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TEEFEE FE
01:25
14 LE
MICROCOPY RESOLUTION TEST CHART
NATIONAL BUREAU OF STANDARDS - 1963
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ORN 0-3230
CONF-670812--2
4 MASTER
HYPERFINE STRUCTURE COUPLING TO 197 AU IN AuMn AS A FUNCTION OF PRESSURE*
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***
**
J. OThomson,
****
D. 0. Patterson,
Paul G. Huray,
and Louis D. Roberts
Oak Ridge national Laboratory
and the
University of Tennessee
University of Tennessee
H.C. $23.00; MN_.65
H.C
M
Many studies have been made of the properties of alloys of the noble
metals in transition metals. The magnetic properties of these systems are
often of special interest and much information has been obtained about the
contribution or the transition element to these properties.
The contribu-
Womat
w
tion of the noble metal to the alloy properties has been relatively diffi-
cult to investigate experimentally, however, and comparatively little is
known about the role of the noble metal in determining the properties of
these materials. In this connection, the Mössbauer effect for 19 Au may
be used to carry out unique studies of alloys and compounds of this noble
metal with the transition elements. Mössbauer measurements on Au in
the intermetallic compound Au, Mn are of particular interest.
Au, Mn is an ordered alloy whose magnetic properties have been studied
by neutron diffraction, 2,5 magnetic susceptibility,2,3 galvanomagnetic,
and resistance techniques.* Neutron diffraction and X-ray investigations
have established that the crystalline structure of this alloy is a layered
tetragonal lattice of the Cac, type with the magnetic moments of the man-
ganese atoms aligned ferromagnetically in planes perpendicular to the
c-axis but having a rotation of approximately 50° between successive planes
at 295°K, thus forming a helical structure as is shown in Fig. 1.
It has further been found that this turn angle is dependent upon
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temperature, pressure, and applied magnetic field, and it has been indi-
cated that the alloy becomes ferromagnetic at room temperature with a pres-
sure of 11 kbar* at zero applied magnetic field, or with an applied field
of 9.6 koe at zero pressure. The nature of the interaction between the
manganese layers which produces this spiral structure has not yet been
determined. This interaction must involve the intervening gold layers
ORNI - AFC-naririni
and it is thus reasonable to expect that a measurement of the monopole,
magnetic dipole, and electric quadrupole interactions of the gold nuclei
with their electronic environment should yield information about the mecha-
nism which produces the spiral structure.
Figure 2 shows the measured hf's splitting of the 77.4 keV resonance
gamma ray of 19 Au în Au, Mn at zero applied pressure. The solid curve
drawn through the data points is a least squares fit of the appropriate
upin Hamiltonians to this data.
The selection of these Hamiltonians was based on the following rea-
soning.
If one assumes that the magnetic moments of the gold atoms are
oriented normal to the c-axis, as are the manganese moments, then the effec-
tive magnetic field at the gold nuclei will also be oriented perpendicular
to the crystalline c-axis. Since every gold atom lies between a plane of
gold atoms and a plane of manganese atoms, one would expect the principal
axis of any electric quadrupole coupling at the gold nucleus to be along
the crystalline c-axis.
Under the above assumptions one is confronted with the problem of
solving for the energy eigenvalues for a magnetic dipole moment in a mag-
netic field and an electric-quadrupole moment in an electric field gradi-
ent, -q.
Thus the Hamiltonian for the system is
84 = 8BÆT + ( 314 - I(I + 1)]
(1)
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M
1 2I - Il
where p =
- 16 the quadrupole coupling constant and we = 1
1(21 - 2
21 + 2
where Q is the intrinsic electric-quadrupole moment of the nuclear charge dis-
tribution. Since the magnetic field at the gold nucleus 16 assumed to lie in
the plane perpendicular to the c-Exis, H.I = HIVThe ground state nuclear
spin for 19 Au is I = 3/2 while the excited state has a nuclear spin of
I* = 1/2. Therefore the Hamiltonian for the ground state 18
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: 78
+
372 - 1)
(2a)
N
and for the excited state 1.8
He -- 2* **+ DET,
(26)
where y and id* are the ground and excited state nuclear magnetic moments.
The quantity AE, is the isomer shift. It is related to the monopole
interaction between the nucleus and the electron charge distribution.'
If one solves the eigenvalue problems for the Hamiltonians, Eqs. 2a
and 2b, it will be found that there are four eigenvalues for H4 and two
eigenvalues for He. These eigenvalues are •
-[ + (912 - 62 + 4)*]
-- }##[ -1+ ( 942 + 6 + 4)%]
(3a)
$4. [ +1 - 1942 - 6 + 4)*]
28--}# ( -2- ( 922 +62 + 4)*]
48, + v*
987-w*
hat
LEGAL NOTICE
(30)
The report me prepared as an account of Government sponsored work, Nolther the Valtod
States, por the Commission, nor any person noting on behalf of the Commission:
A. Makes any warranty or representation, expresand or implied, with respect to the accu-
rioy, completeness, or unehulpelo of the information contaiand in the report, or that the wo
of any information, apparatus, method, or proces, disclosed in this report may not Infringo
prinuly owned righto; or
B. AssumoI LAy Ilabilluns with respot to the une of, or for denega romuns from the
un of any information, apparibus, method, or procon dioolowed in this report.
As und in the above, "person sotiag on behalf of the Commission" Includes any on-
ploys or corrector of the Commission, or employee of ouch cuntractor, to the extent that
such employs or contractor of the Commission, or employs of such contractor preparu,
dlonninates, or provides access to any information pursuant to his employmuat or contract
with the Commisolon, or alo employment with such contractor.
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where 1 = gol
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A schematic representation of this energy spectrum is shown in Fig. 3. The
region of the diagram denoted by (a) represents the unsplit energy levels
of the ground and excited states including only the Mössbauer isomer shift
