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Physical Review Letters, 45, 4, pp. 294-297, 1980-07

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NMR measurement of the hyperfine constant of an excited state of an

impurity ion in a solid

Sharma, K. K.; Erickson, L. E.

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VoLUME 45,+UMBER4

PHYSICAL

REVIEW

LETTERS

28 Jvx,v 1980

(1979);W. Hanke, in I'estkoxPex+vobLeme, edited by

J.

Treusch (Vieweg, Wiesbaden, 1979),Vol. XIX, p.43.

W.Brinkman and

B.

Goodman, Phys. Rev. 149, 597

(1966).

N. O. Lipari and W.

B.

Fowler, Phys. Rev. B2, 3354 (19V0).

E.

O.Kane, Phys. Rev. B4, 1910 (1971). N.

E.

Brener, Phys. Rev. B11,929 (1975).

J.

Bennett and

J.

C.Inkson,

J.

Phys. C 10, 987 (19vv).

S.

T.

Pantelides, D.

J.

Mickish, and A.

B.

Kunz,

Phys. Rev. B10, 5203, 2602 (1974).

A.

B.

Kunz, D.

J.

Mickish, and

T.

C.Collins, Phys. Rev. Lett. 31, 756 (1973).

J.

Hermanson, Phys. Rev. B6, 2427 (1972).

"H.

J.

Mattausch, G. Strinati, and W.Hanke, to be published.

G.S.Painter, D.

E.

Ellis, and A.R.Lubinsky, Phys. Rev. B4, 3610 (1971).

A. Mauger and M. Lanoo, Phys. Rev. B 15, 2324

(19VV).

W. Hanke, G.Strinati, and H.

J.

Mattausch, in

Pro-ceedings of the 1980Annual Conference on Condensed

Matter, Antwerp, Belgium (to be published).

NMR Measurement

of

the

Hyperfine

Constant

of

an

Excited State

of

an Impurity

Ion

in a

Solid

K. K.

Sharma'

and

L.

E.

Erickson

Division of Electrical Engineering, National Research Council ofCanada, Ottawa ElA ORB, Canada

(Received 4February 1980)

An optically detected NMR measurement ofthe hyperfine tensor for an excited state of an impurity rare-earth ion (Pr ) in a solid (LiYF4) is reported. The results have been used to obtain for the first time ameasured value ofthe hyperfine interaction constant

A.

,

=616+51 MHz ofthe D2 excited state. This issomewhat smaller than the calculated

value of754 MHz.

PACS numbers: 76.70.Hb, 71.70.Jp We report the

first

excited-state nuclear mag-netic resonance (NMR) observation. From

a

measurement ofthe orientation and magnitude of

the nuclear Zeeman tensor of the diamagnetic 'D, (16740 cm

')

level of trivalent praseodymium di-lute in the LiYF4 single

crystal,

we have obtained the magnetic hyperfine constant' Az for this

'D,(4f

')

state. Earlier

excited-state magnetic-resonance observations were studies of paramag-netic

levels.

'

'

The large nuclear polarization (and population) required for the NMR observation

is

obtained by

high-resolution optical pumping within

a

strain-broadened inhomogeneous optical line which

se-lects

individual hyperfine

states.

Using this po-larization scheme, Erickson' has studied the ground-state hyperfine interaction in the trivalent praseodymium in

LaF,

and YA10, host

crystals.

We have extended his optical

rf

double-resonance technique to an excited state oftrivalent

praseo-dymium.

Excited-state

studies by Chen, Chiang, and

Hartmann' have determined the hyperf inc splitting

of the

'P,

state of

Pr"

in

LaF,

from their

modu-lated photon-echo experiments. Erickson,

'"

us-ing an enhanced and saturated optical-absorption

technique, has measured the hyperfine splittings

of the lowest level of the

'D,

manifold of

states

of

Pr"

in

LaF,

and YA10,

.

The hyperfine constant A,-was not obtained in those studies. Although in

principle it should be possible to determine A, from the hyperfine splittings alone, the lack of

the

precise

knowledge of the pure quadrupole coup-ling constants and the electronic wave functions make this determination difficult at

best.

A& can,

however, be determined from knowledge of the nuclear Zeeman tensor without knowing the pure quadrupole constants. The

LiYF,

:Pr"

system was chosen for study because (i) the

(4f')

electron

configuration

is

the simplest nontrivial

rare-earth

configuration, (ii)the lowest

states

of 'D, and 'H,

are

singlets, and (iii)

best-fit

crystal-field wave

functions

are

available.

"

The low-magnetic-f ield

study of the

Pr'

ion in this single-magnetic-site host

is

greatly simplified compared to the

three-magnetic-site

LaF,

host. This magnetic

site

is

axially symmetric, further reducing the

complex-ity (and uncertainty) of the analysis.

