Neutron reflection from a liquid helium surface

The reflection of neutrons from a helium surface has been observed for the first time. The ⁴He surface is smoother in the superfluid state at 1.54 K than in the case of the normal liquid at 2.3 K. In the superfluid state we also observe a surface layer ~200 Å thick which has a subtly different neu...

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Veröffentlicht in:	Физика низких температур
Datum:	2008
Hauptverfasser:	Charlton, T.R., Dalgliesh, R.M., Ganshin, A., Kirichek, O., Langridge, S., McClintock, P.V.E.
Format:	Artikel
Sprache:	English
Veröffentlicht:	Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2008
Schlagworte:	Жидкий гелий
Online Zugang:	https://nasplib.isofts.kiev.ua/handle/123456789/116905
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Zitieren:	Neutron reflection from a liquid helium surface / T.R. Charlton, R.M. Dalgliesh, A. Ganshin, O. Kirichek, S. Langridge, P.V.E. McClintock // Физика низких температур. — 2008. — Т. 34, № 4-5. — С. 400–403. — Бібліогр.: 28 назв. — англ.

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spelling	Charlton, T.R. Dalgliesh, R.M. Ganshin, A. Kirichek, O. Langridge, S. McClintock, P.V.E. 2017-05-18T09:42:35Z 2017-05-18T09:42:35Z 2008 Neutron reflection from a liquid helium surface / T.R. Charlton, R.M. Dalgliesh, A. Ganshin, O. Kirichek, S. Langridge, P.V.E. McClintock // Физика низких температур. — 2008. — Т. 34, № 4-5. — С. 400–403. — Бібліогр.: 28 назв. — англ. 0132-6414 PACS: 68.03.–g;67.25.D–;61.05.F– https://nasplib.isofts.kiev.ua/handle/123456789/116905 The reflection of neutrons from a helium surface has been observed for the first time. The ⁴He surface is smoother in the superfluid state at 1.54 K than in the case of the normal liquid at 2.3 K. In the superfluid state we also observe a surface layer ~200 Å thick which has a subtly different neutron scattering cross-section, which may be explained by an enhanced Bose–Einstein condensate fraction close to the helium surface. The application of neutron reflectometry described in this paper creates new and exciting opportunities for the surface and interfacial study of quantum fluids. We gratefully acknowledge help from the ISIS sample environment group. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Физика низких температур Жидкий гелий Neutron reflection from a liquid helium surface Article published earlier
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
title	Neutron reflection from a liquid helium surface
spellingShingle	Neutron reflection from a liquid helium surface Charlton, T.R. Dalgliesh, R.M. Ganshin, A. Kirichek, O. Langridge, S. McClintock, P.V.E. Жидкий гелий
title_short	Neutron reflection from a liquid helium surface
title_full	Neutron reflection from a liquid helium surface
title_fullStr	Neutron reflection from a liquid helium surface
title_full_unstemmed	Neutron reflection from a liquid helium surface
title_sort	neutron reflection from a liquid helium surface
author	Charlton, T.R. Dalgliesh, R.M. Ganshin, A. Kirichek, O. Langridge, S. McClintock, P.V.E.
author_facet	Charlton, T.R. Dalgliesh, R.M. Ganshin, A. Kirichek, O. Langridge, S. McClintock, P.V.E.
topic	Жидкий гелий
topic_facet	Жидкий гелий
publishDate	2008
language	English
container_title	Физика низких температур
publisher	Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
format	Article
description	The reflection of neutrons from a helium surface has been observed for the first time. The ⁴He surface is smoother in the superfluid state at 1.54 K than in the case of the normal liquid at 2.3 K. In the superfluid state we also observe a surface layer ~200 Å thick which has a subtly different neutron scattering cross-section, which may be explained by an enhanced Bose–Einstein condensate fraction close to the helium surface. The application of neutron reflectometry described in this paper creates new and exciting opportunities for the surface and interfacial study of quantum fluids.
issn	0132-6414
url	https://nasplib.isofts.kiev.ua/handle/123456789/116905
citation_txt	Neutron reflection from a liquid helium surface / T.R. Charlton, R.M. Dalgliesh, A. Ganshin, O. Kirichek, S. Langridge, P.V.E. McClintock // Физика низких температур. — 2008. — Т. 34, № 4-5. — С. 400–403. — Бібліогр.: 28 назв. — англ.
