Interatomic Interaction and Structural Ordering in He II Phase
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Interatomic Interaction and Structural Ordering in He II Phase K. A. Chishko1 Received: 7 July 2019 / Accepted: 7 December 2019 © Springer Science+Business Media, LLC, part of Springer Nature 2019
Abstract The Schrödinger equation for a system of two mobile spinless nuclei with Z = 2 and four electrons (4 He2 -dimer) has been solved with exact diagonalization approach. It is found that the ground state of the system (∼ − 4.2 a.u.) is higher than the energy of two separate 4 He atoms (∼ − 5.7 a.u.), and the average internuclear distance R0 ∼ 1.7 Å is a half smaller than the typical lattice constant in solid helium phases. This result corresponds to a metastable state which can be stabilized only at extremely high external pressure estimated as 27,000 GPa. It means that formation of condensed helium phases at saturated vapor pressure (SVP) is possible only due to many-particle interaction. Below 4.2 K at SVP, 4 He behaves as simple liquid without long-range ordering (He I phase), but below 2.17 K it undergoes the λ-transformation into He II phase due to long-range antiferromagnetic ordering in the 4 He spin subsystem with exchange of order 10 K. As a result, the He II phase can be interpreted as ‘spin ice’ built as polytypic structure of close-packed 2D planes on triangular lattice collected in a stack with alternated ordering in the direction perpendicular to the basal planes, but without breaking the closest packing principle between neighboring planes. Keywords Low-energy excitations on He–He bond · Spin-phonon interaction · Spin ice
1 Introduction The difference between two isotopes of helium is only the nuclear spin of 3 He, but they demonstrate the surprising dissimilarity in their physical properties. Whereas 3 He remains a simple liquid down to very low temperatures, the 4 He undergoes the λ-transition to He II phase at saturated vapor pressure. This phase provides a num-
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K. A. Chishko [email protected] B. Verkin Institute for Low Temperature Physics and Engineering, 47, Prospect Nauky, Kharkiv 61103, Ukraine
123
Journal of Low Temperature Physics
ber of special effects (superfluidity, second, third, etc. sounds, vortices and others). Last decade, the microwave response of He II was discovered in a series of works [1–4]. An essential feature of this response is a temperature-dependent absorption line whose position on the frequency axis reproduces exactly the temperature and pressure dependence of the roton gap discovered from neutron measurements [1,3,4]. The temperature dependence of the low-energy resonant effects in quantum condensed media can be explained through spin–phonon interaction in specifically ordered He II phase. Here, we propose the model of interatomic interaction in He II phase based on two- and four-spin antiferromagnetic exchange within an individual 4 He–4 He interatomic bond. Our calculations are based on exact diagonalization procedure developed previously in Refs. [5,6] whose ideology is closely related to an approach used in Ref. [7].
2 Two Interacting Helium Atom
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