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RadioFrequencyEnhancement

< The physics of magnetic Mn | Index | Spin Lattice Relaxation: Redfield treatment for spin greater than 1/2 >

In ferro- and ferri-magnetic materials one exploits their susceptibility, {$(\chi_\parallel, \chi_\perp)$}, where the pedices refer to the easy axis, and the large hyperfine field (typically tens of Tesla). Let's consider two simple geometries in zero external field, with an isotropic hyperfine coupling {$\mu_0\gamma\hbar {\mathbf I} \cdot {\mathbf H}_{hf}$}. In the first geometry consider a radio frequency field {${\mathbf H}_1 \perp {\mathbf M_s}$}, perpendicular to the domain magnetization. In each domain the magnetization will acquire a very small transverse component {$\chi_\perp{\mathbf H}_1$}, hence it will gently wiggle around its preferred axis, following the radio-frequency. Since the hyperfine field follows the domain magnetization it will also acquire a perpendicular component. The effective oscillating field at the nucleus will be thus the much larger prpendicular component due to this mechanism and the radio-frequency field is amplified by:

{$H_{1e}=\frac {H_{hf}} {M_s} \chi_\perp H_1=\eta H_1$}

The numerical factor {$\eta$} can be very large thanks to the huge hyperfine field, typically 10 T/µ_B. This large enhancement factor means that less power is needed to produce a 90 degree nutation. The same enhancement relates the nuclear transverse magnetization {$M_{n\perp}$} and the amplitude of the field modulation in the receiver coil, so that the FID signal is proportional to {$\chi_\perp \frac {H_{hf}} {M_s} M_{n\perp}=\eta M_{n\perp}$}, making magnetic ion NMR much more sensitive. This mechanism works also for antiferromagnets.

The second case is for {${\mathbf H}_1 \parallel {\mathbf M_s}$}. Here the strongest signal comes from nuclei in the domain walls. The field {${\mathbf H}_1$} in this case shifts periodically the balance between the up and down domains of an unmagnetized sample. This is achieved by sweeping certain domain walls back and forth. Assuming an average linear domain size and a domain wall thickness of {$N$} and {$n$} lattice parameters, respectively, the amplitude of the angle {$\theta$} swept by the isotropic hyperfine field at a Fe site inside the domain wall will be roughly proportional to the applied field, {$N H_1/Ms$}, times the angular difference from one site to the next in the wall, {$\pi/n$}. Hence the hyperfine-enhanced radio-frequency field will be now:

{$H_{1e}=H_{hf} \sin\theta\approx \pi \frac {N H_{hf}}{n H_s} H_1$}

Here the enhancement may be even larger, by a factor {$N/n$}, and the same amplification is again obtained in the FID detection. This mechanism is at play only for orders with a macroscopi magnetization, it requiring its coupling to the external field {${\mathbf H}_1$}.

< The physics of magnetic Mn | Index | Spin Lattice Relaxation: Redfield treatment for spin greater than 1/2 >