Magnetic study of the terbium iron garnet, Tbig, along the easy (111) direction : molecular field parameters

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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�

Magnétisme d’Optique Solides, Bellevue, (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 ter-} bium, 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. ²⁰¹⁴ 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.

1. Introduction. ^- The classical work

by

^Pauthenet

(1958)

^{on the}

magnetization

^{of the rare} earth iron

garnets

^{was carried out on}

polycrystalline

^mate-

rials

[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

magne-

tooptical

effects such as

Faraday rotation,

^{the theo-}

retical

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].

2.

Experimental.

^{- In this} paper, ^we

report

^results of our

study

^{of the}

magnetic

behaviour of TbIG

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 magne- tometer in fields _up to 15 k0e. The

single crystal sphere

^is

apparently

^{saturated at 3 k0e at}

liquid

helium temperature. Above this

temperature,

^satu- ration 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

to

Ha

^{= 0}

(the

^{use of}

single crystal

avoids the treat- ment

adopted by

Pauthenet of

extrapolation

^{to infi-}

nite 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 mea-}

surements 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. 1. ^- (M, H) ^{curves in} range 4.2-294 K, along [111] ^direction

for TbIG in external field _up to 15 k0e.

FIG. 2. ^- Variation of the spontaneous magnetization ^versus temperature ^{for TbIG} along [111] ^direction.

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}

FIG. 3. - Temperature variation of the rare earth sublattice

magnetization along ^the [111] ^direction.

earth

spins

^tilt very

slowly

away from the _easy axis

(111)

^{to lie on a cone}

(the

^{cone axis is}

⁽¹¹¹⁾

^{and the}

inclination

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

own mutual interactions. The moment of the rare

earth

(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

magnetiza-

tion

of YIG

from that of TbIG.

Using

^the

magnetiza-

tion

values, MyIG,

^obtained

experimentally (magneti-

zation

[9],

^RMN

[10]),

^we deduced the thermal variation of

Mr (Fig. 4,

^Table

I).

^At

temperature

near 0

K,

the effective moment

Me(T -+ ⁰⁾

^{= 44.66 JlB}

(7.44

liB per

ion)

^is

considerably

lower than

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].

If we suppose the rare earth environment in the

gallate

^{to be the same}

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

Experimental magnetization

ⁱⁿ TbIG and YIG

[10]

and calculated rare earth

magnetization

^{in TbIG}

(*) ^Reference [10].

in

good agreement

^{with that obtained} for the fer- rite

[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

higher

than the free ion

value,

This result shows that the

crystal

^{field effects are}

appreciable

^not

only

^at very low temperature ^{but also} 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] :

the Landc factor of the

Tb " ion g

^{= 1.1 differs}

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 gar- nets

[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 tem-

peratures ; this rhombohedral distorsion which sets

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 corres-}

ponds

^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 bet-

ween 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 Curie- Weiss

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 modu-}

lus).

The molecular field

approximation

^{reduces to the}

assumption

^{that the}

magnetic

interactions between

Fe+3

and

Tb+3

ions are

represented by

^{a mean mole-}

cular field coefficient n. The resultant of the mole- cular fields due to

Fe+3(a)

^et

Fe+3(d)

^ions

respectively

is

given by :

We shall take into account the

magnetic

^interac-

tions 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 satura- tion 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

8p

^{= - 40 K and} temperatures

higher

^{than 45 K}

(Fig. 5);

^{we obtained}

corresponding

^{to a}

compensation temperature

^value of 252 K.

The value of n ^can be

directly

^{deduced from}

and

FIG. 5. ^- Variation of the rare earth sublattice magnetization

versus YIG magnetization for TbIG in _range 4.2-300 K. The Tb +3 moments are measured along [Ill] ^direction.

we found

(after

^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}

approxima- tion, Hex

^is

given by

where gj is the

Lande g

^{factor for a total}

angular

momentum J

[14].

^{In terms of the} parameters,

(which

^{should be constant in the} gamets ^{if we} sup- pose the

exchange

field created

by

^{the iron to be inde-}

pendent

^{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}

Note that in these garnets the distances bet- ween the rare earth ions have

practically

^{the same}

value.

4. Conclusion. ^-

By comparing

^the

temperature

variation for TbIG

magnetization along [111]

^direc-

tion 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 non-}

free-ion character.

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 para- meter and the

single crystal

^{nature of the}

specimen.

In a

subsequent

paper all our results will be used to

interpret

^the

Faraday

rotation evolution.

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