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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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https://nrc-publications.canada.ca/eng/view/object/?id=4acd3e01-f5cc-4430-90df-e97a76730cc1 https://publications-cnrc.canada.ca/fra/voir/objet/?id=4acd3e01-f5cc-4430-90df-e97a76730cc1
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 andJ.
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, andT.
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, inPro-ceedings of the 1980Annual Conference on Condensed
Matter, Antwerp, Belgium (to be published).
NMR Measurement
of
the
HyperfineConstant
of
anExcited State
of
an ImpurityIon
in aSolid
K. K.
Sharma'
andL.
E.
EricksonDivision 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 calculatedvalue of754 MHz.
PACS numbers: 76.70.Hb, 71.70.Jp We report the
first
excited-state nuclear mag-netic resonance (NMR) observation. Froma
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 singlecrystal,
we have obtained the magnetic hyperfine constant' Az for this'D,(4f
')
state. Earlier
excited-state magnetic-resonance observations were studies of paramag-neticlevels.
'
'
The large nuclear polarization (and population) required for the NMR observation
is
obtained byhigh-resolution optical pumping within
a
strain-broadened inhomogeneous optical line whichse-lects
individual hyperfinestates.
Using this po-larization scheme, Erickson' has studied the ground-state hyperfine interaction in the trivalent praseodymium inLaF,
and YA10, hostcrystals.
We have extended his opticalrf
double-resonance technique to an excited state oftrivalent praseo-dymium.Excited-state
studies by Chen, Chiang, andHartmann' have determined the hyperf inc splitting
of the
'P,
state ofPr"
inLaF,
from theirmodu-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 ofstates
ofPr"
inLaF,
and YA10,.
The hyperfine constant A,-was not obtained in those studies. Although inprinciple 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 atbest.
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')
electronconfiguration
is
the simplest nontrivialrare-earth
configuration, (ii)the lowest
states
of 'D, and 'H,are
singlets, and (iii)best-fit
crystal-field wavefunctions
are
available."
The low-magnetic-f ieldstudy of the
Pr'
ion in this single-magnetic-site hostis
greatly simplified compared to thethree-magnetic-site
LaF,
host. This magneticsite
is
axially symmetric, further reducing the
complex-ity (and uncertainty) of the analysis.
We believe
a
variation of this excited-stateNMR technique can be used to obtain the hyperfine
and nuclear Zeeman tensors of other systems
with nondegenerate electronic
states
whichare
VOLUME 45,NUMBER 4 PH
YSICAL
RE VIE%'
LETTERS
28JULY 1980accessible
to the paramagnetic resonancetech-niques. This knowledge will be useful in the
cal-culation of the optical intensities in the presence
of
a
hyperfine interactionfor
the interpretation of the modulated photon-echo experiments.'
ltalso
provides in principle the opportunity to de-termine therole
ofthe configurationinteractions"
and other interactions suchas
J-mixing andrela-tivistic
corrections
in the hyperfine structure inelectronic
states.
Inthe LiYF4
crystal,
"
the trivalentpraseodym-ium impurity ion
occurs
substitutionally for anyttrium ion and has
S,
symmetry".
Eachelec-tronic multiplet
is
split into singlets and doubletsby the crystal field. As in
LaF,
andYA10„
the 'II4 and'D,
manifolds ofstates
both have singletstates
lying lowest. Each singlet electronic stateis
split into three hyperfine doublets by thenu-clear electric
quadrupole and the second-order magnetic hyperf inc interactions. However, the higherrare-earth site
symmetryS,
inLiYF,
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
pureI,
state.
Since4I,
=0
optical transitionsoccur,
the optical pumping cycle couples onlypairs
of levels, which leads toa
different type of population distribution from that in theLaF,
andYA10, experiments.
The 'H,
I',
(0 cm')-'D, I',
(16740 cm')
mag-netic dipole (zero-phonon) transition of
Pr"
(0.
05at.
%)inLiYF,
was excited by o-polarized 2-mm-diam 1-mW focused beam froma
single-mode frequency-stabilizedlaser
at4.
5K.
Anrf
mag-netic field of amplitude0.
30
rms alignedper-pendicular
to
thec
axis was slowly frequency swept. The fluorescence from'D,
r,
(16740 cm')-'H, I',
,
(79cm')
was monitored. Similarto
thePr"
inLaF,
and in YA10, experiments,fluorescence
increases
corresponding to ground-state NMR were observed near9.
5 and19
MHz. These will be discussed elsewhere. Hcnvever,
twodecreases
in fluorescence were observed at5123.
5~0.
9MHz and10244.
6~0.
8 kHz. One of theseis
shown inFig.
1.
Theseresults
werein-dependent of temperature in the range of 2 to
4.
5K.
We believe that these dips represent NMRtransitions in the lowest level of D2.
Amodel ofthe system
is
shown inFig.
2.
Con-sider an impurity ion ata site
such that the2-5
transition
is
resonant with the pumplaser.
Level5
relaxes
to
level 2primarily through intermedi-ate electronicstates.
The population of level 5is
a
function of the number of pump photons while the sum ofthe populations of levels 2 and 5is
constant. As
for
Pr"
in theLaF,
and YA10, hostcrystals,
magnetic dipole transitions between levels 1or
3,
and 2 increase the population of level 2 and therefore increase the optical absorp-tion2-5
and the monitored fluorescence. On the—5/2 CO I-X 76 i 0 O
0
~ ~ ~ 0 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~ ~ lD~(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. Thisisthe ~-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
VOLUME 4$,NUMBER 4
PHYSICAL
RKVIKW
LETTERS
28Jvz, v 1980other 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 and3,
respectively) resulting in a reduction of the optical absorption2-5
at thelaser
frequency anda
reduction in the monitored fluorescence. Arate
equation model confirms these arguments. Magnetic dipole transitions in any intermediate electronic level would also produce reduction ofthe fluorescence at resonance. The lifetimes of
all levels below the lowest 'D, level
are
expected to be muchshorter.
