Exchange constants in ferrimagnetic garnets
C. M. Srivastava, C. Srinivasan, and R. Aiyar
Citation: J. Appl. Phys. 53, 781 (1982); doi: 10.1063/1.329990
View online: http://dx.doi.org/10.1063/1.329990
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Published by the American Institute of Physics.
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Exchange constants in ferrimagnetic garnets
c. M. Srivastava, C. Srinivasan, and R. Aiyar
Department 0/ Physics, Indian Institute o/Technology, Bombay-400 076, India
(Received 27 February 1981; accepted for publication 28 April 1981.)
The exchange constants J IT J TR' and J RR in the garnet series R3FeSOl2 (R = y3+, Gd3+, 103+,
D y3+ , Ho3+ , Er3+ , Tm3+ , or Yb 3+) have been obtained using the molecular field approximation.
The low-temperature magnetization data for all the garnets except Y and Gd garnets have been
fitted assuming a temperature-dependent canting on the rare-earth sublattice. These exchange
constants are found to be comparable to those obtained for the rare-earth intermetallic R Fe4 AIg.
PACS numbers: 75.30.Et, 75.50.Gg
The exchange constants in ferrimagnetic garnets,
R3FeS012 (RIG), where R is y3+ or a rare-earth ion have
been obtained by many workers 1-3 from the data on saturation magnetization Ms or inverse susceptibility X-I, but the
same set of exchange constants has not been used to fit both.
We have attempted to fit both the Ms and X - I data using a
- - TheorotlCal cur.e (Present work I
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single set of exchange constants for the garnet system
R3 Fe S0 12 (R = y3+, Gd 3+, 103+, D y3+, H0 3 +, E~+,
Tm 3 +, or Yb3+). This is important since it is shown by Srivastava et al. 4 that Ms vs T data could be fitted with more
than one set of exchange constants, and the same is true for
X - I vs T data. The data on YIG and GdIG could be fitted
assuming collinear spin arrangement, but in the case of other
rare-earth garnets the saturation magnetization calculated
at 0 1<. from the N~el model is different from that observed
experimentally. This discrepancy has been attributed by
Dionnes to canting within the c sublattice, which is assumed
to arise from the strong anisotropy field of R 3 + ions in comparison to the exchange field on the c sublattice. However,
his assumption of constant canting from 0 OK to the Curie
temperature Tc is not justified since the anisotropy fields and
the Weiss molecular fields are temperature dependent. We
have shown that the canting angle decreases with tempera.
ture, at a temperature less than Tc it falls to zero, and above
this temperature the spins are collinear. It has also been
shown that the magnitude of the exchange constants for garnets is similar to that of R Fe4AIs intermetallics.
The method of calculating exchange constants from the
data on Ms and X - I for a three-sublattice collinear system is
discussed by Srivastava et al. 4 and has been followed here.
Th.oretical cur.. (pres.nt work I
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FIG. 1. Theoretical and experimental curves of (a) magnetization and (b)
inverse susceptibility of yttrium iron garnet (YIG). The theoretical curve
has been calculated from the exchange constants listed in Table I.
781
J. Appl. Phys. 53(1), January 1982
He
FIG. 2. Canting angle as a function of temperature for the rare-earth iron
garnets. The canting angle is calculated from the experimental data on magnetization and the exchange constants listed in Table I.
0021-8979/82/010781-03$02.40
@ 1982 American Institute of Physica
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781
TABLE I. Exchange constants in ferrimagnetic garnets {R 3 Fe,O'21 and rare-earth-transition-ion intermetallics (R Fe4 AI.I.
R
J aa
Y
Gd
Tb
Dy
Ho
Er
Tm
Yb
-
J ad
6.45
6.45
6.45
6.45
6.45
6.45
6.45
6.45
-
J dd
30.40
30.40
30.40
30.40
30.40
30.40
30.40
30.40
-
Garnets (values in KI
J ae
12.05
12.05
12.05
12.05
12.05
12.05
12.05
12.05
0
- 0.60
-0.56
-0.99
-0.66
-0.54
-0.44
- 3.0
J de
J"
0
- 1.8
- 1.01
- 0.99
-0.70
- 0.68
-0.66
- 2.3
0
0
0
0.\0
0
0
0
-0.04
Intermetallics a (values in KI
J RR
J RT
0
0
0
0
0
0
0
-4.1
- 2.1
- 1.5
-0.7
- 0.9
-0.4
- 2.7
In
-
27.72
27.72
27.72
27.72
27.72
27.72
27.72
aK. H. 1. Buschow and A. M. Van der Kraan, 1. Phys. F 8,921 (19781.
Since Te amongst the rare-earth iron garnets is approximately constant it can be assumed that the transition-ion-transition-ion interaction J TT' which is the dominant interaction,
remains constant throughout the series. We have obtained
J aa , J ad, and J dd from the data on YIG and assumed it to be
the same for the rest of the garnets.
