Ferromagnetic relaxation in LPEgrown EuGa substituted yttrium iron garnet
films
B. Uma Maheshwar Rao, P. Mukhopadhyay, and C. M. Srivastava
Citation: J. Appl. Phys. 60, 3656 (1986); doi: 10.1063/1.337572
View online: http://dx.doi.org/10.1063/1.337572
View Table of Contents: http://jap.aip.org/resource/1/JAPIAU/v60/i10
Published by the American Institute of Physics.
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ferromagnetic relaxation in lPE-grown Eu-Ga substituted
yttrium iron garnet fUms
B. Uma Maheshwar Rao, P. Mukhopadhyay, and C. M. Srivastava
Advanced Center for Research in Electronics and Department of Physics, Indian Institute of Technology,
Powai, Bombay-400076, India
(Received 27 April 1985; accepted for publication 15 JUly 1986)
The magnetization, geff and linewidth AHII and AHl for l.iquid-phase-epitaxially grown thin
films ofEu" Y3 _ "Fes _ yGay0 12 (0.2 <;;;x <;;; 1.2; Y = 1.0) have been investigated in the
temperature range 85-420 K. AH versus temperature curves show maxima which occur at
about the same temperature as that observed in bulk single crystals of EuIG, but the width of
the curves is narrower in the LPE films. The temperature and composition dependence of geff
and AH have been explained on the basis of the three sublattice model and a new relaxation
mechanism based on anisotropic exchange.
I. INTRODUCTION
Thin
garnet
films
of
compositIOn
Eu" Y3_xFes_yGayOI2 (0.2<;;;x<;;;1.2, Y = 1.0) have been
grown on [111 J oriented gadolinium gallium garnet
(GGG) substrates using the liquid-phase-epitaxy (LPE)
technique. The dependencies of the ferromagnetic resonance
(FMR) Iinewidth AH andgeff on temperature and composition have been studied in the temperature range 85-420 K at
9.08 GHz. Due primarily to the presence of uniaxial anisotropy, the resonance linewidth in the parallel configuration
(AHII ) is not the same in the perpendicular (tJJfl ) configuration and the temperature dependence of these two
linewidths is different. The magnetization of these films as a
function of temperature can be explained satisfactorily using
the theory of Wolf and Van Vleck. 1
The goff of these LPE grown films increases with temperature, but not as steeply as in bulk europium iron garnet,
EuIG, single crystals. The goff varies from 2.0 to 1.0 when x
changes from 0 to 1.2. An explanation of the observed data
ong.ff , AHII ' and MIL has been attempted based on the effect
ofthe excited states on the ground state and the three sublattice model.
II. EXPERiMENTAL DETAILS
The garnet films were prepared using the LPE technique. A three zone kant hal A-I wound furnace has been
designed and fabricated for this purpose. It is a vertical furnace designed to give a 8-cm-Iong constant temperature zone
with a stability of ± 1 ·C at 11.00·C. Some of the measured
material parameters at 300 K for the films of compositions
Eu x Y3_xFe4,OGaI.0012 (x = 0.2,0.4,0.6,0.8) are given in
Table I.
The magnetization of the EuGa YIG films has been
measured as a function of temperature in the range 85-420 K
using a F arada y balance (George Associates). A typical resuh is given in Fig. 1 for EUO.6 Y2,4 Gal.o Fe4,0 12 ,
The resonance measurements have been made in the
temperature range 85-420 Kat 9.08 GHz using a Varian
E 112 spectrometer. The g.ff has been obtained using the relation z
°
(J)
3656
= reff{ [HII (1.25 HII
+ Hi) ]1/2 -
H II /2}.
J. Appl. Phys. 60 (10),15 November 1986
Here, HII and Hl are the resonance fields for the external
field parallel and perpendicular to the plane of the film and r
is the gyromagnetic ratio.
III. IRESULTS AND DISCUSSION
The results on magnetization, geff' Mill' and Mil and
their analysis is presented in this section. Some of these observations like that on magnetization and g.ff can be analyzed in terms of the existing theories. The observed temperature dependence of the linewidth, however, cannot be
explained on the present theories and a new relaxation mechanism based on anisotropic exchange interaction has been
proposed.
