Electric-field-induced nuclear-spin flips mediated by enhanced spin–orbit coupling

Journal name:
Nature Physics
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Published online

Molecules made of identical nuclei of non-zero spin exist in nuclear-spin modifications, and the interconversion of these spin isomers is often forbidden for isolated states1, 2, 3. The interconversion between the nuclear-spin modifications, however, is promoted by inhomogeneous magnetic fields, such as those present on the surfaces of magnetic materials4. Nuclear-spin conversion on diamagnetic and insulating solid substances, on the other hand, is generally considered improbable. Here we present the observation of nuclear-spin flips of H2 and D2 occurring on amorphous solid water surfaces with time constants of 370−140+340s and 1,220−580+2,980s, respectively. To explain these unexpected conversion processes, we propose a model of electric-field-induced nuclear-spin flips. In this model, giant and inhomogeneous electric fields present on the ice surface5 mix the electronic states of opposite parities by the Stark effect6, and significantly enhance the spin–orbit couplings between the electronic singlet–triplet spin states of the molecules. By virtue of these effects, the intramolecular hyperfine contact interaction induces the nuclear-spin conversion. This concept should have implications for controlling nuclear magnetization using external electric fields7.

At a glance


  1. Schematics of the singlet and triplet states of two identical spin 1/2.
    Figure 1: Schematics of the singlet and triplet states of two identical spin 1/2.

    The configurations of two proton spins are singlet for para-H2 (I=0) and triplet for ortho-H2 (I=1), respectively. Iz is the z-component of the total nuclear spin. The wavefunction of the singlet state is antisymmetric and those of the triplet states are symmetric with respect to the permutation of the two identical nuclei (proton). The antisymmetric nuclear-spin operator ia−ib, where ia and ib are the nuclear-spin operators of proton a and b, couples the singlet (para) state with the triplet (ortho) state. ia,b± represent creation and annihilation operators . In the case of two electron spins, the antisymmetric electron spin operator couples the electron-spin singlet state with the triplet states.

  2. Energy level diagram and measurement of ortho- and para-H2.
    Figure 2: Energy level diagram and measurement of ortho- and para-H2.

    a, Energy level diagram of the rotational motion of H2. The rotational energy is given by BJ(J+1), where J is the rotational quantum number, and B is the rotational constant of ~7.5meV for H2 (~3.8meV for D2) in the electronic ground state. Para-H2 (ortho-D2) has even J, whereas ortho-H2 (para-D2) has odd J (ref. 1). b, Schematic of the experimental set-up used for the dosage and J-state-selective thermal desorption spectroscopy of H2 on an amorphous ice surface. Tunable ultraviolet laser light for REMPI is focused by a spherical plano-convex glass lens (f=400mm) in front of the sample at a distance of ~2mm. c,d, REMPI data for J=0 and J=1 in a series of experiments from the initial H2 dosage to thermal desorption at ~35s (c) and at ~600s (d).

  3. Time evolution of the desorption intensities for J=0 and J=1 and their sum.
    Figure 3: Time evolution of the desorption intensities for J=0 and J=1 and their sum.

    a,b, H2 (a) and D2 (b) on the amorphous ice at 10K (see Supplementary Section SC). The error bars represent the standard deviation of several independent measurements. The solid curves are fits using an exponential function, and the upper and lower limits of the time constant are evaluated by the chi-square test with a confidence level of 95% (see text).

  4. SOC and the ortho-para state mixing under giant and inhomogeneous electric fields.
    Figure 4: SOC and the ortho–para state mixing under giant and inhomogeneous electric fields.

    a, An energy level diagram of the electron spin singlet and triplet states in a Π state. See main text for details of the nomenclature. b, An effective mixing channel of the ortho-H2 (I=1:J=1) with the para-H2 (I=0:J=0) in the electronic ground X1Σg+ state via the electronically excited states through IFCC, SC and ESOC.


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  1. Institute of Industrial Science, The University of Tokyo, Komaba, Meguro-ku, Tokyo 153-8505, Japan

    • Toshiki Sugimoto &
    • Katsuyuki Fukutani
  2. CREST, Japan Science and Technology Agency (JST), Komaba, Meguro-ku, Tokyo 153-8505, Japan

    • Katsuyuki Fukutani


K.F. planned and organized the project; T.S. designed and developed the experimental system, conducted measurements, analysed the data and devised the theory; T.S. and K.F. discussed the results and wrote the manuscript together.

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