Co-occurrence of Superparamagnetism and Anomalous Hall Effect in Highly Reduced Cobalt-Doped Rutile<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mrow><mml:mi>TiO</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mo>−</mml:mo><mml:mi>δ</mml:mi></mml:mrow></mml:msub></mml:math>Films

We report a detailed magnetic and structural analysis of highly reduced Co doped rutile ${\mathrm{TiO}}_{2\ensuremath{-}\ensuremath{\delta}}$ films displaying an anomalous Hall effect (AHE). The temperature and field dependence of magnetization, and transmission electron microscopy, clearly establish the presence of nanosized superparamagnetic cobalt clusters of $\ensuremath{\sim}8--10\text{ }\text{ }\mathrm{nm}$ size in the films at the interface. The co-occurrence of superparamagnetism and AHE raises questions regarding the use of the AHE as a test of the intrinsic nature of ferromagnetism in diluted magnetic semiconductors.