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Physics and Astronomy Publications

Physics and Astronomy

7-1976

Thermoreflectance of V, Nb, and paramagnetic Cr

J. H. Weaver

Iowa State University

David W. Lynch

Iowa State University

, dlynch@iastate.edu

C. H. Culp

Iowa State University

R. Rosei

Istituto di Fisica dell'Universita di Roma

Follow this and additional works at:

http://lib.dr.iastate.edu/physastro_pubs

Part of the

Condensed Matter Physics Commons

The complete bibliographic information for this item can be found athttp://lib.dr.iastate.edu/physastro_pubs/50. For information on how to cite this item, please visithttp://lib.dr.iastate.edu/howtocite.html.

(2)

Thermoreflectance of V, Nb, and paramagnetic Cr

Abstract

Thermoreflectance measurements of V, Nb, and Cr films were performed near 80 and 340 K to investigate the

electronic properties of these metals. The thermoreflectance spectra ΔRR were Kramers-Kronig analyzed to

determine the temperature dependence of the dielectric functions. The results were compared with previous

derivative measurements of Mo and with static measurements of the optical reflectance of the bcc metals.

Interpretation of the structures was guided by recent band calculations. It was shown that the observed

features reflect the behavior of large volumes of the Brillouin zone rather than well-defined singularities.

Keywords

Ames Laboratory, Kramers-Kronig, Brillouin zone

Disciplines

Condensed Matter Physics | Physics

Comments

This article is from

Physical Review B

14 (1976): 459, doi:

10.1103/PhysRevB.14.459

. Posted with permission.

(3)

PHYSICAL REVIEW

B VOLUME

14,

NUMBER 2 15

JULY

1976

Tbermoreflectance

of V,

Nb,

and

paramagnetic

Cr

J.

H. Weaver

Ames Laboratory-ERDA and Department ofPhysics, Iowa State University, Ames, Iowa 50010

and Synchrotron Radiation Center, ~~ University ofWisconsin-Madison, Stoughton, Wisconsin 53589

D.

W. Lynch and C. H. Culp~

Ames Laboratory-ERDA and Department ofPhysics, Iowa State University, Ames, Iowa 50010 R.Rosei~

Istituto diFisica dell'Universita di Roma, Roma, Italy (Received 23 January 1976)

Thermoreflectance measurements ofV, Nb, and Crfilms were performed near 80and 340Ktoinvestigate the electronic properties ofthese metals. Thethermoreflectance spectra

6

R/R were Kramers-Kronig analyzed to

determine the temperature dependence ofthe dielectric functions. The results were compared with previous derivative measurements ofMo and with static measurements ofthe optical reflectance ofthe bcc metals. Interpretation of the structures was guided by recent band calculations. It was shown that the observed features reflect the behavior of large volumes of the Brillouin zone rather than well-defined singularities.

INTRODUCTION

The last few years have seen considerable

inter-est

in the electronic properties of the transition

metals.

'

Numerous studies have been reported

with the predictable outcome that our

understand-ing of the metals has increased dramatically. The contributions of optical studies have been

funda-mental.

For

many of the transition metals,

first

generation optical experiments in which the

reflec-tivity was measured over

a

wide energy range

have been completed,

'

'

and it has been shown that,

while the low-energy optical properties (g v

s

10 eV) vary significantly with the filling of the d bands, the high-energy behavior

is

very similar from metal to metal. The low-energy structure

can be attributed to transitions within the

hy-bridized sp and d bands within which the Fermi

level

lies.

With the horizontal progression

across

the periodic table, the average energy of the d bands drops with

respect

tothe sp bands and the

Fermi level

rises

within them.

'

Accompanying this, the width of the dband

first increases,

reaching

a

maximum with the Cr group, then

de-creases

until, at the noble metals, the d bands

are

completely filled and lie ~2 eV below

E~.

Sim-ilarly, with progression from 3d to 4d to 5d

metals, the dbandwidth

increases.

Such

syste-matics

are

particularly interesting, and the

inter-play between theory and experiment has proved

mutually beneficial. Calculations of the optical

absorption from

first

principles (though generally

without consideration ofwave functions and matrix

elements)

are

becoming more reliable.

