What is T1ρ and How is it Measured?

The time constant for the build up of magnetization along the direction of the main magnetic field, B_o, (the z axis) either after a pulse or upon initially exposing a sample to the magnetic field is called the T₁ relaxation time or spin-lattice relaxation time. It is this relaxation time which determines the rate at which a pulse sequence can be repeated. The time constant for the decay of magnetization in the x-y plane of the rotating frame of reference after a pulse is called the T₂ relaxation time, the spin-spin relaxation time or the transverse relaxation time. It is this relaxation time which determines the natural line width of a particular resonance. There is another relaxation time constant of interest to NMR spectroscopists - T₁ρ. T₁ρ is the time constant for the decay of magnetization along the radio frequency field, B₁, of an applied spin locking pulse in the rotating frame of reference. It is analogous to T₁ except it describes relaxation along the radio frequency field of the pulse (which is static in the rotating frame) rather than relaxation along B_o. T₁ρ's are of interest in ROESY, TOCSY and cross polarization experiments. The T₁ρ is measured by first applying a 90 degree pulse to an equilibrium magnetization vector. A spin locking pulse is then applied. The phase of this pulse is shifted 90 degrees with respect to the excitation pulse such that the field of the spin locking pulse is coincident with the spin vector in the rotating frame of reference. During the spin locking pulse, the large magnetization vector (which was initially polarized in B_o) decays to its equilibrium value in the much smaller field, B₁, with time constant, T₁ρ. The T₁ρ is measured by analysing the intensity of the NMR signal in spectra collected as a function of the duration of the spin locking pulse. This is illustrated in the figure below.