Electronic magnetic relaxation in manganese ferrites
Citation for published version (APA):
Brabers, V. A. M., & Scheerder, A. A. (1988). Electronic magnetic relaxation in manganese ferrites. IEEE
Transactions on Magnetics, 24(2, Pt. 2), 1907-1909. https://doi.org/10.1109/20.11642
DOI:
10.1109/20.11642
Document status and date:
Published: 01/01/1988
Document Version:
Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers)
Please check the document version of this publication:
• A submitted manuscript is the version of the article upon submission and before peer-review. There can be
important differences between the submitted version and the official published version of record. People
interested in the research are advised to contact the author for the final version of the publication, or visit the
DOI to the publisher's website.
• The final author version and the galley proof are versions of the publication after peer review.
• The final published version features the final layout of the paper including the volume, issue and page
numbers.
Link to publication
General rights
Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain
• You may freely distribute the URL identifying the publication in the public portal.
If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, please follow below link for the End User Agreement:
www.tue.nl/taverne Take down policy
If you believe that this document breaches copyright please contact us at: openaccess@tue.nl
IEEE TRANSACTIONS ON MAGNETICS, VOL. 24, NO. 2, MARCH 1988 1907
ELECTRONIC MAGNETIC RELAXATION
IN
MANGANESE FERRITESV.A.M.
Brabers andA.A.
Scheerder, Department of Physics, Eindhouen Uniuersity o f TechnoLogy,P.O. Box 513. 5600 MB Eindhoven. The Netherlands
Abstract
Two electronic magnetic relaxation phenomena are reported for the manganese ferrite system, which are both explained by electron hopping processes between octahedral iron ions: the first one by hopping between Fez+ and Fe3+ ions with a Mn2+-ion as nearest neighbour and the second one by hopping between iron ions with only iron nearest neighbours.
Introduction
It has been well established that in high- permeability spinel ferrites. the dispersion of the dynamic magnetic permeability and the maxima in the loss factor are caused by electron diffusion between cations present in different valency states like e.g. the Fez+ and Fe3+-ions1q2). However, in the manganese ferrite system, MnxFe3-x04. two distinct electronic relaxation phenomena are observed around the composition x = 0 . 8 . with activation energies of 0.015 and 0.06 eV. respectively3). The assignment of these two relaxations to elementary processes is still controversial: inter- and intra-atomic electron transitions between the Fe-ions are claimed as one interpretation. whereas electron transitions between iron ions and/or manganese ions are another4). In the present paper, the composition dependence of the electronic magnetic relaxations in the manganese ferrite system is reported and compared with the analogue Zn ferrite system, from which indications about the origin of the two relaxation processes in the Mn-system are obtained.
Experimental
Polycrystalline manganese and zinc ferrous ferrites toroids with inner and outer diameters of 30 and 35 mm. respectively, were prepared by ceramic techniques. Special precautions were taken to obtain single phase spinel material^^-^). The complex initial permeability was measured by means of a LCR resonance method, using coils wired on the ferrite toroids, in the temperature range of 4-300
K
and frequency range of 20-500 kc/sec. For all the measurements the maximum value of the magnetic induction used in the experiments was 5.10-5 T. independent of the frequency.20
16
12
8
4
0
0
50
100
150
200
250
c;'
Fig. 1 The complex permeability p = p'-jp" for Zn0.4Fe2.604 at 95 kc/s as a function of temperature.
55
44
33
22
11
P"
0
0
T ( K )
I I I I I 1 I I I0
Fig. 2a20
15
10
5
If
0
and bp'* as function of temperature for the Mn and Zn ferrite system with the additional parameter x. the zinc or manganese concentration.
Results and Discussion
For a11 the manganese as well as for the Zn ferrite materials, clear exponential magnetic relaxation effects are found in the complex permeability (p'-jp").
