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One-magnon and two-magnon Raman scattering in MnF2
Journal of Magnetism and Magnetic Materials 54-57 (1986) 1143S1144
ONE-MAGNON
AND TWO-MAGNON
114.1
RAMAN SCATTERING
IN MnF,
M.G. COTTAM Phy.vcs Department,
Unioersity of Essex, Cokhester,
CO4 3SQ. UK
and D.J. LOCKWOOD Nutwnal
Research Council, Ottawu KIA OR6. Cunudu
We report measurements of the one- and two-magnon Raman scattering in MnF2. The results for the magnon frequencies and intensities for temperatures up to 50 K are found to be in good agreement with theory. Values are deduced for the magnitudes of the magneto-optic coupling coefficients.
We report on new light scattering measurements from magnons in the rutile-structure antiferromagnet MnF,(S = 5/2, TN = 68 K.) These include the first observation of the very weak one-magnon Raman scattering [l], while for two-magnon scattering we extend previous work [2] by making a detailed study of the polarization dependence. A comparison with theory is made for each type of scattering. The Raman spectrum was excited with 760 mW of argon laser light at 476.5 nm. Light scattered at 90” was analyzed with a double monochromator at a spectral resolution of 1.8 cm-‘. The sample temperature was controlled to within 0.1 K and corrected for laser heating (= 0.7 K). In specifying the polarization, the X, Y. Z labels refer to the crystal a, h, c axes, respectively. The low-frequency Stokes spectrum of MnF, in Z( XZ)Y and Z(YZ)Y polarizations revealed a peak at 8.5 cm-’ that is assigned to scattering from k = 0 magnons. The linewidth (fwhm) increase from - 2.5 cm-’ at 4 K to = 6.5 cm-’ at 45 K. The integrated intensity for one-magnon scattering is observed to increase with temperature (see fig. la). and this behavior has been analyzed using a Green function theory [3]. The in-phase contribution to the Stokes intensity in zero magnetic field has been calculated including effects of coefficients K and G. representing, respectively, the magneto-optic coupling linear and quadratic in the spin operators. Theory curves are given in fig. la for (XZ) polarization, where the closest agreement is provided by curve W indicating that G/K = 0. This is confirmed by the weak polarization dependence of the intensity. from which we estimate that 1G/K 1= 10-s. This contrasts with FeF, [4], where G/K = 0.44 at 476.5 nm. The fit between theory and experiment can be improved by a smdl admixture of out-of-phase scattering, but we conclude that K is the dominant coupling constant in MnF,. Data for the temperature dependence of the magnon frequency are shown in fig. lb and compared with the predictions of a perturbation theory which takes account of the magnon-magnon interactions [5]. We have assumed HA a (9)” for the
0304-8853/86/$03.50
0 Elsevier
Science Publishers
temperature dependence of the small anisotropy field, where (S’) is the sublattice spin average and n is a positive index (see ref. [l]). The theoretical results for
MnF,
(a) n
1
10
I
20
30
40
50
TEMPERATURE (K1
+
5 (b)
t 41 0
1 10
20 30 40 TEMPERATURE (K)
L 50
Fig. 1. Temperature dependence of (a) the ‘Integrated intensity and (b) the frequency for one-magnon Raman scattering. The crosses and circles refer to (XZ) and (YZ) polarizations, respectively. The theory curves in (a) refer to different values of G/K: W, 0: X, 0.01: Y, 0.1.
B.V.
HnF,
Y
A
i?
0
z (YX) x (YZ) x (ZX)
d
:
8 .
Y
8
Y
.
I ~~~_~ z (XZ) Y
x
50
~~.~~-
_L
0.
60
40
20
TEMPERATURE
1 (dashed
II =
1 h. where latter not
(K)
line) and II = 2 (full
slightly
case. The
better of
line) are shown
agreement
one-magnon
because
only
is obtained
scattering
the
in MnFz
smallness
of
hccause
the
magneto-optic
estimate
it is
= loo-’ of the corresponding
FcF,
The
two-magnon For
magnon
integrated
= NO.
The
scattering spond
intensity
I>‘,+ and
adjustment
of
the expcrimentnl with
intensities temperature From
also
1R,/B, / =
(we
ble with
the in
parameters [7].
