- Email: [email protected]
Coherent tunnelling dynamics of muonium in a disordered medium
Physica B 326 (2003) 61–63
Coherent tunnelling dynamics of muonium in a disordered medium V.G. Storchaka,*, D.G. Eshchenkob, J.H. Brewerc, G.D. Morrisc, S.P. Cottrelld, S.F.J. Coxd a
Kurchatov Institute, Russian Research Centre, Kurchatov Sq. 1, Moscow 123182, Russia b Institute for Nuclear Research, Moscow 117312, Russia c University of British Columbia, Vancouver, BC, Canada V6T 2A3 d Rutherford Appleton Laboratory, Chilton, Oxfordshire OX11 OQX, UK
Abstract Conventional understanding suggests that strong disorder inevitably causes particle localization: states with the same energy are too far apart in space for tunnelling to be effective. We present experimental evidence to the contrary: we have observed coherent tunnelling of Mu atoms in a highly disordered mixture—75% CH4 þ 25% Kr—which forms an orientational glass phase at low temperatures. r 2002 Elsevier Science B.V. All rights reserved. Keywords: Quantum diffusion; Disorder; Coherent tunnelling
To date, most of our knowledge of the tunnelling dynamics of particles in solids comes from extensive studies of crystalline or nearly crystalline materials. In reality, however, the crystalline state is the exception rather than the rule. Disorder is ubiquitous, ranging from a few impurities in an otherwise perfect crystalline host to the strongly disordered limit of alloys or glassy structures. All studies on muon and muonium localization so far have been focused on crystals with weak disorder [1]. In this paper we present experimental studies of muonium tunnelling dynamics under conditions of strong disorder in orientational glasses [2,3].
*Corresponding author. Fax: +7-095-1969-133. E-mail address: [email protected] (V.G. Storchak).
The term ‘orientational glass’ usually refers to randomly diluted (or randomly mixed) molecular crystals. Molecular crystals without such randomness in their chemical composition typically undergo an order–disorder phase transition from the high-temperature ‘plastic crystal’ phase (where the multipole moments associated with the molecules can rotate more or less freely) to a low-temperature phase with long-range orientational order (e.g. N2 ; ortho-H2 ; CH4 ; CD4 ; etc.). This order gets severely disturbed by dilution with spherical atomic species (e.g. Ar in N2 ; Kr in CH4 ; paraH2 in ortho-H2 ; etc.); strong enough dilution leads to a new type of phase in which the multipole moments are frozen in random orientations. The short range, highly anisotropic electric quadrupole–quadrupole or octupole–octupole interaction between two molecules that is responsible for the
0921-4526/03/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 0 2 ) 0 1 5 7 4 - 0
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V.G. Storchak et al. / Physica B 326 (2003) 61–63
orientational ordering is explicitly known. This fact allows one to extract the influence of disorder which can be easily varied (or even switched on and off) by changing the temperature and/or composition, allowing a detailed investigation of the effects of strong disorder on quantum tunnelling of muonium atoms. Conventional understanding suggests that strong disorder inevitably causes particle localization: states with the same energy are too far apart in space for tunnelling to be effective. Here we present experimental evidence to the contrary: we have observed coherent tunnelling of Mu atoms in a highly disordered mixture—75% CH4 þ 25% Kr—which forms an orientational glass phase at low temperatures. At 90:7 K pure methane condenses into an orientationally disordered FCC lattice, the socalled free-rotor phase (phase I). Below 20:4 K it transforms into phase II, with a structure containing eight sublattices. It has been established that as the Kr concentration increases the temperature of the transition from phase I to phase II gradually decreases. Above the critical concentration (about 25%), phase II never forms. Instead, the dynamical orientational disorder of phase I eventually freezes into a static pattern of randomly oriented octopoles, the orientational glass. The experiments were performed on the M20 beamline at TRIUMF and on the EMU beamline of the ISIS Pulsed Muon Facility at the Rutherford Appleton Laboratory. In each experiment mixtures of ultrahigh-purity CH4 and Kr (about 106 impurity content) were condensed from the gas phase into a liquid. Solid samples were carefully grown from the liquid phase at a typical speed of about 5 mm=h under a vertical temperature gradient of about 2 K across the sample cell. At both laboratories positive muons of 28 MeV=c momentum and 100% spin polarization were stopped in the samples and mþ SR time spectra were recorded at various different temperatures and applied magnetic fields. Fig. 1 presents the temperature dependence of the transverse relaxation rate T21 of muonium in pure solid CH4 and in two solid mixtures: CH4 þ 16% Kr and CH4 þ 25% Kr. Between 45 and
