NUCLEAR ACOUSTIC RESONANCE INVESTIGATIONS OF THE LONGITUDINAL AND TRANSVERSE ELECTRON-LATTICE INTERACTION IN TRANSITION METALS AND ALLOYS V. Müller, G. Schanz, E.-J. Unterhorst, D. Maurer
To cite this version:
V. Müller, G. Schanz, E.-J. Unterhorst, D. Maurer. NUCLEAR ACOUSTIC RESONANCE INVES- TIGATIONS OF THE LONGITUDINAL AND TRANSVERSE ELECTRON-LATTICE INTERAC- TION IN TRANSITION METALS AND ALLOYS. Journal de Physique Colloques, 1981, 42 (C6), pp.C6-389-C6-391. 10.1051/jphyscol:19816113. jpa-00221175
HAL Id: jpa-00221175 https://hal.archives-ouvertes.fr/jpa-00221175 Submitted on 1 Jan 1981
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NUCLEAR ACOUSTIC RESONANCE INVESTIGATIONS OF THE LONGITUDINAL AND TRANSVERSE ELECTRON-LATTICE INTERACTION IN TRANSITION METALS AND ALLOYS
V. Miiller, G. Schanz, E.-J. Unterhorst and D. Maurer
&eie Universit8G Berlin, Fachbereich Physik, Kiinigin-Luise-Str.28-30, 0-1000 Berlin 33, Gemany
Abstract.- In metals the conduction electrons contribute significantly to the acoustic-wave-induced electric-field-gradient-tensor (DEFG) at the nuclear positions. Since nuclear electric quadrupole coupling to the DEFG is sensi- tive to acoustic shear modes only, nuclear acoustic resonance (NAR) is a par- ticularly useful tool in studying the coup1 ing of electrons to shear modes without being affected by volume dilatations. By extending previous NAR measurements in Nb, Mo and Ta to superconducting alloys N~I-~MO, it will be shown that the combination of NAR experiments with high-pressure Mossbauer isomer-shift measurements is of interest in a deeper understanding of the coupling of shear modes and volume dilatations to s- and d-electrons in tran- sition metals.
In cubic metals the electric field gradient (EFG) vanishes at a nuclear site. In the presence of an acoustic wave, however, the cubic point symmetry is destroyed period- ically thereby giving rise to a sound-induced dynamic electric field gradient (DEFG) tensor whose components can be measured in nuclear acoustic resonance (NAR). Besides fundamental questions concerning the complex physics behind the EFG /I/, measure- ments of the DEFG are of particular interest in studying the long-wavelength elec- tron-phonon interaction in transition metals since, in the response of the d-el ec- trons to acoustic shear modes, multipole fields are set up due to d-electron charge redistribution, so that the d-electrons are expected to contribute significantly to the electronic part of the DEFG. At a nuclear site and within the range of linear response the DEFG tensor {V. .) 1 J is related to the acoustic strain tensor {E. .) by /2/ Vij = o.v.@ = 1 J I J 6 'ijklCkl where @ is the strain induced electrical potential and isi jkllis the fourth rank "field gradient-strain tensor". Choosing a coordinate system having its axes along the principal axes of the unstrained cubic crystal, the components of the traceless de- CI fined DEFG-tensor Vij = iVij - 6ij~&/3) can be written as
where SI1, S and S44 are the three distinct components of the S-tensor (in Voigt I2A notation) and cij = {E~~- 6. .Tt%/3) are the components of the (in first order) vol- ume-conserving "shear tensor'i . Regarding that the nuclear electric quadrupole in- teraction is invariant against T&, it follows immediately that NAR investigations of the electronic contribution to the DEFG are sensitive to the coupling of elec-
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trons to shear modes only. Consequently, quadrupole NAR enables one to study the coupling of shear modes to electrons without being affected by changes in the elec- tron charge density caused by eventual volume deformations of the lattice unit cells. Confining ourselves to transition metals and applying the usual ansatz
wheretflatt is tho lattice contribution, y_ the Sternheimer antishielding factor and (See the conduction electron contribution within an atomic sphere centered around the nucleus under consideration, it follows from Eqs. (1) and (2):
i) (S1 - S12)ce refers to the conduction electron response to 1inear dilatations of the lattice unit cells (i-e. angular distortions of the d-bonds) ii) (S44)ce refers to the conduction electron response to angular dilatations of the cubic unit cells which predominantly are associated with radial distortions of the d-bonds. Extending the theoretical results of Watson et al. /3/ to the DEFG in transition metals and neglecting s-d transitions, within the frame of a band-orbital model /7/, we find /4/ (also see Ref. (5))
S,2)ce/ [(I-ym)(S1 S12)lattl should be negligible small. i) rI2 = (S1 - -
ii) r44 = (S44)ce/ [(l-yoo)(S44)lattl -N(Ef) , where qo is the electron-phonon coupling parameter as defined in Ref. (10).
