Transition metal and related compounds have been extensively studied over the past several decades. These investigations revealed a wide range of behavior, encompassing colossal magnetoresistance (CMR), high-TC superconductivity, and magnetic semiconductivity, all of which continue to present fundamental challenges to the understanding of such phenomena. There is, however, a close correlation between such characteristics and the appearance of magnetic order. This correlation underlies the present study, which focuses on the magnetic and transport behavior of various Manganese (Mn), Iron (Fe) and Cobalt (Co) containing materials, with particular emphasis on the nature of the magnetic order they display and the critical exponents that characterize the accompanying phase transition. The magnetic and transport properties of two specific systems will be covered: first various doped manganites from the series (La,Pr)1-x(Ca,Ba)xMnO3, and second the magnetic semiconductors Fe0.8Co0.2Si and Ga0.98Mn0.02As. In the manganites, the influence of doping on; (i) the evolution of the metal-insulator transition (MIT) with composition; (ii) the universality class of the magnetic critical behavior associated with the paramagnetic to ferromagnetic transition, which occurs in the vicinity of a MIT with which CMR is associated; (iii) the mechanisms underlying ferromagnetism across the MIT; (iv) the correlation between the appearance of a Griffiths-like phase and CMR, and (v) the origin of Griffiths-like phase have been investigated. Four different systems have been studied: La1-xCaxMnO3 (0.18 ≤ x ≤ 0.27), La1-xBaxMnO3 (x ≤ 0.33), (La1-yPry)0.7Ca0.3Mn16/18O3 (y ≤ 0.85), and Pr1-xCaxMnO3 (x = 0.27, 0.29). In Fe0.8Co0.2Si and Ga0.98Mn0.02As, the scaling between magnetization and conductivity has been the subject of ongoing debate. In bulk Fe0.8Co0.2Si, a novel scaling between the anomalous Hall effect (AHE) and the magnetization enables the anomalous Hall coefficient to be accurately determined. In turn, this enables the universality class for the transition to ferromagnetism to be established independently from the anomalous Hall conductivity. In an epitaxial (metallic) Ga0.98Mn0.02As microstructure, the magnetization has been indirectly determined from the AHE. Subsequent analysis yields magnetic critical exponents consistent with the Mean-Field model, direct support for which had previously been lacking.

Transition metal and related compounds have been extensively studied over the past several decades. These investigations revealed a wide range of behavior, encompassing colossal magnetoresistance (CMR), high-TC superconductivity, and magnetic semiconductivity, all of which continue to present fundamental challenges to the understanding of such phenomena. There is, however, a close correlation between such characteristics and the appearance of magnetic order. This correlation underlies the present study, which focuses on the magnetic and transport behavior of various Manganese (Mn), Iron (Fe) and Cobalt (Co) containing materials, with particular emphasis on the nature of the magnetic order they display and the critical exponents that characterize the accompanying phase transition. The magnetic and transport properties of two specific systems will be covered: first various doped manganites from the series (La,Pr)1-x(Ca,Ba)xMnO3, and second the magnetic semiconductors Fe0.8Co0.2Si and Ga0.98Mn0.02As. In the manganites, the influence of doping on; (i) the evolution of the metal-insulator transition (MIT) with composition; (ii) the universality class of the magnetic critical behavior associated with the paramagnetic to ferromagnetic transition, which occurs in the vicinity of a MIT with which CMR is associated; (iii) the mechanisms underlying ferromagnetism across the MIT; (iv) the correlation between the appearance of a Griffiths-like phase and CMR, and (v) the origin of Griffiths-like phase have been investigated. Four different systems have been studied: La1-xCaxMnO3 (0.18 ≤ x ≤ 0.27), La1-xBaxMnO3 (x ≤ 0.33), (La1-yPry)0.7Ca0.3Mn16/18O3 (y ≤ 0.85), and Pr1-xCaxMnO3 (x = 0.27, 0.29). In Fe0.8Co0.2Si and Ga0.98Mn0.02As, the scaling between magnetization and conductivity has been the subject of ongoing debate. In bulk Fe0.8Co0.2Si, a novel scaling between the anomalous Hall effect (AHE) and the magnetization enables the anomalous Hall coefficient to be accurately determined. In turn, this enables the universality class for the transition to ferromagnetism to be established independently from the anomalous Hall conductivity. In an epitaxial (metallic) Ga0.98Mn0.02As microstructure, the magnetization has been indirectly determined from the AHE. Subsequent analysis yields magnetic critical exponents consistent with the Mean-Field model, direct support for which had previously been lacking.