To better understand the low-energy features

ob-served in the

bcc

transition metals, we have

ex-ploited thermoderivative techniques and measured the thermoderivative of the reflectance, the

ther-moreflectance hR/R. The technique

is

not

a

new

one, and it has seen wide application

for

the noble

metals,

"

semiconductors,

"

and insulators,

"

but few of the transition metals have been so studied.

"

We find, in the present study, that the derivative

spectra

oftransition metals donot

possess

the sharp and distinctive features observed when

dealing with semiconductors since critical-point

contributions

are

minimal. Instead, the broad

structures clearly

arise

from large volumes of

k space. Further, since the interband absorption

persists

to very low photon energies and generally involves states of hybridized angular momentum, line shapes cannot be calculated without detailed

wave functions and matrix elements.

EXPERIMENTAL TECHNIQUE

The thermoreflectance of V, Nb, and

Cr

has been

measured near 80and 340K between

0.

5 and 5 eV. The general techniques ofthermoderivative

spectroscopy"'"

have been described in detail

elsewhere and need be only briefly reviewed here.

The samples were opaque films evaporated by

electron-beam bombardment in vacua of

-10

'

Torr.

They were approximately 3&&25 mm, were

evaporated onto quartz substrates, and had 2—5-Q

electrical resistance.

After evaporation, each

was quickly attached tothe tip of

a

cryofinger-sample-chamber, and the chamber was evacuated

(working pressure

-10

'

Torr).

The thermal excursion of

-1

K deg was provided

by

a

unipolar 7-Hz square wave with

-2-W

power

dissipation. Conventional light sources (W- iodine

(4)

460

J

H~ D~

~

I

INCH,

CUL

AND

R.

RQSE

CLEAVER

I I I

14

„ochromator

(Leiss

lamp and

1000-(pbS cell from

0.

-WXe

arc),

monoc

r

.

5

double-prism), anand detectors

t

3 eV EMI 6256B

7102from 1to e

-in amplifier, an e

a

ted for 100

sec.

Da

a

w

h

asis

with the en '

P01

nature ofthe spec ru

dictated by the na u

d with a

thermo-ature was measure w'

ered adjacent o

couple In- solder

resents only an erature thus repr

measured temper

pie temperature. to the actual samp

approximation o

RESULTSAND DISCUSSION

ermoreflectance

spectra are

The measured thermore ec a

1-3.

Also shown 1n

1

'k'

S

t

en from our

ear

ier

for Mo as taken

r

the temperature

ex-ectra scale

with e

measured spec

bR/R

are

shown in

gn

cu,

a

itudes of

u

hitisun

er

arbitrary units, thoug ' '

r

w

arts

in

10'.

Signgn p

ra are

complica e

The hR/R

spectra

of the dielectric

func-h

t

t

d

ypa

o

f

d

t

1

t't

is

the more fun am

rd

tive of E» b&»

is

h

a

straightforwar

termined throug

a

&R/R. S h

i

analysis of

le

set

of dielectric

func-quires

a

reliable

se

o

analysis requi

1)+ne,

](~R/R)

-

[n(e,

-1

e,

66,

=2[0 e,

— +Pl

r

art

of 4R/R and

w ' e causal counterpart o

1

t

f

t

o

ob-com lex index o

r

'

.

r

we have used dielec

ri

2$3 the analysis, we

easurements. '

tained in our previo us static me

2IOK I 8OK

~

f—340K

(/)

Z

-80K

CL I

0

CCI

K

I I Ct p I Cl

0

/ iJ

540K

0

I I I

I

2

3

4

PHOTON ENERGY (eV)

fNb at approximatetely80

FIG.2. Thermore flectance o a

0.6eV represen ts 340K. The dashed curve below

rs-Kronig analys is.

e used for our

Kramers-the extrapolation use o

ers-Kronig analysis o

ofRE),

st

I the usual Kram

is

well known

a

f

the extrapolations

a

on the nature o e e

ers-dependent up

th derivative Krame

high and low en

er

gy.

. For

e

is

much

less

1

sis

the dependence

is

the shapesof ~,

are

reli-severe.

