Journal of Magnetism and Magnetic Materials 226}230 (2001) 1981}1982
Distant-neighbors exchange constants in Cd Mn Se \V V 夽 from magnetization steps R.A. Cajacuri , X. Gratens , E. ter Haar , V. Bindilatti *, N.F. Oliveira Jr. , Y. Shapira, Z. Golacki Instituto de Fn& sica, Universidade de SaJ o Paulo, C.P. 66.318, CEP 05315-970 SaJ o Paulo, SP, Brazil Department of Physics and Astronomy, Tufts University, Medford, MA 02155, USA Institute of Physics, Polish Academy of Sciences, Pl. 02-668 Warsaw, Poland
Abstract From magnetization measurements at ¹"20 mK on two bulk samples of Cd Mn Se (x"0.59% and x"1.15%), \V V four distant-neighbors antiferromagnetic exchange constants have been measured. The results, in order of decreasing strength, after the two J's for nearest-neighbors pairs, are !0.35$0.01 K, !0.20$0.01 K, !0.10$0.01 K, and !0.08$0.01 K. These results con"rm the long-range character of the distant-neighbor exchange interactions in the Mn-based II}VI diluted magnetic semiconductors. 2001 Elsevier Science B.V. All rights reserved. PACS: 75.30.Et; 75.50.Ee; 75.50.Pp; 75.60.Ej Keywords: Diluted magnetic semiconductors; Exchange constants; Low-temperature magnetization; Cluster model
As part of a systematic investigation on antiferromagnetic (AF) exchange interactions in the Mn-based II}VI diluted magnetic semiconductors (DMS) [1,2], we report experimental results on distant-neighbor exchange constants for Cd Mn Se. Di!erently from the previously \V V studied materials, which are zinc blende, Cd Mn Se \V V has the hexagonal wurtzite structure. Magnetization measurements at 20 mK  and in magnetic "elds up to 90 kOe were performed in two Bridgman grown samples of Cd Mn Se, with \V V x"0.59% and x"1.15%. The relevant part of the magnetization traces for both samples is shown in the top half of Fig. 1. Above 40 kOe the traces show the apparent saturation that precedes the magnetization steps (MS) from J }clusters (starting at 120 kOe) .
夽 This work was supported by the Brazilian agencies CNPq, FAPESP and FINEP. * Corresponding author. Tel.: #55-11-3818-6888; fax: #5511-3818-6984. E-mail address: [email protected]
The magnetization traces in Fig. 1 show a structure of superposed ramps, resulting from sequences of MS. For pairs of Mn>-ions (S") there are "ve MS, related to the AF exchange constant, J(0, by g H "2nJ. L Some of the MS can be clearly distinguished as the marked peaks in the bottom part of Fig. 1, where the derivatives of the magnetization traces are displayed. From a careful analysis of these data, four di!erent exchange constants were extracted: (a) J"!0.35$ 0.01 K, from the series of which the last two MS give the broad peaks marked as H and H in the "gure; (b) J"!0.20$0.01 K, from the series that include the MS at H and H ; (c) J"!0.10$0.01 K, from a series of which the peak at H is the last; and (d) J"!0.08$0.01 K, from the series ending at the peak at H . Table 1 lists the types of neighbors in the hcp structure of the cations, within the sphere of radius 2a (a is the NN-distance), and de"nes a notation for the corresponding exchange constants. The two NN exchange constants are J "!8.1 K, and J"!7.0 K . For the pur pose of identifying the new measured J's we have made computer simulations of the magnetization curves based
0304-8853/01/$ - see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 0 0 ) 0 1 0 8 8 - X
R.A. Cajacuri et al. / Journal of Magnetism and Magnetic Materials 226}230 (2001) 1981}1982 Table 1 Neighbors in the hcp structure: distances in units of the NNdistance a(r ), number (z ) and the associated exchange conL L stants (J ). The superscripts &in' and &out' apply, respectively, to L neighbors in the same and in a di!erent c-plane n r L z L J L
Fig. 1. Top: Magnetization curves for two samples of Cd Mn Se. The magnetization is corrected for the diamag\V V netic contribution of the lattice and normalized to its value at H"50 kOe, M . Bottom: Numerical derivative of the magneti1 zation traces. The arrows identify the peaks associated with M50 from pairs.
samples. For x"1.15% the simulations indicate that it belongs to pairs with z "12, while for x"0.59% the L results indicate that it may be the common value of the exchange constants for two kinds of pairs, with z "12 L and z "6. Due to the complications involved, we did L not attempt the identi"cation of the two remaining constants. For the zinc-blende materials previously studied, [1,2], the strongest exchange constant, after J , is between fourth neighbors, J . Besides, as for the present case, all three or four J's determined for each material are of comparable strength. This gives a long-range character to the distant-neighbor exchange interactions which disagrees with theoretical predictions [5}7].
References on the cluster model and the assumption of a random distribution. Although the cluster statistics are complex, the most important parameter determining the population of a given type of pair, is the corresponding number of neighbors, z . L Comparison of the computer simulations with the data made it possible to conclude that the strongest J after the J 's (J"!0.35 K), is associated with a type of pair with z "6. One possibility is that it is J , as in the zinc-blend L materials. However, there are two other possibilities, J or J , which give indistinguishable simulations. As for J"!0.20 K, the number of pairs involved is bigger, but there are discrepancies between the two
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