The theoretical curves of Ms vs Tand X-I vs Tfor YIG
is given in Fig. 1 along with the experimental points from
AI~onard, 3 Pauthenet, 6 and Geller. 7 The fits obtained for the
other garnets are also equally good.
In the case of garnets other than YIG and GdIG the
saturation magnetization at 0 oK cannot be explained by a
collinear model. Dionne5 accounted for this by assuming a
canting on the c sublattice, but he assumed a canting angle
independent of temperature. In order to fit the magnetization data for these garnets the same method as discussed by
TABLE II. Comparison of exchange constantsJ (Fe' , -Fe" 1in garnets and
spinel (Fe,O.1 with comparable bond angles and bond lengths.
90'
Tetra-tetra
interaction
180'
Octa-tetra
interaction
System
Y,Fe,O"
Fe,04
- 30.4
- 28
- 12.05
- 21
From Anderson's
theory"
- 28
-14
'c. M. Srivastava, G. Srinivasan, and N. G. Nanadikar, Phys. Rev. B 19,
49911979).
TABLE III. Values of canting angles at 4.2 K for garnets from neutron
diffraction data and M, vs T fitting Ipresent work).
Canting angle in degrees
Neutron diffraction data
M, data
(two cones)
(average)
Dy
Ho
Er
Yb
38
63
43
40
3 .,
29 h
5"
25 .,
35
44
48
63
·'S. 1. Pickart, H. A. Alperin, and A. E. Clark, 1. App\. Phys. 41, 1192
(1970).
hA. Herpin, W. C. Koehler, and P. Meriel, C. R. Acad. Sci. (paris) 751, 1359
11960).
782
J. Appl. Phys., Vol. 53, No.1, January 1982
Srivastava et al. 4 has been used except that the c sublattice
magnetization is assumed to be canted by an angle a with
respect to the a and d sublattice magnetizations. The variation of a with temperature has been calculated for all these
garnets and is shown in Fig. 2. Table I shows the values of the
exchange constants for these garnets obtained from Ms and
X - I data.
The J TT interactions in these garnets are dominant
while J RT and J RR are one order of magnitude smaller than
I n · This is understandable since the spatial extensions off
electrons is small and these are also shielded by the outer
electrons.
Similar to J IT interactions in garnets there are interactions in spinel ferrites with identical transition series ions
and ligand ions and approximately the same bond angles and
bond lengths. These interactions can then be compared and
as shown in Table II these are nearly the same.
The garnets with R 3 + ions from Tb 3 + to Yb 3 + have
their c sublattice moments canted with respect to the a and d
sublattices. Several neutron diffraction studies of these garnets K- IO support our estimates of the canting angle as shown
in Table III. Our conclusion that the canting angle is dependent on temperature is supported by the results ofTscheou II
and Kuzminov et al. 12 on TbIG. The former find that at 4.2
K there is canting on the c sublattice while the latter find that
there is no canting from 77 OK to Tc.
We have compared the values of exchange constants for
garnets with those ofthe intermetallics R Fe4 AIg obtained by
Buschow et al. 13 These are shown in Table I. The behavior of
J de as thefsubshell gets filled from Gd+ 3 to Yb 3 + is similar
to the behavior of J R-Fe in the intermetallics. The value of
J Fe -Fe in the intermetallic is - 27.72 K, while in the garnets
it is - 30.4 K. These are quite close in spite of the different
mechanisms of magnetic ordering in the alloy and the
garnet.
1E. E. Anderson, Phys. Rev. A 134, 1581 11964).
'G. F. Dionne, 1. Appl. Phys. 41, 487811970).
'R. AI~onard, 1. Phys. Chern. Solids 15,16711960).
4c. M. Srivastava, G. Srinivasan, and N. G. Nanadikar, Phys. Rev. B 19,
49911979).
'G. F. Dionne, 1. App\. Phys. 47, 4220 11976).
OR. Pauthenet, Ann. Phys. (Paris) 3, 424 (1958).
7S. Geller, 1. P. Remeika, R. C. Sherwood, H. 1. Williams, and G. P. Espin-
Communications
Downloaded 01 Mar 2012 to 14.139.97.76. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions
782
oza, Phys. Rev. A 137,1034 (1965).
"S. J. Pickart, H. A. Alperin, and A. E. Clark, J. Appl. Phys. 41,1192
(1970).
9 A. Herpin, W. C. KOehler, and P. Meriel, C. R. Acad. Sci. (Paris) 751,
1359 (1960).
783
J. Appl. Phys., Vol. 53, No.1, January 1982
'Oy. Allain, M. Bichara, and A. Herpin, J. Appl. Phys. 37,1316 (1966).
"F. Tscheou, Thesis, University of Grenoble France, 1966 (unpublished).
l2y. S. Kuzminov, N. V. Belov, and I. I. Yamzin Kristallografia, 8, 21
(1963); 9, 204 (1964).
13K. H. J. Buschow and A. M. Vander Kraan, J. Phys. F 8, 921 (1978).
Communications
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783