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VALENCE INSTABILITIES IN MAGNETITE DOWN TO 15 K
A. Hirsch, G. Galeczki
To cite this version:
A. Hirsch, G. Galeczki. VALENCE INSTABILITIES IN MAGNETITE DOWN TO 15 K. Journal de
Physique Colloques, 1979, 40 (C2), pp.C2-320-C2-322. �10.1051/jphyscol:19792112�. �jpa-00218482�
JOURNAL DE PHYSIQUE Colloque C2, supplkment au n O 3, Tome 40, mars 1979, page C2-320
A.A. ~ i r s c h + and G. ~ a l e c z k i ~
Department of Physics, Eindhoven University of Technology, Eindhoven, NetherZands
" ~ e ~ a r t m e n t of Physics, Technion-Israel I n s t i t u t e of Technology, Haifa, Israel
Rbsumi5.- Nous discuterons les instabilitbs de la valence des ions du fer dans Ia magnetite sur la base d'un m6canisme de nuclbation de la charge blectrique en cascade de 15 K jusqu's 151 K. Les
fluctuations de la valence sont btudibes en dBtail vers I5 K par effet Gssbauer. Les tempsratures d'instabilitb de la valence, calcul6es par le modsle proposb, sont en bon accord avec les tempbra- tures dsterminbes par les minima du facteur Debye-Waller.
Abstract.- Valence instabilities in magnetite are discussed in terms of a multi-stage charge-nuclea- tion mechanism which starts at 15 K and continues till 151 K. The formation of fluctuating valence states near 15 K is followed in detail by the Mgssbauer effect. The valence-instability temperatu- res obtained by this model agree well with the temperatures at which minima in the Debye-Waller fac- tor were observed.
This paper provides a model for valence insta- bilities in magnetite (Fe30b). A multi-stage charge- nucleation mechanism is assumed in which a quantum- tunneling process across potential barries (with hight Ui and width D;) tends to remove the electrons from metastable states in which they are trapped by thermally induced lattice distortions. The valence stabilization may start well above the Verwey point
(Tv=119 K) and may continue down to a "stabilization temperature" Tst of about 15 K. The phonon-softening in this mixed oxide spine1 which is demonstrated by a sequence of minima in the Debye-Waller factor (f) determined by Mgssbauer spectroscopy /l/, could be due t 3 thermally induced valence instabilities.
Magnetite seems to contain at 0 K four kinds of cations : 17e3+, Fe2+, ~e'+ and ~e'+ in concentra- tion ratios of 3:1:1:1, respectively. We have shown in a previous paper /2/ the existence of ~e"(3d~) and 17e4+(3d4) ions by analyzing the ~Essbauer spectra down tc 7 K. Moreover, a spectrum of ~ e " was well resolved above 15 K. The presence of cations with I+
,and 1.5+ valences in the low-temperature phase have been predicted by Chikazumi et al. 1 3 1 .
We consider here large unit cells (doubled in all three directions, a =2a) with N=192 cations loca- ted into two types of octants. We assume that within a unit cell a charge-cluster of volume L: may be formed which behaves quasi-independently of the other charges in the sample. There are (4!/21)/2 possibilities in which pairs of different cations
+ Permanent address : Department of Physics, Technion, Haifa, Israel.
can be formed. One have also to differentiate between cations belonging to the same octant, and to diffe- rent octants, so that for the valence transitions
12 kinds of pairs have to be considered. The mass (Mi) of the electrons involved in the charge-nuclea- tion within a cluster changes successively in at least 12 stages at specific "valence-instability tem- peratures" Tci. It was pointed out by Iida et al.
/ 4 / that the electron-ordering occuring under stress
may start "locally" with many "independent nuclea- tion centers". The discrete changes in charge and spin densities we expected here may account for the multiple magnetization reversals in the Verwey tem- perature region observed in low fields /S/, as well as for discrete line-rearrangements in the PGjssbauer patterns 161. The nucleation process contributes to the establishment of a high-temperature phase (at about 150 K) in which only Fe3+ and ~ e cations are ~ "
present.
The stabilization temperature Tst could be de- rived from the equality of the quantum-tunneling charge rate and the thermally-activated one : Roexp
1
-(~/H)/PM(X)U(X)] lhdrl
= ROexp(-Ui/kTst) (1 1Y 2
where 21@(r)~(x)] xd' = (2MiUi) Oi, and the width Di is seen as the size L. of the cluster. We obtain a measure for Li from the uncertainty principle by taking the zero-point energy as equal to Ui. When L.=a =2a, we have U =g2/2ma;. With a=8.4 we
1 0 max
obtain U /k=(Tci)max=151 K. The uncertainty prin- max
ciple was recently applied to valence transition problems in NiO 171. The maximum value of Mi in a clusterisM = < D N ml3,where m is the electron mass,
max
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19792112
while <L> is the average number of electrons trans- mainly formed between 16 and 20 K, and they persist ferred from one cation to another. The transfer of
d-electrons is restricted by Hund's rule. (We have estimated <!L>= 1.59 considering only ferromagnetically coupled cations)
.
