How are spin magnetic moment and orbital angular moment in opposition in a d3 ion in octahedral environment?

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I have two queries firstly what does spin exactly mean and secondly how do i decide whether the spin and orbital moment are in opposition or not or is this an experimental fact.


I would also like to know what does it mean by "when the effect of spin orbit coupling is considered it is found that orbital angular momentum is mixed into the ground state from the first excited state of the system."




The electron has the intrinsic property of spin and so this can give rise to a magnetic dipole. Also, the electron in its orbit produces a magnetic field as a result of its orbital motion. An interaction between the two is possible and is called Spin-Orbit coupling. The magnitude of the interaction depends on the atomic number (more accurately as effective charge $Z^4$) and inversely to the principal quantum number $n$ and orbital quantum number $\ell$. (For a 3d electron this has a value $\approx 0.014Z^4\mathrm{cm^{-1}}$). The sign of the coupling depends on the product of orbital and spin quantum number vectors $\vec L\cdot\vec S$. Additionally this product has a certain symmetry and so can couple an excited and a ground state if the product of the three symmetries contain the totally symmetric representation. This interaction can therefore enhance or reduce the spin only values when calculating the magnetic moment.


(It should be added that a full calculation is very complicated and beyond undergraduate level which is why only a summary is given in the quote above. More details, but only a little more can be found in specialist books on spectroscopy and in some phys. chem. textbooks. )


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