Schult EPSL 1970 Curietemp

7/30/2019 Schult EPSL 1970 Curietemp

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EARTH AND PLANETARY SCIENCE LETTERS 10 (1970) 8 1- 86 NORTH-HOLLAN D PUBLISHING COMPANY

E F F E C T O F P R E S S U R E O N T H E C U R I E T E M P E R A T U R E O FT I T A N O M A G N E T I T E S [ (1 - x ) " F e 3 0 4 - x " T i F e 2 0 4 ]

A S C H U L TIns tttu t fur A ngewandte Geop hystk der Ludwtg-Maxtmthans-Umversttat Munchen,8 Mun chen 2, Rtchard- Wagner-Str 1 O, Germany

Recewed 5 October 1970The effect o f pressure up to 60 kba r on the Curie temperature Tc of t l tanomagnetl tes was measured T c mcreasesl inearly over this range For m agnetite the magnetic Grunelsen parameter 7m = d In Tc/d In V equals abou t - 4 +- 10%7m increases m magm tude for increasing ti tanium con tent with a maxtmum of ~'m --- -5 1 + 10% for x ,~ 0 7 Thisresult is consistent w~th relatwe strong an d pos~twe exchang e interaction JBB m th e B -sublattlce one can deduce '

from o the r investigations It is suggested that a large JBB makes self-reversal of magne tization unhkely, which isbased on a change of the predo mina nt magnetlzahon from one sublat tlce to the oth er

1 I n t r o d u c t i o nT h e s t r en g t h o f e x c h a n g e i n t e r a c ti o n s w h i c h a r e

r e s p o n s i b l e f o r t h e o r d e r i n g o f m a g n e t i c i o n s i nf e r r i t e s d e p e n d s c r i t i c a l l y u p o n t h e l n t e r a t o m l cd i s t a n c e s I n s p ln e l s t h e d i f f e r e n t e x c h a n g e i n t e r -a c t i o n s m a y b e d e s c r ib e d b y J A A b e t w e e n A - s it e( t e t ra h e d r a l - s i t e ) i o n s , b y J B B b e t w e e n B - s it e( o c t a h e d r a l - s i t e ) i o n s , a n d b y J A B b e t w e e n A - a n dB - si te io n s T h e s e e x c h a n g e i n t e r a c t i o n s a r e r e l a t e d t ot h e C u ri e t e m p e r a t u r e T c [ 1 ] T h u s t h e v a r i a t i o n o fT c w i t h h y d r o s t a t i c p r e s s u r e p r o v i d e s a m e a s u r e f o rt h e d e p e n d e n c e o f th e e x c h a n g e i n t e r a c ti o n s u p o nl n t e r a to m l c d i s ta n c e s a n d u n d e r c e r t a i n a s s u m p t i o n sa m e a s u r e f o r t h e e x c h a n g e i n t e r a c t i o n s i ts e l f.

S t r e n g t h a n d s i g n o f th e e x c h a n g e i n t e r a c t i o n s a r ei m p o r t a n t f o r t h e b e h a v i o u r o f a p o s s i b le s e l f -r e v er s a lo f m a g n e t i z a t i o n o r ig i n a ti n g f r o m a c h a n g e o f th es u b l a t ti c e m a g n e t i z a t i o n s [ 1 , 2 ] S e l f- r ev e r sa l o fm a g n e t i z a t i o n I n t it a n o m a g n e t i t e s d u e t o t l u sm e c h a n i s m a n d t h e c o n s e q u e n c e s f o r r o c k m a g n e t i s mh a v e b e e n d i sc u s se d b y s e v e ra l a u th o r s [ e g . 3 - 6 ] .

I n t h e p r e s e n t w o r k t h e s h i ft o f t h e C u r i e t e m -p e r a t u re s o f ti t a n o m a g n e t i t e s (1 - x ) F e 3 0 4- x T 1 F e 2 0 4 w i t h p r e ss u r e h a s b e e n m e a s u r e d a n ds o m e c o n c l u s i o n s a b o u t t h e e x c h a n g e i n t e r a c t io n sh a v e b e e n d r a w n . P r e v a o u s i n v e s t ig a t i o n s o f t h e

p r e s su r e d e p e n d e n c e o f t h e C u ri e t e m p e r a t u r e o fn a t u ra l m a g n e t i te w e r e d o n e b y S c h u l t [ 7 ] a n dSa m a r a e t a l [ 8 ]