The
data.
and
r<’
in agreement
measurements
of
with the
in various
including
an analysis
We
shall
also
report
in MnF2,
sities
corre-
are shown
in fig.
as in ref. (61, from
difference
for by theor!.
parameters computed
experiment
III PI 131 [41
A
(within
even closer
(No-magnon
for
T i
on
Raman
further
scattering
where we have observed to the phonon
details
ot
of the damping.
frequencies
from
optic
spin-depenand inten-
T,.
two-magnon which
;fb determined
polarizations
to present
the above results,
dent contributions
symmetries
for FeF,.
we intend
phonons
as
1B,/B, 1= 0.14, 1B,/B, 1= 0.32. 1BJB, 1= 0.007 and are compara-
work
is
frequency
allows The
two-
In later
of the mag-
In the same notation
are
and
to
theory.
the exchange
Raman
much
the
0.66
magnitudes
coefficients.
those found
polarization
is well accounted
uncertainties) lj+
low temperature
with
is of
the
symmetries.
data
between these modes
of
ref. [h]. the results
in
the relative
coupling
Y polarization
polarizations.
I;+
and H,
scattering
ratio
Z( XZ)
frequencies
off-diagonal
exchange
the
deduced
but
coefficient
in Z( YX)I’ in
ha\e been compared
neutron
ment
is
neto-optic
small
H,,.
k’
~\e hate
the
is weak.
however.
at 8 K
scattering peak
in
to the
2. They
scattering,
example.
the one-mugnon
minor
coupling
in fig. in
).
stronger.
using
.,
.
Y
[51
agree-
integrated
increase
(see fig. intensities (as iii ref.
(61
Lvith 3). at
[h]).
[71
M.G. (‘ottam and D.J. Lockwood. Phyh. Re\. 831 ( 1985) 641. See l’or rumple U. Bducani and I’. Tognett~, Iii\. NUCNU C‘im. 6 (1976) 39. and references therein. M.G. Cottam. J. Phvs. CX (1975) 1933. D.J. L,ochuood. M.6. Cortam. V.C‘.Y. So and R.S. Katlyar. .I. Phys. Cl7 (1984) 6009. M.G. Cottam and R.B. St~nchcombe. J. Ph>s. (‘3 (1970) Dl.5. R.B. Stinchcomhe and T.L. Reinccke. Phys. Rev. H9 (1974) 3786. M.G. (‘ottam. V. So. D.J. Lockwood. R.S. K;rtiynr and H.J. Ciuggenhrlm, J. Phys. Cl6 (lYX3) 1741. A. Okaraki, K.C‘. Turherfield and R.W.H. Stevenson. Phys. Lett. X (1964) 9.
ONE-MAGNON
AND TWO-MAGNON
114.1
RAMAN SCATTERING
IN MnF,
M.G. COTTAM Phy.vcs Department,
Unioersity of Essex, Cokhester,
CO4 3SQ. UK
and D.J. LOCKWOOD Nutwnal
Research Council, Ottawu KIA OR6. Cunudu
We report measurements of the one- and two-magnon Raman scattering in MnF2. The results for the magnon frequencies and intensities for temperatures up to 50 K are found to be in good agreement with theory. Values are deduced for the magnitudes of the magneto-optic coupling coefficients.
We report on new light scattering measurements from magnons in the rutile-structure antiferromagnet MnF,(S = 5/2, TN = 68 K.) These include the first observation of the very weak one-magnon Raman scattering [l], while for two-magnon scattering we extend previous work [2] by making a detailed study of the polarization dependence. A comparison with theory is made for each type of scattering. The Raman spectrum was excited with 760 mW of argon laser light at 476.5 nm. Light scattered at 90” was analyzed with a double monochromator at a spectral resolution of 1.8 cm-‘. The sample temperature was controlled to within 0.1 K and corrected for laser heating (= 0.7 K). In specifying the polarization, the X, Y. Z labels refer to the crystal a, h, c axes, respectively. The low-frequency Stokes spectrum of MnF, in Z( XZ)Y and Z(YZ)Y polarizations revealed a peak at 8.5 cm-’ that is assigned to scattering from k = 0 magnons. The linewidth (fwhm) increase from - 2.5 cm-’ at 4 K to = 6.5 cm-’ at 45 K. The integrated intensity for one-magnon scattering is observed to increase with temperature (see fig. la). and this behavior has been analyzed using a Green function theory [3]. The in-phase contribution to the Stokes intensity in zero magnetic field has been calculated including effects of coefficients K and G. representing, respectively, the magneto-optic coupling linear and quadratic in the spin operators. Theory curves are given in fig. la for (XZ) polarization, where the closest agreement is provided by curve W indicating that G/K = 0. This is confirmed by the weak polarization dependence of the intensity. from which we estimate that 1G/K 1= 10-s. This contrasts with FeF, [4], where G/K = 0.44 at 476.5 nm. The fit between theory and experiment can be improved by a smdl admixture of out-of-phase scattering, but we conclude that K is the dominant coupling constant in MnF,. Data for the temperature dependence of the magnon frequency are shown in fig. lb and compared with the predictions of a perturbation theory which takes account of the magnon-magnon interactions [5]. We have assumed HA a (9)” for the
0304-8853/86/$03.50
0 Elsevier
Science Publishers
temperature dependence of the small anisotropy field, where (S’) is the sublattice spin average and n is a positive index (see ref. [l]). The theoretical results for
MnF,
(a) n
1
10
I
20
30
40
50
TEMPERATURE (K1
+
5 (b)
t 41 0
1 10
20 30 40 TEMPERATURE (K)
L 50
Fig. 1. Temperature dependence of (a) the ‘Integrated intensity and (b) the frequency for one-magnon Raman scattering. The crosses and circles refer to (XZ) and (YZ) polarizations, respectively. The theory curves in (a) refer to different values of G/K: W, 0: X, 0.01: Y, 0.1.
