Local hyperfine field

For SMMs at temperatures below the blocking temperature, the magnetisation becomes frozen on the NMR timescale, that is, the local hyperfine fields become static. This is demonstrated spectacularly in [Mni20i2(MeC02)i6(H20)4] 2MeC02H.4H20 by the observation of a Mn (100% natural abundance, I = 5/2) NMR spectrum in zero applied... 

Whereas the paramagnetic shift of the nuclear magnetic resonance frequency for a given applied field is related to the strength of the local hyperfine field at the nuclear site, induced by the electronic moments, the nuclear spin-lattice relaxation rate yields information about the low-frequency spectrum of thermally induced spin fluctuations. The influence of pair-correlation effects on the NMR relaxation in paramagnets was analysed experimentally and theoretically by... 

The paramagnetic states produce local hyperfine fields at nearby Se nuclei (Brown, Moore, and Seymour, 1972) so there is also a shift of the... 

Figure 7.1 Kane s scheme for a quantum computer based in NMR of a solid-state sample. An array of P is inserted in a silicon lattice. Electrical gates of type A control the value of the local hyperfine field, whereas gates of type J control two-qubit interactions. On the right is the estimated NMR resonance shift due to biasing of A-type gates. Adapted with permission from [1].

The third prominent interaction in iron Mossbauer spectroscopy is the magnetic hyperfine interaction of the Fe nucleus with a local magnetic field. As explained in detail in Chap. 4, it can be probed by performing the Mossbauer experiment in the presence of an applied external magnetic field. 

The electron magnetic moment may also interact with the local magnetic fields of the nuclear dipole moments of nuclei around it. A single electron centered on a nucleus of spin I will experience 2/ -f 1 different local magnetic fields due to the 27 - - 1 different orientations of the nuclear spin I in the external magnetic field. This interaction, which is of the order of 10 cm. i, causes a hyperfine structure in the EPR spectrum. This structure is further discussed and illustrated in Section III,B. 

The EPR spectra have always been interpreted2994 using an effective S = 2 spin Hamiltonian including the Zeeman term, /iBB g-S, and the hyperfine term, ICa-A-S, which describes the interaction of the unpaired electrons with the copper nucleus (7Cu = I). The spectra are very sensitive to the ratio between the isotropic coupling constant J and the local zero field splitting of nickel(II), Z)Ni.2982 In the limit J DNi it can easily be shown that the following relations hold ... 

Figure 18-4. ENDOR energy level diagram for an electron Ms = 1/2 in the local magnetic field of a proton Mj = 1 /2. To observe an ENDOR transition, the external magnetic field H0 is positioned on an EPR line, in this case the transition from Ms = —1/2, Ml = +1/2 > to Ms = +1 /2, M, = + 1/2 >. Then a radio-frequency transmitter is scanned through the various NMR frequencies (typically 10-100 MHz). This diagram shows two ENDOR transitions of energy haq and hu2 that correspond to the hyperfine couplings of a nuclear spin with Mj = 1/2...

The g-value is used to characterize the position of a resonance. It is a measure of the local magnetic field experienced by the electron. The g-value is a unique property of the molecule as a whole, and is independent of any electron-nuclear hyperfine interactions that may be present. The g-value is defined as... 

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