A. Magnetization
The dependence of Ms on temperature shown in Fig. I
for x = 0.6 can be explained on the basis of the three sublattice model. Following WolJ and Van Vleck, 1we assume that
the temperature variation of the magnetization of the iron
sublattices, Md and M a, in europium iron garnet (EuIG) is
the same as in yttrium iron garnet(YIG). In the present
study, when gallium is substituted on iron sublattices, the
temperature dependence of Md and Ma is a function of the
distribution of Ga on a and d sites. 3
For example, in {Y}c (Fe z _ y, Gay,) (Fe 3 _ y, Gay, )0 12
the magneton number at 0 K is given by4
no
= 5( 1 + YI
- Yz)Po,
(1)
and the Curie temperature, T c' is
T (
c
YI'Y2
) = 50-Y';2)(1-Y2/3) T (YIG).
5 ( +)
c
YI Y2
(2)
From Eqs. (1) and (2), we have estimated the distribution of Ga ions on a and d sites in our
Eux Y3 ... " Fe s .. yGay 12 films. From the estimates of Y I and
Y2 molecular field coefficients Aaa , Aad and Add have been
obtained by the method described by Roschmann and Hansen.} With these A values, an iterative procedureS has been
used to obtain the temperature dependence ofa and d sublattice magnetizations in these films. The magnetization of the
Eu3+ ion, M Eu ' has been obtained using the iron sub lattice
0021-8979/86/223656-05$02.40
°
@ 1986 American Institute of Physics
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3656
TABLE I. Measured material parameters at 300 K for YEuGaIG LPE films.
Composition
Thickness
Lattice
mismatch
h(JA.)
Au(A)
12.77
'2
195
200
200
190
2.92
magnetizations, Ma and Md in the expression obtained by
Wolf and VanVleck. 1
M Eu =
8N/l1
{
Ed 1 + exp( - E1/kBn]
X [1
+ (~
EI
8 E2 -EI
(Ho
K.
(10' erg/cm3 )
(G)
-0.018
- 0.0172
-0.015
2.49
2.43
ElIo.2 Y2.8 Fe•. o Ga, 00'2
ElIo.4 Y2.6Fe4.0Ga1.0012
ElIo.6 Y z.• Fe•.oGa1.0 0 12
ElIo.8 Yz.zFe•. oGa1.0 0
4-rrM,
+ 2Hex )
l)exp(~)]
kBT
+ ~ (3Ho + 2Hex )exp(
- EI)} .
(3)
16kBT
kBT
Here,E, are 0, 480, and 1330K forJ = 1,2,3, respectively,N
is the numberofEu 3 + ions per unit volume, Ho is the applied
magnetic field, and Hex is the exchange field given by Hex
= AMFe' where A is the molecular field coefficient and M Fe
is the net magnetization of iron sublattice. The M Eu values
obtained in the calculation were then subtracted from
(MrMa) to obtain the magnetization of EuYIGaG. The
computed curve for x = 0.6 is shown in Fig. 1. The exchange
constants used in the calculation have been obtained using
the Roschmann and Hansen) method and are as follows: Jaa
= 7.1 K, J ad = 30.7 K, and J dd = 16.5 K. The theory explains the experimental data satisfactorily for x = 0.6. The
agreement is equally good for other compositions as well.
In EuIG the effective magnetic moment per Eu) + ion at
OK is 0.81; /lB (Ref. 1), but in the present caseit is 0.08 /lB
This is due to the reduction in the magnetization of iron
sublattices because of Ga substitution. When M Fe decreases
because of Ga substitution it decreases Hex' which when
used in Eq. (3) yields a smaller value of M Eu'
yXlO
7
ilH
(Oe)
(rad s-'Oe-')
4
1.63
70
7.6
1.47
1.28
1.04
85
210
10.8
11.8
270
B. Effective 9 factor
The effectiveg factor measured at 300 K varies from 2 to
1 when Eu 3 + concentration, x, changes from 0 to 1.2, as
shown in Fig. 2. Further, the geff increases with temperature
for aU values of x as shown in Fig. 3 for x = 0.6. A number of
workers have attempted to explain the variation of geff with
temperature in EuIG, but all have met with only partial success. As shown below, these expressions for EuIG cannot
explain our data on thin films.