A
typical example is shown in fig. 1 . where the temperature dependence of p' and p" is plotted for Zn0,4Fe2.60? at 95 kc/s. From the exponential shift of the maxima in p" with frequency, activation energies are determined as functions of the compositon of the ferrite.In fig. 2a and 2b. the imaginary part p" is plotted as a function of temperature with the manganese and zinc content
X
as a parameter. In the zinc ferrite system only one electronic relaxation phenomenon is observed, as can be seen from the single peak in the p"-T curve. In the manganese system, however. two relaxation phenomenaA
andB
are observed1908
-
>
W-
a
W0.120
0.096
-0.0 72
0.0
4a0.0 24-
--
-
- 1 1 ' 1 1 1 1 1 ' 1 10
0.2
0.4
0.60.8
1.o
concentration x
Fig. 3 The activation energy of the electronic relaxation in the zinc ferrite system compared with the activation energy of process A in the manganese ferrite system.
for the compositons between 0.6
<
x<
0.9, and only one for compositions with a lower manganese content x<
0.5. In fig. 3 the activation energy of the magnetic relaxation effect in the zinc ferrite system is compared with the energy determined from the manganese system; for the manganese composition between x = 0.6and x = 0.9, the values for the low temperature effect A has been plotted. From the nearly identical values of the energies for the manganese and zinc concentration below x = 0.6 and the rather small and gradual changes in
EA
with increasing Mn-concentration, the conclusion seems to be obvious, that the electronic relaxation phenomenon observed in the zinc ferrite system and the phenomenon A in the Mn-system are due to the same mechanism, i.e. a transfer of electrons between adjacent Fe2+ and Fe3+ ions on the octahedral sublattice of the spinel structure. This conclusion is further supported by the fact that the Zn2+-ions are located on the tetrahedral sublattice of the spinel structure, which results in a concentration of (I-x)Fe2+ ions on the octahedral sites; In the manganese ferrous ferrites. the Mn2+-ions have also a tendency to be located on the tetrahedral sites8), which results in a nearly identical ionic configuration for the octahedral sublattice in both systems: (l-x)Fe2+ ions and ( I+x)Fe3+ ions.Electrical conductivity measurements we performed on single crystals showed further that the composition dependence of activation energy for the conductivity behaves in a similar way as the magnetic activation energy, which is a strong evidence for the proposed Fe2+-Fe3+ electron exchange mechanism.
An additional evidence for the same origin of the Fe2+-Fe3+ relaxation in the zinc ferrite system and the mechanism A in the manganese system is the equal pre-exponential factor -r0 describing the exponential relaxation in both s stems: T ~ =T exp-E'kT: with T~ varying between 10-1z-10-9 s depending on
X
(Mn2+ o r Zn2+ concentration).Now, it seems apparantly to attribute the mechanism
B
in the manganese system to the occurrence of an increasing number of octahedral Mn2+, as it is known that for x = 1.0 up to 202 of the manganese ions can be located on the octahedral lattice. depending on the thermal treatment of the specimens8). In order to study this in more detail, we performed permeability measurements on a specimen Mng.gFe2.204 after different thermal treatments to change the octahedral Mn-concentration. As the absolute value of p*' can also depend on the value of p', due to the microstructureof the specimens, the loss tangent 6 = p ' ' / t ~ ' is now plotted in fig. 4 . The phenomenon A turns out to be independent of the thermal treatment, whereas the strength of relaxation B is strongly influenced by the annealing treatment i.e. by the octahedral Mn-concentration. The relaxation
B
can not be attributed to an electron-transfer between Mn2+ and Mn3+ or Fe3+ ions, because the energy needed for such a transition exceeds 0.3 eV g ) , whereas for the processB
we found values ofE
between 0.060 and 0.075 eV. However, the annealing experiments show clearly that the concentration of the octahedral manganese ions affects the relaxationB!
0.5 I I I I I I
oMn(08)
10
50 100 150 200 250T ( K )
Fig. 4 Temperature dependence of the loss tangent
p " / p ' of Mn0.gFe2.20~ measured on specimens after different heat treatment.
1. As prepared and cooled from 130OOC to room temperature in 2 hours.
2. Annealed at 800°C in sealed silica tube, and cooled within 30 minutes to room temperature. 3 . As 2 but quenched to room temperature.
