CHINESE JOURNAL OF PHYSICS VOL. 47, NO. 1 FEBRUARY 2009 Study of the Magnetic Property in the Systems K 2 Cu x Mn 1−x F 4 R. Masrour, 1, ∗ M. Hamedoun, 1, 2, 3 and A. Benyoussef 3, 4, 5 1 Solid State Physics Laboratory, Sidi Mohammed Ben Abdellah University, Sciences Faculty, BP 1796, Fez, Morocco 2 Expert Aupr` es de l’Acad´ emie Hassan II des Sciences et Techniques, Rabat, Morocco 3 Institute for Nanomaterials and Nanotechnologies, Rabat, Morocco 4 LMPHE, Faculte des Sciences, Universite Mohamed V, Rabat, Morocco 5 Academie Hassan II des Sciences et Techniques, Rabat, Morocco (Received May 8, 2008) The exchange interactions are calculated by using the probability law. The high- temperature series expansions have been applied to the K 2 Cu x Mn 1-x F 4 systems, combined with the Pad´ e approximants method in order to determine the magnetic phase diagram, i.e., T C versus dilution x. The critical exponent associated with the magnetic susceptibility (γ ) is deduced. The obtained value of γ is insensitive to the dilution ratio x and may be compared with other theoretical results based on the XY model. PACS numbers: 71.70.Gm, 75.10.Nr, 76.50.+g I. INTRODUCTION The magnetic properties of randomly mixed spin systems have been investigated extensively in the last few decades [1–10]. The two materials most extensively studied are K 2 NiF 4 [11] and K 2 MnF 4 [12]. In these materials there is a single-ion anisotropy term in the Hamiltonian with a magnitude of 0.2% and 0.4%, respectively, relative to the Heisenberg term. This term acts to align the spins during z behavior, so the materials would be expected to crossover to Ising behavior close to the point. The K 2 Cu x Mn 1−x F 4 systems are mixed materials of K 2 MnF 4 and K 2 CuF 4 . The magnetic structure of K 2 NiF 4 is anti- ferromagnetic with the N´ eel temperature T N = 42.14 K [13], denoting a body-centered tetragonal sub-lattice of magnetic Cu or Mn atoms. The magnetic structure of K 2 CuF 4 is a two-dimensional ferromagnetic phase with T C =6.2 K [14] and K 2 MnF 4 , which is a two-dimensional antiferromagnetic with T N = 42.1 K. The magnetic measurements for K 2 Cu x Mn 1−x F 4 revealed the ferromagnetic (0.8 ≤ x ≤ 1), spin glass (0.5 ≤ x< 0.8), and antiferromagnetic (0 ≤ x< 0.5) phases [12]. The determination of the critical exponents is an important aspect of the theoretical description and experimental characterization of magnetic materials [15]. In this work, the values of the J AB (x) exchange interactions are calculated via a probability law for the systems K 2 Cu x Mn 1−x F 4 in the range 0 ≤ x ≤ 1. The Pad´ e approximant (PA) [16] analysis of the high-temperature series expansions (HTSE) of these correlation functions has been shown to be a useful method for the study of the critical region [17, 18]. In the antiferromagnetic region we use this technique for the magnetic susceptibility to determine the N´ eel temperature, using the results given in Ref. [19], and in http://PSROC.phys.ntu.edu.tw/cjp 71 c  2009 THE PHYSICAL SOCIETY OF THE REPUBLIC OF CHINA