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Physica B 263 -- 264 (1999) 421 -- 423

The vibrational spectrum and giant tunnelling effect of hydrogen dissolved in -Mn
A.I. Kolesnikov *, V.E. Antonov , S.M. Bennington , B. Dorner , V.K. Fedotov , G. Grosse , J.C. Li , S.F. Parker , F.E. Wagner
Institute of Solid State Physics RAS, 142432 Chernogolovka, Moscow District, Russia Department of Physics, UMIST, PO Box 88, Manchester M60 1QD, UK ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, UK Institut Laue-Langevin, BP 156, 38042 Grenoble Cedex 9, France Physik-Department E 15, Technische Universitat Munchen, D-85747 Garching, Germany ( (

Abstract Vibrational spectra of -MnH and -MnD were studied by inelastic neutron scattering at temperatures from 1.7 to 200 K over a wide range of energy and momentum transfers. Together with the high-energy bands of the optical vibrations, pronounced peaks at 6.3 and 1.6 meV were observed in the spectra of the samples loaded with H and D, respectively. The study of the temperature, momentum-transfer and isotope dependence of the spectra demonstrated the tunnelling origin of these peaks. 1999 Elsevier Science B.V. All rights reserved. Keywords: Hydrogen/deuterium tunnelling; Neutron spectroscopy

A recent high-pressure study showed that the solubility of hydrogen in -Mn can be increased up to a few atomic percent [1]. The neutron diffraction investigation of -MnH revealed [2] that hy drogen randomly occupies interstitial sites of the 12e type (space group I43m) which form dumb bells positioned rather far apart, at the centres of the edges and faces of the cubic unit cell of -Mn. Because of the small distance of 0.68 A between the s 12e sites in a dumb-bell, each dumb-bell can accommodate only one hydrogen atom.

* Correspondence address: Department of Physics, UMIST, PO Box 88, Manchester M60 1QD, UK. Fax: #44-161-2003941; e-mail: a.kolesnikov@umist.ac.uk.

An inelastic neutron scattering (INS) study [2] of -MnH at 90 K with the KDSOG-M spectrom eter at JINR (Dubna, Russia) revealed a band of optical hydrogen vibrations split into three peaks at 73, 105 and 123 meV in accordance with the low site symmetry of the hydrogen positions and also a strong peak at 6.4 meV which was tentatively attributed to the splitting of the vibrational ground state of hydrogen due to tunnelling between the adjacent 12e sites forming a dumb-bell. This paper reports on the results of further INS studies which strongly support the assignment [2] of the tunnelling origin of the 6.4 meV peak. These include the INS spectra of -MnH at 5--200 K (Fig. 1) measured with the TFXA spectrometer at ISIS, RAL (UK), the INS spectra of -MnD at

0921-4526/99/$ -- see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 8 ) 0 1 4 0 1 - X


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A.I. Kolesnikov et al. / Physica B 263 -- 264 (1999) 421 -- 423

Fig. 1. The INS spectra of -MnH in the energy range (a) 2--200 meV and (b) 2--12 meV. The spectra in Fig. 1a are shifted along the y-axis. TFXA spectrometer, RAL.

Fig. 3. The H tunnelling peak intensity in the INS spectrum of -MnH measured at 20 K as a function of momentum trans fer. MARI spectrometer, RAL. The solid line shows the result of fitting based on equation of Ref. [4] (see text).

Fig. 2. The difference between the INS spectra of MnD H and -Mn at 2, 15, 29, 44, 60 and 100 K (curves 1--6). The curves are shifted along the y-axis. IN6 spectrometer, ILL.

1.7--180 K (Fig. 2) measured with the IN6 spectrometer at ILL (Grenoble, France) and the neutron momentum transfer dependence of the INS spectra of -MnH at 5--200 K (Fig. 3) measured with the MARI spectrometer at ISIS.

As seen from Fig. 1a, the peaks of the fundamental H optical modes in -MnH are ob served at 74, 107 and 130 meV in fair agreement with Ref. [2]. The intensity of the peak at 6.2 meV decreases with increasing temperature and at 200 K the peak exhibits relaxation behaviour (Fig. 1b). Fig. 2 shows the difference between the INS spectra of the -MnD sample and a sample of pure -Mn measured under the same conditions. The -MnD sample was contaminated with about 0.5 at% H which manifested itself by the peak at 6.3 meV. The peak at 1.6 meV was due to 5 at% D. The positions of these H and D peaks agree with the roughly estimated values, &"5 meV and ""1.5 meV, of the splitting of the hydrogen and deuterium vibrational ground states due to tunnelling. These values follow from the equation +(1/2) exp(!m l/
) of Ref. &"73 meV [2] and [3] if one substitutes ""73/(2 meV for the energy of H and D local vibrations along the line 2l"0.68 A which cons nects the 12e sites in a dumb-bell [2]; m is the mass of the H or D atom. The temperature dependencies of the integral intensities of the H and D tunnelling peaks are shown in Fig. 4 and can be well explained by a Boltzmann thermal population of the corresponding ground states (solid curves in the figure),


A.I. Kolesnikov et al. / Physica B 263 -- 264 (1999) 421 -- 423

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is qualitatively inadequate (dashed curves in the figure). As seen from Fig. 3, the intensity of the 6.3 meV peak of hydrogen in -Mn as a function of momentum transfer, Q, can also be described fairly well by the dependence characteristic of tunnelling peaks: S(Q, )&[1/2!si n(2 l Q )/ (4 l Q )] e x p ( !Qu ) [4]. The value of the fitting parameter, u, the effective mean-square displacement of H atoms, is 0.0256 A. s The remarkable features of the hydrogen tunnelling peak in the INS spectrum of -MnH are its anomalously large integral intensity compared to that of the optical hydrogen band and its anomalously high energy of 6.3 meV which is about 15 times higher than the energy of tunnelling splittings observed earlier for hydrogen in other metals [5]. Deuterium tunnelling in metals was not detected earlier by neutron spectroscopy. We thank the EPSRC for access to the ISIS pulsed neutron source. The work was supported by the Grants No. 96-02-17522 and 96-15-96806 from the Russian Foundation for Basic Research.
Fig. 4. The temperature dependencies of the tunnelling peak intensities for H and D in -Mn obtained from the INS data measured in the regime of neutron energy loss (a, TFXA spectrometer) and neutron energy gain (b, IN6 spectrometer).

References
[1] V.E. Antonov et al., Scripta Mater. 34 (1996) 1331. [2] V.K. Fedotov et al., J. Phys.: Condens. Matter 10 (1998) 5255. [3] S.L. Drechsler et al., J. Phys. F 14 (1984) L243. [4] A. Magerl et al., Phys. Rev. Lett. 56 (1986) 159. [5] H. Wipf, in: H. Wipf (Ed.), Hydrogen in Metals III, Springer, Berlin, 1997, pp. 51--91.

which is proportional to 1/[1#exp(! /k №)] and exp(! /k №)/[1#exp(! /k №)] for the lower and upper states, respectively. The use of a phonon or harmonic oscillator population factor