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Submitted on 1 Jan 1978
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”IMPURITY CONTRIBUTION TO THE LOW TEMPERATURE FMR LINEWIDTH OF Ag-DOPED
CdCr2Se4 SINGLE CRYSTALS”
Jorge Ferreira, M. Coutinho-Filho
To cite this version:
Jorge Ferreira, M. Coutinho-Filho. ”IMPURITY CONTRIBUTION TO THE LOW TEMPERA-
TURE FMR LINEWIDTH OF Ag-DOPED CdCr2Se4 SINGLE CRYSTALS”. Journal de Physique
Colloques, 1978, 39 (C6), pp.C6-1007-C6-1009. �10.1051/jphyscol:19786445�. �jpa-00217923�
JOURNAL DE PHYSIQUE
Colloque C6, supplément au n° 8, Tome 39, août 1978, page C6-1007
"IMPURITY CONTRIBUTION TO THE LOW TEMPERATURE FMR LINEWIDTH OF Ag-DOPED CdCr
2Se
4SINGLE CRYSTALS"*
J.M. Ferreira and M.D. Coutinho-Filho
Departamento de Fisiaa, UniveTsidade Federal de Pernambuao, SO 000 - Reoife, Bvasil
Résumé.- Nous analysons dans ce travail l'effet produit par des ions d'impureté Cr+I* sur la largeur de raies FMR (AH) de monocristaux de CdCr2Se4dopés avec Ag. En supposant que l'ion d'impureté a deux niveaux de basse énergie, nous démontrons que les mécanismes de relaxation lente ou rapide peuvent expliquer la dépendance en température de AH à basse température. Il faut faire des autres expériences au-dessous de 4,2 K pour savoir quel mé- canisme agit réellement.
Abstract.- In this paper x-;e analyse the effect of impurity Cr+l* ions on the FMR linewidth (AH) of Ag-doped CdC^Sei, single crystals. By assuming that the impurity ions has two low- lying energy levels, we show that the slow or the fast relaxation mechanisms can fit the temperature dependence of AH at low temperatures. Further experimental work below 4.2 K is needed to conclude which mechanism is effectively operating.
The effect of impurity paramagnetic ions on the anisotropy and ferromagnetic resonance (FMR) linewidth of ferromagnetic crystals, such as rare- earth ions in Yttrium Iron Garnet (YIG) /l/ and transition-metal ions in garnets /2/ and spinels /3/
has attracted the attention of many workers in the field of magnetism in the last twenty years. In these ferrites the presence of impuritites can in principle, be eliminated (consequently the conduc- tivity) and one can get single crystals with pro- perties close to those of ideal insulators. The situation is quite different in magnetic semicon- ductors where the electrical properties are to be regarded relevant both for applications and basic physical understanding of these materials.
The purpose of this paper is to analyse the effect of impurity paramagnetic ions on the FMR linewidth of the ferromagnetic semiconductor CdCr2Seif doped with Ag /4/. Two peculiar manifesta- tions characterize the observed / 4 / phenomena at liquid Helium temperature : giant anomalous peaks of the resonance field and FMR linewidth (AH) along some particular crystallographic directions. These anomalies have been attributed I hi to the presence of impurity Cr necessary to charge compensate for the Ag+*doping (susbstituting for C d+ 2) . To explain these phenomena we assume that the impurity ion has two low-lying energy levels so that the
anomalies would occur at crossover or nearcrosso- vers of those two levels. The ground state would result from a combined effect of crystalline field, spin-orbit coupling and exchange interaction bet- ween the magnetic moment of the inpurity ion and the crystal magnetization. We show that two diffe- rent mechanism can fit the temperature dependence of AH at low temperatures /4/ : the fast (or trans- verse) l\l and the slow (or longitudinal)/)/ rela- xation mechanism.
The slow or longitudinal relaxation mecha- nism is induced by the delay in establishing the thermal equilibrium values of the population of the impurity ion energy levels. These levels are modulated by the uniform precession via an aniso- tropic exchange coupling between the spin of the impurity ion and the crystal magnetization. For the two-level system the expression for the FMR linewidth reads /l/
AH = ^ £ f (e.« T ^ ^ s e c h * ( J ^ ) , (1)
where
Here u is the resonance frequency, N. is the imp density of impurity ions, AE is the separation between the energy levels, M is the saturation ma- gnetization, 0 and <|> are the angular coordinates of the magnetization with respect to the equili- brium positium, IC is Boltzman constant, T is the
temperature and x is the relaxation time associa- ted with restoring thermodynamic equilibrium in t Work supported by CNPq, CAPES and FINEP (Brazil-
lian Government).
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19786445
t h e p o p u l a t i o n o f t h e two e n e r g y l e v e l s . I t i s w o r t h n o t i c i n g t h a t AH i n E q u a t i o n (1) may have two maxima a s a f u n c t i o n of T .
