HAL Id: jpa-00221211
https://hal.archives-ouvertes.fr/jpa-00221211
Submitted on 1 Jan 1981
HAL is a multi-disciplinary open access
archive for the deposit and dissemination of
sci-entific research documents, whether they are
pub-lished 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.
MAGNETIC FIELD DEPENDENT RESTSTRAHLEN
SPECTRA IN PARAMAGNETIC CeF3
H. Gerlinger, G. Schaack
To cite this version:
H. Gerlinger, G. Schaack.
MAGNETIC FIELD DEPENDENT RESTSTRAHLEN SPECTRA
JOURNAL DE PHYSIQUE
CoZZoque C6, suppZ4ment au n o 12, Tome 42, dgcembre 1981 page c6-499
MAGNETIC F I E L D DEPENDENT RESTSTRAHLEN SPECTRA I N PARAMAGNETIC CeF3
H. Gerlinger and G. Schaack
PhysikaZisches I n s t i t u t der Universitaet lvkerzburg, Roentgenring 8, 87 h'uerzburg, F. R. G.
Abstract.
-
Magnetic f i e l d dependent changes i n the E,-reststrahl en spectram
(frequency s h i f t ? , s p l i t t i n g and r e d u c t i o n o f bandwidths) have been observed a t T = 1.6 K, B = 7 T, d i f f e r i n g i n V o i g t - and Faraday-configuration.I n t r o d u c t i o n .
-
The magnetoelastic i n t e r a c t i o n between 4 f - e l e c t r o n s and Raman-active o p t i c a l phonons i n i o n i c Rare E a r t h (R. E.) compounds gives r i s e t o a s p l i t t i n g of degenerate Eg-modes i n an e x t e r n a l magnetic f i e l d B p a r a l l e l t o t h e o p t i c a l a x i s Z o f an u n i a x i a l c r y s t a l . This i n t e r a c t i o n a l s o s h i f t s t h e phonon frequences w i t h r e - s p e c t t o a diamagnetic m a t e r i a l w i t h o u t 4 f - e l e c t r o n s /l, 2/. The wavenumber d i f f e - rence o f the s p l i t phonon modes, which a r e complex conjugates, f o l l o w s :A5 = ,A: t g h (gpgH/ZkT) ( l ) , where i s t h e s a t u r a t i o n s p l i t t i n g . This e f f e c t has been t h e o r e t i c a l l y i n t e r p r e t e d / 3 / , assuming a phonon-induced mu1 t i p o l a r deformation o f the K. E.-ion due t o v i r t u a l t r a n s i t i o n s w i t h i n the 4 f - c o n f i g u r a t i o n . Theory a l s o p r e d i c t s / 4 ,
5/
the s p l i t t i n g of degenerate i n f r a r e d - a c t i v e Eu-modes. Again the sp1 i t Eu-modes a r e o p p o s i t e l y c i r c u l a r l y p o l a r i z e d and should f o l l o w (1).We have i n v e s t i g a t e d t h e i n f r a r e d a c t i v e Eu-modes o f the CeF3 i n r e f l e c t i o n a t T = 1.6 K i n a magnetic f i e l d B
5
7 T p a r a l l e l t o Z. We s t u d i e d two magnetic con- f i g u r a t i o n s : 1. V o i g t - c o n f i g u r a t i o n ( V . c .): KL
Z, B ' ' Z, E1
Z; 2. Faraday-configu- r a t i o n (F. C.): K ( / Z, B ( 1 Z, EL.Z.
The measurements were made w i t h a Fourier-spectro- meter i n t h e s p e c t r a l range between 60 cm-l and 650 cm-'. The c r y s t a l s were immersedi n s u p e r f l u i d helium.
Experimental Results.
-
I n F i g . 1 t h e r e s t s t r a h l e n spectra f o r d i f f e r e n t e x t e r n a l magnetic f i e l d s i n F. c. a r e shown. F i g . 2 shows the corresponding spectra i n V. C.. The spectra a t B = 0 T a r e i d e n t i c a l w i t h each o t h e r w i t h i n experimental accuracy, b u t d i f f e r i n small b u t meaningful f e a t u r e s from the r e s t s t r a h l e n spectra published by Lowndes e t a l . /6/. A t B > 0 e f f e c t s o f the magnetic f i e l d appear i n both c o n f i - g u r a t i o n s s u r p r i s i n g l y i n d i f f e r e n t manner, e s p e c i a l l y near 320 cm'l and near 170 cm-'. I n F i g . 1 the anomalous slope a t t h e high-wavenumber edge o f the r e f l e c t i o n band near 300 cm-l disappears w i t h i n c r e a s i n g magnetic f i e l d and gives r i s e t o a r e f l e c t i o n d i p . The i n t e n s e band a t 170 cm-' shows a d i s t i n c t change i n i t s form and a second maximum seems t o appear a t h i g h f i e l d s . Generally t h 6 reststrahlen-bands appear more d i s t i n c t l y w i t h i n c r e a s i n g f i e l d and develop steeper slopes. This obvious r e d u c t i o n o f the bandwidth occurs even more c l e a r l y i n t h e V. c. (Fig. 2). I n t h eC6-500 JOURNAL DE PHYSIQUE
same spectral range a s before a new band appears a t 340 cm-l and the s p l i t t i n g of the band near 170 cm-' shows up more c l e a r l y . The reststrahlen spectra i n both con- figurations d i f f e r with increasing f i e l d s beyond the experimental uncertainty
(Fig. 4 ) . This difference has according t o our knowledge not been predicted theore-
t i c a l l y up to now.
