Abstract
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+340 s and 1,220−580+2,980 s, 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.
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Main
In molecules, the nuclear spins of identical nuclei are entangled with each other, thereby classifying the molecule into nuclear-spin modifications according to the total nuclear spin1,2,3 (I). Interconversion between the modifications is typically so slow that different nuclear-spin states behave as independent molecules, which has attracted attention in molecular physics6 as well as in nuclear magnetism8. A straightforward way to accelerate the interconversion is to introduce a perturbation that mixes the nuclear-spin states. In the case of two spins, the perturbation represents an antisymmetric spin operator ia−ib (Fig. 1), where ia and ib denote the nuclear spins of the two identical nuclei a and b. Such a perturbation is realized by the inhomogeneous magnetic fields present on the surfaces of antiferromagnetic materials such as FeO(OH) and Cr2O3 (ref. 4). Even without an apparent magnetic field on the surface, the hyperfine contact interaction between conduction electrons of metal surfaces and the molecular nuclear spins causes such a perturbation4,9. Although this catalytic mechanism is valid for diamagnetic metals such as Cu (ref. 10) and Ag (refs 11, 12), it cannot be applied to diamagnetic and insulating solid substances composed of closed-shell atoms, molecules and ions. Thus, at present, there is no physical theory to describe nuclear-spin conversion on diamagnetic and insulating surfaces, and no direct experimental observations of such processes have been reported so far.
This has a crucial consequence in astrophysics: the dominant interstellar solid surface is amorphous solid water13 (ASW), a diamagnetic insulator. The relative population of the ortho (I=1) and para (I=0) nuclear-spin modifications of hydrogen1 (H2), the Universe’s most abundant molecule14, is thus expected to be preserved long after the formation of molecular clouds, that is the H2 nuclear-spin temperature carries important information on star formation15. As any nuclear-spin conversion of H2 on ASW surfaces would strongly affect the local astrophysical H2 nuclear-spin temperature, we have looked into the possibility of such interconversion processes in laboratory experiments.
Experimentally, we adopt resonance-enhanced multi-photon ionization16 (REMPI) for the highly sensitive and rotational-state-selective detection of molecules in the gas phase. In the case of homonuclear diatomic molecules such as H2, the rotational quantum number (J) is strongly coupled to the total nuclear-spin quantum number (I); that is, the rotational levels of H2 with even and odd J belong to the para (I=0) and ortho (I=1) modifications, respectively1 (Fig. 2a). In combination with thermal desorption spectroscopy (TDS), the REMPI technique therefore enables us to measure the coverage evolution of physisorbed ortho- and para-H2 on surfaces (Supplementary Information Section SA). With this unique approach, we demonstrate quantitatively the nuclear-spin conversion of H2 and D2 isotopes on ASW surfaces and develop a new model for electric-field-induced nuclear-spin flips.
The experiments were carried out in an ultrahigh vacuum (UHV) chamber with a base operating pressure below 2×10−8 Pa. ASW films of 60 layers were grown on a Ag(111) single-crystal surface at 13 K by dosing D2O molecules. The ASW film, held at 10 K, was exposed to a dosage (6.5×1015 molecules) of normal H2 at room temperature with an incidence angle of 45° (Fig. 2b). The sample was heated to 30 K, 1–10 min after the dosage, at a heating rate of 3 K s−1 to induce thermal desorption of H2. During the dosage and the thermal desorption from the sample surface, H2 was J-state-selectively detected by REMPI (Fig. 2b). In the present experiment, only J=0 and J=1 desorption signals were detected because the ortho and para modifications are both at the lowest rotational states of J=1 and J=0 below 30 K (ref. 17). The laser set-up for REMPI is described in detail in a previous paper11. Figure 2c shows typical REMPI data during a series of experiments. At t=0 s, H2 is introduced for 10 s, which results in nearly constant signals for J=1 and J=0. The signals around 35 s correspond to the thermal desorption of H2 from the ASW surface. The desorption signal for J=1 is almost equal to that for J=0. The thermal desorption data taken at 600 s after the H2 dosage, on the other hand, show that the J=1 signal is substantially reduced whereas that for J=0 increases (Fig. 2d). These results indicate the ortho–para conversion of H2 on the amorphous ice surface at 10 K. To evaluate the conversion time constant, we measured the time evolution of the H2 desorption intensities for J=0 and J=1 (Fig. 3a). As the residence time on the ASW surface increases, the intensity for J=1 decreases and that for J=0 increases. Also shown in the figure is the sum of the intensities for these two species, which is constant within the experimental accuracy. Fitting a single exponential function to the J=1 data gives a decay time constant of 370−140+340 s. It is worth noting that the ortho–para ratio just after the adsorption deviates from three, which is also observed on Ag surfaces11,12, and that the total number of H2 is preserved during the experiments even after the ortho–para conversion, which is in contrast to the conversion of H2 on Ag surfaces11,12. To clarify the isotope effect on the nuclear-spin flips on the ASW, we measure the time evolution of the desorption intensities for ortho-D2 (J=0:I=2,0) and para-D2 (J=1:I=1) (Fig. 3b). Fitting a single exponential function to the data gives a decay time constant of 1,220−580+2,980 s. These results indicate that the nuclear-spin flips of H2 and D2 do occur on ASW surfaces with the time constants given above.
