Supplemental Information for Room - temperature local ferromagnetism and its nanoscale expansion in the ferromagnetic semiconductor Ge 1 - x Fe x

In our manuscript, we assumed, that each substitutional Fe atom and each interstitial Fe atom, which exist with the ratio of 85% and 15% of the doped Fe atoms, respectively, contribute equally to the integrated XAS intensity expressed by equation (1) in the main text. Hereinafter, we call this assumption as assumption A in this Supplemental Information. This was used for deriving the following main conclusions (hereinafter referred to as Finding I, II and III, respectively, in this Supplemental Information). I. The first observation of the intriguing expansion of nanoscale local ferromagnetic regions with decreasing temperature, followed by a transition of the entire film into a ferromagnetic state at the Curie temperature as shown in Fig. 7 in the main text. II. There are Fe atoms antiferromagnetically coupled to the substitutional Fe atoms below TC. III. The fraction fSPM of superparamagnetic substitutional Fe atoms and the magnetic moment mSPM per local ferromagnetic region are correlated with TC and the nonuniformity of the Fe concentration; the larger the nonuniformity of the Fe distribution is, the larger each local ferromagnetic region, fSPM, and mSPM become, and the local ferromagnetic regions can be more easily connected magnetically, resulting in a higher TC. Here, we describe that these conclusions do not depend on assumption A.