Orientational ordering in monolayers of ortho–para hydrogen

We discuss orientational ordering in monolayers of solid hydrogen in view of recent experimental findings in NMR studies of (ortho)c–(para)₁–c-hydrogen mixtures on boron nitride substrate. Analysis of the temperature-concentration behavior for the observed NMR frequency splitting is given on the bas...

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Hauptverfasser:	Kokshenev, V.B., Sullivan, N.S.
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spelling	irk-123456789-1289132018-01-15T03:03:57Z Orientational ordering in monolayers of ortho–para hydrogen Kokshenev, V.B. Sullivan, N.S. Physics in Quantum Crystals We discuss orientational ordering in monolayers of solid hydrogen in view of recent experimental findings in NMR studies of (ortho)c–(para)₁–c-hydrogen mixtures on boron nitride substrate. Analysis of the temperature-concentration behavior for the observed NMR frequency splitting is given on the basis of a two-dimensional (J = 1)c–(J = 0)₁–c-rotor model with the quadrupolar coupling constant Г₀ = (0.50 ± 0.03) K and the crystalline field amplitude V₀ = (0.70 ± 0.10) K derived from experiment. The two distinct para-rotational short-range ordered structures are described in terms of the local alignment and orientation of the polar principal axis, and are shown to be due to the interplay between the positive and negative crystalline fields. It is shown that the local structures observed below the 2D site-percolation threshold cp = 0.72 are rather different from the ferromagnetic-type para-rotational ordering suggested earlier by Harris and Berlinsky. 2003 Article Orientational ordering in monolayers of ortho–para hydrogen / V.B. Kokshenev, N.S. Sullivan // Физика низких температур. — 2003. — Т. 29, № 9-10. — С. 980-984. — Бібліогр.: 23 назв. — англ. 0132-6414 PACS: 64.70.Kb, 81.30.Hd http://dspace.nbuv.gov.ua/handle/123456789/128913 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
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language	English
topic	Physics in Quantum Crystals Physics in Quantum Crystals
spellingShingle	Physics in Quantum Crystals Physics in Quantum Crystals Kokshenev, V.B. Sullivan, N.S. Orientational ordering in monolayers of ortho–para hydrogen Физика низких температур
description	We discuss orientational ordering in monolayers of solid hydrogen in view of recent experimental findings in NMR studies of (ortho)c–(para)₁–c-hydrogen mixtures on boron nitride substrate. Analysis of the temperature-concentration behavior for the observed NMR frequency splitting is given on the basis of a two-dimensional (J = 1)c–(J = 0)₁–c-rotor model with the quadrupolar coupling constant Г₀ = (0.50 ± 0.03) K and the crystalline field amplitude V₀ = (0.70 ± 0.10) K derived from experiment. The two distinct para-rotational short-range ordered structures are described in terms of the local alignment and orientation of the polar principal axis, and are shown to be due to the interplay between the positive and negative crystalline fields. It is shown that the local structures observed below the 2D site-percolation threshold cp = 0.72 are rather different from the ferromagnetic-type para-rotational ordering suggested earlier by Harris and Berlinsky.
format	Article
author	Kokshenev, V.B. Sullivan, N.S.
author_facet	Kokshenev, V.B. Sullivan, N.S.
author_sort	Kokshenev, V.B.
title	Orientational ordering in monolayers of ortho–para hydrogen
title_short	Orientational ordering in monolayers of ortho–para hydrogen
title_full	Orientational ordering in monolayers of ortho–para hydrogen
title_fullStr	Orientational ordering in monolayers of ortho–para hydrogen
title_full_unstemmed	Orientational ordering in monolayers of ortho–para hydrogen
title_sort	orientational ordering in monolayers of ortho–para hydrogen
publisher	Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
publishDate	2003
topic_facet	Physics in Quantum Crystals
url	http://dspace.nbuv.gov.ua/handle/123456789/128913
citation_txt	Orientational ordering in monolayers of ortho–para hydrogen / V.B. Kokshenev, N.S. Sullivan // Физика низких температур. — 2003. — Т. 29, № 9-10. — С. 980-984. — Бібліогр.: 23 назв. — англ.
