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428
(paper to be presented at IXth International Conference on Low Tempersture
Proies, Columbus, Ohio, August 31 - September 4, 1964)
ORNL - 428
ITIES
007 91964
م رکه - سیر
S
yperrine Structure Coupling in Ferric Ammonium Sulfate as a function
of Magnetic field and Temperature
F. :. Ovenshain, !. D. Roberts, C. F. Coleran, D. W. Forester
Oak Fidge Tational Laboratory, Oak Ridge, Tennessee
and
J. O, whomson
University o: Tennessee, Knoxville, Tennessee
I: stüdyirs the hyperfine structure coupling in ferromagnetic or
citiierronagrietic materiais by means or the Mössbauer effect the concept
Oi 2. erective magnetic field bon has been widely used. A precise
wurinicion oi !! may ve given in terms of the spin llwmilionian Hi
cucciated with ti: ith magnetic ion of spin S; it: the magnetic solid:
UIT
leemi.
.ini;
+ 5 J., S. , +382 5
(1)
j=i bris
fij
C
Here is is an externally applied magnetic field, I is the nuclear spin
oi tho :" ion, the fourth term is the exchange interaction, the fifth
term is the dipole-dipole interaction and the remaining symbols have their
US
usual reaning. In naterials such as metallic iron and Fe, , the exchange
Research sponsored by the U. S. Atomic Energy Commission under contract
ME
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LEGAL NOTICE ---
with the Union Carbide Corporation.