The peak in the p**-T curve for the relaxation A in the Mn-system can be fitted by one single exponential relaxation, which means that there does not exist a distribution of relaxation times for this mechanism. The same sharp relaxation was observed for the Zn-system but a similar investigation of the relaxation in e.g. nickel ferrous ferrites showed substantial broadening of the p"-T peak indicating a distribution in relaxation times for the Ni-ferrous ferrite systemlo). The different behaviour of the Zn and Mn ferrites on one side and of the nickel ferrite system on the other can be related to the inverse structure of the nickel ferrites. The Ni2+ ions are located on the octahedral sites, by which the electronic energy levels of the iron- nearest neighbours will be influenced by the deviating charge of the Ni2+ ion. In fact, one expects the activation energy for the electron transfer between the iron ions to depend on the number of Ni2+ nearest neighbours, and since the Ni2+ and iron ions will be statistically distributed on the octahedral sites, a distribution in relaxation times is expected. In the zinc ferrites only electronic and no static ionic disorder on the octahedral sites is possible, closely related to the Fe2+ and Fe3+ charge distribution and only one single relaxation time is expected for the electron hops between the adjacent iron ions. For the manganese ferrites we have more or less the same situation as for the zinc ferrites. with an exception for larger Mn concentrations between x = 0.5 and 1.0, where some Mn2+-ions are entering the octahedral sublattice. The
1909 most obvious explanation of the mechanism tor
relaxation B is an electron transfer between Fez+ and Fe3+-ions which are adjacent to an octahedral Mn2+-ion. h e to the bivalent manganese ion and the relative large diameter of the Mn2+-ion. there must be a distinct effect upon the energy levels of the neighbouring iron ions, which results in a quite different relaxation time for an electron hop between Fez+ and Fe3+-ions with or without a manganese nearest neighbour.
For the composition x = 0.8 about 5% of the octahedral sites are occupied by Mn2+ ions7). which seems to be an optimum for the simultaneous appearence of relaxation
A
andB.
Both relaxations can be interpreted on the basis of electrm hopping between Fez+ and Fe3+ ions only, if we take a certain ionic disorder on octahedral sites into account: processB
is caused by electron hopping between iron ions with an octahedral Mn2+ ion as nearest neighbour and processA
is caused by the electron hopping between iron ions without Mn2+ as nearest neighbour. So we can conclude that in the manganese ferrite system the presence of octahedral Mn2+-ions introduces a static ionic disorder, which gives rise to the occurence ofI 8
-
detached electronic magnetic relaxations. two c11 c21 131
c41
~ 5 1 C61 c71P I
c91 ClOl ReferencesJ . Smit and H. Wijn, Ferrites, Eindhoven. Philips
Publ. (1959).
S. Krupicka. Physik der Ferrite, Braunschweig Vieweg. (1973).
A.
Broese van Groenou, Low frequency magnetic relaxations in manganese ferrous ferrites at low temperatures, J. Phys. Chem. Solids28,
325(1967).
S. Krupicka and K. Zaveta. Magnetic-after effects in ferrimagnetic oxidic spinels. J . Appl. Phys. -
39, 930 (1968).
A.L. Stuyts.
D.
Veeneman. Preparation of ferrous zinc ferrites with high saturation magnetization,A. Broese van Groenou. Proc. First Int. Conf. Ferrites, University of Tokyo Press, 236 (1970).
B.
Gillot. R.M. Ben Loucif andA.
Rousset, Electrical conductivity of zinc-iron ferrites in vacuum and in the presence of oxygen. Phys. Stat. Sol.65,
205 (1981).V.A.M. Brabers, Thesis Eindhoven University of Technology (1970).
V.A.M. Brabers. Cation migration, cation valencies and the cubic-tetragonal transition in manganese ferrites,
J.
Phys. Chem. Solids2 .
2181 (1971).V.A.M. Brabers and J . H . Hendriks, Electronic magnetic relaxation in manganese ferrites. Sol. State Comm.
5.