series	Физика низких температур
work_keys_str_mv	AT kokshenevvb orientationalorderinginmonolayersoforthoparahydrogen AT sullivanns orientationalorderinginmonolayersoforthoparahydrogen
first_indexed	2025-07-09T10:13:15Z
last_indexed	2025-07-09T10:13:15Z
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fulltext	Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10 , p. 980–984 Orientational ordering in monolayers of ortho–para hydrogen V.B. Kokshenev Departamento de Física, Universidade Federal de Minas Gerais Caixa Postal 702, Belo Horizonte 30123-970, Minas Gerais, Brazil E-mail: valery@fisica.ufmg.br N.S. Sullivan Physics Department, University of Florida, PO Box 118400, Gainesville, FL 32611-8400, USA We discuss orientational ordering in monolayers of solid hydrogen in view of recent experimen- tal findings in NMR studies of (ortho)c–(para)1–c-hydrogen mixtures on boron nitride substrate. Analysis of the temperature-concentration behavior for the observed NMR frequency splitting is given on the basis of a two-dimensional (J = 1)c–(J = 0)1–c-rotor model with the quadrupolar cou- pling constant �0 = (0.50 � 0.03) K and the crystalline field amplitude V0 = (0.70 � 0.10) K de- rived from experiment. The two distinct para-rotational short-range ordered structures are de- scribed in terms of the local alignment and orientation of the polar principal axis, and are shown to be due to the interplay between the positive and negative crystalline fields. It is shown that the local structures observed below the 2D site-percolation threshold cp = 0.72 are rather different from the ferromagnetic-type para-rotational ordering suggested earlier by Harris and Berlinsky. PACS: 64.70.Kb, 81.30.Hd 1. Introduction Careful studies at low temperatures of the thick films (from 2 to 12 monolayers) [1,2] and monolayers [2,3] of ortho-para hydrogen on boron nitride (BN) substrates revealed at low ortho-H2 concentrations new short-range frozen structures. Besides the ana- logue of known [4–13] quadrupolar glass (QG) phase, that emerges [2] in monolayers below the concentra- tion cp = 0.72, which is apparently close to the site-percolation threshold [14] in honeycomb lattice, the uncommon para-rotational (PR) phases denomi- nated by PR-A and PR-B phases were discovered [2,3]. They are demarcated by a crossover temperature T cx (exp)( ) at which the NMR frequency splitting passes through zero (see 2D diagram in Fig. 1). In- stead of the Pa3 structure known in the bulk hydro- gen, the herring bone (HB) and pinwheel (PW) 2D long-range ordered structures have been the subject of scientific interest since 1979, when Harris and Berlinsky made their famous mean-field theory predic- tions [15]. Meanwhile thorough experimental studies on grafoil [16,17] and BN [2,3] substrates registered only the PW orientational order at sufficiently high concentrations, i.e. above the percolation limit cp. Analysis is given within the scope of the site-disor- dered microscopic 2D (J = 1)c–(J = 0)1–c-rotor model, which is introduced on the basis of the 3D-ro- tor analog developed earlier [18–21] for an indepth study of the QG phase. We will give a microscopic ex- planation of the observed temperature-concentration behavior for the orientational local-order parameters related to the NMR line shapes. We will show that the PR-A and PR-B short-range correlated structures are due to the interplay of the frustrated o-H2-molecular exchange interaction with the molecule-substrate in- teraction. 2. Microscopic description Description of the orientational degrees of freedom of the site-disordered ortho-para-hydrogen system with pure electrostatic quadrupole-quadrupole (EQQ) intermolecular interactions has been discussed extensively within context of the 3D QG problem [6,8,12,18]. In general, the thermodynamic rotational states of a given ortho-molecule located at a site i are characterized by the a second rank local tensor that has only five independent components: the three prin- cipal local axes (given by vector Li) , and the align- © V.B. Kokshenev and N.S. Sullivan, 2003 ment � i zi TJ /� � � �( � )1 