' Ac cordingly, es

re

were no der1vative data below' o g

i

analyses

for Cr,

, an

mers-Kron1g an

4and 5. A

sos

0

shown in

Figs.

1 the tempera

t

ur

re

modulat1on

'

r

contribution to

o e

d

is

difficult to remove. low energy and

is

i i

derivative feature.

to obscure the lowest-energy eriv

1 t' ns have been Numerous recent band calcu

a1o

CA

I-z

2-K o Kl tr) I— 2

Cr-80K

——Cr-340K

CL p g

J

&-2 ft

a

I 2

PHOTON ENERGY (eV)

-4—

I I

2 4

PHOTON ENERGY (eV)

t a roximately 80

fl tance ofVa pp

FIG.

1.

Ther more ec

determined near

ctrum was also e

tdb

th

; i ' at

1.

30eV is indica e

K; its maximum a

Ref.

ceof Cr and Mo (from

(5)

14

THERMORE

FLECTANCE

OF

F V,

V Nb

Nb,

AND P

ARAMAGNE

T

IC

C

r

V)

2

0

ml I

~,

I ~ I ~i I I

H 6 N Z I" A P D N D P F H

FIG.6. Ener

(Ref. 15). gy band

structure ofNb from Matthecss'

I I I I

I 2 5 4

PHOTON ENERGY (eV)

FIG,4. TemTemperature derivative of&2for Nb and V

CC

CQ

0

CV

0

I I I I

I P.

PHOTON ENERGY (eV)

FIG.5. TTemperature derivative of& for Cr and Mo.

performed' for V, Nb, and Mo, and these h

shown ener

an

ese

have

generally good agreement on many of the important

features.

The details still remain

de-pendent upon the choice of starting potential

(atom-ic

configuration) and the handling ofthe

in eraction. Relativistic effects in Nb and Mo

are

also important and tend to lift band degeneracies

a

ong

certai

1'

Nb V and M

g n lines. Because of the sim'la1ar1

't'

les

1n

ofNb

, V, and Mo, we reproduce here only theb

ans

d

Nb as calculated by

Mattheiss" (Fig. 6).

Much ofthe theoretical interest in

Cr

has been

because of ituse o

i

s antiferromagnetic ordering

(T

=312K

for

for bulk

Cr).

16 Recent calculations of theg

e1cp

aseof

Cr

band structure of the paramagn

t'

h

the

have been performed by Rath and C 11

e derivative

spectra

of

Cr

mill be interpreted in terms of th

of-atomic-o ose self-consistent

linear-co

mb'1na

t'

1on-o

-a

omic-orbitals paramagnetic bands8

(Fi

lg.

.

7

1sInore e owest-energy structure in V and Nb

the

prominently seen in nB/ft thann in'

6

g,because of e

free

carrier

contribution to

4e

.

U on co from 340too 800 K, the features sharpen and shift to

slightly lower energy

(Figs.

1 and

2}.

The

maxi-mum in Vshifts from

1.

33 (340K)to

1.

30 (210K

1.

67e

to

1.

27 eV (80 K), and in Nb from

1.

70(340K to

eV(80

K}.

The other structures sh8 ow 1

ess

epen ence on the ambient temperature. Th

ener

ure.

e

low-gy der1vative feature corresponds to the

max-imum in

a,

at

1.

6 eV (V)and

2.

4 eV(Nb)

or

in the

81 seems

o the origin of the structure

as

Z

-

Z

st ll

reasonable. Harmon" has shown that the wave

functions along the Z direction

are

of mixed and

d

character

er,

with

a

greater admixture ofp in the lower Z band. Such

a

m1x1ng~ ~ reduced the expected

weakness of

d-to-d

transitions. Further, the

in-volvement of

states

near and at

E t

ends to enhance the temperature dependence of eo

e,

.

.

I

t

is

' reasonable

a

e spreading ofthe dband

increases

the

en-ergy separation of the bands and moves the

struc-ture to higher energy for Nb than for V.

The energy bands of Cr and Mo have been shown to be very similar in the absence ofsp

in-or

b't

1

p

i

1ng and magnetic ordering. In addition the have the samme general features

as

those of V and

1lonq ey

(6)

J.

H.

%'EA

VER,

D.

W.

I

YNCHs

C.