The experimental results for Mo, Ta, Nb and Nb88M~,2 are shown in Figs. (?a) and (lb). We note that the data of Fig. (la) are corrected for the actual values of the elec- tric quadrupole moments and partly differ from those reported previously /6/.
Mo Ta Nb VPd 0 I I I 0 1 2 N(Er ) I states ev-' atom" N(Ef) I states ev-' atom-'
Fig. 1 a) Coupling of electrons to shear b) Coup1 ing of electrons to modes (o predicted data) volume dilatations The most striking feature of these results is that within experimental error r44 proves to be proportional to N(Ef) Nd(Ef) whereas r12 seems to be insensitive against N(Ef). From Fig. (la) we therefore may conclude that in transition metals with high densities of states (i .e. < lr441) the long-wavelength electron-pho- non interaction with shear modes is dominated by "compressions" and "expansions" of d-electron bonds (transverse electron-lattice coupl ing). Concerning the electron coupling to the longitudinal part of shear modes (i .e. angular distortions of the d- bonds) no conclusions can be drawn yet. The coupl ing of electrons to volume dilata- tions is reflected by (St,+ 2SIz) which, however, cannot be measured in NAR but may be derived /4/ from high-pressure Mossbauer isomer-shifts measurements /8/, /9/. Regarding that only s-type electrons will contribute to the Mijssbauer isomer-shift, and taking into account that Ns(Ef) is nearly constant throughout the transition metal series, experimental evidence is quite in favour (see Fiq. (Ib)) of a relation of the form (S1 + 2SI2) Q NS(Ef). Summarizing our experimental results, we have shown that measurements of the "field gradient-strain" tensor are an important tool in studying the relative significance of s- and d-electron coupling to acoustic shear modes and volume deformations in transition metals.
References
/I/ B. Strobe1 and V. filler, Phys. Rev. By in print /2/ E.F. Taylor, and N. Bloembergen, Phys. Rev. 113, 431 (1959) /3/ R.E. Watson, A.C. Gossard, and Y. Yafet, Phys. Rev. 140, A375 (1965) /4/ V. Miiller, G. Schanz, E.J. Unterhorst, and D. Maurer, to be published /5/ K.H. Bennemann, Phys. Rev. Lett. 42, 676 (1979) /6/ E. Fischer, V. Muller, D. Ploumbidis, and G. Schanz, Phys. Rev. Lett. 40, 796 (1978) /7/ H.A. Harrison, and J.C. Phillips, Phys. Rev. Lett. 3, 410 (1974) /8/ G. Kaindl, D. Salomon, and G. Wortmanil in "lulossbauer isomer shifts", North Holland Publ . Co. (1978) p. 316, and references therein /9/ D.L. Williamson in "Mossbauer isomer shifts", North Holland Publ. Co. (1978) p. 561, and references therein /lo/ K.H. Bennemann, and J.W. Garland in "Supercondt~ctivityin d- and f-Band Metals", AIP Conference Proceedings 4, American Institute of Physics (1972) p. 99