3 22 and the eccentricity �i xi yi TJ J� � � �� 2 2 defined with respect to L i axes. (Here �J i stands for the angular-operator rotational moment of a given ortho-molecule located [8] at site i, and � �... T refers to a thermodynamic average at tem- perature T.) A thermodynamic description, given in terms of the local molecular fields �i , and �i conju- gate to the local order parameters and extended by the crystalline field hi can be introduced [18,19] on the basis of the local-order-parameter fundamental equa- tions, namely � � � � i i i i i / T / T h / T � � � � 1 3 3 2 2 3 2 3 2 cosh ( ) cosh ( ) exp [ ( ) ] ; (1) � � � � i i i i i / T / T h / T � � � 3 3 2 2 3 2 3 2 sinh ( ) cosh ( ) exp [ ( ) ] . (2) These equations follow from the conditions of local equilibrium [10] and they are shown [19] to be con- sistent with the density-matrix representation [7]. In what follows, we restrict our consideration to a re- duced set of local order parameters { , }L i i� with �i � 0 that corresponds to the so-called «powder ap- proximation» common [5] in NMR theory applica- tions. This description ignores the local field �i , conjugate to the local eccentricity �i , and Eqs. (1), (2) (where �i i� and �i � 0) are therefore re- duced to 1 1 2 3 2 � � � � � � � � � � � � i i i ih T exp ( ) with �i ij j j j i z c� � � � J . (3) Here the effective exchange interaction J ij and the crystalline field hi are given by J ij zi zjP L P L� � 3 2 0 20 20� ( ) ( ) and h V P Li zi� 2 3 0 20( ). (4) This reduced mean-field description formally follows from the truncated 2D Hamiltonian given for N quantum rotors with z neighbors placed in the plane, namely � � � �H c c h cN ij i j i j i i i i N j i z i N � � � �� J � � � 11 with � �� i ziJ� �1 3 2 2 . (5) Here ci is a random occupation number whose mean, given by the configurational average, is the concen- tration: c ci c � ; �Jzi is a z-projection of the angular momentum operator in the local principal coordinate system. In turn, �0 stands for the EQQ coupling con- stant and V0 is the crystal-field amplitude; P L /zi i20 23 1 2( ) ( cos )� �� where � i is the polar angle of the principal molecular axis Lj . In bulk hcp solid ortho-para-hydrogen the coupling constant �0 and the amplitude V0 are well established theoretically that is not the case of commensurate 3 3� solid monolayers. The magnitudes of �0 2 0 56 25� Q / R( ) (Q is the molecular electrostatic quadrupole moment and R0 is the nearest-neighbor molecular separation) calculated for graphite and BN substrates are 0.534 K [15] and 0.470 K [2], respec- tively. The approximate estimates for the crystal-field amplitude \| \|(exp)V0 � 0.6–0.8 K for grafoil [22] and \| \|(exp)V0 � 0.6 K for BN [17] were derived from the ob- served NMR line shapes. As seen from Fig. 1, the ex- perimentally established position of the order-disorder Orientational ordering in monolayers of ortho–para hydrogen Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10 981 Fig. 1. Phase diagram for site-disordered monolayers of ortho-para-hydrogen (o-H2)c(p-H2)1–c mixtures. The sym- bols refer to observed changes in the NMR line shapes re- ported in the literature: crosses for hydrogen monolayers on graphite, Ref. 16; open triangles for commensurate hy- drogen monolayers on BN, Ref. 2. The solid symbols refer to NMR studies of Ref. 2: solid circles, transitions to the quadrupolar glass (QG) state; diamonds, transitions to the hindered rotor (HR) state. The inverted triangles re- fer to the vanishing of the small splitting of the NMR lines in the para-rotational state. Insert: theoretical phase diagram from Fig. 2 in Ref. 15; a and b are the tricritical points [15], and c is the minimum in the observed PR-PW transition temperatures. boundary is consistent for the cases of grafoil [16] and BN [2] substrates (shown by crosses and triangles in Fig. 1, respectively). On the other hand, the PW–PR boundary (restricted by points a and b in the insert of Fig. 1) exists only for positive crystalline fields. These yield the following fundamental model parameters �0 0 50 0 03� �( . . ) K and V0 0 70 010� �( . . ) K (6) in order to specify our estimations based on the 2D ( )J c� 1 – ( )J c� �0 1 -rotor model given in Eqs. (3)–(6). 