A Ex. Region (b) represents the same states when one considers the pres-
ence of a magnetic dipole interaction. (These levels can be seen quantita-
tively by setting 1 = 0 in Eqs. (3)). Region (c) represents the situation
with both the magnetic and quadrupole interactions taken into account.
Shirley, Kaplan, and Axle (9) have given the result that the 77 keV
y ray of 19 Au has an E2/ mixing ratio of 0.11 $ 0.01. Therefore, one
obtains an 8 line spectrum corresponding to the selection rule Amp =
0, † 1, $ 2.
Furthermore, in region (c) the simultaneous presence of
magnetic and quadrupoje interactions with perpendicular axes introduces
a mixing of substates and thus any given ground state level cannot be com-
pletely associated with a single magnetic quantum number.
Referring again to Fig. 2, as was mentioned, the solid linė through
the data points is the least square fit for the sum of 8 Lorentzian lines
which is constrained to satisfy eigenvalues given by Eqs. (3. and Fig. 3,
but where the values of */H, H, 1, AE, and the line width 2r are
left as variable parameters. Each individual line is also shown. The
line intensities were also variable parameters but were constrained by
pairs such that I1 = Ig, Ia = Iy, Iz = Ig, and I4 = Is. The values
obtained for these parameters are: 2u^H = 16.130 $ 0.05 mm/sec, H* =
0.420 $ 0.004 nm, H = 1568 i 15 kgauss, 2 = 0.24 $ 0.01, AE, = 2.79 + 0.02
ram/sec referred to metallic gold, 2r = 2.06 = 0.04 mm/sec, and the line
intensities I2 = 0.26 € 0.03, I2 = 1.04 € 0.03, I3 = 1.85 € 0.04 and
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Ij = 2.62 $ 0.04.
The latter correspond to the relative intensities
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0.100 + 0.012, 0.398 $ 0.013, 0.709 † 0.019 and 1.000.
For ^ small compared to 1, and for the mixing ratio given in refer-
ORNI - AC - DEFICIA
ence 9, the relative intensities to be expected theoretically are 0.087
0.391, -0.696, and 1.000 which are in good agreement with our measurements.
The line width 2 = 2.06 1 0.04 mm/sec is in agreement with our previous
measurements of the natural line width for this gamma ray. Also because
of the very good fit obtained for Eys. (3) to the experimental data, it
was possible to obtain it and I to a precision of 1% and 24 H to a pre-
cision of o
The applicability of this spin Hamiltonian to the experimental data
gives one a useful tool for the investigation cî A, , AE, and of 2uºn as
a function of sample environment as well as of the atomic environment of
the gold. In fig. 4 we give results of measurements of H (in terms of
2u*) and of AE, as a function of applied pressure. A Bridgeman anvil
apparatus which has been described previously was used for this work.
Ty measurements were made at 4.2°K.
The spectra obtained under pressure were comparable to that shown
in Figure 2 at zero pressure, except that the statistical accuracy was not
so high because of the reduced count rate available through the B, C anvils.
At the highest pressures, a broadening of the individual lines was observed
which was slightly outside our experimental error in 2r of a few per cent.
This line broadening was due to pressure inhomogenieties and some cold work,
but the evidence available leads us to believe this cold work does not affect
H(p).
As may be seen from Fig. 4, the magnetic field increases by about 8%
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between zero pressure and 25-30 kilobars where, within error the fieid increase
saturates. This 8% increase of H is one of the largest changes of a phys..cal
parameter which has been observed due to the application of pressure to a
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solid in this pressure range.
In previous high pressure measurements on gold
it was shown that
the charge density at the gold nucleus is related to the isomer shift by
. 19 4120960.12.14. + 2)
T4 Aurore
where 14 ur loy(0)22 and 14 Auroyle are the charge densities of the gold
nucleus in the alloy and in pure gold. In Fig. 4 this parameter is seen to
change by about 2% between zero pressure and 30 kbars applied pressure. Thus
the magnetic field at the gold nucleus increases by a inuch larger percentage
than the charge density.
If we suppose that the magnetic field at the gold nucleus is due to
magnetization M of the conduction electrons, then one would expect that
#~M. 14 r.s.coope.
where
the wave function at the Au nucleus for a Fermi surface
electron in the alloy. Then
where p is the applied pressure.
If we also suppose that 147.5.(0)2 18 proportional to 14 alloyroje,
then the principal contribution to the comes from an increase of M. with
pressure. It seems reasonable to assume that this increase of M with pres-
sure is due to the corresponding uncoiling of the manganese spin spiral..?
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'OPN!, AfroOFF GAM
REFERENCES
ORNĮ = AEG=OFFICIAL
Research sponsored by the ü. S. Atomic Energy Commission under contract
with the Union Carbide Corporation.
**Consultant, now at Memphis State University, Memphis, Tennessee.
Oak Ridge Graduate Fellow from the University of Tennessee appointed by
Oak Ridge Associated Universities.
Oak Ridge Graduate Fellow from the University of Tennessee appointed by
Oak Ridge Associated Universities.
Present address:
Texas Instruments, Inc., Dallas, Texas.
1. Herpin, A., Meriel, P., and Villain, J., .C. R. Acad. Sci., Paris
249, 1334 (1959).
2. Meyer, A. J. P., J. Phys., Paris 20, 430 (1959).
3. Meyer, A. J. P., and Taglang, P., J. Phys., Paris 17, 457 (1956).
4. Grazhdankina, N. P., and Rodionov, K. P., Soviet Physics JETP 16,
1429 (1963).
5. Smità, F. A., Bradley, C. C., and Bacon, G. E., J. Phys. Chem. Solids 27,
925 (1966).
6. Herpin A., and Meriel, P., J. Phys., Paris 22, 337 (1961).
7. Roberts, L. D., Becker, R. L., Obenshain, F. E., and J. 0. Thomson,
Phys. Rev. 137, A895 (1965).
8. Parker, B. M., J. Chem. Phys. 24, 1096 (1956).
9. Shirley, D. A., Kaplan, M., and Axel, P., Phys. Rev. 123, 816 (1961).
10. Roberts, L. D., Patterson, D. O., Thomson, J. O., and Levey, R. P.,
ORNL Physics Division Annual Progress Report 3924, 116 (1965).
i
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Omul-AFC-UFMOAL :
#
- ... .
a mamma occa.
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C AXIS