We believe

a

variation of this excited-state

NMR technique can be used to obtain the hyperfine

and nuclear Zeeman tensors of other systems

with nondegenerate electronic

states

which

are

(3)

VOLUME 45,NUMBER 4 PH

YSICAL

RE VIE%'

LETTERS

28JULY 1980

accessible

to the paramagnetic resonance

tech-niques. This knowledge will be useful in the

cal-culation of the optical intensities in the presence

of

a

hyperfine interaction

for

the interpretation of the modulated photon-echo experiments.

'

lt

also

provides in principle the opportunity to de-termine the

role

ofthe configuration

interactions"

and other interactions such

as

J-mixing and

rela-tivistic

corrections

in the hyperfine structure in

electronic

states.

Inthe LiYF4

crystal,

"

the trivalent

praseodym-ium impurity ion

occurs

substitutionally for an

yttrium ion and has

S,

symmetry

".

Each

elec-tronic multiplet

is

split into singlets and doublets

by the crystal field. As in

LaF,

and

YA10„

the 'II4 and

'D,

manifolds of

states

both have singlet

states

lying lowest. Each singlet electronic state

is

split into three hyperfine doublets by the

nu-clear electric

quadrupole and the second-order magnetic hyperf inc interactions. However, the higher

rare-earth site

symmetry

S,

in

LiYF,

re-quires, in the absence of third- and higher-order hyperfine mixing, that the hyperfine tensor

is

ax-ial and each hyperfine state may be described

as

a

pure

I,

state.

Since

4I,

=0

optical transitions

occur,

the optical pumping cycle couples only

pairs

of levels, which leads to

a

different type of population distribution from that in the

LaF,

and

YA10, experiments.

The 'H,

I',

(0 cm

')-'D, I',

(16740 cm

')

mag-netic dipole (zero-phonon) transition of

Pr"

(0.

05

at.

%)in

LiYF,

was excited by o-polarized 2-mm-diam 1-mW focused beam from

a

single-mode frequency-stabilized

laser

at

4.

5

K.

An

rf

mag-netic field of amplitude

0.

3

0

rms aligned

per-pendicular

to

the

c

axis was slowly frequency swept. The fluorescence from

'D,

r,

(16740 cm

')-'H, I',

,

(79cm

')

was monitored. Similar

to

the

Pr"

in

LaF,

and in YA10, experiments,

fluorescence

increases

corresponding to ground-state NMR were observed near

9.

5 and

19

MHz. These will be discussed elsewhere. Hcnv

ever,

two

decreases

in fluorescence were observed at

5123.

5~

0.

9MHz and

10244.

6~

0.

8 kHz. One of these

is

shown in

Fig.

1.

These

results

were

in-dependent of temperature in the range of 2 to

4.

5

K.

We believe that these dips represent NMR

transitions in the lowest level of D2.

Amodel ofthe system

is

shown in

Fig.

2.

Con-sider an impurity ion at

a site

such that the

2-5

transition

is

resonant with the pump

laser.

Level

5

relaxes

to

level 2primarily through intermedi-ate electronic

states.

The population of level 5

is

a

function of the number of pump photons while the sum ofthe populations of levels 2 and 5

is

constant. As

for

Pr"

in the

LaF,

and YA10, host

crystals,

magnetic dipole transitions between levels 1

or

3,

and 2 increase the population of level 2 and therefore increase the optical absorp-tion

2-5

and the monitored fluorescence. On the

5/2 CO I-X 76 i 0 O

0

~ ~ ~ 0 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~ ~ l

D~(r~)

4 LASER -+ 3/2 +1/2 4l 7+— x LLL O Ch Lal K O ~

72-5000 I 5100 FREQUENCY (kHz ) 5200 ~H4(r~) +5/a +-5/2 + 1/Z

FIG.

l.

Optically detected NMH in the lowest D2 level ofPr +in LiYF4. This

isthe ~-p transition. The

solid line is a Gaussian curve least-squares best fit to

the data. The line isdistorted on the high-frequency

side because ofsweep-rate effects. The resonance

fre-quency is 5123.5+

0.

9 kHz. The stated error isthe standard deviation of the least-squares fit.

Iz

FIG.2. Energy level model for the optically detected

excited-state NMR experiment. Each singlet electronic

level is split into three nuclear doublets by the

hyper-fine interaction. The energy levels are labeled by

L,

S,

J, I

(4)

VOLUME 4$,NUMBER 4

PHYSICAL

RKVIKW

LETTERS

28Jvz, v 1980

other hand, magnetic dipole transitions between the populated level 5 and the empty levels 4

or

6 remove these ions from resonance with the opti-cal pump (because they relax only to levels 1 and

3,

respectively) resulting in a reduction of the optical absorption

2-5

at the

laser

frequency and

a

reduction in the monitored fluorescence. A

rate

equation model confirms these arguments. Magnetic dipole transitions in any intermediate electronic level would also produce reduction of

the fluorescence at resonance. The lifetimes of

all levels below the lowest 'D, level

are

expected to be much

shorter.