3. Macroscopic description The phase diagram for the pure J = 1 rotor system on a 2D triangle solid lattice was scaled [15] by Harris and Berlinsky in terms of the EQQ coupling constant �0 and the crystal-field amplitude V0 of both signs (see insert in Fig. 1). The PR phase was postulated by a single ferromagnetic-type structure that can be given as { , }� i i� �0 0� � . Moreover, one can see that equ- ation for the PR alignment �0 obtained by minimi- zation of the relevant free energy (see Eq. (17) in Ref. 15) is equivalent to Eqs. (2)–(6) with adopted z = 6, �i � � �0 0 09� , J ij /� �3 20� and h hi � �0 � 2 30V / that corresponds to a ferrorotational-type (FR type) local-structure given by � �i j� � 0 and � �i � 0. A description for the long-range orientationally disordered, but locally correlated PR-A phase is intro- duced through the short-range order parameter � �A i c PRAc T T( , ) ( ) ( )� � � , where a configurational ave- rage is limited by the temperature-concentration PR-A region shown in Fig. 1. Application of this average procedure to both the sides of Eq. (4) can be presented in the following form, namely PR-A: 1 1 2 3 2 9 8 0 1 1 2 2� � � � � �� A A A A AV T T T exp � � � � � � � . (7) Unlike the case of the QG, we assume here that fluc- tuations of the local alignment (or the quadrupolarization) are small. The same is referred to the crystalline field given by the mean h V /A1 02 3� . The local fluctuations of the molecular field are intro- duced through the mean �1 1 5 2 A A / Azc� J (with J1 1 03 2A A /� � � � and with z = 6) and the variance �2 2 2 4 2 2 23 1 1 8A A Azc c / T� � �J ( )( ) , and are esti- mated* within the Gaussian distribution justified in Ref. 19). With account of the Zeeman-field local po- larization effects [18] given by the mean � � �1 2 2 21A A A Azc /T� � �J ( ) , we have analyzed** a concentration behavior of the observed [22] NMR fre- quency splitting given in Fig. 8 in Ref. 2 for T = = 0.65 K and T = 0.546 K. Analysis is given with the help of Eqs. (2)–(6) where the polar-principal-axis correlation parameters �1A and �2A, namely �1 20 20A zi zj c PRA P L P L� ( ) ( ) ( ) and �2 20 2 20 2 A zi zj c PRA P L P L� ( ) ( ) ( ) (8) are treated as fitting parameters. In the particular cases of the FR type (� �i j� � 0) and AFR type (� i � 0, � j /� 2) locally correlated structures are characterized by � �1 2 1� � and � �1 2 1 2� � � � / , re- spectively. For the PR-A phase we have derived [23] �1 1 3A /(exp) � � and �2 0 75A (exp) .� . This local structure is in a way similar to that in the PW phase modified by orientations of in-plane rotors which show out- of-plane orientations. As seen from Fig. 1, the long-range disordered PR-B phase is stable at low temperatures (T < V0) and low concentrations (c cp! ) where the site-dilu- tion effects are expected to be more pronounced than in the PR-A phase. The short-range orientational ar- rangement results from the interplay between the ran- dom EQQ coupling and the random negative crystal- line fields. Adopting for the latter a Gaussian distribution, and taking into account its variance h2B (with the mean h V /B1 02 3� ) one finds, after elabora- tion of the configurational average in Eq. (3), the ef- fective amplitude of the crystalline field can be intro- duced as V c T V T c T x( , ) ( )(exp) � � � � � � � � � �0 1 for T T cx� (exp)( ) . (9) Here T cx (exp)( ) is a crossover temperature between the PR-A and the PR-B structures that provides a re- construction of the local order from � A c T(exp)( , ) " 0 to 982 Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10 V.B. Kokshenev and N.S. Sullivan * One can show that for the Gaussian average exp( ) exp[ ( ) ]� � � �ax ax ax / G 1 2 2 2 is true for a random value x with mean x1 and variance x2. ** The observable quadrupolarization is introduced by the relation \| ( , )\| ( , )(exp)� #c T c T / d� 3 where # is the NMR frequency splitting and d = 57.67 kHz. �B c T(exp)( , ) ! 