2 E x p e r i m e n t a l p r o c e d u r e a n d r e su l tsT h e C u r i e t e m p e r a t u r e s o f t h e s y n t h e t i c t lt a n o -

m a g n e t i t e s w e r e m e a s u r e d I n a " b e l t " h i g h p r e s s u r ea p p a r a t u s u p t o 6 0 k b a r T h e p r e s s u r e c a l ib r a t i o n w a sd o n e w i t h t h e f o l l o w i n g t r a n s i t i o n s a n d p r e s s u r ev a l u es B I I . I I ( 2 5 5 k b a r ) , T l i l . i i I ( 3 6 7 k b a r ) ,B a i . i i ( 55 kba r ) , a nd B I I I I _V (7 7 k b a r ) [ 9 ]

T h e t l t a n o m a g n e t l t e s i n v e s t i g a t e d w e r e s i n t e r e d a t1 3 0 0 C u n d e r c o n t r o l l ed o x y g e n p r e s su r e ( C O 2 - H 2m a x t u r e ) ( e x c e p t t h a t w i t h x = 0 5 ) A d e t a i le dde s c r i p t i on w i ll be g i ve n e l s e w he r e [ 10 ] B e s i des y n t h e t i c m a g n e t i t e t w o s a m p l e s o f n a t u r a l m a g n e t i t ew e r e i n v e s ti g a t e d a s in g l e c r y s t a l ( p o w d e r e d b e f o r em e a s u r e m e n t ) f r o m P f i t sc h e r j o c h , A u s t ri a a n d ap o l y c r y s t a l h n e s a m p l e f r o m K i r u n a v a a ra , S w e d e n

T h e s a m p l e a s s e m b l y in t h e " b e l t " c o n s i s t e d o f ac o il w o u n d o n a t h r e a d e d t h i n w a l l o f a b o r o n n l tr l d ec y h n d e r w i t h t h e s a m p le o f c o m p a c t p o w d e r I n s id eT h e l o w - f ie l d s e l f - i n d u c t a n c e o f th e c o i l, w h i c h i sr e l a te d t o t h e I n i t ia l s u s c e p t i b i li t y o f t h e s a m p l e , w a sm e a s u r e d a s a f u n c t i o n o f t e m p e r a t u r e a t d i f fe r e n t


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82 A Schult, The Curte temperature o f tttanomagnetttes

65 0 /6 O0' / /

r e c

. , ~ x - - 0 ,15550 // .5 0 0

45 0J, . ~ x = 0 ,3

0 2 0 k b o r 4 0 6 0Ftg 1 Pressure dependence o f the Curie temperatures ofsynthetic tl tanomagnetl tes ( l -x ) Fe 30 4 - x T1Fe204Closed cxrcles deno te Curie points determined m the f trstpressure increasing cycle, open ctrcles m the ftrst pressure de-creasing cycle and further increasing and decreasing cycles

c o n s t a n t p r e s s u r e s , u s i n g t h e H o p k l n s o n p e a k f o r t h ed e t e r m i n a t i o n o f t h e C u ri e t e m p e r a t u r e T h e e x p e r i -m e n t a l t e c h m q u e h a s b e e n d e s c r i b e d i n d e t a d e l s e -w h e r e [ 7 ]

A t t h e C u r i e t e m p e r a t u r e t h e m ~ tm l s u s c e p t i b i li t y

a n d b y t h i s t h e s e l f - I n d u c t a n c e o f t h e c o i i d r o p ss h a r p l y w l t h i n c r e a s in g t e m p e r a t u r e T h e s h i f t o f th eC u r ie t e m p e r a t u r e w i t h p re s s u r e w a s e s t u n a t e d b yf i n d i n g t h e r e l a ti v e s h i f t o f t h e s e l f - i n d u c t a n c e c u r v e su n d e r v a r io u s p r e s s u r e s [ 7 ] T h e r e s u l t s f o r t h ev a r io u s c o m p o s i t i o n s o f th e t i ta n o m a g n e t l te s a r es h o w n i n f ig s 1 - - 3 T h e s e a r e t h e e x p e r i m e n t a l d a t an o t c o r r e c t e d f o r t h e e f f e c t o f p r e s s u re o n t h e e m f o ft h e c h r o m a l -a l u m e l t h e r m o c o u p l e u s e d

