The J-PARC TREK experiment will search for violation of time reversal invariance (T) in the K+→π0μ+;d; decay. The transverse muon polarization (PT) in stopped kaon decay will be measured with high precision (10-4). An active polarimeter will be employed to stop muons and to detect decay positron asymmetry at the same time. The selection of the stopper material is an important issue. In a longitudinal and transverse field μSR experiment at TRIUMF, the muon spin relaxation rates have been measured for alloys of Al and Mg to find the best candidate stopper material. Almost all the alloys tested showed no significant relaxation.