Substituting Ui=Umax, M.=M and1 max Di=ao in equation (I) we get :
Ts t
- n21z
'a t m (0.53 (2)0
with a -16.8 A and N=192 we calculate T -15 K. A st
formula analogous to (2) was previously derived for a spin-nucleation process /8/ applying the quasi- particle approach of equation (I) suggested by Stauf- fer 191.
Both the uncertainty principle and equation (1) give rise to the identity :
(umaxlk) b/Mmax) E (Ui/*) (m/Mi)
%
(3)In a first approximation M./M may be taken as
1 max
11/12 with n=1,2,3,
...
12. Integer values of n could be justified if the changes in the mass of the clus- ter proceed in equal steps during the consecutive stages of the nucleation process. If some cations at B sites become antiferromagnetically coupled we may expect a drop in the spontaneous magnetization (U ), as well as a decrease in the number of transferred electrons. In that case one has to introduce also some noninteger values of n.With U /Ui = (Tci)max/Tci, eq. (l) gives : max
Tci = (Tci)ma, ("/l21 v2 (4) Figure 1 shows that the temperatures T cal-
c i culated from equation (4) are in a very good quan- titative agreement with those at which minima in the f-factor are observed, if n=4,5,6
...
1 1 . There isone exception at T
.
However, with n=7.5 we obtain vTci=119 K. The noninteger n in this case may account for the recently reported lowering in as just below the Verwey point /10/.
I ~ I I ; ~
I I$0.5n=41 5 1 6 7 1 8 ' 9 1 0 1 1 I Z
'c theory:
\
l-
,
l l n.751 I I values,
ot Tci1
"-
80 100 120 140 160 T K
-
Fig. I : Debye-Waller factor of pure magnetite nor- malized with its value at 8 0 K. The theoretically derived valence-instability temperatures Tci are indicated.
even till 8 0 K (Fig. 2(b) and (c)). These valences may be generated by the reactions Fe1+ + Fe2+ # 2Fe1*'+ and ~e'++Fe~+ ~ 2 F e ~ ' ~ + . The sextets a and f3 of the Fe1+ and Fe4+ are most pronounced below 15 K (Fig. 2(a)) as predicted by equation (2). Approaching 117 K (Fig. 2(d)) the profile of the second absorp- tion region become more simple : the A-site line (Y) and the broadened B-site "line".
It should be noted that during the last few years many new features were discovered in magnetite at 10-30 K /]l-131. In our opinion the answer to the
"magnetite problem" must be searched in the very low temperature region.
Fig. 2 : Evoluation of the second absorption region of the Gssbauer patterns in magnetite.
Acknowledgments.- Thanks to V.A.M. Brabers for stimu lating discussions. One of the authors (A.A.H.) ex- presses his gratitude to the Eindhoven University of Technology for a Visiting Research Fellowship in sup- port of this work while being in sabbatical leave from the Technion, Haifa, Israel.
Figure 2 shows in detail the evoluation of the se- cond absorption region of the Gssbauer patterns of pure magnetite. The sextets 6 and 8 of the cations with fluctuating valences of 1.5+ and 3.5+ are
JOURNAL DE PHYSIQUE References
/I/ Galeczki, G., Buckwald, R.A. and Hirsch, A.A., Solid State Commun.
2
(1977) 201./2/ Galeczki, G., and Hirsch, A.A., J. Magn.Magn.
Mater.
2
(1978) 230./3/ Chikazumi, S., Chiba, K., Matsui, M., Akimitsu, J. and Todo, S., Proc.Int.Conf.Magnetism, %scow, Vol. 111 (1973) pp.137-139.
/4/ Iida, S., Yamamoto, M. and Umemura, S., AIP Conf.
Proc. (1973) 913.
/5/ Buckwald, R.A., Hirsch, A.A., Cabib, D. and Cal- len, E., Phys. Rev. Lett.
35
(1975) 878.161 Buckwald, R.A. and Hirsch, A.A., Solid State C o w mun.
17
(1975) 625./7/ Keem, J.E., Honig, J.M. and Van Zandt, L.L., in
"Valence Instabilities and Related Narrorband Phenomena", ed. Parks, R.D.(Plenum Press, New York) 1977, pp.551-554.
/8/ Galeczki, G. and Hirsch, A.A., J.Magn.Magn.Mater.
3 (1976) 309.
-
/g/ Stauffer, D., Solid State Comun.
2
(1976) 533./10/ Umemura, S. and Iida, S., J. Phys. Soc. Japan
9
(1976) 679.
/l11 Todo, S. and Chikazumi, S., J. Phys. Soc. Japan 43 (1977) 1091.
-
1121 Chikazumi, S., AIP Conf. Proc.
13
(1975) 382./l31 Kronmuller, H., J.Magn.Magn.Mater.5 (1977) 280.