The relaxationis
phononas-sisted.
The known energygaps"
allow fouror
less
phononprocesses for
all but the lowest 'G4level. This gives microsecond
or
less
lifetimesfor
thoselevels.
The lowest'6,
level must relax through a, gap of 2500 cm'
ora
five-phononproc-ess
in LiYF4. Since the crystal-field splittingsare
greater for this host than for theLaF„
thernultiphonon
rates
measured by Riseberg andMoos"
give an upper bound of 100 p,s.
Thiscom-pares
toa
measured0.
67 ms lifetimefor
thelow-est
level of 'D,.
Further,
the expected value ofy„=3.
6kHz/G for this1',
state(J,
& &=4), is
much larger than the observed value.
The data were fitted to
a
spin Hamiltonian given byTeplov"'"
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 AE
A gg xx ~ 6j
2 zz P 6j
D„E,
represent the second-order magnetic-hy-perfine-interaction contributions andP,
gare
thepure quadrupole
parameters;
y&—
(-
g»p» —2gi BA&&)/h1(0
i/) In)t'
ff~
j
n~0
'
en—i-'0e„=
energy of level n and A, =hyperfine constantappropriate tothe electronic state studied.
'
The resultsare
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 froma
simultaneousleast-squares
fit ofthe Hamiltonian to 37frequencies measured at fields of 30+
0.
1 G,40+0.
1 Gat many differentangles between the field vector and the crystal
c axis.
The z axis ofthe hf tensoris
found to be parallel tothe crystallographic e axis withina
degree. The
rf
frequency for each channel was measured to an accuracy ofo.
2 kHz. The statederrors
ofD,
E,
and yare
the standard deviations obtained from theleast-squares
analysis.The hyperfine constant A, was determined by
use ofy&
=-
(g»P»+2gp BA«)/h, the measuredval-ues of
y„,
y,
, and the crystal-fieldintermediate-coupling wave functions of
Esterowitz":
Fromy,
A,.=+
60S+40 MHz, and fromy„,
A&=+630
+74 MHz. The value ofA~('D,)
=+754
MHzcal-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 thecrys-tal-field wave functions and ofthe
intermediate-coupling
corrections.
The intermediate couplingstates are
well knownfor
praseodymium. The intermediate-coupling corrections representa
10'%%uo
effect,
and if theyare
known to 10%, give a1%accuracy for the
calculated';.
Thecrystal-field states in
D„symmetry
withJ
= 2are
com-pletely symmetry determined exceptfor
the inter-mediate- coupling coefficients.
SinceEsterowitz"
has demonstrated that the praseodymium
site
symmetry
is
only slightly distorted fromD,
„,
the uncertainty in the"measured" A;
from incompleteknowledge of the crystal-field wave functions
is
small indeed. Interactions such
as
the configura-tion interaction andJ
mixing which have been ig-nored in the analysis may makea
significant con-tribution to the discrepancy."
However,knowl-edge of the Az's
for
several excitedstates
wouldbe required before an experimental estimate can be made of their contributions.
The measured Dg and
D,
for the ground'II,
(0cm
')
and excited 'D,(16740
cm')
states
togetherwith the calculated second-order magnetic hyper-fine contribution
D,
(excited) =—0.
039MHz andD,
(ground)=+3.
262 MHz were used to determinethe pure quadrupole
parameters" P~,
and P4qfor
the ground and excitedstates
[P,
q('H, )=0.
76 MHz,P,
~('D, )=1.
88 MHz, andPz, =0.
71 MHz]. The asymmetry parameter gwas assumed to bezero.
The calculated ratio of
P,
q('D,)/P«('H,
) =2.
47 was used in thisfit.
P&„was assumedto
be the same in the two electronicstates as
the total 4felec-tron shielding ofthe nuclear quadrupole moment
from the lattice
is less
than 3%."
Shielding changes from one electronic state to anotherVOLUME 45,NUMBER 4
PHYSICAL
REVIEW LETTERS
28 JUr.v 1980If the impurity ion
exists
ina site
of lower than axial symmetry, certain modifications in theex-perimental technique
are
required to observeex-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 (level2).
Since the population oflevel 5
is
alwaysless
than that of level 2 at the pump levels used in theseexperiments, no NMR can be observed in the
ex-citedstate.
However, we believe excited-stateNMR of
Pr"
may be observed inLaF,
and YAlO,if the crystal
is
simultaneously radiated at oneor
both ofthe ground-state frequencies in addition totheexcited-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 forPr"
inLaF„
in or-der to obtaina
unique symmetry, andcrystal-field eigenfunctions where the number of
param-eters
is
too large to obtaina
satisfactory fit from the crystal-field energy levels alone.The authors thank
C.
A. Morrisonfor
the wavefunctions used in this
Letter
and Art Linzfor
sup-plying the
Pr'
in LiYF4crystal.
On leave from the Indian Institute of Technology, Kanpur, India.
B.
G.Wybourne, Spectroscopic Properties of RareEarths (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 andF.
Bitter, Phys. Rev. 86, 308 (1952). W.J.
Childs, O. Poulsen, andL.
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, andS.
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 byP.
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).