NUCLEAR ACOUSTIC RESONANCE INVESTIGATIONS OF THE LONGITUDINAL AND TRANSVERSE ELECTRON-LATTICE INTERACTION IN TRANSITION METALS AND ALLOYS

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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:

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JOURNAL DE PHYSIQUE

CoZZoque C 6 , suppZe'ment au n o 22, Tome 42, de'cembre 1981 page C6-389

NUCLEAR ACOUSTIC RESONANCE INVESTIGATIONS OF THE LONGITUDINAL AND TRANSVERSE ELECTRON-LATTICE INTERACTION I N 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

A b s t r a c t . - I n metals t h e conduction e l e c t r o n s c o n t r i b u t e s i g n i f i c a n t l y t o t h e acoustic-wave-induced e l e c t r i c - f i e l d - g r a d i e n t - t e n s o r (DEFG) a t t h e n u c l e a r p o s i t i o n s . Since nuclear e l e c t r i c quadrupole c o u p l i n g t o t h e DEFG i s sensi- t i v e t o a c o u s t i c shear modes only, n u c l e a r a c o u s t i c resonance (NAR) i s a p a r - t i c u l a r l y u s e f u l t o o l i n s t u d y i n g t h e coup1 i n g o f e l e c t r o n s t o shear modes w i t h o u t being a f f e c t e d by volume d i l a t a t i o n s . By extending previous NAR measurements i n

Nb,

Mo and Ta t o superconducting a l l o y s N~I-~MO, i t w i l l be shown t h a t t h e combination o f NAR experiments w i t h high-pressure Mossbauer i s o m e r - s h i f t measurements i s o f i n t e r e s t i n a deeper understanding o f t h e c o u p l i n g o f shear modes and volume d i l a t a t i o n s t o s- and d-electrons i n t r a n - s i t i o n metals.

I n cubic metals t h e e l e c t r i c f i e l d g r a d i e n t (EFG) vanishes a t a nuclear s i t e . I n the presence o f an a c o u s t i c wave, however, t h e cubic p o i n t symmetry i s destroyed p e r i o d - i c a l l y thereby g i v i n g r i s e t o a sound-induced dynamic e l e c t r i c f i e l d g r a d i e n t (DEFG) t e n s o r whose components can be measured i n n u c l e a r a c o u s t i c resonance (NAR). Besides fundamental questions concerning t h e complex physics behind t h e EFG / I / , measurements o f t h e DEFG are o f p a r t i c u l a r i n t e r e s t i n s t u d y i n g t h e long-wavelength e l e c - tron-phonon i n t e r a c t i o n i n t r a n s i t i o n metals since, i n the response o f t h e d-el ec- t r o n s t o a c o u s t i c shear modes, m u l t i p o l e f i e l d s are s e t up due t o d - e l e c t r o n charge r e d i s t r i b u t i o n , so t h a t t h e d - e l e c t r o n s a r e expected t o c o n t r i b u t e s i g n i f i c a n t l y t o t h e e l e c t r o n i c p a r t o f t h e DEFG.

A t a n u c l e a r s i t e and w i t h i n t h e range o f l i n e a r response t h e DEFG t e n s o r {V. .)

1

J

i s r e l a t e d t o t h e a c o u s t i c s t r a i n tensor {E. .) by /2/ Vij =

o.v.@

=

1

J

I J

6

' i j k l C k l where @ i s t h e s t r a i n induced e l e c t r i c a l p o t e n t i a l and

isi

jkll

i s t h e f o u r t h rank " f i e l d g r a d i e n t - s t r a i n tensor". Choosing a coordinate system having i t s axes along the p r i n c i p a l axes o f the u n s t r a i n e d cubic c r y s t a l , t h e components o f t h e t r a c e l e s s de-

CI

f i n e d DEFG-tensor Vij = i V i j

-

6 i j ~ & / 3 ) can be w r i t t e n as

where SI1, S and S44 a r e t h e t h r e e d i s t i n c t components o f t h e S-tensor ( i n V o i g t

I 2 A

n o t a t i o n ) and cij = { E

-

~6. .Tt%/3) a r e t h e components o f t h e ( i n f i r s t o r d e r ) v o l - ~

'i

ume-conserving "shear t e n s o r

.

Regarding t h a t t h e n u c l e a r e l e c t r i c quadrupole i n - t e r a c t i o n i s i n v a r i a n t a g a i n s t T&, i t f o l l o w s immediately t h a t NAR i n v e s t i g a t i o n s o f t h e e l e c t r o n i c c o n t r i b u t i o n t o t h e DEFG a r e s e n s i t i v e t o t h e c o u p l i n g o f e l e c -

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C6-390 JOURNAL DE PHYSIQUE

trons t o shear modes only. Consequently, quadrupole NAR enables one t o study the coupling of shear modes t o electrons without being affected by changes in the electron charge density caused by eventual volume deformations of the l a t t i c e

u n i t

cells. Confining ourselves t o t r a n s i t i o n metals and applying the usual ansatz

wheretflatt i s tho l a t t i c e contribution, y_ the Sternheimer antishielding f a c t o r and

(See

the conduction electron contribution within an atomic sphere centered around the

nucleus under consideration, i t follows from Eqs. ( 1 ) and ( 2 ) :

i ) _(S1

-

S12)ce r e f e r s t o the conduction electron response t o 1 inear d i l a t a t i o n s of the l a t t i c e unit c e l l s ( i - e . angular d i s t o r t i o n s of the d-bonds)

i i ) (S44)ce r e f e r s t o the conduction electron response t o angular d i l a t a t i o n s of the cubic u n i t c e l l s which predominantly a r e associated

w i t h

radial d i s t o r t i o n s of the d-bonds.

Extending the theoretical r e s u l t s of Watson e t a l . /3/ t o the DEFG in t r a n s i t i o n metals and neglecting s - d t r a n s i t i o n s , within the frame of a band-orbital model /7/, we f i n d /4/ ( a l s o see Ref. ( 5 ) )

i )

_{r I 2}

₌_(S1

-

S,2)ce/ [(I-ym)(S1

-

S12)lattl should be negligible small.

i i ) r44 = (S44)ce/ [(l-yoo)(S44)lattl -N(Ef)

,

where qo i s the electron-phonon coupling parameter a s defined

i n

Ref. (10).

The experimental r e s u l t s f o r Mo, Ta, Nb and Nb88M~,2 a r e shown i n Figs. ( ? a ) and (lb). We note t h a t t h e data of Fig. ( l a ) a r e corrected f o r the actual values of the elec- t r i c quadrupole moments and p a r t l y d i f f e r from those reported previously

/6/.

Mo Ta Nb V P d

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 t o shear b ) Coup1 ing of electrons

t o

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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.