795 (1968).1910 IEEE TRANSACTIONS ON MAGNETICS, VOL. 24, NO. 2, MARCH 1988
LOW T E M P E R A T U R E ELECTRICAL PROPERTIES O F PlAGNETITE A N D Mn-FERRITES
Zdengk SirnSa and V i c t o r A . M . B r a b e r s ( 1 )
I n s t i t u t e o f P h y s i c s , C z e c h o s l o v a k Academy o f S c i e n c e s , 1 8 0 4 0 P r a g u e 8 , C z e c h o s l o v a k i a 5 6 0 0 MB E i n d h o v e n , The N e t h e r l a n d s ( 1 ) O e p a r t r n e n t o f P h y s i c s , Eindhoven U n i v e r s i t y o f T e c h n o l o g y E 1 e c t r i ca 1 res i s t i v i t y a n d t h e rmoe 1 e c t r j c: power' m e a s u r e m e n t s h a v e b e e n made o n s i n g l e c r y s t a l s of manganese f e r r i t e s , MnxFeg.404 ( x
=
0 , 0 . 5 , O . ' l , 0 . 8 , 0 . 9 a n d 0 . 9 5 ) i n t h e t e m p e r a t u r e r a n g e 10 K t o 300 K . Below t h e Verwey t r a n s i t i o n Tv of m a g n e t i t c , t h e thcrmo- e1ectri.c power i s s t r o n g l y i n f l u e r i c e d by t h e o x y g e n n o n s t c ) i . c h i o m e t r y o f t h e samp.les w h e r e a s t h e r e s i s t i v i t y e x h i . b i t s hard1.y a n y d e p e n d e r i c c on t h e c h a n g c s of t h e o x y g e n c o n t e n t . S t a r t i n g f r o m t h o ].owest t e m p e r a t u r e s , t h e e l e c t r i c a l p r o p e r t i e s are e x p l a i n e d i n terms of t h e i m - p u r i t y b a n d , v a r i , i h l e r a n g e h u p p i n g , small. p o l a r o n lxind a n d s m a l l p o l a r o n h o p p i n g c o n d u c t i o n mechanisms w h e r e t h e l o r i g - . r a r i g e a n d t h e s h o r t - r a n g e o r d e r i n g s h a v e t o be t a k e r i i n t o account,.
-. 1 nt. . ... ..- r o d u c . . .. . t j on _ _ F:xtensive e x p e r i m e n t a l a n d t h e o r e t i c a l . work h a v e b e e n d o n e t o u n d e r s t a n d t h e e J ec t on i. c 6 t, ruc t id re a n d c: 1 e c t r i c a l t, 3'811s p o r t mechanj.smc, i n m a g n e t i t c ( E ' e 3 0 4 ) a n d o t h e r s p i n e l f e r r i . t t : s . S t a r t i n g w i t h t : a r l y i n v e c t i - g a t ' i o n s oi Vcrwey [ 1 , 2 1 who d i s c o v e r e d a jump o f t w o - o r d e r s of magnjl.ude of t h e e l e c t r i c a l r e s i s t i v i t yp
, of m a g n e t i t e a t Tv w 1 2 0 K , a v a s t number ok p a p e r s h a v e b e e n d a v o t e d t o s t u d y i n g 0 1 t h i s f i - r s t - o r d e r ct.rur;l,ura3., rilagnetic a n d e l e c t r i c a l p h a s e t r a n s i t , i o r i ( s e e 111 t h e same t i m e , work o n t h o e l e c t r i c a l properLir:n o f the: " . s u l J : i t i t u t e d m a g i i e t i t c r , " , s mixed f e r r i t e s l i k e c o b a l t f e r r j LasL S l ,
manganesc f e r r i t c s[ l o ,
SI],
n i c k e l f e r r i t a s [123 e t c . was g o i n g o n , r e v e a l i n g t h a t t h e c l a s s i c a l s e m i c o n d u c t o r o n e - el c t c t r o n b a n d p i c t u r e b r e a k s down. A new concept.. o f mort; o r less 1 o c a l i . z e d charge c:arric:.rt; ( m a l 1 p o l a r o n s ) was d e v e l o p o d t o a c c o u n t . l ' o r t h c o b s o r v c d e l e c t r i c a l , m a g n e t i c a n d o p t i c a I properties c f m o n o x i d e s ,si0 s q u i. o K i t i c s ;I tid mo rc.: ccmp :le x m:rgne;. t i r; o x i d i c r n a l e r . i a l s ( i ' c x r r e v i e w s see e . g . [13--161). . ~ u n L a s p l i t . t . i n g of t h e ccinduc- w a s p o s s i b l e t o e x p l a i n a com- e . g . [ z - - s j j . p1.c.:~ l l ~ h a v i o u r o f t h c tliermoelectric power a n e a r
T,
i n t h e c a s e of m a g n e t i t e [l6,17]. Howcvor, thc: o h s e r v e d d e p e n , l e n c e s o f e 1 e c l . r i c a l . p r o p c r t i e s o f f e r r i t e s at. low t e n i p c r a t u r c : ; r e v e a l e d e a r l y .>n t h a t t h e simple s m a l l p c l l a r m p i c t u r e must. be m o d i f i e d i n a t J.car,t, t.wc ways: u J i m p r i r j t i 6 s p r e s e n t i n f e r r i t r ? s i n t r o d u m b a n d c o n d u c t . i o r i or h o p p i n g of c h a r g e c a r r i e r s w h i c h becomes i m p o r t a n t a t low t e m p a rCi t u rt : c; ; b ) corr-el at,i 011 e f f e c t s m u s t b e i n t r o d u c e di r i t c , Ltil; srn:iLJ polariiri t l i e o r i e s .