In the three sublattice models, the effective gyromagnetic ratio, refT is given by
reff =
M
S
(4)
(Mdlrd) - (Ma1ra) - (Mc1rc)
For EuIG, Le Craw et al. 6 find that rc is very large due to the
damping associated with the Eu 3 + ions. In that case, one has
geff =g(YIG) [Ms (EuIG)IMs (YIG)].
(5)
7
It has been shown by Sekerka that the temperature depen-
dence of geff in EuIG is described more satisfactorily by an
equation
(6)
Here, me (n is the temperature dependence of the reduced
c-sublattice magnetization.
Sinha and Le Craws have modified Eq. (6) on the basis
2.4
-
2
Theoretical curve
E_perimental points
1.6
200
4 TTMs
0.8
(G)
100
o
100
200
o
300
T 'K)
FIG. 1. Variation of
Ella.• Yz.4Fe•. oGa1.00'2 film.
3657
magnetization
with
temperature
J. Appl. Phys., Vol. 60, No. 10, 15 November 1986
0.4
0.8
1.2
x-
for
FIG. 2. Variation of geff with Eu 3 + ion concentration at 300 K.
Rao, Mukhopadhyay, and Srivastava
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3657
oftheir theory of magnon-phonon interaction for the relaxation in EuIG, according to them
golf =g(YIG)[1 - 0.45 Z(n-I),
(7)
TABLE II. The values of g, and gJ obtained as a function of x in
Y,_ ,EuxFe4oGaI.OO.2 films.
x
-gc
gJ
where
Z(T) = 1 + 3 exp( - 5OOIT).
(8)
The best fit among Eqs. (5), (6), and (7) is obtained
with Eq. (6) for EuIG.
None of these expressions agree with the data on EuGaYIG film shown in Fig. 3 for x = 0.6. To explore the
applicability of the three sub lattice model, Eq. (4) was used
relaxing the condition of Le Craw et 01. 6 that Ye is very large.
It is possible to have a reasonable fit to the experimental data
with Eq. (4) for EuIG if we assume a temperature independent Ye and gc = 15. The temperature variation of geff will
then come from the temperature dependence of a and d sublattice magnetization.
The ge values which fit the present data for different
values of x are given in Table n. It is significant that the
experimental values of ge for thin films are negative. In fact,
on account of strong LS coupling the c sublattice will have an
effective g factor given by ge = 2(gJ - 1). Using this relationgJ as a function ofx is calculated and given in Table II.
A theoretical curve based on Eq. (4) is drawn in Fig. 3.
The sublattice magnetization Mo, M d , Me have been obtained as discussed above, ga = gd = 2. ge has been taken to
be independent of temperature and its composition dependence is given in Table II. The agreement of experiment with
theory is satisfactory.
C. Linewldth
The theory of ferromagnetic resonance in rare-earth
iron garnets has been extensively discussed by several
workers. 9 - 12 This has been compared with results on bulk
single crystals. Very few studies on thin films have been reported so far.
The relaxation mechanisms operative in these systems
are broadly classified into two groups, one based on the
transverse or so called fast relaxation mechanism and the
other on the longitudinal (slow) relaxation mechanism. The
former was developed by de Gennes et 01.,9 while the latter
has been developed by Clogston,10 Teale and Tweedale, II
1.8
1.6
-
Thea. curve!
o
Exp. points
o
o
1.2
100
300
400
T (K)
FIG. 3. Variation of gdr with temperature for EIlo. 6 Y2 .• Fe•.o GaI.OO.2·
3658
J. Appl. Phys" Vol. 60, No.1 0, 15 November 1986
0.2
0.4
0.6
0.8
1.0
0.46
0.46
0.46
0.31
0.25
0.77
0.77
0.77
0.85
0.88
Van Vleck and Orbach, 12 Le Craw et 01., \3 Galt, 14 and Hartman-Bourtron. 15 In both mechanisms low temperature peak
is expected in the linewidth versus temperature curve. However, the frequency dependence of these curves is different
for the two mechanisms. In case of the fast spin relaxation
the resonance linewidth llH is proportional to the frequency
w over the entire temperature range, whereas in the case of
the slow spin relaxation mechanism, llH is proportional to
11w below the temperature T m, where the peak in llH occurs
and is proportional to w, above T m •
Le Craw et 01.13 have studied the ferromagnetic relaxation in bulk single crystals of EuIG, between 4 and 300 K.