work_keys_str_mv	AT charltontr neutronreflectionfromaliquidheliumsurface AT dalglieshrm neutronreflectionfromaliquidheliumsurface AT ganshina neutronreflectionfromaliquidheliumsurface AT kiricheko neutronreflectionfromaliquidheliumsurface AT langridges neutronreflectionfromaliquidheliumsurface AT mcclintockpve neutronreflectionfromaliquidheliumsurface
first_indexed	2025-11-25T21:07:27Z
last_indexed	2025-11-25T21:07:27Z
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fulltext	Fizika Nizkikh Temperatur, 2008, v. 34, Nos. 4/5, p. 400–403 Neutron reflection from a liquid helium surface T.R. Charlton1, R.M. Dalgliesh1, A. Ganshin2, O. Kirichek1, S. Langridge1, and P.V.E. McClintock2 1 ISIS, STFC, Rutherford Appleton Laboratory, Harwell Science and Innovation Campus, Didcot, OX11 0QX, UK E-mail: o.kirichek@rl.ac.uk 2 Physics Department, Lancaster University, Lancaster, LA1 4YB, UK Received November 6, 2007 The reflection of neutrons from a helium surface has been observed for the first time. The 4He surface is smoother in the superfluid state at 1.54 K than in the case of the normal liquid at 2.3 K. In the superfluid state we also observe a surface layer ~200 Å thick which has a subtly different neutron scattering cross-section, which may be explained by an enhanced Bose–Einstein condensate fraction close to the helium surface. The application of neutron reflectometry described in this paper creates new and exciting opportunities for the surface and interfacial study of quantum fluids. PACS: 68.03.–g Gas–liquid and vacuum–liquid interfaces; 67.25.D– Superfluid phase; 61.05.F– Neutron diffraction and scattering. Keywords: neutron reflection, liquid helium, surface, Bose–Einstein condensate. The importance of liquid helium for physics can hardly be overestimated. Its unique ability to remain liquid right down to absolute zero makes helium an ideal ex- perimental sample for studying quantum phenomena in condensed matter. Helium-4 was first liquefied by Ka- merlingh Onnes in 1908. Since then the properties of bulk helium liquid (including 4He, 3He and isotopic mixtures) have been studied in detail, resulting in the discovery of many fundamental phenomena including, especially, su- perfluidity. However the free surface of liquid helium has attracted significantly less attention than the bulk liquid, perhaps due to the relatively complex experimental meth- ods that are needed for surface studies. Currently the best-known approaches are probably optical ellipsomet- ry, surface tension measurements, and investigations of two-dimensional charge sheets above and below the sur- face. Optical ellipsometry was exploited for measuring the thickness and density profile of the liquid helium surface [1]. It was shown in experiments that the vertical thick- ness within which the density changes from 90 to 10% of the bulk liquid density increases slightly with tempera- ture from 1.4 to 2.1 K , with an average value of 9.4 Å at 1.8 K. There was also evidence of a rise of up to 3 Å between 2.1 K and the superfluid transition temperature (� point). A very close value for the vertical thickness, of (9.2 ± 1) Å at 1.13 K, was obtained in experiments where liquid-vapor density profiles of thick 4He films were mea- sured using x-ray reflectivity [2]. The surface tension of liquid helium can be measured by various experimental methods [3,4] and may be com- pared directly with the values derived from theoretical models [5,6]. However, establishing the relationship be- tween surface tension and the dynamical properties of superfluid helium remains a rather complex task [7]. Perhaps the most powerful experimental technique for studying the surface properties of liquid helium is through measurements on two-dimensional charge sys- tems including surface electrons (SE) and layer of ions trapped under the surface of liquid helium [8]. The exis- tence of the quantized capillary surface waves, or rip- plons, earlier proposed by Atkins [7] in order to explain surface tension data, has been clearly proven in experi- ments with a two-dimensional plasma resonance in sur- face electrons [9]. Later, ripplons [10] as well as scatter- ing of surface electrons with Fermi quasi-particles from bulk liquid [11] were detected on liquid 3He. Soon after that, it was found that the mobility of surface electrons on 3He deviates drastically from the single-electron-ripplon scattering theory below 70 mK [12]. In contrast, the mo- © T.R. Charlton, R.M. Dalgliesh, A. Ganshin, O. Kirichek, S. Langridge, and P.V.E. McClintock, 2008 bility of surface electrons on 4He follows the single-elec- tron-ripplon scattering theory down to 20 mK, the lowest temperature achieved in the experiment. This may sug- gest a crossover to the long-mean-free-path regime, im- plying