Download (111) direction : molecular field parameters

Magnetic study of the terbium iron garnet, Tbig, along
the easy (111) direction : molecular field parameters
M. Guillot, H. Le Gall
To cite this version:
M. Guillot, H. Le Gall. Magnetic study of the terbium iron garnet, Tbig, along the easy
(111) direction : molecular field parameters. Journal de Physique, 1977, 38 (7), pp.871-875.
<10.1051/jphys:01977003807087100>. <jpa-00208650>
HAL Id: jpa-00208650
https://hal.archives-ouvertes.fr/jpa-00208650
Submitted on 1 Jan 1977
HAL is a multi-disciplinary open access
archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d’enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.
LE JOURNAL DE PHYSIQUE
TOME
38,
JUILLET
1977, ,’.
871
Classification
Physics Abstracts
8.500
MAGNETIC STUDY OF THE TERBIUM IRON GARNET, TbIG,
ALONG THE EASY (111) DIRECTION : MOLECULAR FIELD PARAMETERS
M. GUILLOT
C.N.R.S. Laboratoire Louis
Néel, BP 166 X, 38042 Grenoble Cedex, France
and
H. LE GALL
C.N.R.S., Laboratoire de Magnétisme et d’Optique des Solides, 92190 Meudon Bellevue, France
(Reçu le 12 janvier 1977, revise le 18 mars 1977, accepté le 30 mars 1977)
Résumé. 2014 Des mesures d’aimantation et de susceptibilité effectuées sur le ferrite grenat de terbium, TbIG, suivant la direction (111), conduisent à une température de Curie et à une constante
de Curie très différente des valeurs précédemment obtenues par Pauthenet dans des échantillons
polycristallins. L’effet de champ cristallin reste très important dans toute la gamme de température
étudiée, 4,2-295 K. Les coefficients de champ moléculaiie représentant les interactions d’échange
sur
l’ion terre
rare sont
calculés.
Abstract.
Magnetization and susceptibility measurements, over the range 4.2-295 K have
been made on single crystal TbIG along the (111) direction. The paramagnetic Curie point and the
Curie constant are markedly different from the values established by Pauthenet in polycrystalline
samples. The effects of the crystalline field are found to be important over all the temperature range
studied. From the experimental results, we deduce molecular fields parameters representing the
magnetic interactions on the rare earth sublattice.
2014
1. Introduction.
The classical work by Pauthenet
(1958) on the magnetization of the rare earth iron
garnets was carried out on polycrystalline materials [1]. We believe it is the only determination of
the exchange fields parameters acting on the rare
earth ions.
This determination was obtained from the magnetic
susceptibility value at the compensation temperature.
Later (1965), the large anisotropy introduced by most
of the rare earth ions was established when single
crystals of high purity became available [2, 3, 4]. All
the low temperature spontaneous magnetization values
given in these references are higher than those reported
by Pauthenet but no indications about magnetic
susceptibility and exchange parameters were presented
In this situation, it is very difficult to analyse magnetooptical effects such as Faraday rotation, the theoretical study showing than one expects the effect
caused by each magnetic ion to be proportional to
its magnetic moment evolution in a wide range of
circumstances (especially temperature and magnetic
field dependences) [5].
-
Experimental. In this paper, we report results
of our study of the magnetic behaviour of TbIG
2.
-
when the applied field is parallel to the easy (111)
direction. Magnetic measurements were made over
the temperature range 4.2-295 K with a Foner magnetometer in fields up to 15 k0e. The single crystal
sphere is apparently saturated at 3 k0e at liquid
helium temperature. Above this temperature, saturation is not attained. The figure 1 gives some typical
magnetization curves for different temperatures; the
variation of the moment versus field is linear. To
determine the spontaneous magnetization of the ferrite
written MTbIG (corresponding to two formula units
Tb3Fe5012), we extrapolate the magnetization curves
0 (the use of single crystal avoids the treatto Ha
ment adopted by Pauthenet of extrapolation to infinite fields which may be doubtful). Magnetization,
MTHIG, versus temperature is plotted in figure 2.
At low temperature, our values do not differ markedly
from results obtained by Harrison [4] and Geller [3].
The compensation point value, 249 K, is 3 degrees
higher than previous determinations [1, 3]. Figure 3
shows the temperature variation of the inverse of the
susceptibility, x, for one gram molecule and also the
values given by Pauthenet [1]. Faraday rotation measurements and a magnetooptical effects analysis will
be presented in a subsequent paper.