The data above 300 K are not available. They have observed
Tm close to 240 K and have made an attempt to explain their
data on the basis of the slow spin relaxation mechanisms,
although they have not completely ruled out the presence of
the fast relaxation process. The two physical processes considered by Le Craw et 01. 13 for relaxation are (i) the interaction with the iron lattice magnons resonant with the transitions between J = 0 and J = 1 levels of the Eu 3 + ions and
(ii) the orbit lattice interactions between the three components of J = 1 level. The relative importance of (i) and (ii)
has been discussed by Huber, 16 who concludes that it is difficult to decide which of the two dominates in the case of
EuIG.
In an attempt to study the relaxation mechanism in thin
films with large uniaxial anisotropy we have carried out
FMR studies in our films. On account of the presence of
uniaxial anisotropy in these films, llHl! and llHl are different in magnitude for the same sample and their variation
with temperature also shows differences. Representative
data are shown in Fig. 4 and the general features are as follows:
(i) The linewidth versus temperature curves for both
AlII! and llH, general.ly contain two peaks in the temperature range 100-300 K for Eu concentrations varying from
x = 0.2-0.8.
(ii) The first peak T ~ for llH, ties around 215 K while
second T~ is around 255 K. For all compositions
(0.2<x < 0.8), T:" and T~ lie within ± 10 K of these vatues.
(ii) Close to Curie temperature, Tc,llH ll and llHl both
show abrupt increase in linewidth. This occurs within 30 K
of Te. Just below this temperature, the linewidth is almost
independent of temperature and the magnitude in this region
is approximately the same for both the parallel and perpendicular configurations. The magnitude of linewidth in this
Rao, Mukhopadhyay. and Srivastava
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3658
400
Q/
(10)
Here C is the ratio of Eu 3 + to Fe3 + ions and E1 is the
energy of the level measured from the ground' = 0 level.
In obtaining Eq. (9) we have replaced CUll the frequency of
the splitting of the level due to the crystal field used by Le
Craw et al. 13 by the exchange frequency splitting CUe.' which
is given by
'1
300
0
'1
::I:
<l
200
x = 0.8
CUe.
100
400
Q/
0
=
300
e.
Mi =
<l
i.
m 2 ( T)tanh (
T
1.2 m (T) )
T
200
0
lC
100
= 0.-'
1SO
x = 0.2
Q/
100
o
::I:
.to
<l
100
(12)
1 + 3 exp( - 480/T)
Equation (12) explains the observed dependence of Ml
on T only in the temperature region of 0-300 K. Above the
region in which the relaxation due to exchange splitting
ceases to dominate the linewidth is independent of temperature. Also, near Tc there is a sharp increase in Mi. It has
been shown by de Gennes et 01. 9 that the sharp increase in
Mi as we approach Tc occurs because a significant fraction
of spins begins to relax by the process of critical point fluctuation. In this process, the ferric spins flip locally. Contribution to the linewidth due to the spin fluctuations has been
calculated by de Gennes et 01. H and is given by
Q/
0
(11)
X _..:..ex...,!p...:,(_----:.4.:...80:.:.,/_T..:..}_
200
<l
(O)m(T),
where CUe. (0) is the exchange frequency at 0 K and m (T) is
the reduced magnetization of the resonant iron sub lattice (d
sublattice). Combining Eqs. (9), (10), and (11) we obtain
::I:
::I:
CUe.
-t.Hl
-t.HII
200
Mi
_ NBI(l + 1 )S(S + 1 )YAHO
MZT
(13)
flue -
FIG. 4. The vanatJon of AHII and t:.H, with temperature for
Eu xY3 _xFe4.oGaLoO,2(x = 0.2.0.4,0.6,0.8) films.
plateau region varies with Eu-ion concentration and is proportional to x.
