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OBSERVATION OF CRITICAL FLUCTUATIONS USING MÖSSBAUER SPECTROSCOPY
G. Hoy, M. Corson
To cite this version:
G. Hoy, M. Corson. OBSERVATION OF CRITICAL FLUCTUATIONS USING MÖSS- BAUER SPECTROSCOPY. Journal de Physique Colloques, 1980, 41 (C1), pp.C1-225-C1-226.
�10.1051/jphyscol:1980172�. �jpa-00219741�
JOURNAL DE PHYSIQUE Colloque C l , supplcfment au n O 1 , Tome 41, janvier 1980, page (21-225
G.R. Hoy and M.R. Corson
Department o f Physics, Boston University, Boston, Massachusetts 02225, USA.
Critical fluctuations in the neighborhood of a magnetic phase transition can be observed using M8ssbauer spectroscopy if the spin fluctuation rate of the atom containing the MBssbauer nucleus slows down sufficiently at the critical tempera- ture.l We have observed such a critical slowing down of the spin fluctuations near the N6el tem- perature of the antif erromagnet K2Fe04.
Consider an iron-57 atom with: no orbital angular momentum, totalelectronic spin S=1, and non-degenerate atomic eigenstates Sz=l, 0, and -1. Assume, for simplicity, that the
XI - 3
hyperfine interaction can be represented by an effective magnetic field in the z-direction at the nuclear site, and that this magnetic field takes on the values -H, 0, and +H when Sz=l, 0, and -1, respectively. If the atom undergoes transi- tions among these eigenstates due to relaxation in the solid, we must determine the magnetic field that the nucleus experiences.
Consider the cases of slow, fast, and inter- mediate relaxation shown in figure 1. By the time-energy uncertainty principle, the time re-
FAST
--"'-
I IINTERMEDIATE p v
quired for a nucleus to measure a hyperfine mag- netic field is approximately the Larmor period of the nucleus in that field, which for iron-57 is typically sec. If the atomic relaxation is slow, and an atom spends many Larmor periods in each eigenstate, then a Mtissbauer nucleus experi- ences a magnetic field -H, 0, or +H depending on the state of the atom containing the nucleus. In this case, the Mtissbauer spectrum is the Boltzmann- weighted sum of three spectra characteristic of these three fields. An example is shown in the upper curve in figure 1. The four outer peaks are from nuclei which experience magnetic fields H and -H, and the large central peak is from nuclei of atoms in the state Sz=O, i.e., H = O .
If the atomic relaxation rate is fast compared to the Larmor frequency, then the nucleus cannot respond to the individual fields H, 0, and -H, and all nuclei experience the same, single valued, hyperfine magnetic field which is the Boltzmann- weighted average of these three values. A typical spectrum is shown as the middle curve in figure 1.
Note that the central peak in the slow relaxation spectrum is completely absent under conditions of fast relaxation because the magnetic field of zero has lost its individual identity. 'Furthermore,
the overall width of the fast relaxation spectrum is less than that of the slow relaxation spectrum.
If the atomic relaxation rate is comparable to the nuclear Lamor frequency, then the hyper- fine magnetic field experienced by the nucleus is FIGURE 1 not well defined. This gives rise to a "relaxation
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1980172
cl-226 JOURNAL DE PHYSIQUE broadened" spectrum, t h e lower c u r v e i n F i g u r e 1.
K2Fe04 i s a n a n t i f e r r o m a g n e t w i t h a Ne'el t e m - p e r a t u r e TN = 3 . 6 ~ . l The i r o n atom i n K2Fe01, i s i n a nominal 6+ c h a r g e s t a t e , and t h e two remaining d - e l e c t r o n s a r e coupled w i t h p a r a l l e l s p i n s and no o r b i t a l a n g u l a r momentum t o y i e l d J = S = 1. The p o i n t s i n Fig. 2 show o u r e x p e r i - m e n t a l Mgssbauer t r a n s m i s s i o n s p e c t r a of p o l y c r y s - t a l l i n e K2Fe04 a t 3.6K and 3.55K. Although t h e s e
VELOCITY (mm/sec)
'FIGURE 2
s p e c t r a e x h i b i t some r e l a x a t i o n broadening, a com- p a r i s o n w i t h F i g u r e 1 shows t h a t t h e 3.6K spec- trum i s c h a r a c t e r i s t i c of S = l s l o w r e l a x a t i o n , and t h e 3.55K spectrum i s c h a r a c t e r i s t i c of f a s t r e l a x a t l o n . Note t h a t t h e c e n t r a l peak which i s prominent a t 3.6K i s m i s s i n g a t 3.55K, and t h a t
t h e o v e r a l l width of t h e spectrum a t 3.6K is g r e a t - e r t h a n a t 3.55K. T h i s slow atomic r e l a x a t i o n a t 3.6K mzy b e due t o t h e proposed c r i r i c a l s l o w i n g down o f t h e i r o n atom s p i n f l u c t u a t i o n s a t t h e N6el t e m p e r a t u r e .
We have used t h e s t o c h a s t i c r e l a x a t i o n t h e o r y of l i n e s h a p e of C l a u s e r and ~ l u m e ~ , ~ t o f i t o u r e x p e r i m e n t a l Miissbauer s p e c t r a o f K2Fe04 between 0.16K and 4.2K. The d e t a i l s o f o u r c a l c u l a t i o n w i l l b e p u b l i s h e d e l s e w h e r e . Two of t h e s e t h e o r e t i c a l s p e c t r a are shown as s o l i d c u r v e s i n F i g u r e 2. The atomic r e l a x a t i o n r a t e and micro- s c o p i c magnetic o r d e r i n g p a r a m e t e r d e r i v e d from t h e c a l c u l a t i o n a r e shown i n T a b l e 1. It c a n b e s e e n t h a t t h e r e l a x a t i o n r a t e drops by
Temperature (OK) 3.60 3.55 3.50 3.00 2.50 1.00 0.16
Magnetic Ordering Parameter
0.004 0.45 0.55 0.70 0.80 1.0 1.0
R e l a x a t i o n R a t e ( s e c - l ) 5.5 x
l o 6
1 . 5 x 1 0 9 1 . 2 ~ 1 0 9 7.1 x
l o 8
3 . 1 x 1 0 8 0.0 0.0 TABLE 1
a l m o s t t h r e e o r d e r s of magnitude a t t h e Ndel tem- p e r a t u r e , i n agreement w i t h t h e above d i s c u s s i o n . Furthermore, t h e m i c r o s c o p i c magnetic o r d e r i n g parameter can b e s e e n t o f o l l o w a m a g n e t i z a t i o n - t y p e c u r v e from low t e m p e r a t u r e s up t o t h e Ndel t e m p e r a t u r e of 3.6K. Above 3.6K, t h e Mtissbauer s p e c t r a of t h e two samples we have s t u d i e d d i f f e r . We a r e c u r r e n t l y a t t e m p t i n g t o r e s o l v e t h i s d i s - crepancy.
We wish t o thank P r o f e s s o r R. H, Herber f o r s u p p l y i n g t h e samples ofK2Fe04, and Dr. S. Redner and D r . P. Reynolds f o r v a l u a b l e d i s c u s s i o n s .
*
Work s u p p o r t e d b y N.S.F., Grant CDMR 77-19017 [ l ] HOY, G.R., CORSON, M.R., B u l l . Amer. Phys.Soc.
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(1979) 427, JG7.[ 2 ] OOSTERHUIS, W.T., BARROS, F. De S . , J. Chem.
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