H.

C

UI

P,

AND

R.

ROSE

I

-2

z

4J

FIG.7. Energy bands inparamagnetic Cr from Bath

and Calla@ay (Bef.17).

bands has an important influence on the low-energy

optical properties. The Ztransitions identified

as

being responsible for the

first

structure in bR/A

for

V and Nb

are still

possible

for

Cr

and Mo,

though they might be expected to appear at higher

energy and be weaker since the x'espective

Fermi

levels

are

no longer involved, but additional

struc-ture due to transitions along

4

also come into play. The degeneracy of the

6,

bands in

Cr is

lifted by relativistic effects in Mo and

%,

Rnd the

optical features associated with the

62(6,

}

-&,

(4„&,

)transitions

reflect

the changes. In

Cr,

only

a

single feature

is

observed infl

or

AR/A;

in Mo,

static

measurements failed to resolve the splitting ofthe initial

states,

'

but the derivative

spectra

clearly showed the separation'

(see Fig.

3);

in W, the spin-orbit splitting

is

-0.

5eV, and

static

measurements4 were able to resolve

struc-tures

in ARnd &,

.

Hence, the assignment ofthe

first

structure in

Cr

as

4,'

4,

seems

secure.

The identification ofthe second derivative

struc-ture in V and Nb and the third in

Cr

and Mo

is

dif-ficult, but large volumes ofk space

are

certainly

involved. Intheir xecent relativistic-augmented-plane-wave calculations for Mo, Koelling et gl.

"

concluded that the experimental feature in

z,

at

4.

1eV was built up from transitions between bands along

I,

6,

and Z.

Cr

would be expected to have

an analogous structure in &» but the extrapolation

of those transitions to the

Cr

bands of Rath and

Callaway

is

thwarted: Examination shows the band separation at

E

to be about 2 eV, at G

to

be

2.

6 eV, and along Zto be about

2.

3eV. Few new "high-symmetry*' candidates present themselves. Transitions like P~—

P,

are

allowed by selection rules, have large joint densities of

states,

and

would probably have non-negligible matrix

ele-ments since

P,

wave functions

are

=100% d-like

and those at

P,

are

20%

p-like,

80%

d-like.

"

Nevertheless, though the energy difference

is

ap-proximately

correct

in

Cr(-3.

5 eV), it

is

too great to account for the features in the other

bcc

metals,

based upon existing energy bands

for

those metals.

Probably, then, the

P

transitions

are

of minimal

importance. Transitions like

4,

,

b,

,

can also be discounted by analogy to Mo and%' since, if such

transitions were evident in

Cr,

they could be

ex-pected to

carry

over to Mo and %'and result in

pRlx'8 ofstructul es& the sepRx'Rtlon ofwhich would

grow with the spin-orbit splitting. No such

fea-tures were observed.

The recent calculations of Pickett and Allen"

indicate that the d bands in the txansition metals

Nb and M0 tend to be flatter array from symmetry

lines than along them. Their calculations showed

that major contributions to the g, structure in Nb

near

4.

3 eV and in Mo near

4.

1eV

arose

from the

region around k = (—,

',

—,

',

—,

'}.

Though there have been

no calculations of

a

similar nature fox V and

paramagnetic

Cr,

one might expect that the

ex-perimental features in

Cr

near

3.

5 eV

(4e,

)or

3.

3

ev (o),

and in Vnear

2.

5

ev

(ae,

)

or 2.

35(&,)

could be explained by transitions in that part of

the Brillouin zone. The consequence of the

Pic-kett-Allen calculations was that structures which

is

observed in the experimental

spectra

can

arise

from off-symmetry parts of the zone.

It

is clear

from our measurements that the de-rivative features in the transition metals Rre

broad, thereby indicating that large volumes of

k space

are

contributing tothe

structures.

It

is

also apparent that the last word

is

not in

as far

as calculations

are

concerned, and identifications such

as

those put forth tentatively here

are

sub-ject

to improvement. This refining must come

after

good agreement with experimental data

is

achieved; such agreement must result from the inclusion ofmatrix elements in the calculations.

The derivative

spectra

reported here provide yet another

set

of experimental data to which the

theorist must compare his calculations.