E x c e p t f o r m a g n e t i t e t h e c h a n g e o f th e C u r mt e m p e r a t u r e w a s n o t r e v e r s ib l e u p o n l o w e r i n g th ep r e s s u r e a f t e r t he f i rs t ri s i ng c yc l e ( t he c l o s e d c i r c le si n f ig s 1 - 3 r e p r e s e n t d a t a o b t a i n e d b y t h e f i rs tp r e s s u re r i se ) T h e C u r i e t e m p e r a t u r e s w e r e in c r e a s e di r re v e r s ib l y ( a t z e r o p r e s s u r e ) i n t h e o r d e r o f 2 0 H o w e v e r , a f t e r t h e f i rs t r is i ng a n d l o w e r i n g c y c l e t h es h i ft w a s r e v er s ib l e i n a s e c o n d a n d t h i r d c y c l e N oe x p l a n a t i o n c o u l d b e f o u n d f o r t h e i r r e v e r s i b l e I n -c r e as e o f t h e C u r ie t e m p e r a t u r e s A d e t a il e d X - r a ys t u d y o f t h e s a m p l es m a y s o l v e t h is p r o b l e m I nt h e f o l l o w i n g d i s cu s s ] o n o n l y t h e r e v e r s ib l e s h i f t o ft h e C u r i e t e m p e r a t u r e s w i t h p r e s s u r e w i ll b e c o n s ] d e r e d

T h e C u r i e t e m p e r a t u r e s s e e m t o i n c r e a s e l i n e a r l yw i t h p r e s s u r e i n a l l c a s e s The s l ope s d T c / d p t a k e nf r o m f ig s 1 - 3 w e r e a ll c o r r e c t e d f o r t h e e f f e c t o fp r e ss u re o n t h e e m f o f th e c h r o m e l - a l u m e l t h e r m o -c o u p l e u s e d a c c o r d i n g t o t h e r e s u lt s o f H a n n e m a n e ta l [11 ] Th e f ina l s lope s d T c / d p f o r t h e v a r i o u s c o m -

400

35 OTc300:

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20 0

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x= 0 , 5

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. 1 t .

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. J x= 0 ,66Tco c

1 5 0 ~ i r -

lOO / x = 0 , 845 C /

0 0 20 kbor 40 60Fig 2. See fig 1 Fig 3 See fig. l


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A Schu lt , The Curie temperature o f t t tanomagnet t tes 83p o s m o n s o f s y n t h e t i c t ~ t a n o m a g n e t l t es a re s h o w n mf i g . 4 T a b l e 1 c o m p a r e s v a l u e s o f d T c / d p f o r n a t u r a la n d s y n t h e t i c F e 3 0 4

3 D i s c u s s i o nI t xs u n i f o r m l y s u g g e s t e d t h a t t h e C u r i e t e m p e r a -

t u r e i s a l i n ea r f u n c t m n o f t h e e x c h a n g e i n t e r a c t i o n sJ q

r = % s ( 1 )qT h e A q a re c o n s t a n t s T h e e x c h a n g e l n t e r a c t m n s v a r yw i t h v o l u m e (1 e w i t h l n t e r a t o m l c d is t a n c e s ) T h ev a r l a t ao n c an b e d e s c r i b e d b y t h e s o - c a l l e d " m a g n e t i cG r u n e l s e n p a r a m e t e r " [ 1 2 ]

d I n T d T c d p Vc = d l n ~ A q J q / d l n V7 m - d l n V d p T c d V tl ( 2 )dV[ Vdp is the isothe rmal volume compress lbdltynear the Curie temperature These values are nota v a d a b le . W e h av e a d o p t e d t h e r e f o r e t h e u n i f o r mv a lu e 5 5 + 0 3 1 0 - 4 / k b a r , t h e c o m p r e s s i b i l i t y o fm a g n e m e a t r o o m t e m p e r a t u r e ( c l t . I n [ 8] ) . I t c an b ea s s u m e d t h a t t h e c o m p r e s s l b d l t y IS n o t d r a s t i c a l l y

Table 1Pressure dependence o f the Curie tempera tu re o f na tu ra l andsyn the t ic magne t i teSample d T c / dp R ef(C/kbar)Na tura l f rom 2 3 +- 10% [7]Ktrunavaara, SwedenNa tural 2 05 +- 5% [8]Natura l f rom 1 9 +- 10% Pres ent wo rkPfitscherjoch, AustriaNatura l f rom 1 85 -+ 5% Present work-Ktrunavaara, SwedenSynth etic 1 85 + 5% Present work

d i f f e r e n t f r o m t h i s v a l ue f o r t h e t l t a n o m a g n e t l t e s a tt h e i r C u r i e t e m p e r a t u r e s T h e v a l u e s o f ~m d e t e r -m i n e d b y e q ( 2 ) a r e s h o w n m f i g 5

A q u a n t l t a t w e i n t e r r e l a t i o n s h i p b e t w e e n T c a n dt h e v a r i ou s ex c h a n g e l n t e r a c t t o n s m F e 3 0 4 w a s g i ve nb y K o u v e l [ 1 3 ] .