The relaxation

is

phonon

as-sisted.

The known energy

gaps"

allow four

or

less

phonon

processes for

all but the lowest 'G4

level. This gives microsecond

or

less

lifetimes

for

those

levels.

The lowest

'6,

level must relax through a, gap of 2500 cm

'

or

a

five-phonon

proc-ess

in LiYF4. Since the crystal-field splittings

are

greater for this host than for the

LaF„

the

rnultiphonon

rates

measured by Riseberg and

Moos"

give an upper bound of 100 p,

s.

This

com-pares

to

a

measured

0.

67 ms lifetime

for

the

low-est

level of 'D,

.

Further,

the expected value of

y„=3.

6kHz/G for this

1',

state

(J,

& &

=4), is

much larger than the observed value.

The data were fitted to

a

spin Hamiltonian given by

Teplov"'"

II

=Q,

y&H&I&+D[I,

'

3I(I+1)]+E[I„'

I„'],

XqP q& where D=D,

+P,

E

=E,

+

3gP,

with A xx vv A

E

A gg xx ~ 6

j

2 zz P 6

j

D„E,

represent the second-order magnetic-hy-perfine-interaction contributions and

P,

g

are

the

pure quadrupole

parameters;

y&—

(-

g»p» —2gi BA&&)/h

1(0

i/) In)

t'

ff

~

j

n~0

'

en—i-'0

e„=

energy of level n and A, =hyperfine constant

appropriate tothe electronic state studied.

'

The results

are

D =+

2561+0.

6kHz, I&I

=17~

8 kHz,

y,

=-1.

653+

0.

020 kHz/G,

y„=

y,

=—

1.

480+0.

020 kHz/G. The magnetic splitting parameters were derived from

a

simultaneous

least-squares

fit of

the Hamiltonian to 37frequencies measured at fields of 30+

0.

1 G,

40+0.

1 Gat many different

angles between the field vector and the crystal

c axis.

The z axis ofthe hf tensor

is

found to be parallel tothe crystallographic e axis within

a

degree. The

rf

frequency for each channel was measured to an accuracy of

o.

2 kHz. The stated

errors

of

D,

E,

and y

are

the standard deviations obtained from the

least-squares

analysis.

The hyperfine constant A, was determined by

use ofy&

=-

(g»P»+2gp BA«)/h, the measured

val-ues of

y„,

y,

, and the crystal-field

intermediate-coupling wave functions of

Esterowitz":

From

y,

A,.

=+

60S+40 MHz, and from

y„,

A&

=+630

+74 MHz. The value ofA~('D,)

=+754

MHz

cal-culated from the formulas ofWybourne' (with

cor-rections for intermediate couplings) and the ex-perimental ground-state value from Teplov

"

is

significantly higher. The reliability of the

"meas-ured" A,.

is

dependent on the accuracy of the

crys-tal-field wave functions and ofthe

intermediate-coupling

corrections.

The intermediate coupling

states are

well known

for

praseodymium. The intermediate-coupling corrections represent

a

10'%%uo

effect,

and if they

are

known to 10%, give a

1%accuracy for the

calculated';.

The

crystal-field states in

D„symmetry

with

J

= 2

are

com-pletely symmetry determined except

for

the inter-mediate- coupling coeff

icients.

Since

Esterowitz"

has demonstrated that the praseodymium

site

symmetry

is

only slightly distorted from

D,

„,

the uncertainty in the

"measured" A;

from incomplete

knowledge of the crystal-field wave functions

is

small indeed. Interactions such

as

the configura-tion interaction and

J

mixing which have been ig-nored in the analysis may make

a

significant con-tribution to the discrepancy.

"

However,

knowl-edge of the Az's

for

several excited

states

would

be required before an experimental estimate can be made of their contributions.

The measured Dg and

D,

for the ground

'II,

(0

cm

')

and excited 'D,

(16740

cm

')

states

together

with the calculated second-order magnetic hyper-fine contribution

D,

(excited) =—

0.

039MHz and

D,

(ground)

=+3.

262 MHz were used to determine

the pure quadrupole

parameters" P~,

and P4q

for

the ground and excited

states

[P,

q('H, )

=0.

76 MHz,

P,

~('D, )

=1.

88 MHz, and

Pz, =0.

71 MHz]. The asymmetry parameter gwas assumed to be

zero.

The calculated ratio of

P,

q('D,

)/P«('H,

) =

2.

47 was used in this

fit.

P&„was assumed

to

be the same in the two electronic

states as

the total 4f

elec-tron shielding ofthe nuclear quadrupole moment

from the lattice

is less

than 3%.