Although, in the present case, the first peak at T ~ appears at the same temperature as in the case of bulk EuIG
single crystals, there is a distinct difference in the shape of
the two curves. The curve is sharper and shows two maxima
in the LPE films while there is only one broad peak in bulk
sample. An attempt to explain the present results in LPE
films on the basis of the theory of Le Craw et a/. 13 was not
successful since their theory yields a much broader curve
than what is observed. From this, it was concluded that the
processes (i) and (ij) described above are not dominant in
the LPE films. This is likely since uniaxial anisotropy which
is present in LPE films but not in bulk samples plays a dominant role in the dynamics of the spin system. It is likely that
because of the anisotropic exchange interaction the' = 1
level will be split. This splitting is temperature dependent
and in this case the linewidth can be written as
(9)
where N B and I are the number of the spins of the rare-earth
ion, H 0 is the resonance field, M ;, YA , and S are the magnetization, gyromagnetic ratio, and spin of the magnetic atoms
on the iron sublattice. Equation (13) can be written as
MiHu• = Ocu/MiT,
(14)
where 0 is a constant and cu = yAHo is the resonance frequency.
To obtain the existence of the plateau region in the Mi
vs T curves, we have to understand how the relaxation in the
200
o
o'"
100
200
T( K)
300
400
FIG. 5. The temperature dependence of AHi for ElIo.4 Y 26 Fe4.oGaI.OO'2
film. The solid line represents the theoretical curve drawn using Eq. (15).
where
3659
A
J. Appl. Phys., Vol. 60, No.1 0, 15 November 1986
Rao, Mukhopadhyay, and Srivastava
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3659
300~------------------------------~
between b.Hflux and x; but for low concentrations ofEu ions
it is reasonable to assume that this term also varies linearly
withx. In Fig. 6 we have plotted b.H as a function ofx at 300
K. A linear dependence as expected is observed.
200
QI
o
IV. CONCLUSION
.....
::I:
<I
100
o
0.2
0.6
x
0.8
FIG. 6. Variation of ttil1 with Eu·ion concentration, x, at 300 K.
spin system changes from that described by Eq. (12) to the
one given by Eq. (13). The transition from coherent mode
relaxation to an independent spin fluctuation would occur
gradually as the temperature is increased. We assume that a
fraction I (t) of spins relaxes by the coherent mode and
[1 -I (t) 1 relaxes by the fluctuating mode at any reduced
temperature t = T ITc. Here.! (t) is a function of t which
can be fixed from the experiment. It is obvious that at t = 0,
1(0) = 1, and at t= 1/(1) =0. Using this approach we
can express the linewidth as
MI = [1 - l(t) 1tlH.x
+I
(t)tlHfluc •
(15)
ExperimentaHy, we find the best fit with
l(t) = t4.
Here Mlex and b.Hfluc are given by Eqs. (12) and (13),
respectively. Figure 5 gives the theoretical curve based on
Eq. ( 15) along with the experimental points for
EUo.4 Yz.6Fe4.0GalOOI2 for MIL' The general features of the
experimental curve are satisfactorily expJ.ained. The plateau
in MI vs T curves near Tc occurs because the exchange contribution begins to fall in this region while the contribution
from fluctuations increases, thereby making MI independent of T in this region.
The composition dependence of MI is easy to explain.
As we vary the Eu concentration, c in Eq. (9) increases linearly with x. We cannot arrive at any simple relationship
3660
J. Appl. Phys., Vol. 60, No. 10,15 November 1986
The magnetization, rolf' MIll' and MIL for LPE grown
thin films of composition Eu" Y3_xGal.oFe4.0012 have been
studied. in the temperature range 85-400 K and with x varying from 0.2 to 0.8. The gyromagnetic ratio is found to depend on both temperature and composition and the dependence has been explained on the basis of the temperature
variation of the three sublattices and the dependence of the g
factor of the c sublattice on composition. The magnetization
follows the usual temperature dependence based on the three
sublattice analysis. The analysis of the linewidth shows that
exchange splitting of the excited state J = 1 is the dominant
mechanism of relaxation in thin films below Tc. Another
process which contributes to the linewidth near Tc through
critical point fluctuations has also been considered. Using
these two contributions the temperature dependence of
linewidth in thin films has been satisfactorily explained.
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( 1965).
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Rao, Mukhopadhyay, and Srivastava
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3660