Journal ArticleMagnetization measurements down to 10 mK of Cd, _ x Mn, Te for Mn concentrations 0.01<x<0.15 show spin glass behavior. Such behavior is attributed to short-range exchange and dipolar interactions. Both interactions are used to explain the concentration dependence of the spin freezing temperatures for 0.01<*<0.6, the short-range exchange dominating at high concentrations, and the dipolar interaction at low concentrations

Novak, M. A.

Symko, Orest George

English

The University of Utah: J. Willard Marriott Digital Library

Spin glass behavior of Cd 1 _ x Mnx Te below the nearest-neighbor percoiation limit M. A. Novak,a) O. G. Symko, and D. J. Zhengb) Department oj Physics, University oj Utah. Salt Lake City. Utah 84112 S. Oseroff Department oj Physics. San Diego State University. San Diego. California 92182 Magnetization measurements down to 10 mK of Cd, _ x Mnx Te for Mn concentrations 0.01 ..;;x..;;0.15 show spin glass behavior. Such behavior is attibuted to short-range exchange and dipolar interactions. Both interactions are used to explain the concentration dependence of the spin freezing temperatures for 0.01'x<0.6, the short-range exchange dominating at high concentrations, and the dipolar interaction at low concentrations. INTRODUCTION Dilute magnetic semiconductors have been the subject of considerable interest in recent years not only for their semiconductor behavior but also for their magnetic proper-ties. The magnetic property of interest here is the spin glass behavior at low temperatures. Cd, _ x Mnx Te, a member of this group of materials, has been studied extensively down to -1.4 K. There was evidence J- 3 for a spin glass phase below a spin freezing temperature Tg for concentrations above the nearest-neighbor percolation limit, x::::O.2. Below this per-colation limit, it was generally believed that CdMnTe re-mains in the paramagnetic phase. However, preliminary magnetization measurements4 below 1 K for 0.OOO5,x ,0.05 concentrations have shown that for x = 0.05 there is spin glass behavior, even though it is below the percolation limit presumably due to more distant neighbors. The tem-perature dependence of EPR 1inewidth data suggests3 spin freezing temperatures below 1 K. We report here an investi-gation of this problem for a wide range of concentrations. Contrary to general belief, spin glass behavior occurs for concentrations below the percolation limit, thus supporting our preliminary measurements. With this information a new magnetic phase diagram is presented extending the concen-tration range well below the percolation value and showing spin glass behavior down to the limit of our measurements, 0.01 K. To explain our results, a model. based on short-range exchange and long-range dipolar interactions is presented. This model is also extended successfully to other studies of this system. EXPERIMENTAl- DETAILS The samples came from the same source as in Ref. 3. Their composition and homogeneity were analyzed by atom-ic absorption and density measurements. The agreement between the measured and nominal concentrations was bet-ter than 2%. The single crystalIine samples were crushed, ground, and then passed through a sieve #400. The fine powder was pressed inside an epoxy, Epibond cylinder, the '1 Present address; Department of Physics. Federal University of Rio de Jan-eiro. Brazil. b)On leave from the Institute of Physics of Chinese Academy of Sciences, Peking. China. sample size being 0.2 cm in diameter by 0.6 cm long. Magne-tization measurements were taken with a SQUID magne-tometer. Each sample was field cooled in 1 Oe down to 10 mK inside the mixing chamber of a 3He_ 4He dilution refrig-erator. Temperatures were measured by a CMN thermom-eter also located inside the mixing chamber. Measurements were taken by heating the sample in small steps from 10 mK up to 4 K. Figure 1 shows the magnetization for x = 0.10 normalized to field and concentration. At a certain temperature there is a kink in the magneti-zation and we call it the spin freezing temperature Tg • A similar characterization of Tg for this material was done by other groups for higher concentrations.3 All the other sam-ples, with x = 0.01, 0.05, 0.125, and 0.15, had similar behav-ior, each concentration showing its characteristic kink at Tg • As the concentration was reduced, the kinks were l.ess pro-nounced. To show more dearly the spin freezing a plot of log M vs log T is made and is presented in Fig. 2. A similar kink is observed in the dc susceptibility measurements on E\Io.1 SrO.9 S by Maletta and Fesch.5 In fact, their ac suscepti-bility cusp corresponds to a nearly invisible kink in the dc data. Below Tg , the magnetization still increases as the tem-perature is lowered due to free spins and groups of spins. DISCUSSION AND CONCLUSIONS Since the samples are field cooled, there is no cusp in the magnetization as a function of temperature. There is, how-ever, a kink for each concentration as a result of a sudden change in slope of the magnetization. For every sample, we define the spin freezing temperature Tg as the temperature for the occurrence of the