The t e m p e r a t u r e dependence of T i s d e t e r - mined by t h e t h e r m a l b a t h which we can assume t o c o n s i s t of phonons o r magnons / I / . For d i r e c t pro- c e s s e s i n which a phonon ( o r magnon) i s absorved o r e m i t t e d , t h e r e l a x a t i o n time h a s t h e same tempe- r a t u r e dependence, namely
T = T O t a n h (
-
)2 K ~ T
I n t h e t r a n s v e r s e o r f a s t r e l a x a t i o n me- chanism, t h e t r a n s v e r s e p a r t of t h e e f f e c t i v e f i e l d a c t i n g on t h e i m p u r i t y i o n e x c i t e s t h e p r e c e s s i o n of i t , a s i n a paramagnetic r e s o n a n c e e x p e r i m e n t , and e n e r g y i s t r a n s f e r r e d from t h e f e r r o m a g n e t i c system t o t h e t h e r m a l b a t h . I n t h e c a s e of two e n e r g y l e v e l s , and Mw << A E , t h e e x p r e s s i o n f o r t h e FMR l i n e w i d t h c o r r e s p o n d i n g t o t h i s p r o c e s s i s g i v e n by /
11
N . Imp w
AH = 4-- A E
t g h
-
w i t h No i s t h e d e n s i t y o f ~ ri o n s forming t h e + ~ m a g n e t i c a l l y o r d e r e d subsystem. We s h o u l d n o t i c e
t h a t A E i n E q u a t i o n ( 4 ) h a s a maximum a t T = 0 and d e c r e a s e s w i t h i n c r e a s i n g t e m p e r a t u r e .
I n F i g u r e 1 we p r e s e n t a f i t o f t h e A H peak u s i n g t h e mentioned mechanism. W e have sub- t r a c t e d t h e r e s u l t s o f AH f o r t h e d i r e c t i o n from t h e ones f o r t h e
fi
1fl
d i r e c t i o n , t o i s o l a t e t h e c o n t r i b u t i o n form t h e i m p u r i t y i o n s ( s e e Figu- r e 5 i n t h e second p a p e r of R e f e r e n c e 1 4 1 ) . To produce t h e f i t of F i g u r e 1 t h e f o l l o w i n g r e s u l t s f o r h e and T O where o b t a i n e d :A c = 24 K and-c0 = 3 . 3 ~ 1 0 - 1 3 s , a n d A e : 3.54 K and T O = 1 . 4 ~ 1 0 - 1 0 s , f o r t h e f a s t and t h e slow mecha- nism r e s p e c t i v e l y . We have u s e d M = 4480 Oe / 5 / and w = 6 . 2 8 ~ 1 0 ~ ~ s - ~ 141. On t h e o t h e r hand, t o j u s t i f y t h e magnitude of AH a t 4.2 K u s i n g t h e f a s t r e l a x a t i o n mechanism i t would r e q u i r e a doping of 1.5 % ( a g a i n s t t h e e x p e r i m e n t a l nominal doping of 1.34 % / 4 / ) , w h i c h i s a r e a s o n a b l e r e s u l t . The r e q u i r e d v a l u e of N imp £(@,I$) u s i n g t h e s l o w r e l a - x a t i o n mechanism f o r t h e same p u r p o s e would b e 8 x E n ( c m - ' ) ~ p e r c d
,
which i s of t h e o r d e r of t h e r e s u l t found f o r Mnx F 04 161.eY
F u r t h e r e x p e r i m e n t a l i n v e s t i g a t i o n s f o r temperatu- r e s below 4.2 K a r e needed t o a c c o u n t f o r t h e b e h a v i o r of AH i n t h i s t e m p e r a t u r e r a n g e and con-
s e q u e n t l y a d e f i n i t e c o n c l u s i o n a b o u t which mecha- nism i s e f f e c t i v e l y o p e r a t i n g .
F i g . l a .
8 0 , . , , I I I I I
F i g . Ib.
F i g u r e 1 : S o l i d L i n e i s t h e f i t t o t h e d a t a ( d o t p o i n t s ) o f Bairamov e t a 1 ( R e f e r e n c e / 4 / ) u s i n g : a ) E q u a t i o n (4) f o r t h e f a s t r e l a x a t i o n mechanism, b) E q u a t i o n ( 1 ) f o r t h e slow r e l a x a t i o n mechanism.
R e f e r e n c e s
/ I / See e . g . , Gurevich
,
A.G., Ageev, A.N., and K l i n g e r , PI.T., J. Appl. Phys.2
(1970) 1295; S p a r k s , M., J. Appl. Phys.
2
(1967) 1031; Van Vleck, J.H., J . Appl. Phys.2
(1964) 882./ 2 / See e.g. S t u r g e , M.D., Gyorgy, E.M., Le Craw, R.C., and Remeika, J.P., Phys.
Rev.
180
(1969) 413./ 3 / See e.g. Gurevich, A.G., Karpovich, V . I . , R u b a l s k a y s , E.V., Bairamov, A . I . , Lapovok, B.L., and Emiryan, L.M., Phys. S t a t . S o l . (b)
69
(1975) 731./ 4 / Bairamov, A . I . , Gurevich, A.G., Emiryan, L.M., and P a r f e n o v a , N.N. Phys. L e t t . 62A (1977) 242; Bairamov, A . I . , Gurevich, A.G. Karpovich, V.I., Kalinni'hov,
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V.T., Aminov, T . G . , and Emiryan, L.H., F i z Tverd. T e l a 18 (1976) 687 p o v . Phys.-
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