I . .
.
fswq-mg-ta m V7c*' Void - Cmtiwalinl
~ m D ) l o O l D o V/&'Fig. 1
+
2 : B-dependence of E,-reststrahlen-spectra of CeF3I# U 9) U I 8 U 7)
: Wavenumber s h i f t of transverse and longitudinal
phonons, B J I Z , i n V . c.
For the evaluation of the experimental data we have used Kramers-Kronig-analysis and, more successfully, a Lorentzian o s c i l l a t o r - f i t . The Faraday-spectra a r e the superpo-
s i t i o n of two orthogonally c i r c u l a r l y polarized spectra /5/, which can only be ana-
lyzed by an o s c i l l a t o r - f i t . Here we present the r e s u l t s f o r the V . C.. We have cal-
culated the r e f l e c t i o n spectra, using the generalized Kurosawa r e l a t i o n a s given i n
where v"! means the complex longitudinal frequency, C D the transverse frequency and
j yq, y, J t h e damping f a c t o r s respectively.
The magnetic f i e l d dependence of 5:. ij: i s shown i n Fig. 3. The o s c i l l a t o r f i t
y i e l d s f o r $he band near 170 cm-l three o s c i l l a t o r s , which a r e c l e a r l y separated a t
high f i e l d s (Fig. 2 ) . A very unusual behaviour shows the band a t 300 cm-l. A t low
f i e l d s i t was d i f f i c u l t to obtain a s a t i s f y i n g f i t in t h i s region. We had t o take
i n t o account an additional o s c i l l a t o r which disappears a t higher f i e l d s (see below)
W find one case where the transverse and longitudinal frequencies of one E,-mode e
1
( S 367 cm- ) s h i f t i n opposite directions, l i k e the two components of a s p l i t Eg-
phonon damping
F i g . 4 : E u - r e s t s t r a h l e n spectra i n r a n d F. C., B = 7 T.
f i e l d . Frequency s h i f t s i n t h e order o f 7 cm-' t o h i g h e r frequencies are observed i n several cases. These s h i f t s behave l i k e a s p l i t Eg-phonon component according t o ( I ) and s a t u r a t e a t 3
-
4 T, they a r e n o t explained by e x i s t i n g theory. The damping f a c - t o r o f the l o n g i t u d i n a l mode a t 319 cm-' decreases w i t h i n c r e a s i n g f i e l d s from 32 cm -l t o 11 cm-l i n t h e same form as found i n Raman-experiments /2/.Discussion.
-
Magnetic f i e l d dependent frequency s h i f t s and changes o f i n t e n s i t y o f Eu-phonons were p r e d i c t e d by Anastassakis e t a l . (e. g. / 4 / ) u s i n g symmetry argu- ments alone. Our observations a r e i n f u l l agreement w i t h these considerations. A s p l i t t i n g o f a reststrahlen-band due t o magnetoelastic i n t e r a c t i o n and p r e d i c t e d by Thalmeier and Fulde i n a microscopic treatment /5/ i s observed perhaps i n one case (170 cm-').The a d d i t i o n a l o s c i l l a t o r a t l c l r magnetic f i e l d s near 300 cm-l i s t e n t a t i v e l y a t t r i - buted t o magnetic f l u c t u a t i o n s , which a r e t r a c e d by the phonons. O p t i c a l phonons w i t h a l a r g e magnetoelastic i n t e r a c t i o n seem t o s p l i t a l r e a d y a t B = 0 T when t h e timescale o f these f l u c t u a t i o n s exceeds t h e phonon l i f e t i m e . These f l u c t u a t i o n s a r e suppressed w i t h i n c r e a s i n g magnetic f i e l d . The d i f f e r e n c e s i n the spectra o f the two c o n f i g u r a t i o n s , obtained a t h i g h f i e l d s , have t o be a t t r i b u t e d t o the macroscopic Coulomb-field, which couples w i t h the phonon i n V. c. b u t n o t i n F. c. and has t o be taken i n t o account i n a d d i t i o n t o t h e magnetoelastic i n t e r a c t i o n . The j o i n t e f f e c t s o f b o t h i n t e r a c t i o n s r e q u i r e an e l l i p t i c a l p o l a r i z a t i o n o f s p l i t phonon modes i n V. c. w i t h the appearance o f a q u a s i - l o n g i t u d i n a l component i n t h e spectrum as a consequence (Fig. 2, ,340 cm-l)
.
References:
/ l / Ahrens, K. and G. Schaack: Phys. Rev. L e t t . 42, 1488 (1979)
/2/ Ahrens, K. and G. Schaack: Proc. Conf. L a t t i Z Dynamics, ed. by M. Bal kanski
,
Flammarion, Paris, 257 (1978)
/3/ Thalmeier, P. and P. Fulde: Z. Physik B 26, 323 (1977)
/4/ Anastassakis: Dynamical P r o p e r t i e s o f S o F d s Vol. 4, ed. by G. K. Horton and A. A. Maradudin, N o r t h Holland, Amsterdam p. 157 (1980)
/5/ Thalmeier, P. and P. Fulde: Z. Physik B 32, 1 ( 1 9 7 8 )
/6/ Lowndes, R. P,, 3. F. P a r r i s h and C. H. E r r y : Phys. Rev. 182 (3), 913 (1969) /7/ Lamprecht, G. and L. Merten: Phys. s t a t . s o l . ( b )
