## The Spin Lock

A spin lock is a relatively long (1-400 ms), low-power (usually 12-33% of the B1 amplitude of a hard pulse) radio frequency pulse applied on the same axis as the desired sample z

Spin lock

Figure 8.37

Figure 8.37

magnetization. It can be either continuous wave or a long series ("train") of pulses of varying length and phase. It can be used to remove artifacts, to "grab and drag" the sample magnetization, and to get transfer of magnetization (either by NOE or by J couplings). First, we will look at the continuous-wave spin lock.

### 8.10.1 Locking the Sample Magnetization

In the rotating frame of reference for an on-resonance peak, the Bo field is exactly canceled by a fictitious field created by the rotation of the axes, so that for nuclei that are on-resonance the only field present is the B i field during the spin lock (Beff = Bi). If we place the sample magnetization on the y' axis of the rotating frame with a 90o hard pulse (phase -x), the spin lock can be placed on the y' axis (phase y). While the spin lock is on, the sample magnetization is "locked" on the y axis and will not undergo precession, as the only field present is the Bi field and the sample magnetization is on the same axis as the Bi field (Fig. 8.37).

8.10.2 Fate of Magnetization Perpendicular to the Spin Lock: Purge Pulses

If instead we start by putting the sample magnetization on the x axis (90o hard pulse on y) and then apply the spin lock on the y axis, the sample magnetization will rotate around the spin lock axis (y axis) at the rate v 1 = yB 1/2n. For typical spin-lock power levels this rate is between 3000 and 9000 Hz. The rotation occurs in the x-z plane (from x to — z to —x to z, and back to x). As the vector rotates, the individual spins that contribute to it began to "dephase" because different parts of the sample experience different B i amplitudes and the sample magnetization from each region rotates at a slightly different rate. Although the Bo field is carefully shimmed to be homogeneous to parts per billion (10—9) variation throughout the sample, the B1 field is quite inhomogeneous and varies significantly in amplitude in different parts of the sample. So this "fanning out" occurs rapidly and all components of the net magnetization that are not on the spin-lock axis rapidly decay to zero. We can see this "fanning out" effect by doing a pulse calibration and continuing far beyond the 360o point (Fig. 8.38). This is a measure of B1 field homogeneity, usually expressed as the ratio of signal intensity for an 810o pulse to the intensity for a 90o pulse. Even though probe designers strive for the best B1 homogeneity possible, you can see that after 100 or 200 cycles there will be no more signal left. If the pulse calibration data are fit to an exponential decay (Fig. 8.38, inset) we get a half-life of 116 |xs for the magnetization rotating around the spin-lock axis. This means that after a 1 ms spin lock at this power level (high power), the net magnetization has rotated 31.25 times around B1 (1000 ^s/(4 x 8 |xs)) and has been cut in half 8.6 times (1000 ^s/116 |xs). After eight half-lives the net

Figure 8.38

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