(3 )w h e r e

0 2 = S A ( S A + 1 ) , o 2 = S B ( S B + 1 ) ( 4 )

2

1,5d p

1o K

k b a rO,5

(l-x) e3Ot . ~ x Fe2T , O~I I0 ,2 x 0 ,4 0 , 6 O ,B 1

\0 ,2 x ~ 4 ~ 6 ~ B

Fig 4 Sh if t o f the Curie tempera tu re d T c / d p as a func tmn ofthe com pos i t ion o f the t l tanomagne t t te s d T c [ dp was deter-mined from the s lopes o f the curves m f igs 1 - 3 and correc tedfor the e ffec t o f p ressure on the emf o f the chromel-a lumelthe rmocouple used accord ing to Hanneman e t a l . [1 1] .

- 6

d t ~ T ~d i n V

- 5

0

F t g 5 . M a g n e t i c G r u n e l s e n p a r a m e t e r - rm = d In T c / d n Va s a f u n c t m n o f t h e c o m p o s ~ t t o n o f t h e t ~ t a n o m a g n e t ~ te s

( l - x ) F e 3 0 4 - x T t F e 2 0 4


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84 A Schult, The Curie temperature of ntanomagnetttesk I s th e B o l t z m a n n c o n s t a n t S A a n d S B a re t h ea v e r ag e s p in s o f e l e c t r o n s a s s o c m t e d w i t h t h e i r o nm o m e n t s o n A - a n d B - s~ te s, r e sp e c U v e l y S A a m o u n t st o - ~ be c a us e t he A - s ~ te s a r e oc c up i e d b y F e 3+ s onsThe a ve r a ge va l ue f o r S13 c a n be w r H t e n ( Fe 2+ a ndF e 3 + i o n s ) S B = l 4 s 2 5( ~ + 5 ) = 2 W e a s s u m e n o w t h a tJ A A is n e g h g i b l y s m a l l w i t h r e s p e c t t o J A B a n d J BBT h i s h a s b e e n p r o v e d b y t h e o r e U c a l a n d e x p e r i m e n t a lr e s u lt s f o r f e r n t e s b y B la ss e [ 2 ] a n d p a m c u l a r l y f o rm a g n e t i t e b y G la s s er e t a l [ 1 4 ] E q ( 3 ) r e d u c e s t o

kT c ~ 4 N/~2 AB OA OB -- 2JB B O'~'~ (5 )T h e e x c h a n g e i n t e r a c ti o n s a r e a s su m e d t o d e p e n d o n l yo n v o l u m e b u t n o t n e c e s s a r i l y m t h e s a m e w a yD e r i v in g e q ( 5 ) m t h e s a m e w a y a s e q ( 2 ) y i e l d s a f t e rs o m e s u b s U t u t l o n s

d I n T c d I n J A B d I n J B B3'm - d In V - ( I - 1/a) d I n V ( a - 1 ) d I n V '

(6 )w i t h

4 V ~ o A o B J A Ba - (7)2 0 2 J B BJ A B i s a n i n d i re c t e x c h a n g e m t e r a c t i o n b e t w e e nc a t i o n s v m a n o x y g e n i o n w h e r e a s i t ~s e v i d e n t f r o mt h e o r e U c a l a n d e x p e r t m e n t a l I n v e s t I g a U o n s t h a tJ B B is a d i r e c t c a t i on - c a t i o n i n t e r a c t i o n [ 2 , 15 ]B l o c h [ 1 2 ] h a s s h o w n t h a t i n s u n p l e f e r n t e s , o x i d e sa n d g a r n e t s t h e I n d i r e c t e x c h a n g e i n t e r a c t i o n s v a r ya s t h e l o p o w e r o f t h e v o l u m e (1 e 3 'r n = - 3 3 3 ms im p l e c o m p o u n d s w i t h a n y o t h e r th a n t h e m & r e c te x c h a n g e m t e r a c u o n s n e g h gl b le ) T h e & r e c t e x c h a n g ei n t e ra c t i o n s a r e m u c h s t r o n g e r d e p e n d e n t o n t h em t e r a t o m l c d is t a n c e s [ 1 5 ] W e a s s u m e t h e r e f o r e t h a tt h e r e l a t i v e l y l a r g e 7 r n f o u n d f o r m a n o m a g n e t l t e s( s ee f ig 5 ) is r e l a t e d t o t h e s t r o n g ( p o s l t w e ) & r e c te x c h a n g e i n t e r a c t i o n s J B B

