We have calculated the linear magnetoconductance across a vertical parabolic Quantum Dot with a magnetic field in the direction of the current. Gate voltage and magnetic field are tuned at the degeneracy point between the occupancies N=2 and N=3, close to the Singlet-Triplet transition for N=2. We find that the conductance is enhanced prior to the transition by nearby crossings of the levels of the 3 particle dot. Immediately after it is depressed by roughly 1/3, as long as the total spin S of the 3 electron ground state doesnt change from S=1/2 to S=3/2, due to spin selection rule. At low temperature this dip is very sharp, but the peak is recovered by increasing the temperature.
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