a connection to the Rayleigh-like waves predicted theoretically in [13,14]. A peculiar temperature depend- ence was also observed during studies of the surface ten- sion of liquid 3He [4], behavior that could not be ex- plained in terms of ripplons and the quasi-particle-scat- tering contribution. Capillary waves on the surface of thick superfluid 4He films have been detected via the dielectric ponderomotive effect [15]. This method allowed measurement of the spectrum and damping of capillary waves within the wavelength range 3.3–20 �m. The damping was orders of magnitude smaller than the value predicted theoretically. In some respects, the SE, surface tension and capillary wave methods provide rather indirect ways of studying the liquid helium surface experimentally, inevitably lead- ing to ambiguities in the interpretation of the data. A com- plementary experimental approach that might facilitate direct studies of the microscopic properties of liquid he- lium surface, thus illuminating this fascinating subject, is therefore much to be desired. In this paper we propose a new experimental method based on the unique combination of neutron reflection and ultralow-temperature sample environment: small-an- gle neutron reflection from the liquid surface, opening new opportunities for studying the interface properties of quantum liquids. We also present our preliminary mea- surements of reflection from the superfluid and normal liquid 4He surfaces. Note that a range of classical optical phenomena such as reflection, refraction and interference can be also ob- served for slow neutrons [16,17]. For a neutron approach- ing a plane surface at a glancing angle �, the refractive in- dex at the boundary between two media is defined as: n k k � � � � cos cos � � , (1) where k and k� are the neutron wave vectors inside and outside the medium. Since n � 1, a limiting case occurs when cos �� 1, characterized by the critical angle � c such that cos � c n� . For � �� c we have total external reflec- tion. The phenomenon is analogous to the total inter- nal reflection of light; the difference is in the sign of ( )n �1 . For the thermal neutrons � c �� 1 we can write cos � � �1 22 / , which leads to � c n� �2 1( ) . (2) Total reflection of slow neutrons was first reported by Fermi and co-workers [18,19] and since been extensively applied to range of problems. The specular reflection of neutrons gives information on the neutron refractive in- dex profile normal to a surface. The refractive index is simply related to the scattering length density and hence specular neutron reflection can provide important infor- mation about the composition of surfaces and interfaces. Similar information can be obtained from x-ray reflection experiments. There are many instances, however, where the neutron method provides distinct advantages. For ex- ample, the neutron’s ability to penetrate through bulk samples and their containers, including cryostats, is much higher than that of x-rays. It allows for an easy combina- tion of neutron scattering with an ultralow-temperature sample environment. Our experiments were performed on the CRISP instru- ment, which was designed as a general purpose reflec- tometer for the investigation of a wide spectrum of inter- faces and surfaces. It uses a broad-band neutron time-of- flight method for determination of the wavelength at fixed angles. Figure 1 shows a schematic diagram of the instrument. The sample geometry is horizontal, allowing investigation of liquid surfaces. The instrument uses the pulsed neutron beam from the ISIS neutron facility and passage via a 20 K hydrogen moderator provides neutron wavelengths in the range 0.5–6.5 Å at the source fre- quency of 50 Hz, extending up to a maximum of 13 Å if operated at 25 Hz. The incident beam is well collimated by both coarse and fine adjustable collimating slits (S1–S4) to give a variable beam size and angular diver- gence, with typical dimensions of 40 mm wide (horizon- tal direction) and anything up to 10 mm in height (vertical direction). A variable aperture disc chopper defines the wavelength band, and prompt pulse suppression is achie- ved by a nimonic chopper. Additional frame overlap sup- pression is provided by the nickel-coated silicon wa- fer frame overlap mirrors, which remove wavelengths greater than 13 Å. The instrument has two types of detec- tors, a 3He single detector and a 1D position-sensitive multidetector. The instrument can also be run in a polar- ized mode allowing polarized neutron reflectivity mea- Neutron reflection from a liquid helium surface Fizika Nizkikh Temperatur, 2008, v. 34, Nos. 4/5 401 ? M on it or 1 S1 S up er m ir ro r F ra m e ov er la p m ir ro rs F ra m e ov er la p m ir ro rs S2M on it or 2 