Gadolinium Spin Decoherence Mechanisms at High Magnetic Fields

Favorable relaxation processes, high-field spectral properties, and biological compatibility have made spin-7/2 Gd3+-based spin labels an increasingly popular choice for protein structure studies using high-field electron paramagnetic resonance. However, high-field relaxation and decoherence in ensembles of half-integer high-spin systems, such as Gd3+, remain poorly understood. We report spin–lattice (T1) and phase memory (TM) relaxation times at 8.6 T (240 GHz), and we present the first comprehensive model of high-field, high-spin decoherence accounting for both the electron spin concentration and temperature. The model includes four principal mechanisms driving decoherence: energy-conserving electron spin flip-flops, direct “T1” spin–lattice relaxation-driven electron spin flip processes, indirect T1-driven flips of nearby electron spins, and nuclear spin flip-flops. Mechanistic insight into decoherence can inform the design of experiments making use of Gd3+ as spin probes or relaxivity agents and can be used to measure local average interspin distances as long as 17 nm.

show field-swept echo-detected EPR spectra acquired around the central m = −1/2 → m = 1/2 transition for Gd-DOTA and Gd-PyMTA, respectively.Spectra were acquired using a two-pulse echo of the form P 1 − τ − P 2 − τ −echo, where P 1 , τ, P 2 were kept fixed and the echo was recorded as a function of magnetic field.Field sweeps were centered at 8608 T.Only the m = −1/2 → m = 1/2 transition contributes to the peak shown at the center of the field sweep.All other transitions form a broad baseline which covers ±0.4.S3 The echo intensity outside of the central m = −1/2 → m = 1/2 transition was at most <5% of the echo intensity at the peak of the central transition.
T M measurements were carried out at the peak of the central m = −1/2 → m = 1/2 transition using a two-pulse echo of the form P 1 − τ − P 2 − τ −echo.The integrated echo magnitude squared was recorded as a function of inter-pulse delay τ .Representative echo decay curves are shown in Figures S4 and S5.The phase memory time T M was extracted by fitting the square of the echo magnitude E(2τ ) 2 with a function of the form E(2τ ) 2 = A exp(−2τ /2T M ) + C. Echo decays were observed to be well-described by a single exponential.A repetition period of 800 µs was used.
T M experiments performed on Gd-DOTA were carried out with pulses P 1 = 175 ns and P 2 = 275 ns.Echo decay experiments were also performed with longer pulses P 1 = 300 ns and P 2 = 510 ns to confirm that instantaneous spectral diffusion was not significantly contributing to echo decay (Figure S4).T M experiments performed on Gd-PyMTA were carried out using pulses P 1 = P 2 = 350 ns (Figure S5).  2.
T 1 measurements were carried out using an echo-detected saturation-recovery experiment with a pulse sequence of the form P sat − T − P 1 − τ − P 2 − τ − echo, with saturation pulse P sat = 300 µs.Representative datasets are shown in Figure S6.For Gd-DOTA, pulses P 1 = 175 ns, and P 2 = 275 ns were used.For Gd-PyMTA, pulses P 1 = P 2 = 350 ns were used.
τ was kept fixed and was between 0.9 µs and 1.2 µs.The integrated echo was recorded as a function of the recovery period T .T 1 was extracted by fitting the integrated echo E(T ) with a function of the form E(T ) = A exp(−T /T 1 ) + C (Figure S6.

Comparing flip-flop models
Figure S8 shows the temperature-dependent flip-flop rate R M for Gd-DOTA and Gd-PyMTA (from Figure 4e in the main text), along with fits to the temperature dependence predicted by Equations 10 (using the ubiquitous flip-flop model) and 1 (using the crystalline flip-flop model.Fitting parameters for both models are shown in Table SS1.We note that from a conceptual standpoint, the crystalline model underestimates the prevalence of energyconserving electron spin flip-flops taking place at nearly every temperature, since frozen Gd 3+ centers are randomly oriented and display a wide distribution of zero field splitting parameters.S3 Table S1: Model parameters extracted from fits fo the concentration-dependent decoherence rate R M to Equation 10, using the ubiquitous flip-flop model, and to Equation S1, using the crystalline flip-flop model. Ubiquitous flip-flop model Crystalline flip-flop model Gd-DOTA Gd-PyMTA Gd-DOTA Gd-PyMTA A1/10 − 3 1.5 ± 0.1 0.9 ± 0.3 3.2 ± 0.2 1.2 ± 0.6 A1 (µs) 1.4 ± 0.2 1.4 ± 0.4 2.9 ± 0.2 2.3 ± 0.3       4) and ubiquitous (Equation 6) models.S1.

Figure
Figure S1 shows T M plotted as a function of temperature (data from Figure 3 in the main text), along with fits to the full model of electron spin decoherence (Equation 10 in the main

Figure
Figure S7 compares the temperature dependence of the flip-flop-driven decoherence term using either the crystalline model or the ubiquitous flip-flop models for S=7/2.The crystalline flip-flop model predicts a sharper initial temperature dependence, which flattens out at around 20K, while the ubiquitous flip-flop model predicts the temperature-dependent flip-flop rate continues to increase with temperature through 50 K.The crystalline flip-flop model predicts the concentration-dependent decoherence rate R M to be

Figure S1 :
Figure S1: Inverse phase memory time 1/T M of (a) Gd-DOTA and (b) Gd-PyMTA.Dashed lines represent a fit to Equation 10, the full model of 1/T M concentration and temperature dependence.

Figure S5 :
Figure S5: Electron spin-echo decay experiments carried out with a pulse sequence of the form P 1 − τ − P 2 − τ −echo, where P 1 = P 2 = 350 ns.The integrated echo magnitude squared was recorded as a function of inter-pulse delay τ .

Figure S8 :
Figure S8: Concentration-dependent rate R M plotted as a function of temperature, from Figure 4e.Solid lines indicate fits to Equation 9 using the ubiquitous flip-flop model.Dashed lines indicate a fit to Equation 9 using the crystalline flip-flop model, using the fitting parameters shown in TableS1.