B.V.
HnF,
Y
A
i?
0
z (YX) x (YZ) x (ZX)
d
:
8 .
Y
8
Y
.
I ~~~_~ z (XZ) Y
x
50
~~.~~-
_L
0.
60
40
20
TEMPERATURE
1 (dashed
II =
1 h. where latter not
(K)
line) and II = 2 (full
slightly
case. The
better of
line) are shown
agreement
one-magnon
because
only
is obtained
scattering
the
in MnFz
smallness
of
hccause
the
magneto-optic
estimate
it is
= loo-’ of the corresponding
FcF,
The
two-magnon For
magnon
integrated
= NO.
The
scattering spond
intensity
I>‘,+ and
adjustment
of
the expcrimentnl with
intensities temperature From
also
1R,/B, / =
(we
ble with
the in
parameters [7].
The
data.
and
r<’
in agreement
measurements
of
with the
in various
including
an analysis
We
shall
also
report
in MnF2,
sities
corre-
are shown
in fig.
as in ref. (61, from
difference
for by theor!.
parameters computed
experiment
III PI 131 [41
A
(within
even closer
(No-magnon
for
T i
on
Raman
further
scattering
where we have observed to the phonon
details
ot
of the damping.
frequencies
from
optic
spin-depenand inten-
T,.
two-magnon which
;fb determined
polarizations
to present
the above results,
dent contributions
symmetries
for FeF,.
we intend
phonons
as
1B,/B, 1= 0.14, 1B,/B, 1= 0.32. 1BJB, 1= 0.007 and are compara-
work
is
frequency
allows The
two-
In later
of the mag-
In the same notation
are
and
to
theory.
the exchange
Raman
much
the
0.66
magnitudes
coefficients.
those found
polarization
is well accounted
uncertainties) lj+
low temperature
with
is of
the
symmetries.
data
between these modes
of
ref. [h]. the results
in
the relative
coupling
Y polarization
polarizations.
I;+
and H,
scattering
ratio
Z( XZ)
frequencies
off-diagonal
exchange
the
deduced
but
coefficient
in Z( YX)I’ in
ha\e been compared
neutron
ment
is
neto-optic
small
H,,.
k’
~\e hate
the
is weak.
however.
at 8 K
scattering peak
in
to the
2. They
scattering,
example.
the one-mugnon
minor
coupling
in fig. in
).
stronger.
using
.,
.
Y
[51
agree-
integrated
increase
(see fig. intensities (as iii ref.
(61
Lvith 3). at
[h]).
[71
M.G. (‘ottam and D.J. Lockwood. Phyh. Re\. 831 ( 1985) 641. See l’or rumple U. Bducani and I’. Tognett~, Iii\. NUCNU C‘im. 6 (1976) 39. and references therein. M.G. Cottam. J. Phvs. CX (1975) 1933. D.J. L,ochuood. M.6. Cortam. V.C‘.Y. So and R.S. Katlyar. .I. Phys. Cl7 (1984) 6009. M.G. Cottam and R.B. St~nchcombe. J. Ph>s. (‘3 (1970) Dl.5. R.B. Stinchcomhe and T.L. Reinccke. Phys. Rev. H9 (1974) 3786. M.G. (‘ottam. V. So. D.J. Lockwood. R.S. K;rtiynr and H.J. Ciuggenhrlm, J. Phys. Cl6 (lYX3) 1741. A. Okaraki, K.C‘. Turherfield and R.W.H. Stevenson. Phys. Lett. X (1964) 9.