S c h w o b [ 1 6 ] a s s u m e d t h a t t h e & r e c t e x c h a n g eI n t e r a c t i o n s a r e i n v e r s e l y p r o p o r t i o n a l t o t h e s q u a r eo f t h e c u b i c c r y s t a l li n e - f ie l d s p h t t m g o f t h e s o ne n e r g y le v e ls B y t h e a id o f p a r a m a g n e t l c r e s o n a n c es p e c t r a m e a s u r e m e n t s W a l s h [ 1 7 , 1 8 ] d e t e r m i n e d f o ri r o n 1 on t h a t t h e c u b l c c r y s t a ll i n e -f i e ld s p h t t m g i sp r o p o r U o n a l t o t h e - 2 1 p o w e r o f th e m t e r a t o m l cd i s t a n c e s T h i s l m p h e s t h a t t h e d i r e c t e x c h a n g e

Interaction JBB s h o u l d v a ry as th e - 1 4 p o w e r o f t hev o l u m e W e s et t h e r e f o r e I n e q ( 6 ) f o r d I n JAB/d I n V = - 2 4 G r a s s e r e t a l [ 1 4 ] o n b o t h e x p e r u n e n t a la n d t h e o r e t i c a l g r o u n d s h a v e s h o w n t h a t i n m a g n e t i t eJ BB ~ - - 0 1 J A B ( w i t h J A B n e g a t w e ) U n d e r t h ea s s u m p u o n t h a t o A a n d o B a re i n d e p e n d e n t o f p re s -s u r e e q u a u o n ( 6 ) y i e l d s 3 'm = - 3 7 w h i c h i s m a g r e e -m e n t w i t h t h e m e a s u r e d v a lu e o f a b o u t - 4 w i t h i n t h ee x p e r u n e n t a l e r r o r s

T h e l a r g e r 7 m ( m m a g m t u d e ) f o r x > 0 4 ( f ig 5 )unp i l e s t ha t a l s o t he r a t i o JJBB/JABI( JBB pos i t ive) I sl ar ge r f o r th e s e U t a n o m a g n e U t e s t h a n f o r m a g n e m eU n d e r c e r t a i n c o n d l t J o n s a c a l c u l a t i o n o f t h e JBB/JABr a U o xs pos s i b l e w i t h t he a i d o f N 6e l ' s [ 1 ] t he o r yf r o m t h e c h a n g e o f t h e s h a p e o f t h e s p o n t a n e o u sm a g n e t i z a t i o n v e r s us t e m p e r a t u r e c u r v es ( M s ( T ) -c u r ve s ) i n a s ohd s o l u t i on s e r i e s [ 2 ]

I n th e n o t a t i o n o f N 6 e l [ 1 ] t h e e x c h a n g e r a te r -a c t i o n s JAB, J B B a n d J A A a r e h n e a r l y r e l a t e d t o t h em o l e c u l a r f i e l d c oe f f i c i e n t s n , n /3 a nd na r e s p e c t i v e l yI f e g m F e 3 + ( F e 2 + F e 3 + ) O 4 t h e i r o n i o n s m o c t a -h e d r a l s i te s ( p u t m b r a c k e t s ) a r e r e p l a c e d b y d l a -m a g n e u c i o n s t h e ra U o o f th e s p o n t a n e o u s s u b la t t~ c em a g n e t i z a t i o n s a t 0 K MA/MI3 i nc r e a s e s ( s t a r t i ngwlthMA/MB < 1 ) N o w i t is a g a i n a s s u m e d t h a t JA Ai s ve r y w e a k ( i e a ~ (3 ) The n i t fo l l ow s & r e c t l y f r o mN 4 e l ' s [ 1 ] t h e o r y t h a t t h e M s ( T ) - c u r v e IS o f th eP - t y p e forMA/MB va l ue s be t w e e n 1 a nd ( 1 - f l) a ndo f t h e N - t y p e forMA/MB be t w e e n 1 a nd ( 1 + ~3 ). Fo rMAIMB = 1 t h e M s ( T ) c u rv e i s o f t h e L - t y p e a n d f o ra ll o t h e r M A / M s v a l u es o f t h e Q - t y p e ( se e f i g 6 )F r o m t h e s e q u e n c e o f t h e d i f f e r e n t M s ( T ) c u r ve s as af u n c t i o n Of MA/MI3 t h e s i g n o f / 3 c a n b e d e t e r m i n e da n d f r o m t h e c o n c e n t r a t i o n r a n g e in w h i c h t h e c u r v esc h a n g e t h e i r s h a p e t h e m a g n i t u d e o f / 3 ( s ee f ig 6 )

