The origin of ferromagnetism in semimagnetic III-V materials is discussed. The indirect exchange interaction caused by virtual electron excitations from magnetic impurity acceptor levels to the valence band can explain ferromagnetism in GaAs(Mn) in both degenerate and nondegenerate samples. Formation of ferromagnetic clusters and the percolation picture of phase transition describes well all available experimental data and allows us to predict the Mn-composition dependence of transition temperature in wurtzite (Ga,In,Al)N epitaxial layers.

The indirect exchange interaction between magnetic impurities localized in a graphene plane is considered theoretically, with the influence of intrinsic spin-orbit interaction taken into account. Such an interaction gives rise to an energy gap at the Fermi level, which makes the usual RKKY model not applicable. The results show that the effective indirect exchange interaction is described by a range function which decays exponentially with the distance between magnetic moments. The interaction is also shown to depend on whether the two localized moments belong to the same sublattice or are located in two different sublattices.

Litvinov and Dugaev Reply: The Comment [1] contains statements that require discussion. The statements are as follows:(i) The Litvinov and Dugaev (LD) Letter [2] indicates the Bloembergen-Rowland (BR) mechanism [3] is responsible for ferromagnetism in III-V(Mn) materials. That is incorrect since Larson has proved that the BR contribution in semiconductors is small and irrelevant.(ii) In nondegenerate magnetic semiconductors, the magnetic coupling (if not due to the BR mechanism) is due only to superexchange. Larson et al. [4] have shown that superexchange, involving two holes, is antiferromagnetic. Although they discussed particularly the case of II-VI compounds, these conclusions are general and remain valid for the III-V system.(iii) The LD Letter claims that the hole density is too small. However, experimental data clearly indicate the existence of carriers in GaMnAs. The 5% doped GaMnAs clearly exhibits metallic behavior.(iv) As we further increase the doping, the superexchange term is suppressed, while RKKY coupling strongly increases and becomes dominant. This scenario is confirmed experimentally.(v) In the LD Letter, T c is proportional to J 2 pd . This relation cannot be correct in the strong coupling limit.We believe that Statement (i) stems from a terminology misunderstanding. The indirect exchange interaction discussed in the LD Letter is not the BR mechanism discussed by Larson et al. [4]. It is of ''BR-type'' in the sense that both mechanisms rely on virtual excitations between given energy levels and could exist in crystals with no carriers in the valence and conduction bands. However, the energy states involved are different, which makes the magnitude of the interaction different. The original BR mechanism is caused by electron-hole excitations across the band gap, that produce a small BR indirect interaction, which becomes exponentially smaller as the band gap increases, and almost irrelevant when the magnetic state is considered. The LD Letter discusses the mechanism associated with the virtual transitions between the valence band and a narrow impurity band created by Mn in GaAs. The mechanism of indirect exchange via Mn impurity-valence band excitations was also discussed in Ref. [5].Statement (ii) concerns diluted magnetic semiconductors, where the Fermi energy lies in the band gap (no RKKY coupling). The comment that states the coupling between magnetic impurities is due only to a superexchange mechanism does not seem correct. There are the double exchange mechanisms, and also another one indicated in the LD Letter. Superexchange dominates for two close Mn ions located in neighboring positions. For two magnetic ions at a larger distance, the superexchange is much weaker than the interaction discussed in the LD

The one-loop diagram calculation of the Ruderman-Kittel-Kasuya-Yosida exchange interaction in one and two dimensions is done. The method allows us to handle correctly the nonanalytical behavior of the integrand in the range function in the one-dimensional electron gas. ͓S0163-1829͑98͒01732-9͔

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