ACKNOWLEDGMENTS

The authors gratefully acknowledge

correspon-dence with

J.

F.

Alward

and%.

E.

Pickett.

We ax'e grateful tothem

for

sharing their results

prior

to publication. The encouragement ofthe Directox'

ofthe Synchrotron Radiation Center,

E.

M. Rowe,

(7)

THERMORE FLECTANC

E

OF V,

Nb,

AND

PARAMAGNETIC

Cx'

~Permanent address.

~Supported under NSFGrant No. DMB-7415089.

Gruppo Nazionale di Struttura della Materia (GNSM) of

&the Consiglio Nazionale delle Hicerche.

Present address: Interand Corporation, Chicago, Ill. 60611.

«For detailed reviews ofthe literature, see the

refer-ences cited in Befs.

2-8.

2J. H.%eaver, D.

%.

Lynch, and C.G. Olson, Phys.

Bev.

8

7, 4311 (1973), Nb.

3J.H.%eaver, D.

%.

Lynch, and C. G.Olson, Phys.

Bev.

810,

501(1974),.V, Mo, Ta.

4J.H.%eaver, C. G. Ol.son, and D.%.Lynch, Phys.

Bev.

812,

1293(1975), %.

5J.H.Weaver, C. G. Olson, M.Piacentini, and D.%.

Lynch, Solid State Commun. 16, 163 (1975), Mo

thermoreflectance.

6D.W. Lynch, C. G. Olson, and

J.

H.Weaver, Phys.

Hev.

8

ll,

3617(1975), Ti, Zr, and Hf.

VJ.H. %'eaver, Phys. Rev.

8

11, 1416 (1975), Bh, Pd,

Ir, Pt; and

J.

H.%eaver and

B.

L.Benbow, i&id. 12, (1975), Pd.

J.

H.%eaver and D.

%.

Lynch, Phys. Hev.

8

7, 4737

(1973)and

J.

H.Weaver and C.G.Olson. (unpublished),

Y.

~L. Hodges, R.E.%atson, and H. Ehrenreich, Phys.

Hev.

8

5, 3953(1972).

«OB.Hosei and D.

%.

Lynch, Phys. Bev.

8

5, 3883

(1972), Al, Au, and Cu;

B.

Bosei, C. H. Culp, and

J.

H.Weaver, ibid. 10, 484 (1974),Ag; C.G. Olson, M. Piacentini, and D.%.Lynch, Phys. Hev. Lett. 33,

644 (1974), Au; %.

J.

Scouler, ibid. 18, 455(1967),Au.

See, for example, M. Cardona, Modulation

Spectr0s-eopy (Academic, New York, 1969);and B.Batz,

Sengi-conduetors and Semimetagg, edited by

B.

K.%illardson

and A. C.Beer(Academic, New York, 1972) Vol. 9,

p. 316.

«2J. Hanus,

J.

Feinleib, and

%.

J.

Scouler, Phys. Bev. Lett. 19, 16 (1967), Ni; and D.%.Lynch,

B.

Bosei,

and

J.

H. Weaver, Solid State Commun. 9, 2195(1971),

Ni. Seealso Ref. 5.

«3B.Bosei, Phys. Bev.

8

10, 501 (1974).

'4A. Balzarotti,

E.

Colavita, S.Gentile, and B.Bosei, Appl. Opt. 14, 2412 (1975).

«5L.

F.

Mattheiss, Phys. Bev.

8

1, 373(1970).

«6For results of optical measurements of

antiferromag-netic Cr and Cr alloys, see L.W. Bosand D.%.

Lynch, Phys. Bev.

8

2, 4567(1970);A. S.Barker and

J.

A.Ditzenberger, ibid. 1, 4378(1970); D.

%.

Lynch,

R.Bosei, and

J.

H.Weaver, Phys. Status Solidi A27, 515(1975).

ath and

J

CaI,laway Phys Bev

8

8 5398(1973) B.N. Harmon (private communication).

«BD.D.Koelling,

F.

M. Mueller, and B.

%.

Veal, Phys.

Bev.

8

10, 1280(1974).

0%.E.Pickett and

P.

B.Allen, Phys. Bev.

8

11, 3599

References

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