T h e s ~ t u a t l o n f o r t h e t l t a n o m a g n e t l t e s i s s h o w n mf ig 7 . TheMA/MB r a t io a s a f u n c t i o n o f x w a sd e d u c e d f r o m t h e c a t i o n d i s t r i b u t i o n g w e n b yO ' R e l l l y e t a l [ 1 9 ] T h e M s ( T ) c u rv e s a re o f t h eQ - t y p e f o r x < 0 6 a n d o f t h e P - t y p e f o r x > 0 6a c c o r d i n g to A k l m o t o e t a l [ 2 0 ] W i t h th e c o n v e r s i o nf r o m t h e e x c h a n g e i n t e r a c t i o n r a t i o J B B = - - 0 1 J A Bf o r m a g n e t i t e t o t h e m o l e c u l a r f i e ld c o e f f i c i e n t o n eg e t s f l = + 0 0 5 F o r x = 0 6 w h e r e t h e Q - t y p e c h a n g e st o t h e P - t y p e f o l l o w s M A / M B = 1 - j3 (see f ig s 6 an d7 ) F r o m t h e c a t i o n d i s t ri b u t io n [ 1 9 ] f o r x = 0 6

2+ 3+ (Fe2+ 2 3+ 4+Fe 0 4 Fe 0 6 Fe 0 2 TI 0 6 ) 04 (8 )


5/6

A Schult, The Curie temperature of tttanomagnetztes 85

i ' +. _ ! } P /,%/"/Q P L N o '

[

Fig 6 Change of types ofM s(T )cu rve s - gwen at the bot-tom of the figure - as a funct mn ofMA/MB The abscissadenotes a vanat mn in chemmal cornpositaon (e g substatutaonof paramagnetl c runs by daamagnetlc ions m the B-sublattace)For increasing MAIMB the sequence of the Ms( T) curve typesas Q ~ P -'> L ~ N ~ Q' for /3 posatlve (as shown in t he figure)and Q ~N ~L ~P ~Q ' for 13negatwe If 3 is large the com-positi on ranges of P- and N-ty pe curves are also large andvice versa

o n e findsMA/M B = 0 79 a nd / 3 = + 0 21 a nd f i na l l yJ B B = - - 0 42 J A B ( J B B p o s it iv e ) W i t h t h e a p p r o x l m at l o n t h a t t h e r e la t m n f o r t h e C u r ie t e m p e r a t u r e g w e nm e q u a t m n ( 5 ) xs a l so v a l id f o r t h e t l t a n o m a g n e t l t e se q ( 6 ) y i e ld s 3'm = - 4 6 a g a in i n a g r e e m e n t w i t h t h em e a s u r e d v a l u e o f a b o u t - 5 ( f o r x = 0 6 ) w i t h i n t h ee x p e r i m e n t a l e r r o r s

G e n e r a l l y i t c a n b e s a i d th a t t h e b e h a v m u r o f t h ee x c h a n g e i n t e r a c t i o n s i n t ] t a n o m a g n e t ) t e s d e d u c e df r o m t h e h i g h p r e s s u r e m e a s u r e m e n t s i s c o n s i s t e n tw i t h t h e r e s u l ts o n e g e t s f r o m o t h e r i n v e s t i g a ti o n s W et h e r e f o r e a s s u m e t h a t " )'rn v a r ie s a s a f u n c t i o n o f xq u a h t a t w e l y m t h e w a y a s s h o w n i n fi g 7 (/3 s h o u l dv a r y m a s im i l ar w a y a s 3 % s h o w n i n fi g 5 )

