A novel single-crystal growth method was developed, using arc plasma and metal melt, for a quick survey of high melting point materials. Single crystals of Yb-doped Lu2O3, Lu0.388Hf0.612O1.806, and Lu0.18Hf0.82O1.91, with melting points of 2460, 2900, and 2840◦C, respectively, were grown by an indirect heating method using arc plasma. We refer to this indirect heating growth method as the core heating (CH) method. The CH-grown Yb1%-doped Lu2O3 sample showed a full width at half maximum of 286 arcsec in the X-ray rocking curve. This value is better than the 393 arcsec obtained for the crystal grown by the micro-pulling-down (µ-PD) method. The Yb charge transfer state (CTS) emission was observed at 350 nm in the Yb1%-doped Lu2O3 and Lu0.18Hf0.82O1.91. In the case of the µ-PD method, using a rhenium (Re) crucible, absorption due to Re contamination and a resulting reduction in the Yb CTS emission were confirmed. However, contamination did not influence the properties observed in the crystals grown by the CH method.