Magnetic percolation in diluted magnetic semiconductors L. Bergqvist, 1 O. Eriksson, 1 J. Kudrnovsk´ y, 2 V. Drchal, 2 P. Korzhavyi, 3 and I. Turek 4 1 Department of Physics, Uppsala University, Box 530, 751 21 Uppsala, Sweden 2 Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, CZ-182 21 Prague 8, Czech Republic 3 Department of Materials Science, Royal Institute of Technology, SE-10044,Stockholm, Sweden 4 Institute of Physics of Materials, Academy of Sciences of the Czech Republic, Zizkova 22, CZ-616 62 Brno, Czech Republic We demonstrate that the magnetic properties of diluted magnetic semiconductors are dominated by short ranged interatomic exchange interactions that have a strong directional dependence. By combining first principles calculations of interatomic exchange interactions with a classical Heisen- berg model and Monte Carlo simulations, a theory that does not use any adjustable parameters is proposed, and we show that the observed critical temperatures of a broad range of diluted magnetic semiconductors, involving Mn-doped GaAs without and with As-antisites, Mn-doped GaN as well as Cr-doped ZnTe, are reproduced with good accuracy. We show that agreement between theory and experiment is obtained only when the magnetic atoms are randomly positioned on the Ga (or Zn) sites. This suggests that the ordering of diluted magnetic semiconductors is heavily influenced by magnetic percolation, and that the measured critical temperatures should be very sensitive to details in the sample preparation, in agreement with observations. The suggestion of magnetic ordering in semiconduct- ing devices 1,2 has spurred a tremendous interest in the so called diluted magnetic semiconductors (DMS), i.e. semiconductors that have been doped with magnetic elements. One of the most frequently studied sys- tems is Mn doped GaAs, 3–6 but other III-V semicon- ductors have also been investigated, e.g. Mn doped GaP 7 and GaN 8 . Among the II-VI semiconductors there have been experimental reports of Cr doped ZnTe 9 and Mn doped ZnO 10 , whereas for more complex semicon- ducting/insulating materials one may note Mn doped ZnGeP 2 11 and Co doped SnO 2 12 and TiO 2 13 . In all these studies one comes to the conclusion that the magnetic properties, in particular the ordering temperature and the magnetic moment, depend critically on the details in the sample preparation: the Mn-concentration, possi- ble clustering of Mn-atoms as well as the concentration of non-magnetic defects. Hence, the critical temperature can vary over a large range, sometimes reaching room temperature 9 . This is a very important finding since for applications one needs ordering temperatures above room temperature 1,2 . Several DMS materials with a critical temperature close to, or above, room temperature have been reported, 7–13 but it is likely that some of these re- ports represent magnetic properties of impurity phases and/or clusters. Theoretically there have been several attempts to calculate the magnetic properties of these materi- als, especially the critical temperatures, using model Hamiltonians 14 even for random distribution of magnetic atoms 15 . Unfortunately these works rely on assumed forms of the exchange interactions between the magnetic atoms in the semi conducting host. Typically one as- sumes either an RKKY or a double exchange interaction to be relevant. In order to have predictive capability, it would clearly be advantageous to avoid any such assump- tions, something a first principles approach provides. Some attempts to estimate the critical temperature of DMS materials have been made, by calculating in- teratomic exchange interactions from first principles and then using mean field theories for the evaluation of the critical temperature. 6,16 These calculations seem always to overestimate the critical temperature. In addition there have been attempts using the random-phase ap- proximation (RPA-VCA) 17 or Monte Carlo simulations (MC-VCA) 5 in the framework of the virtual-crystal treat- ment of a random Heisenberg Hamiltonian (the average lattice) providing similar results. In the present report we have attempted to make realistic calculations of the critical temperature of DMS systems in which we have abandoned the approximation of an ordered lattice and treated the effect of randomness properly. We have cho- sen to compare our theoretical results to experimental data for Mn doped GaAs 3–6 and GaN 8 as well as Cr doped ZnTe 9 , since in these systems the reported mag- netic properties seem to reflect the true nature of DMS systems, and not clustering or impurity effects which can be avoided by a proper synthesis yielding a more or less random distribution of magnetic atoms. We have calculated interatomic exchange interactions using a first principles theory, and then simulated the critical temperature using a Heisenberg Hamiltonian with magnetic atoms distributed randomly. The criti- cal temperature was calculated by means of Monte Carlo simulations. For materials with large atomic spins a clas- sical Heisenberg Hamiltonian has good accuracy as was recently demonstrated for the case of transition metal ferromagnets 18 . In principle, exchange interactions between atoms i and j, J ij , have to be determined for each geometry of the Monte Carlo simulation cell (typically 50000 atoms) using ab initio electronic structure calculations. Since this is computationally impossible we have made the approximation to calculate them using the coherent- potential approximation (CPA) and using the local spin density approximation (LSDA), as implemented in the