S3 D et ec to r S4 Fig. 1. Schematic diagram of the CRISP reflectometer showing the major components. Items used for polarization handling have been removed from the drawing since they were not used in the experiments described. surements as well being able to perform full polarization analyses. The experimental arrangement is extremely flexible and, with the neutron beam inclined at 1.5° to the horizon- tal, provides well for the study of liquid surfaces. Provi- sion for liquid surfaces angles of less than 1.5° is achie- ved by the insertion of a supermirror. The sample position is designed to be vibrationally isolated from the rest of the instrument, further aided by active anti-vibration damp- ing. Much of the instrument is automated allowing for precision control and a high degree of reproducibility. A large variety of sample environment equipment in- cluding cryostats and ultralow-temperature refrigerators is available. For the experiment to be described, we used an Oxford Instruments Variox BL cryostat for neutron scattering experiments with a variable temperature insert (VTI). The temperature range of the VTI is 1.25–300 K. A cylindrical cell made of aluminium alloy 6082 with inner diameter 31.4 mm, internal length 74.0 mm and wall thickness 0.5 mm was attached to the sample stick of the VTI. The temperature of the cell was measured with a cal- ibrated Cernox sensor. In order to estimate the influence of the cell and sam- ple environment on the signal from the scattered neu- trons, we performed neutron reflection calibration mea- surements from the surface of liquid D2O at room temperature in the same experimental setup. The test demonstrated a negligible influence of the sample envi- ronment on the experimental data. In our experiments we attempted to study neutron re- flection from the surfaces of both liquid 4He and 3He. However, due to the large cross-section for neutron scat- tering from the 3He nucleus in the vapour phase, we could not detect a reflection signal from the 3He liquid surface within the experimental temperature range down to 1.25 K. The 3He vapour pressure decreases rapidly with temperature, and we therefore believe that the tempera- ture reduction below ~1 K should solve this problem. In the experiment we condense approximately 10 litres of helium gas (at STP) into the cell, which is kept at a tem- perature of 2 K. After the reflection signal is detected, the temperature of the cell is stabilized and controlled for a sufficient period of time to collect neutron reflection data over a range of values of wave vector transfer Qz perpen- dicular to the reflecting surface (see the diagram in the in- set of Fig. 2), which typically takes a few hours. We have measured the reflectivity of the liquid 4He surface as a function of Qz at temperatures of 2.3 K and 1.54 K, obtaining the results presented in Figs. 2 and 3, respectively. As a general feature both data sets show a slight downward slope of the reflectivity approaching the critical value, Qc ~ 0.006 1/Å, attributable to absorption of neutrons by traces of 3He at the natural isotopic ratio of about 2·10–7 in the supplied 4He gas. Without absorption the signal below Qc would be completely flat. Past Qc, from Qz > 0.08 1/Å where the Born approximation applies we observe the typical ~ Q z �4decrease in the reflectivity curve indicating, qualitatively, that the surface is smooth. To extract quantitative information from the data we compare the reflectivity profile with an optical model. In its simplest form, the model reduces to the quantum me- chanical problem of a particle incident on a potential step. In our case, the optical potential has three distinct regions 402 Fizika Nizkikh Temperatur, 2008, v. 34, Nos. 4/5 T.R. Charlton, R.M. Dalgliesh, A. Ganshin, O. Kirichek, S. Langridge, and P.V.E. McClintock 10 –4 10 –3 10 –2 10 –1 1 0.006 0.010 0.050 Data Calculation ki kf Qz Liquid HeN or m al iz ed re fl ec ti vi ty , a rb . u ni ts Fig. 2. The reflectivity of the liquid 4He surface as a function of Qz measured at 2.3 K. The inset shows the orientation of the incoming ki and outgoing kf wave vectors as well as the mo- mentum transfer vector Qz in relation to the liquid helium sur- face. 0.006 0.010 0.050 Data Calculation 10 –4 10 –5 10 –3 10 –2 10 –1 1 N or m al iz ed re fl ec ti vi ty , a rb . u ni ts Fig. 3. The reflectivity of liquid 4He surface as a function of Qz measured at 1.54 K. (vacuum, near surface, and bulk) with the transition be- tween adjacent steps calculated as an interface roughness. The reflectivity is calculated from the optical potential using a recursive definition of the reflectivity, taking into account multiple reflections [20]. The numerical descrip- tion of the interface roughness follows that of