Fig. 1. Temperature dependence of muonium relaxation rate T21 in pure solid methane (circles) and solid mixtures of CH4 þ 16% Kr (triangles) and CH4 þ 25% Kr (stars) in a transverse magnetic field of B ¼ 5 G:
55 K T21 is independent of temperature and is almost identical for pure CH4 and CH4 þ 16% Kr. In pure CH4 such ‘plateau’ behaviour is identified with coherent band-like tunnelling of Mu atoms [4]. The fact that addition of 16% impurities into the host does not influence the muonium relaxation rate suggests that substituting 2 out of 12 nearest neighbours does not destroy the coherence in the Mu band regime. This is a remarkable feature: typically, the presence of even B103 impurities in a crystal is enough to destroy coherent tunneling [1,5]. Although addition of 25% Kr to CH4 does change the muonium T21 ; in the temperature range between 50 and 60 K the Mu relaxation rate is again temperature independent, which means that even substitution of three nearest neighbours out of 12 still does not destroy the coherence. The 2 * bandwidth DB10 K determined in the CH4 þ 25% Kr mixture is remarkably high, only slightly * less than DB3 102 K in pure CH4 ; about the same as that in pure solid nitrogen [6] and an order 3 * of magnitude higher than DB10 K in pure solid CD4 [4]. In conclusion, we have observed coherent muonium band dynamics that is remarkably insensitive to the presence of as much as 25% impurity atoms in a crystal. This work was supported by the Canadian Institute for Advanced Research, the Natural
V.G. Storchak et al. / Physica B 326 (2003) 61–63
Sciences and Engineering Research Council of Canada, the National Research Council of Canada (through TRIUMF), the Engineering and Physical Sciences Research Council of the United Kingdom and the Russian Research Center ‘Kurchatov Institute’. Two of us (VGS and DGE) were also supported by the INTAS Foundation (through grant 97-30063), the Royal Society of London, NATO (through grant PST.CLG.977687) and NSF.
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References [1] V.G. Storchak, N.V. Prokof’ev, Rev. Mod. Phys. 70 (1998) 929. [2] U.T. Hochli, K. Knorr, A. Loidl, Adv. Phys. 39 (1990) 405. [3] K. Binder, J.D. Reger, Adv. Phys. 41 (1992) 547. [4] V.G. Storchak, J.H. Brewer, D.G. Eshchenko, S.P. Cottrell, S.F.J. Cox, Phys. Rev. Lett. 82 (1999) 2729. [5] A.J. Leggett, Yu.M. Kagan (Eds.), Quantum Tunnelling in Condensed Media, North-Holland, Amsterdam, 1992. [6] V.G. Storchak, J.H. Brewer, W.N. Hardy, S.R. Kreitzman, G.D. Morris, Phys. Rev. Lett. 72 (1994) 3056.
Coherent tunnelling dynamics of muonium in a disordered medium V.G. Storchaka,*, D.G. Eshchenkob, J.H. Brewerc, G.D. Morrisc, S.P. Cottrelld, S.F.J. Coxd a
Kurchatov Institute, Russian Research Centre, Kurchatov Sq. 1, Moscow 123182, Russia b Institute for Nuclear Research, Moscow 117312, Russia c University of British Columbia, Vancouver, BC, Canada V6T 2A3 d Rutherford Appleton Laboratory, Chilton, Oxfordshire OX11 OQX, UK
Abstract Conventional understanding suggests that strong disorder inevitably causes particle localization: states with the same energy are too far apart in space for tunnelling to be effective. We present experimental evidence to the contrary: we have observed coherent tunnelling of Mu atoms in a highly disordered mixture—75% CH4 þ 25% Kr—which forms an orientational glass phase at low temperatures. r 2002 Elsevier Science B.V. All rights reserved. Keywords: Quantum diffusion; Disorder; Coherent tunnelling
To date, most of our knowledge of the tunnelling dynamics of particles in solids comes from extensive studies of crystalline or nearly crystalline materials. In reality, however, the crystalline state is the exception rather than the rule. Disorder is ubiquitous, ranging from a few impurities in an otherwise perfect crystalline host to the strongly disordered limit of alloys or glassy structures. All studies on muon and muonium localization so far have been focused on crystals with weak disorder [1]. In this paper we present experimental studies of muonium tunnelling dynamics under conditions of strong disorder in orientational glasses [2,3].
*Corresponding author. Fax: +7-095-1969-133. E-mail address: [email protected] (V.G. Storchak).
