CRITICAL PHENOMENA OF ANISOTROPIC SPIN GLASS ZnMn

Longitudinal (11 c) and transverse (LC) nonlinear susceptibilities have been measured on the Ising-type ZnMn spin glass. The critical exponents obtained from the scaling hypothesis depend on the anisotropy/exchange ratio, which can suggest a crossover effect from Heisenberg to Ising spin glasses in real RKKY systems. Critical behaviors of the nonlinear susceptibility in spin glasses have been extensively studied by various experiments and numerical calculations. Recently, Yeshurun and Sompolinsky [I] have shown that the nonlinear susceptibility in CuMn is affected by the presence of random Dzyaloshinsky-Moriya (DM) anisotropy induced by Au impurity and suggested that there exists an anisotropy-induced crossover effect from Heisenberg to Ising behavior. More detailed investigations by Courtenay et al. [2] for CuMn and AgMn alloys have defined two sets of critical exponents: Ising type in the range of small field and temperature near T, and Heisenberg type in high field and temperature far from T,. Numerical studies also have shown the importance of the anisotropy. It was suggested that the spin-glass transition does not occur at finite temperature for a three-dimensional (3D) Heisenberg model 131 but that weak anisotropic interactions induce a spin-glass transition at T, # 0 [4]. Recently, we have studied the uniaxially anisotropic spin glass ZnMn [5] over a wide range of the Mn impurity concentration c. Since in ZnMn it is possible to control the ratio of the anisotropy to the variance of the random exchange interaction ( D / J ) by changing the Mn impurity concentration, systematic study for the effect of the uniaxial anisotropy D on the spin-glass critical behavior could be done in this system. Therefore, we have performed detailed measurements of the longitudinal (11 c) and transverse ( Ic ) ac susceptibilities x 11 and X I of ZnMn single crystal at various fields parallel t o the ac field. As we previously reported, ZnMn with 270, 390 and 600 pprn Mn show the two successive paramagnetic (P) longitudinal (L) mixed longitudinal and transverse (LT) spin glass transitions and the Ising like P-L transition only occurs for c 5 150 ppm. The nonlinear part of the susceptibility is extracted from X I I N L = X 11 (0) X 11 H 11) in the longitudinal, direction and X I N L = X I (0) X I ( H I ) in the transverse direction as shown in figure 1 for ZnMn (270 pprn). Here, we assume from the maximum of x 11 and XI that the first P-L transition occurs at T, 0.53 K and the second L-LT transition occurs at T,I = 0.09 K. The obtained temperature and field dependence of the nonlinear susceptibility for the two directions is independently analysed in the framework Fig. 1. Temperature dependence of the longitudinal and transverse nonlinear susceptibilities XNL (H) x (0) x (H) of ZnMn (270 ppm) at various fields parallel to the ac field. of the scaling hypothesis: XNL / rP = f ( H ~ / rB+') , where r is a reduced temperature (T T,) / T,, /3 and 7 are a critical exponent. Figure 2 is the double logarithmic scaling plot of XNL / 7@ US. H~ / T ~ + ~ for ZnMn with 270 pprn Mn in the longitudinal and transverse directions respectively, by using the best fitted value of /3 = 1.0 f 0.2 and 7 = 3.0 f 0.3 for X ((NL and /3 = 1.0 f 0.2 and 7 = 2.7 f 0.3 for x INL. The scaling plot by using the mean-field value of /3 = 7 = 1 is also shown in figure 2 for comparison. We have done the same scaling analysis for ZnMn with 150, 390 and 600 pprn Mn. We found that the best fitted value of /3 is in the range of , B = 1.0 f 0.2 for all the present samples in the longitudinal and transverse directions. The 7 value is dependent on the Mn concentration. The obtained critical exponent 4 = /3 + 7 is shown as a function of D / J in figure 3. Here, we use the D / J value estimated previously in reference [5]. From figure 3, it is found that the 4 value for the longitudinal and transverse directions increases with increasing the relative anisotropy D / J and that 4 11 is slightly larger than +I at any D / J ratio where two successive transitions occur. We can roughly estimate the value of the "Heisenberg" limit from the extrapolation of D / J -+ 0 a s P ~ = 1.0 * 0.2, = 1.8 f 0.3, and therefore 4~ = 2.8 f 0.4 for both direcArticle published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19888483