Observation of isotropic magnetic contribution to the refractive index of ABF3-type cubic crystals

Solid State Communications, Vol. 19, pp. 185—188, 1976.

Pergamon Press.

Printed in Great Britain

OBSERVATION OF ISOTROPIC MAGNETIC CONTRIBUTION TO THE REFRACTIVE INDEX OF ABF3-TYPE CUBIC CRYSTALS P.A. Markovin, R.V. Pisarev, G.A. Smolensky and P.P. Syrnikov A.F. loffe Physico-Technical Institute of the Academy of Sciences of the U.S.S.R., Leningrad 194021, U.S.S.R. (Received 5 January 1976 by R. Loudon) Isotropic magnetic contribution to the refractive index of cubic crystals was observed by studying temperature dependences of the index in perovskite-type crystals KMnF3, KCoF3, KNiF3 and KMgF3. At low temperature magnetic contribution in KNiF3 is t5flm 33 x iO~.Magnetic contribution was found to exist well above the temperature of magnetic ordering due to short-range ordering effects. THE TRANSITION of a crystal from paramagnetic to magnetically ordered state is accompanied by the change of its magnetic and electronic structure and as a consequence by the change of its optical properties. At the present time these changes are widely studied by different optical and magnetooptical methods. Recently the magnetic linear birefringence was successfully used for a study of transitions to the ordered state in fern- and 16 antiferromagnetic crystals. But as far as we know no attempt was made to observe a transition to the ordered state by the refractive index measurements. In the present paper we report on results of our investigation of the temperature dependences of refractive indices in ABF3 perevskite-type cubic crystals. In this study we were able to find the contribution to the refractive index connected with the isotropical magnetic interaction. First let us discuss what changes of dielectric constant or refractive index are expected in a magnetically ordered state in comparison with the paramagnetic one. These changes can be found from the energy & of the interaction of the light with magnetic crystal. From the symmetry considerations for the cubic crystal in which magnetic order is described by one magnetization vector the density of the energy & can be written in the form 2E2 + X 2 & = ~ [e1~E~+ A1 m 2(mE) + A 3(m~E~ + m~E~ + m~E~) (1) -

.

of magnetization but does not depend either on the orientation of m or E relatively to the crystal axis or on their relative orientation. This term may be called isotropic and the magnitude of A1 is defmed by isotropic exchange interaction. The term proportional to A2 also does not depend on the orientation of m and E in the crystal, but it depends on their relative orientation. The laston twotheterms in (1) proportional to A3 and in A., the depend orientation of the magnetization crystal and on the relative orientation of m and E as well. These two terms give anisotropic contribution to the dielectric constant of cubic (in paramagnetic state) crystal. The parameters A 3 and A4 are defined by spin— orbit coupling, dipole—dipole interaction, etc. The components of the symmetric dielectric tensor e~jare deduced from (1) =

.

2 e~+ 2A1m 2 + 2(A2 + A3)m1

(2) As it was shown in reference 7 this tensor can be diagonalized only in two cases, namely when the magnetization lies in (110) or (010)-type crystallographic planes. Form J. [010] in cubic crystals of 432, 43m and m3m classes the following expressions for the three main values of the refractive indices and for magnetic birefringence can be obtained

X4(m~E~ + m~E~ + m~E~) where e~is the magnetization independent part of the dielectric constant, E is the electric field vector of the

n1

=

n0+

~m2+~2

+_A3)2

1A2+ 1

A2

—

1

1/2

(A + A

+

±- 2

3 m2~

cos 4i,1i~

—

(3)

fl

~

0

light wave, A1ForA2theA3, A4 areof the phenomenological parameters. crystals cubic classes 432, ~3m ,

e~,= 2A2m~m1.

2 and m3m we may take A., = 0, for the 23 and m3 classes all four parameters A, differ from zero in general case. important conclusions can be drawn from (l). The Some term proportional to A 1 depends only on the value

2

2 2

=

(4)

~~uu1,3 = 1~ul A2-— fl3 =1 2 1A2 + m 2(A2 + A3) 185

~i,

j

m n0 + X~

n

,

2

—

1/2 cos 4iP)

(5)

186

REFRACTIVE INDEX OFABF3-TYPE CUBIC CRYSTALS

Vol. 19, No. 3

1

T~NN 9F5 105_g

-

0%

0 -

~ 3

-

KCoF~

4~~AUOO%~

—

~

AL L&

—

R~000r 14

—

1100

200

300 400 T(°~)

500

600

700

Fig. I. Temperature dependence of the refractive index n of KMnF3, KCoF3 KNiF,~and KMgF3 crystals. The values of n in all crystals are fixed to zero at T = 700 K. ,

where A = A2/(A2 + A3) is the parameter of the magneto-optical anisotropy,’ iJi is the angle between m and [1001 axis in (010) plane. From expressions (3)—(5) we see that taking into account and magnetic orderingcontributions causes the appearence of isotropical anisotropical to the refractive index of magnetic cyrstal. It is important to underline that by measuring the magnetic birefringence L~n [expression (5)] or magnetic linear dichroism 6 we can determine onlyinAthe absorption band region 2 and X3-parameters but by measuring the refractive index the A 1 -parameter can be also found. The temperature variations of refractive indices were measured by the homodyne detection method. A single mode 6328 A helium—neon laser was used in the experiments. With this method we were able to measure the phasethrough difference between twothe beams (one of which traveled the ç~ crystal) with accuracy 4(2ir/l00). With such an accuracy and with the samples of 2—3 mm in thickness the changes of the refractive index iO~could be measured. These changes were calculated using the expression A dl (n 1) 6T (6) 217] ldT where I is the sample thickness and dI/IdT is the linear expansion coefficient. The expansion coefficients were =

—

—

—

—

taken from references 8 and 9 and the indices of refraction from reference 10.