The term ‘orientational glass’ usually refers to randomly diluted (or randomly mixed) molecular crystals. Molecular crystals without such randomness in their chemical composition typically undergo an order–disorder phase transition from the high-temperature ‘plastic crystal’ phase (where the multipole moments associated with the molecules can rotate more or less freely) to a low-temperature phase with long-range orientational order (e.g. N2 ; ortho-H2 ; CH4 ; CD4 ; etc.). This order gets severely disturbed by dilution with spherical atomic species (e.g. Ar in N2 ; Kr in CH4 ; paraH2 in ortho-H2 ; etc.); strong enough dilution leads to a new type of phase in which the multipole moments are frozen in random orientations. The short range, highly anisotropic electric quadrupole–quadrupole or octupole–octupole interaction between two molecules that is responsible for the
0921-4526/03/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 0 2 ) 0 1 5 7 4 - 0
62
V.G. Storchak et al. / Physica B 326 (2003) 61–63
orientational ordering is explicitly known. This fact allows one to extract the influence of disorder which can be easily varied (or even switched on and off) by changing the temperature and/or composition, allowing a detailed investigation of the effects of strong disorder on quantum tunnelling of muonium atoms. Conventional understanding suggests that strong disorder inevitably causes particle localization: states with the same energy are too far apart in space for tunnelling to be effective. Here we present experimental evidence to the contrary: we have observed coherent tunnelling of Mu atoms in a highly disordered mixture—75% CH4 þ 25% Kr—which forms an orientational glass phase at low temperatures. At 90:7 K pure methane condenses into an orientationally disordered FCC lattice, the socalled free-rotor phase (phase I). Below 20:4 K it transforms into phase II, with a structure containing eight sublattices. It has been established that as the Kr concentration increases the temperature of the transition from phase I to phase II gradually decreases. Above the critical concentration (about 25%), phase II never forms. Instead, the dynamical orientational disorder of phase I eventually freezes into a static pattern of randomly oriented octopoles, the orientational glass. The experiments were performed on the M20 beamline at TRIUMF and on the EMU beamline of the ISIS Pulsed Muon Facility at the Rutherford Appleton Laboratory. In each experiment mixtures of ultrahigh-purity CH4 and Kr (about 106 impurity content) were condensed from the gas phase into a liquid. Solid samples were carefully grown from the liquid phase at a typical speed of about 5 mm=h under a vertical temperature gradient of about 2 K across the sample cell. At both laboratories positive muons of 28 MeV=c momentum and 100% spin polarization were stopped in the samples and mþ SR time spectra were recorded at various different temperatures and applied magnetic fields. Fig. 1 presents the temperature dependence of the transverse relaxation rate T21 of muonium in pure solid CH4 and in two solid mixtures: CH4 þ 16% Kr and CH4 þ 25% Kr. Between 45 and
Fig. 1. Temperature dependence of muonium relaxation rate T21 in pure solid methane (circles) and solid mixtures of CH4 þ 16% Kr (triangles) and CH4 þ 25% Kr (stars) in a transverse magnetic field of B ¼ 5 G:
55 K T21 is independent of temperature and is almost identical for pure CH4 and CH4 þ 16% Kr. In pure CH4 such ‘plateau’ behaviour is identified with coherent band-like tunnelling of Mu atoms [4]. The fact that addition of 16% impurities into the host does not influence the muonium relaxation rate suggests that substituting 2 out of 12 nearest neighbours does not destroy the coherence in the Mu band regime. This is a remarkable feature: typically, the presence of even B103 impurities in a crystal is enough to destroy coherent tunneling [1,5]. Although addition of 25% Kr to CH4 does change the muonium T21 ; in the temperature range between 50 and 60 K the Mu relaxation rate is again temperature independent, which means that even substitution of three nearest neighbours out of 12 still does not destroy the coherence. The 2 * bandwidth DB10 K determined in the CH4 þ 25% Kr mixture is remarkably high, only slightly * less than DB3 102 K in pure CH4 ; about the same as that in pure solid nitrogen [6] and an order 3 * of magnitude higher than DB10 K in pure solid CD4 [4]. In conclusion, we have observed coherent muonium band dynamics that is remarkably insensitive to the presence of as much as 25% impurity atoms in a crystal. This work was supported by the Canadian Institute for Advanced Research, the Natural
V.G. Storchak et al. / Physica B 326 (2003) 61–63
Sciences and Engineering Research Council of Canada, the National Research Council of Canada (through TRIUMF), the Engineering and Physical Sciences Research Council of the United Kingdom and the Russian Research Center ‘Kurchatov Institute’. Two of us (VGS and DGE) were also supported by the INTAS Foundation (through grant 97-30063), the Royal Society of London, NATO (through grant PST.CLG.977687) and NSF.
63
References [1] V.G. Storchak, N.V. Prokof’ev, Rev. Mod. Phys. 70 (1998) 929. [2] U.T. Hochli, K. Knorr, A. Loidl, Adv. Phys. 39 (1990) 405. [3] K. Binder, J.D. Reger, Adv. Phys. 41 (1992) 547. [4] V.G. Storchak, J.H. Brewer, D.G. Eshchenko, S.P. Cottrell, S.F.J. Cox, Phys. Rev. Lett. 82 (1999) 2729. [5] A.J. Leggett, Yu.M. Kagan (Eds.), Quantum Tunnelling in Condensed Media, North-Holland, Amsterdam, 1992. [6] V.G. Storchak, J.H. Brewer, W.N. Hardy, S.R. Kreitzman, G.D. Morris, Phys. Rev. Lett. 72 (1994) 3056.