0 (shown by dashed line in Fig. 1). The explicit form in Eq. (9) follows from h B2 � � � � �( ) ( )( )$h V T /i c PRB / x /2 1 2 0 1 22 2 3 where Tx is ap- proximated by the observed PRA–PRB boundary. An analysis of the observed PR-B quadrupolarization �B is given through averaged Eq. (9), namely PR-B: ln ( )(exp)1 1 2 1 9 0 2 � � � � �� B B x B V T T c T �0 2 21 0 T c B B � � � � � � � �� ( ) . (10) Treating the PR-B phase as a precursor of the 2D QG phase, we have omitted in Eq. (10) all molecu- lar-field local ordering effects. Similar to the QG case, we have therefore adopted � � � � i c PRB B ( ) 1 em- ployed in Eq. (7) for the PR-A phase. Analysis of the available experimental data for c = 0.44 (with Tx (exp) � 1.64 K, see Fig. 12 of Ref. 2) on temperature dependence of the short-range orientational order pa- rameter in the PR-B given with the help of Eq. (5) results [23] in, approximately, �1 0B � , �2 1B � , that in a way is characteristic for the QG local order. The observed order parameters � A (exp) and �B (exp) vanish at a certain crossover temperature T cx( ) associ- ated with the PRA-PRB boundary T cx (exp)( ) (shown by the dashed line Fig. 1). For concentrations c cp% , this boundary can be therefore deduced from the con- ditions � �A x B xc T c T( , ) ( , )� � 0. To satisfy the boundary observation conditions, the interplay be- tween the fluctuating crystalline and Zeeman-type molecular fields for T T Tx0 ! % is made implicit in the form 8 9 00 0 2 2V T T c T( ) ( , )� � � , where T0 � � 9 82 2 0h / V plays a role of Tx when the competing fluc- tuations the EQQ field are ignored. The variance h2 was studied [20] in detail for the 3D disordered PR phase in o-p-H2 systems for temperatures 0.80 K < T < < 4.9 K. As seen from the right insert in Fig. 2, unlike the mean of the crystal-field h D 1 3( ), its variance de- pends strongly on the overall concentration, i.e., h c c cD M2 3( ) & �( ) and disappears at the highest con- centration for the 3D QG state, cM = 0.55 (for the 3D phase diagram see Fig. 2 in Ref. 19 ). In the 2D case cM is very close to the threshold concentration cp. Therefore, we adopt V c c cp2 & �( ) that reduces the aforegiven boundary observation condition to the fol- lowing cubic equation T T c T c c Vx x 3 0 2 2 0 4 0 3 2 1 2 � � � � � � � � � ( ) ( ) � � = 0 (11) with T V c c c cp p 0 0 2 8 1� � � � � � � � � � � � � � � � � ' . Treating ' as an adjustable parameter characterizing a scale of the crystal-field fluctuations, we analyze in Fig. 2 the physical solution Tx of Eq. (11) by com- paring it with the observed PRA–PRB boundary. Taking into account the above analysis for PR-B and PR-A phases, we adopt �2 � 1 as a typical value. As seen from Fig. 2, the idea that the disordered PRB phase is constructed from mostly disordered «in-plane» rotors is corroborated by experimental ob- servations [2]. On the other hand, our consideration of the reduced orientational degrees of freedom fails to give quantitative descriptions above c = 0.45. The unphysical value �2 " 1 deduced from experimental data in Fig. 2 signals the existence of ignored local order parameters (e.g. q� �� 2), which (similar to the case of the 3D QG given in Eq. (6) in Ref. 18) can play an appreciable role near the crossover tem- perature. A complete analysis should be given beyond the «powder approximation» and based on fundamen- tal order-parameter Eqs. (1), (2) given for both the local alignment and the eccentricity. Orientational ordering in monolayers of ortho–para hydrogen Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10 983 Fig. 2. Pararotational A–B crossover temperature against concentration. The symbols refer to the experimental points represented in Fig. 1: solid inverted triangles, van- ishing of NMR doublet, Ref. 2; open triangles, onset of PW state in the anomalous upturn region of the phase transition boundary, Ref. 2. The lines designate solutions of Eq. (6) for an adjustable parameter ' � 23. . Other pa- rameters shown include the fitting parameter �2. Insert: left; concentration dependence of the effective crystalline field at distinct temperatures derived from experiment [2] using Eq. (9); right, the variance of the crystalline field in bulk ortho-para-H2 (squares, from insert in Fig. 5 of Ref. 20). 