Interconversion between the ortho and para modifications in the electronic ground X1Σg+ state requires perturbations that induce the state mixing (Supplementary Information Section SB). On the basis that giant electric fields (1010–1011 V m−1) with steep atomic-scale gradients (1020–1021 V m−2) are present on ASW surfaces5 and that H2 on ASW is infrared active through the induced electric dipole moment18, we propose that intramolecular Fermi contact coupling4 (IFCC; Supplementary Information Section SC) is effective for the nuclear-spin conversion through Stark coupling (SC) and spin–orbit coupling (SOC). Although these two couplings are normally small and can be neglected, we argue in the following that the SC is significant, and that the SOC is substantially enhanced in the molecules.
An external electric field mixes the electronic states with opposite parities (gerade–ungerade) and even–odd rotational states6. This is called SC, where the mixing is caused by the perturbation due to an electric-dipole moment. The typical value of the electric-dipole matrix element of H2 is ∼ea0 (refs 19, 20), where e is the elementary charge and a0 is the Bohr radius, respectively. At an electric field of 1010–1011 V m−1, the energy scale of the Stark matrix element becomes of the order of an electronvolt, which is the same order as the energy difference between the electronic ground and excited states of H2. Under such a strong electric field, the SC coefficients become of the order of unity (Supplementary Information Section SB). It should be noted that ionization of molecules can be neglected because the electric field is inhomogeneous on an atomic scale, which is in contrast to the homogeneous electric fields in intense light fields21.
The SOC is induced by the magnetic interaction of the electron orbital motion with its spin. The form of the intrinsic spin–orbit Hamiltonian of molecular hydrogen is , where ξi is the intrinsic spin–orbit interaction coefficient, and and si are the angular momentum relative to the centre of mass of the molecule and the spin of the ith electron, respectively22. Under an external electric field E, an electron moving around the nuclei feels an additional spin–orbit interaction due to the centrifugal component of the electric field E·ri/|ri|. The form of the extrinsic spin–orbit Hamiltonian is , where ri is the position vector of the ith electron relative to the centre of mass, m is the electron mass, c is the light speed, and ℏ is the Planck constant divided by 2π. We emphasize here that the expectation value of E·ri/|ri|2 is non-zero only when E is inhomogeneous on an atomic scale. As a result, the spin–orbit interaction under an inhomogeneous electric field is expressed as , where the first and second terms represent the intrinsic and extrinsic spin–orbit interactions, respectively. The first-order perturbation due to HSOtot lifts the degeneracy of the electron spin triplet state according to the total angular momentum, whereas the second-order perturbation combines the singlet and triplet states having the same total angular momentum, as schematically shown in Fig. 4a. The SOC coefficient between the triplet (3Π1) and singlet (1Π1) states is described by A/Δt−s, where A=|ξ(n l)+η(E)| and Δt−s are the matrix element of HSOtot and the energy difference between the triplet and the singlet states, respectively. The value of Δt−s for the (1s σg)1(n lπ)1 electron configuration corresponding to single-electron excitation becomes smaller as n or l increases23,24,25, where n and l are the main and azimuthal quantum numbers in the united atom picture. This can be intuitively understood by considering that the electron wavefunction has an extended feature at larger n and l (ref. 23), and that the singlet–triplet energy difference reflects the electron–electron repulsion22. As the intrinsic SOC is determined by the electron–nucleus attractive Coulomb force, ξ(n l) also decreases as n or l increases. On the other hand, the value of the extrinsic SOC is almost independent of n or l, with η(E) being ∼10−4 eV in an electric field gradient of 1020–1021 V m−2. Consequently, at high-n, l states, the SOC coefficient of A/Δt−s leads to η(E)/Δt−s. This is an enhancement of the SOC induced by a giant and inhomogeneous electric field. In the case of the (1s σg)1(4dπg)1 configuration, the SOC coefficient of r3Πg with R1Πg can be enhanced to the order of 0.1 as a result of the small energy difference Δt−s∼0.7 meV (refs 24, 25).
