Magnetic moment with external magnetic field on a lattice?
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Consider a system in which atoms are located in a regular lattice, each atom having a spin 1/21/2 and an associated intrinsic magnetic moment μ0>0μ0>0. Assume that each atom interacts only weakly with other atoms so that all the other atoms act as a heat reservior. If the system is placed in an external magnetic field H0z^H0z^, then the Hamiltonian is given by:
H^=−μ0H0∑iσziH^=−μ0H0∑iσiz
where σziσiz are (the zz components of) the Pauli matrices, at the iith site.
For the magnetic moment μ=±μ0μ=±μ0, the corresponding magnetic energy of the atom is E=∓μ0H0E=∓μ0H0.
H^=−μ0H0∑iσziH^=−μ0H0∑iσiz
where σziσiz are (the zz components of) the Pauli matrices, at the iith site.
For the magnetic moment μ=±μ0μ=±μ0, the corresponding magnetic energy of the atom is E=∓μ0H0E=∓μ0H0.
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Explanation:
The displaced magnetic moment produced by the radio frequency driving pulse, precesses around the external magnetic field and itself generates a radio frequency signal.
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