Larmor precession, mechanism

The mechanics of EPR spectroscopy as to Larmor precession and the nteraction of the spin S in the applied radiation are exactly similar to that... 

It is sometimes useful to compare the quantum mechanical and classical pictures of magnetic nuclei pictured as tiny bar magnets. A bar magnet in an externally applied magnetic field undergoes the motion called precession as it twists around the direction of the field (Fig. 13.18). The rate of precession is proportional to the strength of the applied field and is in fact equal to y l2n) Bo, which in this context is called the Larmor precession frequency, Vl. 

Quantum mechanics does not allow the orbital angular momentum to line up with the magnetic field as assumed in the previous example. Instead L projects a component, lime on the B-direction as was shown in Chapter 2. A magnetic field exerts a torque on a magnetic moment according to L = p,M x B. This torque is perpendicular both to the field B and the L, which is along the p.b therefore, the effect is to cause a precession of L about B. This precession is knovm as Larmor precession and takes place with the Larmor frequency... 

This is the Larmor equation. Since co = Ittv, this expression is equivalent to Equation 15.7. The two approaches are different one leads to the frequency of the quanta which separates both energy states and the other to the mechanical precession frequency. These two frequencies have the same value. 

In spherically symmetric systems the induced diamagnetism depends primarily on the mean square radius of the valence electrons as the small contribution from the inner-shell electron core can usually be neglected 1 ). In the case of molecules with symmetry lower than cubic, the quantum mechanical treatment by Van Vleck 23> indicates that another term must be added to the Larmor-Langevin expression in order to calculate correctly diamagnetic susceptibilities. This second term arises because the electrons now suffer a resistance to precession in certain directions due to the deviations of the atomic potential from centric symmetry. The induced moment will now be dependent on the orientation of the molecule in the applied magnetic field and thus in general the diamagnetic susceptibility will not be an isotropic quantity 19-a8>. 

After the rf field Hj is turned off, the magnetization will precess freely. In an actual experiment, the precessing magnetization decays owing to various mechanisms which usually are the objects of an NMR study. In a coil with its axis perpendicular to the laboratory field, this decaying magnetization will induce an rf current at the Larmor frequen-... 

At very high frequencies, domain walls are unable to follow the field and the only remaining magnetisation mechanism is spin rotation within domains. This mechanism eventually also shows a dispersion, which always takes the form of a resonance. Spins are subjected to the anisotropy field, representing spin-lattice coupling as an external field is applied (out of the spins easy direction), spins experience a torque. However, the response of spins is not instantaneous spins precess around the field direction for a certain time (the relaxation time, r) before adopting the new orientation. Fig. 4.62. The frequency of this precession is given by the Larmor frequency ... 

As Mo is a property of the bulk system, one can define all three components simultaneously and use classical mechanics to describe its evolution. Mo will precess around Bq at the Larmor frequency, coq (see Figure 1). The Larmor frequency is equivalent to the frequency of photons required to induce transitions between the energy levels and is defined as ... 

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