=
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01977003807087100
872
FIG. 3.
earth
- Temperature variation of the rare earth sublattice
magnetization along the [111] direction.
spins
tilt very
to lie
on a cone
slowly
away from the easy axis
axis is (111) and the
(the
angle is 300) [6]. In his original paper Neel
envisaged a partitioning of the magnetic moments
into three sublattices, which are aligned parallel or
antiparallel to each other because of their mutual
interactions [7]. In TbIG, the (111) direction is the
only one for which the molecular field calculations
neglecting the strongly anisotropic action of the
crystal field and the exchange field are convenient.
The Fe + 3 ions, in the two different sites (a) and (d),
are strongly coupled antiferromagnetically by their
(111)
cone
inclination
FIG. 1.
-
curves in range 4.2-294 K, along [111] direction
for TbIG in external field up to 15 k0e.
(M, H)
own
earth
mutual interactions. The moment of the rare
(site c) is antiparallel to the resultant Fe
magnetization [8].
Considering the relatively weak interactions ac
and dc between the rare earth and iron ions, we adopt
the usual method of determining the Th" sublattice
magnetization, M,,,, by subtracting the magnetization of YIG from that of TbIG. Using the magnetization values, MyIG, obtained experimentally (magnetization [9], RMN [10]), we deduced the thermal
variation of Mr (Fig. 4, Table I). At temperature
44.66 JlB
near 0 K, the effective moment Me(T -+ 0)
is
than
lower
(7.44 liB per ion) considerably
expected
value for the 7F6 state of six free ions Tb+3 (54 IzB);
note the spin only value is equal to 36 PB. This result
confirms that the Tb + 3 ion is exposed to the crystalline
field produced by the surrounding dodecahedral
0-’ ions. Previous determinations gave 46.4 JlB [3]
and about 45 PB [4].
=
FIG. 2.
-
Variation of the spontaneous magnetization
temperature for TbIG along [111] direction.
versus
3. Discussion.
First, let us remark that in TbIG
the spins are all aligned along the (111) axis in the
70-300 K range. In the vicinity of 70 K, the rare
-
If
we
suppose the
rare
to be the same
earth environment in the
polyhedron of oxygen ions as
in the ferrite, it should exhibit the same quenching
properties. In pulsed magnetic field up to 200 kOc,
one of us has measured at 2.6 K for the gallate of
terbium a magnetic moment equal to 47.5 ± 1 JlB
gallate
873
from the two curves that the thermal variation of the inverse of the susceptibility disagrees
markedly with the free ion Curie Weiss law as found
by Pauthenet. In the second place, the value of the
paramagnetic Curie point, 0p (defined by extrapolation
to zero of the 11x line), - 40 K, is five times larger
than the measured value for polycrystalline materials.
In a subsequent paper, we will show that the evolution
of the Faraday rotation TF with the applied field
confirms this value of 0p (experiment performed at
1,15 J1 under 20 k0e). (åCPF/åHJ-1 is proportional
to x-1 or proportional to the temperature. We
verified such a proportionality from which is deduced
the same value of 0p [12].
The Curie constant obtained along the (111) direction, 1.79 x 10-2 deg (JlB mole-’ Oe -1 ) -1 is much
higher than the free ion value,
can see
FIG. 4.
Temperature variation of the inverse of the susceptibility
in range 4.2-294 K for TbIG in low external field applied along [l 11]]
direction.
-
TABLE I
Experimental magnetization in TbIG and YIG [10]
and calculated rare earth magnetization in TbIG
crystal field effects are
low
temperature but also
appreciable
only
in the 100-300 K range. Previous investigation of the
Faraday rotation in TbIG in the infrared region
(6.5 p under 8 kO) supports this conclusion [13] :
1.1 differs
the Landc factor of the Tb " ion g
from its single ion value 1.5 in the temperature range
from 25 to 350 K.
