Spin properties of two interacting electrons in a quantum dot (QD) embedded in a nanowire with controlled aspect ratio and longitudinal magnetic fields are investigated by using a configuration interaction (CI) method and exact diagonalization (ED) techniques. The developed CI theory based on a three-dimensional (3D) parabolic model provides explicit formulations of the Coulomb matrix elements and allows for straightforward and efficient numerical implementation. Our studies reveal fruitful features of spin singlet-triplet transitions of two electrons confined in a nanowire quantum dot (NWQD), as a consequence of the competing effects of geometry-controlled kinetic energy quantization, the various Coulomb interactions, and spin Zeeman energies. The developed theory is further employed to study the spin phase diagram of two quantum-confined electrons in the regime of cross over dimensionality, from quasi-two-dimensional (disk-like) QDs to finite one-dimensional (rod-like) QDs.
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