I n :,u(:h i~ way, t h e b n h a v i u u r of t h e ' v i t,y a n d ~ , } - i ~ - ~ r ~ i [ . , p [ i w f ~ I ~ of the.
e t l rnagnnt,i-te. [ 181 a f l d
I.ow t o m p c r a 1.1 op' !r t it: J t l i < , i c e 1 f < ; J-I' ;
C
191 were d e s c r i b e d . C o n s i d e r i n g t h e c o r r e l a t i o n e f f e c t s of s m a l l p o l a r o n s ( l c a d i i i g t o s h o r t r a r i g e o r d e r i n g ) I h l e a n d Loreriz [20] w e r e a b l e t o e x p l a i n t h e c o n d u c t i v i t y m a x i m u m o c c u r r i n g i n m a g n e t i t e a t a b o u t 300 I(. I n t h i s r e p o r t , a more detailed i n v e s t i g a t i o n of t h e e l e c t r i c a l r e s i s t i v i t y a n d t h e r m o e l e c t r i c powcr. o f s e v e r a l sdmple?, c i f m a g n e t i t e i s mads i n o r d r - r t c J r;l:irify t f i c b e h a v i o u r of a b a l o w T,J M e n s i r r r m t A n t s of e l e c t r i c a l p r o p e r t i e s o f i r o n - r i c h n i d r i g a n o s s f e r r i t e s g i v e f u r t h e r i n f o r m a t i o n s on t h e i n f l u e n c c of s u b s t i t u t i o n a l d i s o r d e r o n t h c b e h a v i o u r of c l i a r & e c a r r i e r s S i n g l e c r y s t a l s of m a g n e t A t e a n d m a n g a - ncsc: f e r r i t e s i.n t h e s y s t a i n MnxF'c3_ x04 were p r e p a r c d by t h o t r a v e l l i n g - m o l t e n ~ curie t e c h n i q u e a s d e s c r i b e d e l s e w h e r e [ 2 1 ] . A f t e r g r o w t h t h e s i n g 1 e c r y s t a l r o d s ( a p p r o x.
!)mm i n d i ame t e r ) w o r e add i. t i o n a 1 1 y Th=14'70 K f o r 70 hours a n d s l o w l y c o o l e d t oroom t e m p e r a t u r e i r i c o r k t r o l l e d atmusphere:; , t,o s e c u r e t h e a d j u s t e d o x y g e n s t o i c h i o m e t r y
.