The report m. peenrnd au u account of Doren.nl ornsond work. Neither Une Valls
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A, MIL MJ varrinty of ropesenulim, por or impiind, 10 roinnt um arru.
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of any information, maritus, methind, or procesu delom in wo report wy not infring
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As im le the above, "prm kung an half of the cowalielon" includes any on.
porn or contracur of the Connulou, of implor of me contractor, no tent that
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diomainte., provides accmi be, any Inor sulton pureut to do amoy on or contrat
0 Comiuolan, or to employmel nid oernali actor.
-2-
hüür.cüica is much larger than thie other terms in Hi, including in
vichar the hyperfine structure coupiing. Correspondingly the spin-
5, relaxation time I will be very short compared with the nuclear
2000sion time I r when the temperature T is below the Curie temperaivre
fonetic orderins efi'ects suppress the of? diagonal terms in AI;S;.
i
till
;-+
>>] the hyperfine interaction may then be described approximately
19 fs = 5nPne fiziert
la)
were
cap = A <$iz> 16
43, +$426 = H149/372 ***/*T.
To incore effective field model gives a good description of Mössbauer
C.Vishnuments of the nis splitting occurring in metallic iron
and
I woübü be of interest to expiore magnetically dilute materials in which
wie reiüive magnitudes of the terms in Hi may differ markedly from those
cor le or 0203
Be substance of interest is the dilute parumagnetic material
FC 1:50: 19.12!1,0. Here the exchange interaction is many orders of mag-
z wcie smaller than in metallic iron, and the dipule-dipole interaction is
rolig
oc order or magnitude smaller. In this salt the dinolc-dipole
izveracüion is thought to be much larcer than the exchance term in Hi, which
now contains an additional term D(5,- 1/3 S(S + 1)). The coefficient D
as riot iven measured, but may be of comparabic magnitude' to the di polizm
ciäpoic orm. Vagnetic ordering in this material for 11 2 0 is presumably
due to the D torn and dipolc-dipcle interaction and ling a Néel temperature
".shent 0.04**. Is one applies a magnetic field of about 10" oorsteds to
tric salt ai temperatures in the iiquid helium ranga, a value for <S >
carnetic saturation may be produced. In the measurcnents described
bilo: we have chosen to make a Szilabout one order of magnitude larger
this tire siipole-iipole nná o terms which in turn are large compared to the
oilier terms in 11. The magnetic ordering is now duc primurily to the
ested field, in contxnst to metallic iron, where the spin ordering is
Osü entirely due to the exchange interaction. Onc muy ühen inquire how
um tho nas spectra observed in these measurements may be correlated with
thic predictions of the effective fielú model. An additional interest in
this measurement derives from the fact that ferrio alum has been used for
man piy years in magnetic cooling studies.
ás radioactive source wil3 prepared by diffusing about 70 mc of "Co into
0.0003 inch thick copper foil. The diancter of the active arcas was
approximately 2.2 cm. The absorber was a polycrystalline sample of
54:2, 650,19.1211,0 containing 20 mg/cm- of natural Fc, pressed into the form
SW.
the same liquid helium bath, but the macnetic field was applied only to the
übsorber. The direction of the magnetic field was normal to the planc or
tio alisorber and parallel to the Y-ray propagation direction. Picasurements
were made at H/T values of 14.10, 10.65, 8.0, 6.50, 5.72, 4.30, 2.86 ind
We
zero koc/ºk. A selection from these results is shown in Fig. l.
11
At the largest 11/m vnluc or 14.10 koe/ºk, Fix, la, a hyperfire
structiire op:0c truri of f'our lines was obverved in which the relative Bpac-
incu oi' lines corresponded to those observed in ferromagnetic iron,
and ind i the lineu showed widtho 10.05 mm/sec. me line width found for
.càü source at W.2°x using a Xilc(08)6:311,0 absorber at 300°K was 0.47 mm/sec.
me rehatively smali line brondering in this spectrum compared with that
51
(
Co
TO
vidad for the smaller 11/" values discussed below results from the fact
wiūt liere 2 SM is near cuturation, i.c., the electron spins spend most
0:' the time in the energetically most favored orientation S, E. 5/2. For
O
v ürini single crystal or the onlt one would expect the lines to approach
üeir ilüural width as 11/" approacics infinity. Assuming for the xresent
ühjat I, is opposite in sien to the applied lielu II, and using Eqs. (2-4)
é to extrapolato to saturation magnetization, the observed splitting corresponds
101... = 991 20 koe at < 5,> /SE 1. This may be compared with the
vallie 552 10 koc measured at 1.2°% for antiferromagnetic reg.g, in which
tric iron utoms are also in the i'erric state.
mici!
2
3
p
The other spectru, or which i'ie. 10 is a typical example, show a very
marked procressive asynmetric brondening and decrense of ampiitude of the
outer lines us !1/7 decreases. In sharp contrast with this, within statisti-
IS
SOS
cal error the amplitudes and widths of the inner lines are very nearly in-
deperdicat 08 !1/over the range from 14.10 to 2.86 koe/ºk. The arrows in
.. i show where the peaks of the outer lines would appear if their positions
con lowesi 993. (2-).
Tie separations of the outer line pair and those of the inner pair for
üll of our data are shown as a function of B11/kt in Fig. 2. mie solid curves
- 5
are a plot of <1,> given by Eq. (") normalized in each case to the
splitting of the corresponding line pair at the largest value of H/T.
Tuc spacing of the inner pair appears to follow the Brillouin function
CG. () within the statistical uncertainties of the measurements, but
me Sureme
the peak separation of the outer lines clearly falls above the calculated
curve as 11/T decreases.
In discussing these measurements, three characteristic times are of
C
@
importance. These are the nuclear life time are the spin-spiti relaxation
time 2a and the nuclear precession time 7. Clearly T / Ty must be
small compared with one in order to have a resolved spectrum and TIT
must be large compared vith one so that fluctuations of the electron spin
riacnetization may have a negligible eifect on the line widths. As mentioned
avove, these conditions are well satisfied in metallic iron. In contrast,
Cr17, in ferric ammonium alum is much smaller and possibly comparable
with unity. llere fluctuation effects may be expected to have a strong in-
fluence on the observed Mössbauer spectrum.
In this context one may note
that the broadening effects are much more pronounced for the outer lines,
for which /(m 4/I. - m4/I) I is large, than for the inner lines, and
that is the outer lines become broader they also become progressively more
asymmetric. This asymmetry can be attributed to the selection rules correspond-
ing to the dipole-dipole and D terms which give rise to the electronic spin-
spin relaxation process.
These selection rules are such that spins in
energetically highly unfavored orientations, which will have very few neighbors
suitably oriented for spin exchange, will relax unusually slowly towards
more probable orientations. Another possible contribution to the asymmetry
may come from én, = 0 transitions. Because of the presence of off-diagonal
OXTC
TON
Il
terus in the spin Hamiltonian, these transitions will not be completely for-
bidder.
he is spectrum of ferric ammonium alum was also observed under field-
free cordiitions at temperatures of 1.7, 2.25, 4.2, and 300°. In each case
Q
res
the spectrum showed a sincle rather broad linę, the width at 4.2°K being
1.3 m/sec. This is to be contrasted with the resolved multi-line spectra
r
observer under field-free conditions in magnetically very dilute materials
by hertheim et al.
It is clear that under the conditions of this experiment the effective
s'iclü model does not give an adequate description of the behavior of f'erric
üonium alum. The discrepancies are quantitative, in its failure to account
.
for the positions of the outer peaks, and qualitative, in that the model
assumes that the lines will show only the natural wirith associated with the
ili clear lifetime. Both types of discrepancy may well be removed by a theory
which takes account of fluctuations in the electron spin magnetization.
-7-
REFERENCES
1. Visiting scientist from the Atomic Energy Research Establishment,
arvell, England.
Oak Ridge Graduate Fellow from the University of Tennessee, Knoxville,
Tennessee.
York (1962).
H. 3. S. Preston, S. S. llanna and J. Heberle, Phys. Rev. 128, 2207 (1962).
5. %. Ono, Y. Ishikawa, A. Ito, and E. Hirahara, J. Phys. Soc., Japan,
Suppl. B-I, 17, 129 (1962).
6. m. 7. Cooke, Proc. Phys. Soc. (London) A62, 269 (1949).
8. G. E. Wertheim and J. P. Remeika, Bull. Am, Phys. Soc. 2, 464 (1964).
FIGURE CAPTIONS
rico? - Pyperfine structure spectra of 'l'e in ferric ammonium alum
a) 11.= 24.0 koe, T = 1.70K
b) 1 = 24.0 koe, T = 4,2°K
Fig. 2 - Peas separations in nyperfine structure spectrum of ferric ammonium
alum as a function of BH/KT.
Solid circles - separation of outer peaks
Open circles - separation of inner peaks
For explanation of curves see text.
Curves S
UNCLASSIFIED
ORNL-DWG 64-3044 R
so

H = 24.0 koe
T = 1.7 °K
runkát, ki
-
war, wa
ARBITRARY UNITS
(0)

Castindo
H = 24.0 koe
r = 4.2°K
de
ARBITRARY UNITS
***
14
12
10
8
8
10
12
14
6 4 2 0 2 4 6
RELATIVE VELOCITY (mm/sec)
Iron-Ammonium Alum.
Figure 1
Avo (mm/sec)
20
0.25
0.50
a=0.67x104 HT
0.75
Figure ?
1.00
1.25 ;
ORN-OVG (:--0145
UNCLASSIFIED)
4.50
Avi (mm/sec)
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