Quantum anomalous Hall effect with a permanent magnet defines a quantum resistance standard

The quantum anomalous Hall effect (QAHE)(1-6) is a transport phenomenon where the Hall resistance is quantized to the von Klitzing constant due to the spontaneous magnetization of a ferromagnetic material even at zero magnetic field. Similar to the quantum Hall effect (QHE) under strong magnetic fields, the quantized Hall resistance of QAHE is supposed to be universal, independent of the details in the experimental realization(7,8). However, the quantization accuracy of QAHE reported so far(9-11) is much poorer than that of QHE. Here we demonstrate a precision of 10 parts per billion of Hall resistance quantization in QAHE. By directly comparing QAHE with QHE, we confirm that the quantization accuracy of QAHE satisfies the required level as a primary standard of electric resistance. We achieve this high accuracy of quantization by using a weak magnetic field supplied by a permanent disc magnet to align the magnetization domains. Our findings establish a milestone for developing a quantum resistance standard without strong magnetic fields.