Figure 1 shows index variations with temperature in KMgF3, KMnF3 KCoF3 and KNiF3 crystals. For convience the values of n at T= 700°Kin all crystals were fixed to zero. 1 the diamagnetic studied earlier’ slopeInofallthe curve n(T) crystals or the temperature variation dn/dT decreases while the temperature is lowered. This is also the case for diamagnetic crystal KMgF 3 as shown in the Fig. 2. In a quite different way the index is changed in KNiF3 which orders antiferromagnetically 6Beginning at T = 550°K(that below TN = 246°K. corresponds to 2.2TN) the index of KNiF3 grows more rapidly than in isostructural KMgF3. The most rapid variation takes place in the region of TN (Fig. 2). In KCoF3 and KMnF3 beginning at T 250°Kthe temperature dependence of dn/dT also grows. This 2.2TN forternperature corresponds approximately to KCoF 3TN for KMnF 3 (TN = 1 14°K)and to 3 (TN = 88°K).But in these crystals magnetic contribution to the refractive index is masked by the rapid growth of it due to a structural transition at 11 4°Kin KCoF3 and at 180°Kin KMnF3. We shall discuss in detail the magnetic contribution ,

—

to the refractive index only in KNiF3. Both KNiF3 and 8 Thus KMgF3 have the same cubic perovskite structure and very small difference in the lattice parameters. we believe that the magnetic contribution to the index of KNiF 3 can be found as a difference between observed changes of indices in these two crystals (Fig. 3). At low

Vol. 19, No.3

REFRACTIVE INDEX OFABF3-TYPE CUBIC CRYSTALS I

0

6

-

-

-

.

-

•

187

etc. These measurements gave the same temperature variation of the index. Due to the existence of antiferromagnetic domains and short-range ordering below and above TN there is some isotropic contribution index connected with 2/no) astoit the follows from (3). Anisothe termangle (A2 +dependent A3Xm terms in cubic crystals do not tropical

•

KN F 5 0 •

-

•

•~ -

-

.

~

0•

Y•

::

4

.00000000

:1~ %5~o.

•~..

K Mg F5

0

100

I 300 400 T(°1<)

200

500

600

700

Fig. 2. Temperature derivative dn/dT of the refractive index of KNiF3 and KMgF3. ________________ •0~••• -

...

~-

••

~

$0

2

T~P~)

~

S

-

Cl

S

/

•

— —

-‘-

••.

/

—~r~ t 100 200

—

—

/

00

that phenomenological expression (1) describes only a part of the observed changes of n. We see that fluctuations of the antiferromagnetic ordering both below and above TN = 246°Kgive a significant contribution to the index. Such a contribution must exist also in noncubic crystals as was shown by the method of linear birefringence Let us discuss briefly the possible origin of the observed changes of the refractive index in terms of a general theory of optical dispersion.~The temperature dependence of the index is described by the expression 2--1 = l~ aLfjN,v~ dn 1 aLfiNi F n dT ~ 2 2 I~7, zn (vs—v) (7) where (1)dv, 1 df 1 d’y ‘V = x~=— v~ dT F= --—

0

I0

give any contribution to the index. anisotropical contribution can be observed only ifThis there is preferred direction of magnetization (connected with external magnetic field or uniaxial stress), that was supported by the measurements of magnetic linear dichroism in 6 (see the inset in the Fig. 3). In Fig. 3 we show the temperature variation of KNiF3 the square of the antiferromagnetic moment of KNiF 3. From the comparison of this curve with that of the magnetic contribution to the refractive index we conclude,

300

~‘

—

f,, ~

•••

i 400

(~~)

—,

500

600

T (°K) Fig. 3. Isotropic magnetic contribution to the refractive index of KNiF3 (dotted line), the square of antiferromagnetic moment (solid curve) and the contribution of fluctuations of an antiferromagnetic moment to the refractive index below TN (dashed curve). In the inset the temperature variation of magnetic linear dichroism near TN in KNiF3 ~6 —

are the strength, density and frequency of osdillators respectively, v is the light frequency, ‘y is the volume of the crystal and a, are the constants. As a rule it is assumed that there is no change in the oscillator strength with temperature in cubic crystals and

F, = 0.11 The third term in (7) was estimated using the results of reference 9 and found to be non-important. Estimations showed also that the main contribution to the index is connected not with 8the weak 3d74pd—d transition transitions rather with strong situatedbut approximately at v 3d 1 55.000—60.000 6~mcm’ Using this value and the experimental value 3.3 x l0~we found for the shift ~v 1 220—250 cm~. In 3A2g termsground of molecular approximation state offield Ni2~ion is 426 cm’the ,14splitting We see of observed magnetic contribution to the refractive that -*

—

temperatures nitude 6nm the 3.3 magnetic x l0-~.Itcontribution is importantreaches to notethe themagexistence of magnetic contribution far above TN = 246°Kdue ordering, In ordertotoshort-range be sure that the observed variation of the index in KNiF 3 is connected with the isotropical contribution described by the term proportional to A1 in (1), the measurements were taken different ization of the incident light, such as E for II [100], ElI polar[101]

~

index in KNiF3 is caused not only by the exchange splitting of the ground 1).state, but also by that of excited one ~ 650—670 cm

188

REFRACTIVE INDEX OFABF3-TYPE CUBIC CRYSTALS

Vol. 19, No.3

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