BODY-CENTERED TETRAGONAL
SPIRAL STRUCTURE OF
MANGANESE SPINS IN Aug Mn
Auz Mn
O Au
o Mn
rug. 2
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1.01
T
1
2
3
4
5
6
7
8
1.0
PA
als
0.99
RELATIVE INTENSITY
0.98
0.97
Auzon
0.96
INCREASING GAMMA RAY ENERGY
0.95 LI
14
4
_ L
-4
-8
-12
DOPPLER VELOCITY (mm/sec)
Fig. 2. Hyperfine splitting of the 77.4 keV resonance gamına ray for 19 Au
in Au, n.
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m* =
12

24* H
-
AE,

i
m* = +12
77 kev
FROM AU IN Pt
SOURCE

m = -3/20
1 3
m=-1/2,4
T
-
-
m=+1/2 -
m= + 3/29

3uH
HI
la
16)
(0)
Fig. 3. Energy level diagram for the ground and first excited states of
the 19' Au nucleus, (a) in zero fiela, (b) in a magnetic field, and
(c) in the crossed electric and magnetic fields which occur in
Aug Mi.
IVDUATU-Wov - TVOU
18.0
.
.
---
-
..
-
-
-
--
---
-
-
---------------
17.5
Zlect Here (mm/sec)
-
PRESSURE
(k bars)
O
Heff
(kgauss)
1568+30
1630+32
1690+33
I
l
15.4
31.1
-
16.0 L
1.40
alco, M0110m
1.35
-
-
-
-
-
.
. -
-
-
.
..
-
2160) A = d.
(Estil
P = 18.0
l
30
2
50
0 10 20 30 40
APPLIED AVERAGE PRESSURE (kbars)
24* Heff and P for 197 Au in Aug Mn as a Function of
Pressure.
Fig. 4.
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