Figure 4b shows a possible channel for effective mixing of the ortho-H2 (I=1:J=1) with the para-H2 (I=0:J=0) in the X1Σ+g state under giant electric fields (1010–1011 V m−1) with steep atomic-scale gradients (1020–1021 V m−2). The SC is as large as the order of unity, which leads to actual coupling coefficients of , where N denotes the number of the coupling states. With the IFCC and the enhanced SOC (ESOC) coefficients of ∼10−5 and ∼10−1 for the and r3Πg−R1Πg, respectively, the total coupling coefficient can reasonably be estimated to be ∼10−8 for H2. The magnetic dipole moment of the deuteron is about three times smaller than that of the proton9, which results in a smaller total coupling coefficient for D2 than for H2 (Supplementary Information Section SC). As the deuteron nucleus has a quadrupole moment of ∼0.28 efm2 (ref. 8), the nuclear quadrupole interaction with the electric field gradients leads to the D2 para–ortho coupling between J=1 and J=0 in the X1Σg+ states. The nuclear quadrupole matrix element of ∼10−11 eV and the energy difference of ∼7.5 meV leads to the nuclear quadrupole coupling coefficient of ∼10−9, which is similar to the coupling due to the IFCC–SC–ESOC mechanism. From these coupling coefficients, (∼10−8 for H2 and ∼10−9 for D2), the order of the conversion time of H2 and D2 is estimated to be ∼102 s and ∼103 s (refs 4, 9), respectively, which is in good agreement with our experimental results. Finally, it is worth noting that the magnetic interaction with water nuclear spins is not significant for conversion times of this magnitude (Supplementary Section SD).
The possibility of nuclear-spin conversion of H2 and D2 on diamagnetic and insulating ASW surfaces is demonstrated both experimentally and theoretically. Although the intrinsic SOC in H2 and D2 is small, giant electric fields with steep atomic-scale gradients significantly enhance the SOC and validate the IFCC without ionization of the molecules. In contrast to the conventional theory, our new model indicates that diamagnetic and insulating solid substances composed of closed-shell polar molecules and ions have the potential to serve as a catalyst for nuclear-spin conversion through their surface electric fields26, which also has profound implications for controlling nuclear magnetization by external electric fields. This new concept, at the present stage, is qualitative and further deep theoretical analysis will be a subject for future study. Furthermore, the spin-conversion time-constant obtained in this work will be a key parameter in understanding the dynamics of interstellar molecular clouds on the basis of the increasingly available data on the astronomical ortho/para ratio.
Methods
Preparation of the Ag(111) substrate. The Ag(111) single-crystal substrate was cleaned by cycles of Ar+ bombardment at 500 eV and annealing at 700 K for 1 min in a UHV environment. The surface cleanliness and crystalline order of the substrate were checked using Auger-electron spectroscopy and low-energy electron diffraction (LEED), respectively. Auger-electron spectra revealed that the substrate was chemically clean silver with no trace of oxygen contaminant to induce dissociative adsorption of water molecules. LEED revealed a clear 1×1 pattern with the three-fold symmetry of a face-centred cubic (111) surface structure. From these preparatory experiments, we confirmed that the substrate was chemically clean and well-ordered Ag(111).
Preparation of the ASW film. The D2O water sample, with a purity of 99.96 atom % D as purchased from ISOTEC, was carefully pre-degassed in a baked UHV gas line by repeated freeze–pump–thaw cycles. The ASW film of 60 bilayers was grown by D2O deposition through a molecular beam gas doser in the surface normal direction onto Ag(111) at a substrate temperature of ∼13 K. The deposition rate was 0.11 bilayers per second. Here, the water coverage was normalized by the bilayer density (∼1.1×1015 molecules cm−2) for the crystalline ice-Ih. For the deposition rate used here, the ice film grown at 13 K is known to be amorphous27,28. The ice film was annealed at 55 K to avoid any structural changes during the H2 adsorption and desorption experiments, which were conducted in the temperature range of 10–30 K. The ice film was characterized by TDS and LEED. When the sample was heated from 13 K to 300 K with a heating rate of 2 K s−1, the zeroth-order single TDS peak was observed at around 170 K, which was in good agreement with previous TDS studies of water on Ag(111) (ref. 29). Here, we emphasize that there was no desorption peak around 50 K corresponding to desorption of O2 (ref. 30). The LEED pattern of the ice film at 13 K revealed no diffraction spots, indicating that there was no ordered structure on the surface. From these preparatory experiments, we confirmed that the ice film was in an amorphous state.
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Acknowledgements
We thank T. Kawauchi and T. Okano for assistance with apparatus development, M. Matsumoto and K. Niki for assistance with the experiments, K. Yamakawa for fruitful discussions and M. Wilde for manuscript corrections. This work was supported by Grant-in Aid for Scientific Research (A) of the Japan Society for the Promotion of Science (JSPS). T.S. acknowledges support as a Research Assistant of the Global Centre of Excellence for the Physical Science Frontier of Tokyo University, Japan.
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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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Sugimoto, T., Fukutani, K. Electric-field-induced nuclear-spin flips mediated by enhanced spin–orbit coupling. Nature Phys 7, 307–310 (2011). https://doi.org/10.1038/nphys1883
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DOI: https://doi.org/10.1038/nphys1883
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