We have developed a novel technique for detection of spin polarization with a quantum dot weakly coupled to the objective device. The disturbance to the object in this technique is very small since the detection is performed through sampling of single electrons in the object with very slow rate. We have applied the method to a quantum point contact (QPC) under a spin-orbit interaction. A high degree of spin polarization in the vicinity of the QPC was detected when the conductance stayed on a plateau at a half of the unit conductance quantum ($G_{rm q}/2equiv e^2/h$), and also on another plateau at $2e^2/h$. On the half-quantum plateau, the degree of polarization $P$ decreased with the bias source-drain voltage of the QPC while $P$ increased on the single-quantum plateau, manifesting that different mechanisms of polarization were working on these plateaus. Very long spin relaxation times in the detector quantum dot probably due to dynamical nuclear spin polarization were observed. Anomalous decrease of $P$ around zero-bias was observed at a Kondo-like resonance peak.
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