PHYSICAL REVIEW B 83, 224421 (2011) MOKE experiments and theory of uniform and nonuniform distribution of magnetic nanoscrystals: Mn 5 Ge 3 in Ge Fabio Ricci, 1,2 Franco D’Orazio, 1,3 Alessandra Continenza, 1,3 Franco Lucari, 1,2 and Arthur J. Freeman 4 1 Dipartimento di Fisica, Universit` a di L’Aquila, I-67010 Coppito, L’Aquila, Italy 2 Consiglio Nazionale delle Ricerche–Istituto Nazionale di Fisica della Materia (CNR-SPIN) at Dipartimento di Fisica, Universit` a di L’Aquila, I-67010 Coppito, L’Aquila, Italy 3 Consorzio Nazionale Interuniversitario Scienze Fisiche della Materia (CNISM) at Dipartimento di Fisica, Universit` a di L’Aquila, I-67010 Coppito, L’Aquila, Italy 4 Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, USA (Received 9 February 2011; revised manuscript received 3 May 2011; published 27 June 2011) We present a theoretical and experimental study of the magneto-optical (MO) Kerr effect (MOKE) on inhomogeneous systems. Starting from ab initio calculated band structures and using the effective medium approximation or the recently proposed alternating composition layers approximation [Phys. Rev. B 78, 134411 (2008)], we show that the complex Kerr angle can be reproduced also when a nonuniform distribution of the inhomogeneities is present. Applying our formalism to Mn-Ge–based systems, we find that a realistic account of the inhomogeneous concentration of Mn-rich precipitates in a Ge matrix is a necessary condition in order to describe, within the theoretical approach, the experimental Kerr spectra. The agreement between theoretical and measured MOKE spectra shows the validity of the model considered and establishes its predictive power also for a continuously varying concentration distribution of magnetic species in the system. DOI: 10.1103/PhysRevB.83.224421 PACS number(s): 71.15.−m, 78.20.Ls, 75.50.Tt, 75.75.Fk I. INTRODUCTION Inhomogeneity is largely exploited in materials since it often gives rise to new phenomena or enhances features that are appealing for fundamental physics and technological applications as well. However, its presence may constitute an obstacle to the detailed description of the material when the interpretation of the experimental characterization relies on theoretical models that need to be adapted to such complex systems. For example, the study of magnetic nanoclusters in non- magnetic media represents an issue in itself and a challenge to achieve technological exploitation of composite inho- mogeneous materials suitable for read and write magnetic devices with relatively cheap techniques. 1 In this paper, we show how different approaches can be considered within an ab initio–based model and how these compare with experiments in specific cases. In particular, we consider inhomogeneities present in diluted magnetic semiconductors (DMS), which have recently attracted the interest of the scientific community, due to possible applications in the field of spintronics. 2,3 Among different possible systems, group-IV semiconductors (Si, Ge, and Si 1−x Ge x ) doped with magnetic atoms have gained a lot of attention thanks to their integrability with modern electronic Si-based devices. 4,5 In particular, Mn x Ge 1−x shows significantly different Curie temperatures, T C , depending on the growth conditions. T C up to 116 K was found by Park et al. in Mn x Ge 1−x (001) films grown on both Ge and GaAs(001) substrates by molecular beam epitaxy (MBE), 6 whereas T C near room temperature (RT) was reported for MBE-grown MnGe on a Ge(100) substrate. 7–10 Ion implantation techniques (IIT), employed on a Ge matrix maintained at 300 ◦ C, also give T C close to RT for samples containing (2–4) × 10 16 Mn at./cm 2 . 11,12 However, the observed enhanced magnetic ordering temper- ature was usually ascribed to the presence of crystalline nanoclusters (principally Mn 5 Ge 3 ) often dispersed in the DMS phase. 13–16 The present paper reports a combined experimental and theoretical study of the properties of Mn x Ge 1−x inhomoge- neous samples realized with different methods: MBE and IIT. Within the universal approach to magneto-optical (MO) properties of multilayered structures, 17,18 we used either the effective medium approximation (EMA) or the alternating composition layers approximation (ACLA) to account for compositional inhomogeneities. 19,20 We show that these mod- els allow us to fully consider, in the calculation, the nanoscopic structure of the samples: including not only its granular character, but also a varying concentration of the grains inside a matrix, we obtain good agreement with experimental measurements of the MO Kerr effect (MOKE) and we establish a reliable procedure that allows the prediction and, there- fore, the design of sample inhomogeneities to meet specific requirements. In a previous paper, we developed the appropriate method- ology to simulate the MO spectra of inhomogeneous layered materials implementing two different approaches, namely EMA and ACLA. 20 Successively, 21 we presented a preliminary application of one of the considered models (EMA) to a par- ticular sample. In the present paper, we go beyond this work: we extend the model to noncubic structures (such as uniaxial Mn 5 Ge 3 ) and consider application of our methodology to various samples grown with different techniques and thus with large differences in their inhomogeneous morphology. This extensive study and the comparison between theory and experiments on such different samples set the validity and the applicability of the proposed procedure to interpret and design inhomogeneous materials for specific magneto-optical applications. 224421-1 1098-0121/2011/83(22)/224421(5) ©2011 American Physical Society