Below about 80 K a significant deviation from the
Curie Weiss law is found (Fig. 3), the curve however
shows no abrupt changes. This result may be explained
by the saturation of the Tb + 3 moments when at low
temperature only some of the states of the rare-earth
are populated. The garnet in question is magnetically
saturated in moderate fields at temperatures near 0 K
and as such it belongs to the category in which the
rare earth moment is locked in by crystalline field
effects. Such a phenomenon has been observed in
the Al and Ga garnets [14, 11]. Note that for both
Tb+3 and Ho+3, the results are very similar in both
the Al and Ga compounds in contrast to the observed
results for Dy+3 and Er+3; this gives some support
to the supposition that any deductions about crystal
fields for these paramagnetic garnets can also be
applied to the corresponding ferrimagnetic iron garnets [15]. In reality the situation is more complicated :
the relatively strong electric field affects the overall
magnetic anisotropy. The extent to which the rare
earth moments deviate from the [111] direction
depends on the anisotropy of both the magnetic g
tensor and anisotropic exchange G tensor. The
results obtained by Bertaut et ale [16, 6] (neutron
investigation on a polycristalline specimen) are in
agreement with the conclusion advanced by Wolf
et al. [15] that the crystal field causes canting relatively
to the ferrimagnetic alignment direction. The umbrella
structure has a rhombohedral character at low temperatures ; this rhombohedral distorsion which sets
This result shows that the
not
at very
=
(*) Reference [10].
in good agreement with that obtained for the ferrite [11].
In low external fields, the variation of the Fe + 3 ions
is very weak in the 0-300 K range (the molecular fields
acting on the Fe+3 ion are in the 4 000 kOe range);
the susceptibility of the ferrite is only induced by the
Tb + 3 evolution. Figure 3 shows two very important
differences with respect to the results previously
obtained for polycrystalline samples [1]. First, we
874
in below 200 K becomes important near 70 K. The
components at 4.2 K of the Tb+3 moment (8.5 JlB)
parallel and perpendicular to the [111] axis are 7.35
and 4.25 respectively [16] ; this parallel value corresponds to M, 44.10 JlB in excellent agreement with
=
our experimental result (Table I). Usually, only the
magnetic interaction between Fe+3 and Tb+3 is
taken into account in evaluating the exchange G
tensor. Nevertheless, the magnetic interactions between rare earth ions also may affect the anisotropic
character of the exchange term as the exchange integral
depends on the orbital state which are modified by
the crystalline fields. Our remarks which have been
proposed to explain the deviation from the CurieWeiss law, as of a qualitative nature it is probable
that two contributions to the susceptibility must be
considered : increasing the field tends to rotate the
rare earth moment in closer parallelism with the easy
direction ; the second contribution is the classical
susceptibility (change of the magnetic moment modulus).
The molecular field approximation reduces to the
assumption that the magnetic interactions between
Fe+3 and Tb+3 ions are represented by a mean molecular field coefficient n. The resultant of the molecular fields due to Fe+3(a) et Fe+3(d) ions respectively
is given by :
We shall take into account the magnetic interactions between rare earth ions which are represented
by the molecular field coefficient ncc.
In zero external field, the classical equation of the
spontaneous Tb" sublattice magnetization may be
written :
when crystalline effects are absorbed into x and 8p
is proportional to ncc. We have assumed that saturation effects can be neglected. From eq. (2), Me is
expected to be proportional to MnG. Using the values
of table I, we verified such a proportionality for
40 K and temperatures higher than 45 K
8p
(Fig. 5); we obtained
=
FIG. 5.
versus
we
Variation of the rare earth sublattice magnetization
YIG magnetization for TbIG in range 4.2-300 K. The
Tb +3 moments are measured along [Ill] direction.
-
found
units conversion, Pauthenet’s value is
17.875 x 103 O liB 1). For example, the molecular
field due to the iron ions acting on a Tb + 3 ion is
about 120 kOe at room temperature. It may be of
interest to compare the size of the exchange field,
Hex, found in TbIG along the [111] direction with
that in the other garnets. The molecular field acts on
the total magnetic moment and is related to the
exchange field which acts only by means of spin
angular momentum S. In the free ion approximation, Hex is given by
(after
-
Lande g factor for a total angular
[14]. In terms of the parameters,
where gj is the
momentum J
corresponding
to a
of 252 K.
The value of n
compensation temperature
can
be
directly
value
deduced from
(which should be constant in the gamets if we supexchange field created by the iron to be independent of the nature of the rare earth ion), we
obtained 17°. For comparison the value of the same
parameter was found to be 25° in GdIG [1], 24° in
pose the
and
875
EUIG [14] and between 14 and 19° in TmIG [15].
Note that only qualitative significance must be
attached to this comparison because the free ion
approximation is far from the reality in TbIG, as
mentioned before.
From the relation 8p
nee C, we found
=
corresponding to an exchange integral Jcc 1.56°.
