There are two compounds which arguably demonstrate the highest potential for studying novel spintronics-related phenomena: (Ga,Mn)As, the 'canonical' dilute ferromagnetic semiconductor (DFS)  and (Ga,Mn)N, the emerging member of this family [1,2]. Whereas (Ga,Mn)As has become the model material to test semiconductor spintronics concepts, the importance of (Ga,Mn)N stems from a different origin of magnetism and the already dominating role of GaN in photonics and high power electronics. Due to the strong p-d hybridization the Mn^2+/3+ acceptor level occupies the mid band gap position in GaN, and, interchangeable, either a high p-type doping or high Mn content x is possible. Nevertheless, in uncompensated films, where Mn³⁺ ions prevail, the superexchange interaction becomes ferromagnetic for all Mn-Mn distances resulting in a ferromagnetic order [1] characterized by the Curie temperature T_C = 13 K for x = 0.10 [3].

In this context it becomes of a paramount importance to provide the most comprehensive characterization of the magnetic ground state of this insulating DFS. To this end we investigate the static critical behavior of MBE grown (Ga,Mn)N layers [3] with 0.04 < x < 0.10 and compensation free, high-T_C (Ga,Mn)As layer, utilizing direct DC field dependent magnetization and temperature dependence of AC susceptibility. From the analysis we establish for each sample its T_C and critical exponents a, b, and g. In both systems we find g @ 2.6 to exceed about twice its typical value for most common (Stoner) ferromagnets, a value indicative of the profound role of disorder [positional of Mn in (Ga,Mn)N and electrical in (Ga,Mn)As] in the setting of the ferromagnetic state in these two system. We further find that, the Widom relation, d = 1 + g/d, holds precisely only in (Ga,Mn)As. Such calculated d in (Ga,Mn)N considerably overshoots its experimental value. This interesting discrepancy needs further clarification.

The work has been in part supported by FunDMS Advanced Grant of ERC within the Ideas 7th FP of EC and by (Polish) National Science Centre through project MAESTRO "Quantum phase transitions in magnetic layers driven by an electric field" (Decision 2011/02/A/ST3/00125).

[1] M. Sawicki, T. Devillers, S. Gałęski, C. Simserides, S. Dobkowska, B. Faina, A. Grois, A. Navarro-Quezada, K. N. Trohidou, J. A. Majewski, T. Dietl, and A. Bonanni, Phys. Rev. B 85, 205204 (2012).

[2] G. Kunert, S. Dobkowska, Tian Li, H. Reuther, C. Kruse, S. Figge, R. Jakieła, A. Bonanni, J. Grenzer, W. Stefanowicz, J. von Borany, M. Sawicki, T. Dietl, and D. Hommel, Appl. Phys. Lett. 101, 022413 (2012).

[3] S. Stefanowicz, G. Kunert, Tian Li, H. Reuther, C. Kruse, S. Figge, W. Stefanowicz, A. Bonanni, M. Sawicki, T. Dietl, and D. Hommel, in preparation, arXiv 2013.

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