PhD work: Piegay (2002), Marion (2002), Baudin (2010)

Collaborative research projects: WideNMR (2016-2019), IMAGINE (2013-2016), DIPOL (2007-2011)

Introduction

Conventional descriptions of nuclear magnetic resonance (NMR) ignore collective effects for spin dynamics and the evolution of local magnetisation is described by a simple linear Bloch equation. This approach, usually justified in weakly polarised systems, turns out to be inappropriate for a liquid where nuclear polarisation is large. In such a liquid, dipolar magnetic interactions introduce a significant non-linear and non-local contribution to the Bloch equation that leads, for instance, to precession instabilities at large tip angles [1], [2], [3]. A variety of new phenomena related to the non-linear evolution of nuclear magnetisation in highly polarised liquid samples have been described in the past decade. In most cases they result from the intricate combination of (i) the non-linear coupling between the transverse nuclear magnetization and the detection coil (radiation damping, RD, a well-known NMR artefact) and (ii) the enhanced contribution of long-range magnetic interactions, not averaged out by the Brownian motion (distant dipolar fields, DDFs). Similar effects have been are in fact met in a wide range of other physical systems (such as Bose-Einstein condensates, superfluid 3He, two-dimensional atomic hydrogen gas or quantum entangled spin systems). The work carried out with laser-polarised noble gas atoms is expected to contribute to a better understanding of the spin dynamics in highly magnetised liquids. We perform NMR experiments at low field (2 mT) on bulk samples (0.5 cm³) of liquid helium mixtures that consist in hyperpolarised ³He atoms (with a high nuclear orientation obtained by MEOP in the gas phase at room temperature ) condensed in superfluid ⁴He. In these mixtures intrinsic longitudinal relaxation times are many hours long at low ³He concentrations [4]. Thanks to the hyperpolarisation process, dipolar fields reach a few µT (to be compared to the few nT obtained for proton at equilibrium in a standard 12T spectrometer) and bring a dominant contribution to the evolution of magnetisation in the liquid. This model system provides a great freedom for the control of key experimental parameters (diffusion coefficient, dipolar field strength), though the choice of operating conditions (temperature, concentration, and nuclear polarisation).

Investigation and control of NMR instabilities in hyperpolarised 3He solutions

In highly polarised ³He-⁴He mixtures, after a 90° pulse, free induction decay signals vanish in few tens of milliseconds (instead of typically one second at low magnetisation densities) [5]. This collapse is an evidence of the onset of dipolar instabilities, and results from the development of inhomogeneous magnetisation patterns that grow exponentially in time during transverse precession [6]. We have launched a study of dipolar instabilities using spin echo techniques, to determine the characteristic length scales of these magnetisation patterns. At high magnetisations, a simple 180°rf pulse fails to refocus transverse magnetisation. We therefore use a Magic Sandwich pulse sequence (a linked series of adequately phased 180° rf pulses, originally developed in solid-state NMR for strongly-coupled dipolar systems) to drive a time-reversed evolution of the magnetisation (at half the pace of the free evolution). Using a series of Magic Sandwich sequences, transverse magnetisation can be repeatedly refocussed and its lifetime can be increased by up to 3 orders of magnitude  [7],  [8],  [9]. A quantitative analysis of the decay of the dynamically stabilised magnetisation has been carried out (E. Baudin, PhD work, 2010), both experimentally and numerically. For these studies, an active feedback scheme has been implemented on the NMR detection system to control its back-action on magnetisation [10] and to observe the intrinsic dipolar instabilities in the hyperpolarised mixtures.

Computed (left) and observed (right) echo trains obtained with repeated magic sandwiches. Long NMR signal lifetimes are thus recovered.

The efficiency of time reversal has appeared to be very sensitive to homogeneity of the applied radiofrequency field. Work is in progress to perform experiments with improved rf coils and higher nuclear polarisations. The same feedback device will then be used to enhance (rather than decrease) radiation damping field, in order to investigate the behaviour of the magnetisation under the joint effect of DDF and RD. Radiation damping and dynamic instabilities actually play an increasing role due to sustained technological efforts to improve NMR signals, in particular in high-resolution NMR spectroscopy (a very powerful tool with applications in condensed matter physics, analytical chemistry, structural biology, or medicine). It is expected that our recent theoretical breakthroughs and the deeper understanding of rf-driven time evolution already obtained in a variety of situations (with/without DDF, RD, or spatial inhomogeneities of applied field) will lay the ground to new developments in this field. In particular, generic ways have been found to taylor robust composite pulses and to design more efficient NMR sequences. They will be experimentally validated.