From t h e r o d s , r e c - t a n g u 1 . a r s a m p l e s of 1 ~ 5 x 1 2 tr1n13 w e r e c u t a n d f i n e l y p o l i s h e d . The r e n i a i n j iig p a r t s of t h e c r y s t a l s w e r e u s e d f o r c h e m i c a l a n a l y s i s t o d e t e r m i n o f i n a l c o n t e n t s of c a t i o n s a n d t h e a c t i v e o x y g e n . R e s u l t s of t h e a n a l y s i s , p a r t i a l o x y g e n p r e s s u r e s d u r i n g h e a t - t r e a t m e n t a n d c r y s t a l a x e s a r e l i s t e d i n T a b l e 1 . I t was f o u n d t h a t t h e g r a d i e r i t . ? , i n c h e m i c a l c o m p o s i t i o n s a l o n g or across t l i e s a m p l e s were w i t h i n t h e e r r o r 1 . i m i . t ~ rrif c h e m i c a l a n a l y s i a ( i . e . 0 . 0 2 a n d 0 . 0 0 2 f o r x a n da'
r c s p . ) . E l e c t r i c a l . c o n t a c t s w e r e m s d c by r u b b i n g i n an e u t e c t i c In-Ga alloy a t t h e o p p o s i t e f a c e s of t h e s a m p l e s . h e a t - t r e a t c d a t A f o u r p o i n t d c p o t e n t i o m c t r i c method w a s u s e d t o d c t e r m i ne t h e e l e c t r i c a l re;i:.,t,ivi t yof L h c l a t r r e s i n t i v c s a m p l e s at ~ ; ~ c ; ~ . ~ i i ~ . c u r r e n t d c r l s i t . i e!.;. Kcsi:it.anr:e:; (acc1.11
I > u t . t c r . than 1 X j V I C : I ' C d e t c r l n i r ~ c r l a{
c u r r c r i t valucs wlicre 0hm's l a w was P u l i ' i l l e , ] A t 1 o w t r: nipe r a t u r $2 s whc n r C: a the: d
10'; 52 t i v(>lt.age d r o p at, prober; was dettjrmiclcd u s i n g :.I K c i t h l c y 6 4 0 el.ectroirieitar wit11 t h e i r l
p u t r e s i s t a n c e e x c e e d i n g Q . A t v e r y hig1-1 r e s i . s t a n c e s (>lo1'. Q ) a t w o p o i n t method e x p l o i t i n g a f e c d - b a c k l o o p o f t h e e l o c t r c l - meter w a s u s e d . Sample t e m p e r a t u r e w a s v a r i e d by means of a l i q u i d h e l i u m c o n t i n u o u s - f low c r y o s t a t ; t e m p e r a t u r e c o n t r o l ( w i t h a c c u r a c y of 0 . 1 1 0 w a s a c h i e v e d w i t h a DTC 2 ( O x f o r d i n s t r u m e n t s ) con t r o l l e r c o n n e c t e d t o a C . L . T . S . s e n s u r .
IherNjaals.c;tria.
.gmr=.r. re ;:i s t a I i u e 5 To d e t e r m i n e t h e t h e r m o e l e c t r i c power p e r 1 1C (Seeback c o e f f i c i c n t a ) t h e o p p o s i t e erldn o f t h e sample wcre c l a m p e d i n t h e arnis of t h oalurni n j . z e d s a m p l e h o l d e r ( e n a t l i r l g a good t h e r m a l c o n t a c t a n d s e c u r i n g a h i g h elect.ri.ca1 i s o l o t i u t i n f sample from t l i c h o l d e r ) , The a r m -
c o u l d b o i n d i v i d u a l l y h e a t e d t o e s t a b l i s h a trmpur;aturc: g r a d i e n t s u p t o 5 K / c m a l o n g t h e s a m p l e i n b v t k d i r e c t i o n s . T e m p e r a t i i r e s n f a r m s wc2ro m e a s u r e d b y A u + 0 , 0 3 %Fe v s , ctiromc:l t h e r m o r w u p l e s a n d t h e t h e r m o p o w e r s g e n e r a t e d liy Leuipt?ratiAKe g r a d i e n t . . ; were d e t e r m i n e d b y o p e n itipiut K e i t h l e y 6 4 0 e l e c t r o m e t e r . SI opes o f t , l i e t.tiamiop,ower V . T . t e m p e r a t u r e d i f f e r e n c e s pl.cts were u s e d t o c a l c u l a t e t h e v a l u e s of u . EGZ!AltZ Magr!.2t.lt.ns
.
