MAGNETIC-BEHAVIOR OF CD1-XMNXSE

Abstract We report EPR and magnetic susceptability measurements in single crystals of Cd 1− x Mn x Se as a function of concentration and temperature. The data indicate that there is a critical concentration x ≈0.22 which we identify with the percolation critical point x c .

Semiconducting systems with controlled quantity of magnetic elements have recently received considerable attention [1,2]. Cdl_xMnxSe is a new semiconductor With a large gap and wurtzite structure within a wide range of concentration (0 ~<x ~< 0.5).
Electron paramagnetic resonance (EPR) has been found to be useful technique to study spin-spin interactions as well as effects related to magnetic phase transitions [3]. Broadening of the EPR linewidths and changes of the gyromagnetic factors (g) with decreasing temperatures have been observed in systems undergoing ferromagnetic, antiferromagnetic and spin glass phase transitions [4][5][6].
In this work we have measured the EPR spectra and magnetic susceptibility (×) in a single crystals of Cd 1 _xMnxSe for different concentrations (0.0005 ~<x ~< 0.45). By fitting the broadening of the resonance linewidth and the shift of the resonance field as a function of temperature to a modified Huber expression [1][2][3] we have deduced the concentration dependence of the order-disorder transition temperature (Tc). At 1 Work supported in part by CONICIT, Venezuela. 2 Work supported by National Science Foundation Grant, no. DMR77-08469. 3 Work supported in part by the Swiss National Science Foundation.
0.2 ~<x <~ 0.25, we find a discontinuity in T c suggestive of a percolation critical point. Solid solutions of Cd l_xMnx Se were grown using a modified Bridgrnan technique; good quality crystals were obtained for x up to 0.45. The concentration was measured by atomic absorption. The EPR measurements have been made at 9 GHz using a Varian spectrometer as a function of temperature (1.5 ~ T ~ 300 K). The Faraday method was used to obtain the X data between 90 <~ T ~< 300 K.
The reciprocal susceptibility is shown as a function of temperature in fig. 1. In the range of temperature measured, the data obey a Curie-Weiss la~v Xmlol Mn = T -O/C. Values for the Curie constant C and the asymptotic Curie temperature O are shown in table 1, where C should be compared with the free ion value C = 4.375 K cm3/mol Mn; The EPR spectra of Cdl_xMnxSe have been studied for low concentration (x <~ 0.005), and a well separated hyperf'me structure is observed [7]. As the concentration is increased beyond x ~ 0.005, the hyperfine lines initially broaden due to the dipole-dipole interaction, eventually becoming a single broad line for x 0.015. Then, the line narrows with a further increase ofx due to exchange narrowing, with the minimum linewidth corresponding to x ~ 0.03. For larger concentration we observed a single, symmetrical resonance 8  line which broadens monotonically with increasing concentration. The line shope is qualitatively lorentzian characteristic of exchange narrowing.
In fig. 2 we present our measurements of the EPR linewidth as a function of temperature for 0.05 ~< x <~ 0.45. A significant increase in linewidth as a function of decreasing temperature is observed for all samples. In fig. 3 the values of the gyromagnetic factors are shown as a function of temperature for 0.15 ~< x ~< 0.25; for other values of x, changes ofg were not observed Since we were limited, either because the linewidth becomes comparable to the resonance field at 9 GHz (the case for x > 0.25), or our lowest available temperature of 1.5 K (the case for x < 0.15). We have measured the angular dependence of the EPR line and found that there is a small variation of linewidth ~3% independent of concentration.
The observed broadening of the EPR linewidth with Table 1 Values measured as a function of x in Cdl_xMnxSe of the Curie temperature ®, and the Curie constant C; temperatures TczXH and Tog and critical exponents aAH and C~g as obtained from the temperature dependences of A//and g.

TcAH
where z.k/-/denotes the EPR linewidth, a the critical exponent, T c the temperature of the order-disorder transition and B(O/T + 1) is the high temperature linewidth. The first term on the right accounts for the dynarrdcal contribution and is valid for T close to T c, and the second explains the decrease of the linewidth over a region of temperature where T >> T c. The change of the g-factor with tqmperature can be analyzed with an expression similar to eq. (1), where the second term on the right is replaced by the value of the gyromagnetic factor measured at high temperature (g ~ 2.00). Since this formula is expected to be valid near To, the values of T c, aAH and ag listed in table 1, were obtained using only low temperature data. The solid lines shown in figs. 2 and 3 are a least squares fitting of the experimental points with eq. (1).
From the parameters listed in table 1, we can separate the data into three regions of concentration: x < 0.20, 0.20 ~< x ~< 0.25, and x > 0.25. In theories of the site percolation problem, it is found that the mean cluster becomes infinitive above a certain critical concentration x c. Long range magnetic ordering does not take place for x < x c where only finite clusters of magnetic ions exist. In this region short range magnetic ordering occurs and the behavior can be analyzed in terms of a duster model [8]. This model could explain, in our case, the rising linewidth and shift of the resonance field in the region ofx < 0.25, as originated from the growth of short-range magnetic correlations. For x > 0.25, T c is larger and increases linearly with concentration, as is shown in table 1. The rapid change in T c occurs at x ~ 0.22 which we identify with a percolation critical point x c. A similar result is obtained for Cd l_xMnxTe [1].
Preliminary magnetization measurements at low de magnetic field in Cdl_xMnxSe and Cdl_xMnxTe indicate that these systems have micromagnetic behavior above x = 0.2 [9]. As a conclusion, our EPR data indicate that there is a value of critical concentration in the region of 0.2 ~<x c ~< 0.25. This value agrees with the results of calculations based on a series expansion of the mean cluster size, considering the nearest neighbors [ 10]. However, more data (ac and de magnetic susceptibility, specific heat, etc.) are needed to understand the magnetic behavior of this system.
We would like to thank Professor W. Giriat for supplying the crystals.