Ref. 21. The results of the calculation are shown as lines through the data in Figs. 2 and 3 with the optical potential shown in Fig. 4. From the calculations it is clear that, near the surface, a region with higher scattering power exits in the 1.54 K case as compared to the 2.30 K calculations. Also the transition from bulk to vacuum at 2.30 K occurs grad- ually over a large 800 Å distance while, at 1.54 K, the transition is compressed into ~400 Å. We can suggest a possible explanation for this observation. Experiments on liquid 4He with both neutron scatter- ing [22,23] and x-ray diffraction [24] indicate a signifi- cant change in the structure of liquid as it cools through the superfluid transition. This observation was also sup- ported by Monte Carlo simulations [25] where it was shown that, when Bose condensation takes place, the liq- uid 4He becomes more disordered in Cartesian space with some rearrangement of atoms occurring to create the nec- essary space for delocalization to occur. If there is an en- hanced Bose–Einstein condensate fraction close to the surface of the superfluid [26,27], an increase in disorder could be expected, possibly accounting for the alteration in the neutron scattering structure factor. However, thor- ough theoretical modelling is now required to establish whether the results observed in the experiment can be ac- counted for quantitatively on this basis. In conclusion, we have observed neutron reflection from the 4He surface for the first time. The surface is smoother in the superfluid state at 1.54 K than in the case of the normal liquid at 2.3 K. We have also observed a sur- face layer ~200 Å thick with a subtly different neutron scattering cross-section in superfluid 4He. The new ex- perimental method described in this paper opens up fresh opportunities in the study of quantum fluids and solid quantum surfaces and interfaces. For example, it could be used for direct observation of Fomin surface excitations on liquid 3He [13], or in the search for a superfluid transi- tion in 2D 3He on the surface of micro-separated 3He–4He liquid mixture [28]. We gratefully acknowledge help from the ISIS sample environment group. 1. D.V. Osborne, J. Phys.: Condens. Matter 1, 289 (1989). 2. L.B. Lurio, T.A. Rabedeau, P.S. Pershan, Isaac F. Silvera, M. Deutsch, S.D. Kosowsky, and B.M. Ocko, Phys. Rev. Lett. 68, 2628 (1992). 3. K.N. Zinoveva, ZhETF 29, 899 (1955). 4. K. Matsumoto, Y. Okuda, M. Suzuki, and S. Misawa, J. Low Temp. Phys. 125, 59 (2001). 5. K.R. Atkins, Can. J. Phys. 31, 1165 (1953). 6. A.D. Singh, Phys. Rev. 125, 802 (1962). 7. K.R. Atkins and Y. Narahara, Phys. Rev. 138, A437 (1965). 8. Yu. Monarkha and K. Kono, Two-Dimensional Coulomb Liquids and Solids, Springer (2004). 9. C.C. Grimes and G. Adams, Phys. Rev. Lett. 36, 145 (1976). 10. K. Shirahama, S. Ito, H. Suto, and K. Kono, J. Low Temp. Phys. 101, 439 (1995). 11. K. Shirahama, O.I. Kirichek, and K. Kono, Phys. Rev. Lett. 79, 4218 (1997). 12. O. Kirichek, M. Saitoh, K. Kono, and F.I.B. Williams, Phys. Rev. Lett. 86, 4064 (2001). 13. I.A. Fomin, Sov. Phys. JETP 34, 1371 (1972). 14. Yu.B. Ivanov, Sov. Phys. JETP 52, 549 (1980). 15. P. Roche, G. Deville, K.O. Keshishev, N.J. Appleyard, and F.I.B. Williams, Phys. Rev. Lett. 75, 3316 (1995). 16. A.G. Klein and S.A. Werner, Rep. Prog. Phys. 46, 259 (1982). 17. J. Penfold and R.K. Thomas, J. Phys.: Condens. Matter 2, 1369 (1990). 18. E. Fermi and W. Zinn, Phys. Rev. 70, 103 (1946). 19. E. Fermi and W. Marshall, Phys. Rev. 71, 666 (1947). 20. L.G. Parratt, Phys. Rev. 95, 359 (1954). 21. L. Nevot and P. Croce, Rev. Phys. Appl. 15, 761 (1980). 22. V.F. Sears and E.C. Svensson, Phys. Rev. Lett. 43, 2009 (1979). 23. E.C. Svensson, V.F. Sears, A.D.B. Woods, and P. Martel, Phys. Rev. B21, 3638 (1980). 24. H.N. Robkoff, D.A. Ewen, and R.B. Hallock, Phys. Rev. Lett. 43, 2006 (1979). 25. J. Mayers, Phys. Rev. Lett. 84, 314 (2000). 26. A. Griffin and S. Stringari, Phys. Rev. Lett. 76, 259 (1996). 27. A.F.G. Wyatt, Nature 391, 56 (1998). 28. P.A. Sheldon and R.B. Hallock, Phys. Rev. Lett. 77, 2973 (1996). Neutron reflection from a liquid helium surface Fizika Nizkikh Temperatur, 2008, v. 34, Nos. 4/5 403 0.2 0.4 0.6 0.8 1.0 1.2 0 200 400 600 800 1000 T = 2.30 K T = 1.54 K Depth, Å S ca tt er in g po te nt ia l, 10 1/ –6 Å 0 Fig. 4. The scattering potential profiles obtained by numerical simulation, using the reflectivity data for 2.3 and 1.54 K. The abscissa corresponds to vacuum below 0 Å, to the near-surface region between 0 and 800 Å, and to bulk liquid 4He above 800 Å. Note that the optical potential is proportional to the density and scattering power of the material.

Neutron reflection from a liquid helium surface

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