The r e l a t i ve l a r ge a nd pos i t i ve / 3 ( s t r ong J B B

x o , s i" - " - I ,

Q P

Fag 7 Behaviour of MAIMB, 1 + 3 and 1 -/3 and types ofMs(T ) curves as a funct mn of x for tatanomagnetates

(1 - x) Fe3 04 - x TaFe204

/ T ~ O ~ Q - t y p e~ , T , o,/,. ' \ pm N

Fig 8 Chemical composltmn of natural (catmn deflment)tatanomagnetlte s an basalts after Schult [6] Probable bordersbetween ranges with different types of Ms(T) curves are

indicated with broken lines

i n t e r a c t i o n ) h a s s o m e c o n s e q u e n c e s f o r s e lf - re v e r sa lm o d e l s d i sc u s se d o n t h e b a c k g r o u n d t h a t t l t a n o -m a g n e t i t e s c a n p r o d u c e s i n g l e p h a s e c a t i o n d e f i c i e n ts p ln e l s b y s l o w o x i d a t i o n a t l o w t e m p e r a t u r e s S t a r t i n gf r o m a g w e n c a t i o n d i s t r i b u t i o n a n d a n o c t a h e d r a l s i t ep r e d o m i n a n t m a g n e t i z a t io n s ev e ra l a u t h o r s s h o w e dt h e o r e ti c a ll y a n d e x p e r i m e n t a l ly ( e g r ef s [ 3 - 6 ] ) t h a tw i t h s l o w o x i d a t i o n v a c a n c i e s c a n b e f o r m e d o nB - s i t e s p r o d u c i n g a n A - s i t e p r e d o m i n a n t m a g n e t i z a -t i o n a f t e r l o n g e n o u g h o x i d a t i o n ( o n l y p o s s i b l e f o rx > 0 5 ) A s t h e e x c h a n g e i n t e r a c t i o n i n th e B -s u b l a t tl c e I S p o s l t w e t h e s e q u e n c e o f t h e M s ( T ) c u r v et y p e s f o r i n c r e a si n g d e g r e e o f o x i d a t i o n ( t h a t ismcreaslngMA/MB ra t io) i s Q -* P ~ L -~ N ~ Q '( f ig 6 ) ( Q ' d e n o t e s a M s ( T ) c u r v e w i t h A - s u b l a t t lc ep r e d o m i n a n t a t a n y t e m p e r a t u r e b e l o w t h e C u ri et e m p e r a t u r e , a c o m p l e t e " i r r e v e r s ib l e " s e lf - re v e rs a l o fm a g n e t i z a t i o n t a k e s p la c e w h e n t h e c o m p o s i t i o n i ss h i f t e d o v e r t h e b o r d e r N / Q ' ) T h e r e la t iv e l a rg e 3 -p a r t i c u l a r ly f o r x > 0 5 - l m p h e s t h a t t h e c o n c e n t r a -t i o n r a n g e in w h i c h t h e M s ( T ) c u r v e s c h a n g e t h e i rs ha pe i s a l s o l a r ge ( s e e f ig 6 ) Th i s i s i n a g r e e m e n t w i t hi n v e s t i g a t i o n s o n n a t u r a l t l t a n o m a g n e t l t e s a s s h o w n i nfig. 8 [6]

I t m u s t b e k e p t i n m i n d , h o w e v e r , th a t t h e s l o pe o fth e MAIMB c u r v e m f ig 6 ( a s a f u n c t i o n o f th ed e g r e e o f o x i d a t i o n ) d e t e r m i n e s t h e e x t e n s i o n o f t h ec h em ) c al c o m p o m l o n o f t h e d i ff e re n t t y p e s o f M s ( T )c u r v e s a s s h o w n i n f i g 8 a s w e l l T h e s l o p e d e p e n d s o nt h e c a t i o n d i s t ri b u t io n w h i c h i s n o t e x a c t l y k n o w na n d w e d o n o t i n t e n d t o & s c u s s th i s p r o b l e m h e r eA f t e r a l l i t c a n b e a s s u m e d t h a t t h e c o m p o s i t i o n r a n g e


6/6

86 A Schult, The Curie temperature of tttanomagnettteswith the Q'-typ e Ms (T ) curve - if there is any - Isrelatively far away from the Fe304-Fe2T104 join infig 8, proba bly near or above the Fe203- FeT1 03 join

The tltanomagnetltes in the hypothetical Q'-rangeshould be highly cation deficie nt. Until now it hasnot been definitely shown that they exist, neither forsynthetic nor for natural titanomagnetltes Composi-tions of iron- titan ium minerals in the range inquestion sometimes reported seem more to be averagecompositions of mixed phases and not those of asingle spinel phase