4. Conclusions We have discussed the short-range orientationally correlated structures discovered [2,3] in monolayers of (o-H2)c–(p-H2)1–c on BN substrate. Analysis of the temperature-concentration behavior for the observed NMR line shapes, related to the short-range order parameter �( , )c T is given on the basis of the 2D (J = 1)c–(J = 0)1–c-rotor model, for which a 3D ana- log was employed earlier [18,19] for the QG problem. In the current study the focus is on the nearest-neigh- bor correlated structures observed by the NMR spec- troscopy in the orientationally disordered phases (shown in Fig. 1). In spite of the fact that fundamen- tal order-parameter equations are consistent with the corresponding Eq. (17) in Ref. 15, the observed PR-A and the PR-B structures are rather «antiferromag- netic» than «ferromagnetic» as suggested in Ref. 15 for a unique PR phase. This conclusion follows from our analysis of the observed [2,3] macroscopic quad- rupolarizations � A c T( , ) and �B c T( , ) adjusted through the polar-axis correlation parameters given in Eq. (8). We have shown that the short-range corre- lated PR-A phase is driven by positive crystalline fields, for which thermal and spatial fluctuations overwhelm those of the short-range EQQ interactions. With decreasing temperature, the interplay between the EQQ coupling and the crystalline fields, which are both sensitive to the site-dilution and thermal- fluctuation effects, results in the PRA–PRB boundary T cx (exp)( ), along which both the quadrupolarizations are zero (see analysis in Fig. 2). The low-temperature PR phase, denominated as the PR-B phase, is driven by negative crystalline field given near the boundary Tx (exp) in Eq. (9). Similar to the case of the QG phase (see Fig. 4 in [19]), this phase is expected to be richer than the PR-A phase, and more order parameters are therefore needed to give a complete description of the observed �B c T(exp)( , ). Unfortunately, this data (such as on $q T TB i i c PRB� � � �� 2 2( ) ( ) ( ) is at present time not available experimentally. Acknowledgments The authors acknowledge financial support by the CNPq (V.B.K.) and by the NSF-DMR-98 (N.S.S.). 1. K. Kim and N.S. Sullivan, Phys. Rev. B57, 12595 (1998). 2. K. Kim and N.S. Sullivan, J. Low Temp. Phys. 114, 173 (1999). 3. K. Kim and N.S. Sullivan, Phys. Rev. B55, R664 (1997). 4. N.S. Sullivan, C.E. Edwards, Y. Lin, and D. Zhou, Phys. Rev. B17, 5016 (1978). 5. A.B. Harris and H. Meyer, Can. J. Phys. 63, 3 (1985). 6. V.B. Kokshenev, Solid State Commun. 55,143 (1985). 7. Y. Lin and N.S. Sullivan, Mol. Cryst. Liq. Cryst. 142, 141 (1987). 8. V.B. Kokshenev and A.A. Litvin, Fiz. Nizk. Temp. 13, 339 (1987) [Sov. J. Low Temp. Phys. 13, 195 (1987)]. 9. U.T. Höchli, K. Knorr, and A. Loidl, Adv. Phys. 39, 405 (1990). 10. V.B. Kokshenev, Phys. Status Solidi B164, 83 (1991). 11. K. Binder and J.D. Reger, Adv. Phys. 41, 547 (1992). 12. K. Walasek, Phys. Rev. B46, 14480 (1992); Phys. Rev. 51, 9314 (1995). 13. V.B. Kokshenev and N.S. Sulivan, J. Low Temp. Phys. 122, 413 (2001). 14. M.B. Isichenko, Rev. Mod. Phys. 64, 961 (1992). 15. A.B. Harris and A.J. Berlinsky, Can. J. Phys. 57, 1852 (1979). 16. P.R. Kubik and W.N. Hardy, Phys. Rev. Lett. 41, 257 (1978). 17. P.R. Kubik, W.N. Hardy, and H. Glattli, Can. J. Phys. 63, 605 (1985). 18. V.B. Kokshenev, Phys. Rev. B53, 2191 (1996). 19. V.B. Kokshenev, J. Low Temp. Phys. 104, 1 (1996). 20. V.B. Kokshenev, J. Low Temp. Phys. 104, 25 (1996). 21. V.B. Kokshenev, J. Low Temp. Phys. 111, 489 (1998). 22. K. Kim, NMR Studies of Thin Films of Solid Hydrogen, Ph. D. Dissertation, University of Florida (1999), unpublished. 23. N.S. Sulivan and V.B. Kokshenev, New J. Phys. 5, 35.1 (2003); URL: stacks.iop.org/1367-263/5/35. 984 Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10 V.B. Kokshenev and N.S. Sullivan

Orientational ordering in monolayers of ortho–para hydrogen

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