II rc d c:p*-:n den C E s of t h a e 1 e c t r i c a 1 v,=, .l/'r
r e p r e s c n t , a t i o n arc shown i n F i g s . < , 2 . Le s a m p l e s in l v g I t i s st-rfo t h a t wit.11 t h e e x c e p t i o n of t h e h i g l i l y nor1 R t,ciii:hioniet-ric s a m p l e A a l l o t h e r s p e c i i n e n s Iiave i d c n t i c a l t e m p e r a t u r e d e y e n d e n c c s of r e s i s t i v i t y down t o 1 0 K. AlthoiJgh t h c c o n c e p t of a c t i v a t i o n e n e r g y h a s d i f f c r e n t m c a n i n g s i n v a r i o u s t h e o r i e s uf t r a n s p o r t mcchanisms i t i s w o r t h w h i . l e ( f o r t h esake of c o m p a r i s o n and e s t i m a t i o n ) t o d e f i.ne a c o n d u c t i v i t y a c t i v a t i o n e n e r g y a3 ( 1 ) E ( e V ) = 1 . 8 9 5 * 1 0 - . 4 d ( l o g p ) / d ( l / T ) V a l u e s of E a s d e t e r m i n e d for t h e m a g n e t i t e s a m p l e s j u s t a b o v e a n d j u s t b e l o w t h e Verwey t r a n s i t i o n a n d a t 10 K a r e l i s t e d i n T a b l e 2 . I I
'2t
2 4 6 K i g . 2 . Temperature d e p e n d e n c e s o f t h e r e s i s t i v i . t i . e . s o f m a g n e t i t e s a t 10K
t o 1 0 0 K ( s e x T a b l e 1 f o r s a m p l e d e t a i l s ) . The t c m p e r a t u r e d e p e n d e n c e s of t h e t h e r m o e 1 e c t r i . c power for r e p r e s e n t a t i v e s a m p l e s o:f m a g n e t i t e a r e d e p i c t e d i n F i g . 3 . 'l'h-2 o t h e r s a n i p l c s d i s p l a y i n t e r m e d i a t e b e h a v i o u r arid, t o a v o i d p o s s i b l e c o n f u s i o n , were ncr,t i n c l u d e d i n F i g . 3 . A s a l i e n t f e a t u r e i.7 l . h e s t r o n g d e p e n d e n c c of a b c l o w Tv 'II th<l-. h c n t t . r e a t r n e n t c o n d i t i o n s of s a m p l e s , a s c~ppo:~e<l t o t h e s m a l l c h a n g e s of a a b o v e T V w i t h u r e m a i n i n g p r a c t i c a l l y c o n s t a n t u p t o room t c r r i p e r a t u r s . The m o s t r e m a r k a b l e i s t l i c behavioi.ir o f s a m p l e G w h e r e a t r a n s i t i o n from i i - t y p c t , c p t y p e c o n d u c t i v i t y occurs a t l ( l l J 1: f o l l c 8 w c : d Gy a maximum a t 8 0 K a n d a n ~ . ~ t , I w r t i . n t l : , i I i , ' J r l t i o n typc: at, a b o u t 50 K . U t . I o r < / t r ~ K , I I 1 :;ampI.%a b e h a v e i n a s i m i l a r ~ I I ~ ~ I I I I S : ~ . wi 1 . 1 1 a 7 0 f-jrT-0.
1912
1
150 loo T [ U ] 50 I I 2 4 6 6 10 F i g , 5 , l ' t ; m y r , - r n t u r c d e p e n d s n z e s o f t l i c c1c:ctri c a l r e s i r , t i v i t i e s o f Mn --f c r r i t c s i n 10I< t o 1rJCl I< i-agi.<>n. 'rhc s y m b o l s i n d L c a L e t h e va r i o u s c un tent :5 CI f mangan r~ :; e
.
In E i g
.
G ternpcrat ur'e dcpcndcii5ccs <.if thf: SeeLei-k c ; o u f l ' i c i c n t s of Mn- f e r r i t e s a r c r u p r c s e n t e d , S t a r t i n g a t r o c m t e m p e r a t u r e a s l i g h t i . n c r e a s c ' rjf a i n d c c r e a s i r i gt e m p e r a t u r e : , i s f i r s t 01JscrVed. l r i thc: 1511 K t o 50 K r e g i o n u reache.-; a maxiniuni iollowed b y a r e g u l a r dec:i-c;tst: ( d ~ w n t < J z t - r ~ i ) w!-~er. T ~~, (J.
