. Bednarsky, J. Cisowski, J.Cryst.Growth 159, 1018 (1996). [5]M. Sawicki, M.A. Brummel, P.AJ. de Groot, G.J. Tomka, D.E. Asbenford and B. Lunn, J.Cryst.Growth 138, 900 (1994). [6]J.A. Gaj, N. Grieshaber, C. Bodin-Deshayes, J. Cibert, G. Feuillet, Y. Merle d'Aubigne and A. Wasiela, Phys. Rev B 50, 5512 (1994). [7]S.R. Jackson, J.E. Nicholls, W.E. Hagston, P. Harrison, T. Stirner, J.H.C. Hogg, B. Lunn and D.E Ashenford; Phys. Rev. B 50, 5392 (1994). [8]S.K. Chang, A.V. Nurmikko, LA. Kolodziejski, R.L. Gunshor and S X.C. Zhang. Datta, Phys. Rev B 31, 4056 (1985). [9]X.C. Koonin, D.C. Meredith (Addison-Vesley Publishing Co.) The Advanced Book Program (1997). [10JL.L. Chang, Superlattices and Microstnictures 6, 39 (1989). [lla]M. Sawicki, S. Kolesnik, T. Wojtowicz,.G. Karczewski, E.Janik, M. Kutrowski, A. Zakrzewski, T. Dietl and J. Kossut Superlattices and Microstnictures 15, 475 (1994). [llb]a=0.8; see The Proceeding of the XXIV International School of Semiconducting Compounds Jaszowiec (1995) M. Sawicki, T. Dietl, T. Skoskiewics. [12]J.A. Cowen, J. Bass, P. Granberg, L. Lundgren and R. Stubi, Physica B 169, 299(1991). [13]K.K. Galazka, S. Nagata and P.H. Keesom, Phys. Rev. B 22, 3344 (1980). [14]A. Abounadi, A. Rajira, M. Averous and J. Calas, Phys.Stat.Sol.(b): 189, 265 (1996). [15]H. Yang, A. Ishida, H. Fujiyasu and H. Kuwabara, J.App.Phys. 65, 2838, (1989). 14

Captions

Figure 1:

From ref. 5 (figure 5), Comparison of the susceptibilities x of a 100 A thick layered DMSC and of a Cd ] _xMnxTe/CdTe ML with 100 A thick DMSC component. Continuous lines denote zero-field cooled and dashed ones denote field cooled measurements. Although both answers show SG behaviour at low temperatures (T< TgQ = 40K), there is an additional paramagnetic contribution to the % of the SL magnetic layer.

Figure 2:

Magnetic phase diagram of Cd}_xMnxTe/CdTe SL reduced to the P-SG line transition. The solid, dotted and dashed lines represent our own results, for ( n ; m ) = (20; 27,10 and 2 respectively). The symbols are experimental data: "the square" corresponds to the 3d associated DMSC [4] TSG values, "the cross" to the (27; 27, 12, 6) quasi-2d SL [10] TSG values and "open circle" to the (16; 27,10,2) SL (x = 0.5) TSG values deduced from the data obtained in ref. 11 (closed circle). T is the reduced temperature

T (x) T

, when TfO is

f0

associated to the referential SL (n;m) = (20; 27) and x = 0.65.

Figure 3:

Comparison between P-SG line transitions in the magnetic phase diagram of the referential SL. Solid line corresponds to results developed for the model formulated in section A and dots are the Monte Carlo simulations. The other symbols are experimental data as in Fig. 2.

15

Figure 4:

Magnetic phase diagram of the referential SL reduced to the dilution for which the bulk inner part cannot order yet (antiferromagnetically). The MC simulation results obtained for nx=15 and for 16000 MCS, are joined by lines representing the Para-order line transitions for interfaces with J ^ O . 9 Jo and oci=2ao, l.loto, O.9ao, 0.5 ao corresponding to the third situation characterised hi the text.

Figures 5 & 6: Influence of the ratio Ji / Jo on the answer of the low magnetic field susceptibility /

of the Cdi^Mni^Te/CdTe

SL versus

temperature, specially for T