If the highly cation deficient titanomagnetltes inthe Q'-reglon exist it would be more likely that alsothe somewhat less cation deficient tltanomagnetltesin the N-region exist The N-type tltanom agnetl teshave been found rarely but only with compensationtemperature s below room temperatures [6] Thismeans that these tlt anoma gnetl tes are located in theN-range closer to the P-range than to the Q'-rangeThe higher cation deficient tltan omagn etlte s m theN-range near the Q'-range should have a compensa-tion temperature above room temperature, but thesetltanomagnetltes have not been found until now,despite an enormous numb er o f existing measure.ments o fM s( T ) curves and remanence versus tempera-ture curves above room tempe rature On the otherhand the composition range of these N-type tltano-magnetites should be fairly large because of thestrong JBB Inter act ion We regard therefore t heself-reversal mechanism discussed here to have noimportance in rock magnetism

AcknowledgementsThe author is indeb ted to Dlpl -Phys U Blell,

Instltut fur Angewandte Geophyslk, Mianchen, andDr W O'Rel lly, University of Newcastle upon T yne,for providing him with the tltan omagn etlt e samplesI thank Dlpl.-Phys. U.Blefl, Dr E.Schmld bauer andDr H Soffel for several stimulating discussions andProf G Angenhelster for his support and encourage-men t The financial help of the Deutsche Forschungs-gemeinschaft is gratefully acknowledged

References[ 1 ] L N~el, Proprl&6S magn&ignes des ferrltes fernmag-n&lsme et antlferromagn&isme, Ann Phys 3 (1948)137[21 G Blasse, Crystal chemistry and some magnetic proper-txes of mixed metal oxides with spinel structure. PhlhpsRes Rept Suppl No 3 (1964)p 1[3 ] J Verhoogen, Oxidation of iron-titanium oxides inigneous rocks, J Geol 70 (1962) 168[4] W O'Reilly and S K Banerjee, The mechamsm of oxida-tion m tltanomagnetites a magnetic study, MineralMag 36 (1967) 29[5] N Sakamato, P I Ince and W.O'Reilly, The effect ofwet-grmdlng on the oxidation of tRanomagnetites,J Geophys 15 (1968) 509[6] A Schult, Self-reversal of magnetization and chemicalcomposition of tltanomagnetltes in basalts, EarthPlanet Scl Letters 4 (1968) 57[7] A Schult, The effect of pressure on the Curie temperatureof magnetite and some other ferrltes, Z Geophys 34(1968) 505[8] G A Samara and A A Glardmi, Effect o f pressure on theN6el temperature of magnetite, Phys Rev 186 (1969)577[9] Symposmm on the accurate characterization of the highpressure environment, Nail Bur. St U S Oct 1968[ 10] U Bleil, in preparation.[11] R E Hanneman and H M Strong, Pressure dependence ofthe electromotive force of thermocouples to 1300Cand 50 kbar, J Appl Phys 36 (1965) 523[12] D Bloch, The 10/3 law for the volume dependence ofsuperexchange, J Phys Chem Solids 27 (1966) 881[ 13 ] J S Kouvel, Specific heat of a magnetite crystal at liquid

helmm temperatures, Phys Rev 102 (1956) 1489[14] W L Glasser and F J Milford, Spin wave spectra ofmagnetite, Phys Rev 130 (1963) 1783[15] J B. Goodenough, Magnetism and the Chemical Bond(Wiley and Sons, New York, 1966)[ 16] P Schwob, Die magnetischen Elgenschaften derEuroplum-Chalkogenlde unter hydrostatlschem Druck,Phys Kondens Matene 10 (1969) 186[ 171 W M Walsh, Effect of hydrostatic pressure on theparamagnetic resonance spectra of several iron groupions in cublc crystals, Phys Rev 122 (1961) 762[18] W M Walsh, Temperature-dependence crystal field andhyperfine interactions, Plays Rev 139 (1965) A 1338[ 19] W O'Rellly and S K Banerjee, Cation distribution intitanomagnetltes ( l- x) Fe30 4-x'Fe2T104, PhysLetters 17 (1965) 237[20] S Aklmoto, T Katsura, and M Yoshlda, Magneticproperties of Fe2T104-Fe30a system and their changewith oxidation, J Geomagn Geoelec 9 (1957) 165

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