"

Shielding changes from one electronic state to another

(5)

VOLUME 45,NUMBER 4

PHYSICAL

REVIEW LETTERS

28 JUr.v 1980

If the impurity ion

exists

in

a site

of lower than axial symmetry, certain modifications in the

ex-perimental technique

are

required to observe

ex-cited-state

NMR. It can be shown in the steady state that optical pumping in the absence of ground-state magnetic dipole transitions com-pletely depopulates the pumped level (level

2).

Since the population oflevel 5

is

always

less

than that of level 2 at the pump levels used in these

experiments, no NMR can be observed in the

ex-cited

state.

However, we believe excited-state

NMR of

Pr"

may be observed in

LaF,

and YAlO,

if the crystal

is

simultaneously radiated at one

or

both ofthe ground-state frequencies in addition tothe

excited-state

frequency.

In conclusion, this experiment demonstrates the feasibility of study of the excited-state hyperfine interaction of impurities in solids through optical-ly detected NMR measurements. The results will be useful in the calculation of optical intensities in the presence of the hyperfine interaction. This technique will broaden the study ofthe configura-tion interactions through the use of the knowledge

gained by

excited-state

NMR experiments. This hyperfine knowledge might also serve to supple-ment the crystal-field data in lower-symmetry situations-, particularly for

Pr"

in

LaF„

in

or-der to obtain

a

unique symmetry, and

crystal-field eigenfunctions where the number of

param-eters

is

too large to obtain

a

satisfactory fit from the crystal-field energy levels alone.

The authors thank

C.

A. Morrison

for

the wave

functions used in this

Letter

and Art Linz

for

sup-plying the

Pr'

in LiYF4

crystal.

On leave from the Indian Institute of Technology, Kanpur, India.

B.

G.Wybourne, Spectroscopic Properties of Rare

Earths (Interscience, New York, 1965), p.

115.

B.

Cognac,

J.

Brossel, and A.Kastler, C.R.Acad.

Sci.246, 1827(1958). This paper concerns the optical detection ofNMR in diamagnetic ground state.

J.

Brossel and

F.

Bitter, Phys. Rev. 86, 308 (1952). W.

J.

Childs, O. Poulsen, and

L.

S.Goodman, Phys.

Rev.A 19, 160(1979).

Dietmar Stehlik, in Excited States, edited by Edward

C.Lim (Academic, New York, 1977), Vol. 3; K.

P.

Dinse and C.

T.

Winscom, Semicond. Insulat. 4, 263

(1978)

.

S.Geschwind, in Electron Paramagnetic Resonance,

edited by S.Geschwind (Plenum, New York, 1972);

J.

P.

Hessler and C.A.Hutchison,

Jr.

, Phys. Rev. B8, 1822

(1973).

L.

E.

Erickson, Opt. Commun. 21, 147 (1977). Y.C.Chen, K.Chiang, and

S.

R.Hartmann, Opt. Commun. 29, 181 (1979).

L. E.

Erickson, Phys. Rev. B16, 4731 (1977).

L.

E.

Erickson, Phys. Rev. B19, 4412 (1979). L.Esterowitz,

F.

J.

Bartoli, R.

E.

Allen, D.

E.

Wortman, C.A. Morrison, and R.

P.

Leavitt, Phys.

Rev. B 19, 6442 (1979);

L.

Esterowitz,

F.

J.

Bartoli,

and R.

E.

Allen,

J.

Lumines. 21, 1(1979).

B.

G.Wybourne, SPectroscoPic ProPerties of Rare Earths (Interscience, New York, 1965), p. 151.

R.

E.

Thoma, C.

F.

Weaver, H. A. Friedman, H.

Ins-ley,

L.

A.Harris, and H.A. Yakel,

Jr.

,

J.

Phys. Chem. 65, 1096(1961).

L.

A. Riseberg and H. W. Moos, Phys. Rev. 174, 429 (1968).

M.A.Teplov, Zh. Eksp. Teor.

Fiz.

53, 1510(1967)

[Sov.Phys. JETP 26, 872 (1968)].

The sign ofg„P„terms in Teplov's Eq. (2) should be

negative. See

B.

Bleaney, in Proceedings ofthe Third International Conference on Quantum Electronics, Paris, 1968, edited by

P.

Grivet and N. Bloembergen

(Colum-bia Univ. Press, New York, 1964), p.607.

S.Hufner, OPtical SPectra ofTransParent Rare Earth

ComPounds (Academic, New York, 1978);

B.

R.Judd,

Operator Techniques in Atomic Spectroscopy (McGraw-Hill, New York, 1963), p.

91.

K. D.Sen and

P.

T.

Narasimhan, Phys. Rev. B16,

107(1977).

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