kink. Such identification of the spin freezing temperature is justified by the fact that exactly the same method has been used for higher-concentration samples by other groups,3 al-though the higher-x samples show a sharper kink than our Iower-x samples. Because edMnTe has a large energy gap (1.6 eV and increasing with Mn concentrations) it behaves like an insula-tor, there being no RKKY interactions. Actually the inter-action between spins is a short-range antiferromagnetic ex-change J (R ) depending strongly on the distance R between spins. It is usually written in the form 3418 J. Appl. Phys. 57 (1),15 April 1985 0021-8979/85/013418-03$02.40 @ 1985 American Institute of PI1ysics 3418 It) I o ,... x () J: -~ 0.5 1 ~O J(R) = Jo(R )exp( - aR ) (1) and was first proposed by Bloembergen and Rowland.6 with subsequent analysis and modification by Abrikosov/ and Bastard and Lewiner8 as to the spatial dependence of Jo(R ). The damping factor a is equal to [2Eg (m. + mh )/~1/2 for semiconductor with a band gap Eg and electron and hole masses me and mh' When the damping term a is large. as in CdMnTe. the exchange interaction is short ranged. Thus it was reasonable to take as a model a nearest-neighbor percolation limit corre-sponding tox:::::O.2. the system remaining paramagnetic be-low this limit. However. other internal interactions must eventually cause ordering in the system as it cannot remain paramagnetic down to 0 K. This is exactly what our results show: the spin freezing at low concentrations occurring mainly because of dipolar interactions. It is a long-range in-teraction varying as 1/ R 3 and hence it will be effective in u :c -~ let 10~ I 1 3419 J. Appl. Phys., Vol. 57, No.1, 15 April 1985 11.5 T(K) FIG. 1. Magnetization ofedo .• MIIoI Te as a function of temperature. Arrow in-dicates spin freezing temperature, Tg • coupling spins at low concentrations. Since 1/ R 3 is propor-tional to x. the dipolar interaction will depend on x. Also, since Jo(R ) has a 1/ R 3 dependence, combining the dipolar and exchange interaction leads to Tg =Ax + Bx exp[ - a(x)x-1/3]. (2) We assume Tg is proportional to the mean effective field at the Mn site. The damping term in the exchange depends on x because the energy gap depends9 on x (we neglect the con-centration dependence of the effective masses). We fit this expression to our data, which are presented on the new mag-netic phase diagram in Fig. 3, with the following values: Tg (x) = (2.4 K)x + (7200 K)x xexp[ - 2.8(1.6 + l.59x)J/2X-1/3]. (3) The solid line in Fig. 3 shows the best fit to the data. Agree-ment for the concentration range O<x<O.6 is excellent. Ear-T(K) FIG. 2. Log of magnetization as a function of Log T for x = 0.15 to 0.01 samples. Ar-rows indicate spin freezing temperatures T,. Novak etal. 3419 Q ~ 2 10 p • MIXED ICRYSTA PHASES FIG. 3. Magnetic phase diagram of Cd, _. Mn. Te. The squares are data from Ref. 2 and the triangles from Ref. 3; the circles are our data. The solid line is a fit to all data using Eq. (3). lier we had fit our data to only an x 2 dependence; this was valid only for a small concentration range and had no phys-ical significance. Our model, based on exchange and dipolar spin glass behavior, is used to explain the magnetic phase diagram of CdMnTe alloys and the results of other groups, without the need for percolation theory. The anomaly in the specific heat in Cdo9 Mno.1 Te ob-served by Galazka et al. 1 at T = 0.5 K corresponds to our 3420 J. Appl. Phys., Vol. 57, No.1, 15 April 19B5 Tg = 0.54 for the x = 0.1 sample. Their specific heat is that of a spin glass. At low x, susceptibility measurements of Oseroff3 and specific-heat data 1 were analyzed in terms of clusters larger than expected from a random distribution of spins. Our model with the onset of a dipolar spin glass at low x explains these results. Although our model on which Eq. (3) is based is a phen-omenologicalone, the order of magnitude of the parameters is reasonable. Further work is necessary to relate these pa-rameters to the more detailed characteristics of the system. ACKNOWLEDGMENTS We would like to thank Professors S. Foner, G. La-marche, R. Orbach, and W. Wolffor interesting and stimu-lating discussions. This work was partially supported by the National Science Foundation, Grant No. DMR-7916243. JR. R. Galazka, S. Nagata, and P. H. Keesom, Phys. Rev. B 22,3344 (1980). 2M. Escome and A. Mauger, Phys. Rev. B 25, 4674 (1982). 's. B. Oseroff, Phys. Rev. B 25,6584 (1982). 4M. A. Novak, S. B. Oseroff, and O. B. Symko, Physica I07B, 313 (1981). ~H. Maletta and W. Felsch, Phys. Rev. B 20, 1245 (1979). 6N. Bloembergen and T. J. Rowland, Phys. Rev. 97,1679 (1955). 7A. A. Abrikosov, Adv. Phys. 29, 869 (1980). "G. Bastard and C. Lewiner, Phys. Rev. B 20, 4256 (1979). 9N. Bottka, J. Stankiewicz, and W. Giriat, J. Appl. Phys. 52, 4189 (1981). Novak eta/. 3420 

Spin glass behavior of Cd1-xMnxTe below the nearest-neighbor percolation limit

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Spin glass behavior of Cd1-xMnxTe below the nearest-neighbor percolation limit

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