Pauthenet’s value is 0.56 x 103 Oe Jlul. The Tb+3
interaction is equivalent to a field of about 45 kOe
at 100 K. Pauthenet’s data indicated in GdIG (the
determination in TbIG was only to within an order
of magnitude) for which 0p
32 ± 5 K, a rare
earth coupling of about 50 kOe at the same temperature. Note that in these garnets the distances between the rare earth ions have practically the same
value.
=
=
-
4. Conclusion.
By comparing the temperature
variation for TbIG magnetization along [111] direction and YIG properties, it is possible to show the
effects of the crystal field on the rare earth ion. The
measurement of the susceptibility confirmed the nonfree-ion character.
-
Except for the molecular field coefficient n (which
represents the magnetic interactions between Fe+3
and Tb+3 ions) all our results are different from those
in polycristalline samples. We now consider possible
origins of the discrepancies between present data
and that due to Pauthenet. In the first place, our
experiments are on a single crystal and we have no
averages of the anisotropic effect. It is doubtful that
the differences are caused by the presence of substantial amounts of impurities in the garnet ; this appears
to be in contradiction with the excellent agreement
of the compensation temperature. It must be pointed
out that the lattice constant reported for the terbium
iron garnet by Pauthenet (12.452 A) is slightly different to that reported by G. P. Espinosa (12.436 A)
[19]. It is known that the properties of the rare-earth
ions are extremely anisotropic and sensitive to the
precise nature of the environment and that the
exchange integral depends strongly on the distance
between the ions and also on the angle subtended
by these ions. It seems probable that the discrepancies
between the present data and that of Pauthenet
originate with the disagreement of the lattice parameter and the single crystal nature of the specimen.
In a subsequent paper all our results will be used to
interpret the Faraday rotation evolution.
References
[1] PAUTHENET, R., Ann. Phys. 3 (1958) 424.
[2] GELLER, S., WILLIAMS, H. J., SHERWOOD, R. C., REMEIKA, J. P.
and ESPINOSA, G. P., Phys. Rev. 131 (1963) 1080.
[3] GELLER, S., REMEIKA, J. M., SHERWOOD, R. C., WILLIAMS, H. J.
and ESPINOSA, G. P., Phys. Rev. 137 (1965) A 1034.
[4] HARRISON, F. W., THOMPSON, J. F. A. and TWEEDALE, K.
in proceedings of the International Conference on Magnetism, Nottingham 1964 (The Institute of Physics and The
Physical Society, London 1965), p. 660.
[5] CROSSLEY, W. A., COOPER, R. W., PAGE, J. L. and VAN STAPELE, R. P., Phys. Rev. 181 (1969) 896.
[6] SIVARDIÈRE, J., TCHÉOU, F., C. R. Hebd. Séan. Acad. Sci.
271 (1970) 9.
[7] NÉEL, L., C. R. Hebd. Séan. Acad. Sci. 239 (1954) 8.
[8] BERTAUT, F. and FORRAT, F., C. R. Hebd. Séan. Acad. Sci.
242 (1956) 382.
[9] ANDERSON, E. E., Phys. Rev. 134 (1964) 1581.
[10] GONANO, R. L., Phys. Rev. 156 (1967) 521.
[ll] GUILLOT, M., PAUTHENET, R., C. R. Hebd. Séan. Acad. Sci.
259 (1964) 1303.
[12] TRAN KHAN VIEN, LE GALL, H., LEPAILLER MALECOT, A.,
[13]
MINELLA, D., GUILLOT, M., Magnetism and Magnetic
Materials 1974 (20th Annual Conference San Francisco).
CHETKIN, M. V. and SHALYGIN, A. N., J. Appl. Phys. 39
(1968) 561.
[14] BALL, M., GARTON, G., LEASK, M. J. M. and WOLF, W. P.,
J. Appl. Phys. 32 (1961) 267 S.
[15] WOLF, W. P., BALL, M., HUTCHINGS, M. T., LEASK, M. J. M.
and WYATT, A. F. G., J. Phys. Soc. Japan 17 (1962) 443.
[16] BERTAUT, E. F., SAYETAT, F., TCHÉOU, F., Solid State Commun.
8 (1970) 239.
[17] WOLF, W. P. and VAN VLECK, J. H., Phys. Rev. 188 (1960) 1490.
[18] CASPARI, M. E., KACKI, A., KOICHI, S. and WOOD, G. T.,
Phys. Lett. 11 (1964) 195.
[19] ESPINOSA, G. P., J. Chem. Phys. 37 (1962) 2344.