Multiple spin echoes in highly magnetised liquids

Joint experiments have been performed with the team of H. Desvaux (LSDRM, CEA Saclay) to investigate other DDF-induced new phenomena, thanks to the DIPOL project (“Non-linear NMR in polarised liquids”, funded by the ANR). We have in particular studied the characteristics of multiple spin echoes (MSE) observed in highly magnetised liquids. This work has been carried out both with solutions of optically pumped ¹²⁹Xe in cyclohexane (at room temperature and 11.7 T, in Saclay) and our hyperpolarised He solutions (at low temperature and 3mT, at LKB) [11]. Two 90° pulses, separated by a phase-encoding period τ with an applied gradient, are followed by a train of echoes. These echoes are formed under the influence of the imprinted longitudinal magnetisation pattern if a strong initial magnetisation is present in the liquid.

Example of multiple spin echoes recorded in hyperpolarised 3He -4He liquid mixtures. Slower diffusion leads to many more echoes for 129Xe dissolved in cyclohexane.

Several NMR experiments had been performed in the 1980s on thermally polarised solid ³He, liquid ³He and water for observing MSE due to dipolar fields. Our thorough investigation has used hyperpolarised liquids, thereby exploring ranges of average dipolar field that are one order of magnitude larger than that usually obtained with thermally polarized spin systems. We have thus reached regimes in which precession instabilities compete with the refocusing action of the gradient (Fig. below), which deserves further investigations. Moreover, we have benefited from the additional flexibility provided by the use of either ³He and ¹²⁹Xe solutions, that have very different diffusion properties.

  Example of data obtained by computer simulation of spin dynamics, for increasing distant dipolar field strengths. Inset: Experimental data obtained in a highly polarised liquid sample.

We have also performed extensive numerical lattice simulations including the effects of diffusion, magnetic field gradients, dipolar couplings, and rf field.

For realistic 3D simulations, with up to 2×10⁶ coupled magnetic moments, the computational load was heavy but manageable. The major outcome of our combined experimental and numerical studies is a detailed knowledge of the different contributions to the measured echoes amplitudes and, in particular, a reliable assessment of the finite size effects (usually overlooked or underestimated for analysis of echo attenuation). This quantitative knowledge provides the basis for a truly reference-free absolute measurement of magnetisation (a holy grail for NMR with out-of-equilibrium nuclear polarisation), just by comparison of relative amplitudes within a recorded echo train.

References:

[1] K.L. Sauer, F. Marion, P.-J. Nacher, and G. Tastevin, Phys. Rev. B. 63, 184427 (2001)

[2] P.-J. Nacher, G. Tastevin, B. Villard, N. Piegay, F. Marion, and K. L. Sauer, J. Low Temp. Phys. 121, 473 (2000)

[3] Y.Y. Lin, N. Lisitza, S.D. Ahn, and W.S. Warren, Science 290, 5489 (2000)

[4] N. Piegay, and G. Tastevin, J. Low Temp. Phys. 126, 157 (2002)

[5] P.-J. Nacher, N. Piegay, F. Marion, and G. Tastevin, J. Low Temp. Phys. 126, 145 (2002)

[6] J. Jeener, J. Chem. Phys. 116, 8439 (2002)

[7] M.E. Hayden, E. Baudin, G. Tastevin, and P.-J. Nacher, Phys. Rev. Lett. 99 (2007) 137602 (Open access archive HAL)

[8] E. Baudin, M.E. Hayden, G. Tastevin, and P.-J. Nacher, J. Low Temp. Phys. 150 (2008) 168 – 173 (Open access archive HAL)

[9] E. Baudin, M.E. Hayden, G. Tastevin, and P.-J. Nacher, Comptes Rendus Chimie 11 (2008) 560 – 567 (Open access archive HAL)

[10] E. Baudin, K. Safiullin, S.W. Morgan, and P.-J. Nacher, J. of Phys. : Conf. Series 294 (2011) 012009 (Open access)

[11] S.W. Morgan, E. Baudin, G. Huber, P. Berthault, G. Tastevin, P.-J. Nacher, M. Goldman, H. Desvaux, « Multiple dipolar echoes observed in dissoved laser-polarized noble gas solutions », Eur. Phys. J. D. (2013) 67 : 29 (Open access archive HAL)