A nuiabsr o f c o n d u c t i o r i m c c l i m i i:.,tn;.> G I C t suggest.,cd t o a c c u u n t . f o r t h e complex b i ; h i v i . r u r of t i l e t e m p e r a t . u r l : depcnderice of t l - 1 , . e l c c t r i . c a 1 r e c i s t i v i t y o f m a g n c t i t c . L r i a g r e e m e n t w i t h o t h e r e x p e r i m e n t s [ 2 2 , 2.3 J c ' u r low t e m p e r a t . u r e s m e a s u r e m e n t s c o n f i r n ; t l t t : i m p o r t a r i c e o f t h e i m p u r i t y c o n d u c t i o n mechanism. The i m p u r i t i e s i n t h e f o r m o f c a t i o n v a c a n c i e s a r e i n t r o d u c e d i n m a g n e t i t e a5 a r e s u l t of t h c o x y g e n r t o n s t o i c t i i ~ ~ m e t ~ - y ( s e e T a b l e 1 ) a c t i n g a s d o n o r c e n t r e s . I n manganese f e r r i t e s , t h e i m p u r i t y l e v e l s a r e a l s o f o r m e d by t h e e l e c t r o n s t r a p p e d a t . o c t a h e d r a l M i l 3 - + i o n s i t e s or i n t h e n e i g h b o u r i n g i r o n i o n s ( f o r d i s c u s s i o n of t h e t r a p p i n g c e n t e r s see [ 10,313. 'The t h e o r y of c CI r re 1 a t e d t o i m p u r i t y b a n d c o n d u c t i o n 1 2 4 1 y i e l d s f o r !.he t e m p e r a t u r e dopundcrice of r e s i s t i v i t y t h e f o l l o w i r i g f o r m u l a h o p p i rig t r a n s p o r t 1 e ;3. d i rig ( 2 )
c
=
p.
T-n R e l a t i o n ( 2 ) scenis t.o be w e l l f i u l f i 1 7 i : d i n c ~ i . i rm e a s u r e m e n t s a s may be seen o n F i g . '7 wlticb shows the l i n c u r d e p c n d e n c c o f l o g y v s . 10gT a t '1' .: 4 0 K . 1 I I 1 I 1 I
T
h-1
10
20
40
?O
100
200
1913 t Ii21
-1
/
go
"'O-I
F i g . 3 , D~.:nicrt:;Lration o f t l t o M o t t ' s l a b . ; f l > rmagtictit,::; arid M u - f c i - r j t e : ,
.
S y n i t i u l s indii_rrit,c: t h e varic9u:. sample c o m p o s i t i o n s .A t . h i g l i c r t e m p e r a t u r e s ( ?' ,' 40 I< ) t.1.1~
1914 f ~ ~ ~ ' i l , t ? s , " Phye.5t.~t..5ol, , v o ? . ( h i ? < ? , p p . 5 - - 4 8 , 1 9 7 7 . [ I S ] S . K r u p i E k a , P h y z i k d e r F e r r i t e und v e r - wiiiidten m a g n e t i s c h e n O x i d e , Braunschwei g : Vieweg, 19'73. ' " I ' h e r n i o c l e c t r i c p r o p e r t i e s of m a g n e t i t e a t the Verwey t r a n s i t i o n , " P h y s . R e v . , v o l . B 1 4 , p p . 1 4 0 1 - 1 4 0 5 , 1 9 7 6 " E l e c t r i c a l t r a n s p o r t i n m a g n e t i t e n e a r t h e Verwey t r a n s i t i o n , " v o l . E B 0 , p p . 5 9 4 - 6 0 0 , 1 9 7 9 . M.R.B. J o n e s , "The l o w - t e m p e r a t u r e r e s i s - t i v i t y a n d S e e b e c k c o e f f i c i e n t of f l u c i - r i n e - s u b s t i t u t e d m a g n e t i t e , " P h i l . M a g . , v o l . R 4 0 , p p . 3 8 9 - 3 9 9 , 1 9 7 9 . V . A . E . I . B r a b e r s , " E l e c t r i c a l c o n d u c t i v i t y a n d t h e r m o e l e c t r i c power of n i c k e l fer- r o u s f e r r i t e . V a r i a b l e r a n g e h o p p i n g a n d t h e Coulomb g a p , " P h i 1. Mag. , v o l . B54, p p . 5 0 5 - 5 2 1 , 1 9 8 6 . [ 2 0 1 D . I h l e a n d B. L o r e n z , " S m a l l - p o l a r o n c o n d u c t i o n a n d s h o r t - r a n g r e o r d e r i n Fe; 0 4 , " J . P h y s . C : S o l . S t a t e P h y s .
