Parker, R. Physica X X 1954 1314-1315

LETTER TO THE EDITOR

T h e n a t u r e of t h e i n s u l a t i n g l a y e r s in f e r r o m a g n e t i c s e m i c o n d u c t o r s

A number of ferromagnetic semiconductors exhibi t a strong dispersion in their A.C. resist ivi ty arid dielectric properties in the audiofrequency range. This phe- nomenon has been interpreted by K o o p s 1) as being due to the presence of thin layers of much greater resist ivi ty than tha t of the bulk of the material . I t is the purpose of this note to offer an interpretat ion of the l~hysical nature of these barrier layers and to discuss some interesting, results published recently by V o 1 g e r 2) on manganites of composition La(t_8)MeaMnO 3, where Me represents a divalent metal and 1 > 6 > 0.

I t is clear from the results of J o n k e r and V a n S a" n t e n s) tha t above their Curie points these manganites behave electrically like ordinary semiconductors, exhibit ing the usual log ~ versus 1/T relationship *). The advent of ferromagnetic order is, however, associated with a striking departure from this simple law, the new value of log ~ being very much smaller than tha t extrapolated from the paramagnet ic region. Our first assumption is tha t this departure is a direct result of the appearance of the spontaneous magnetizat ion I s. Secondly it will be supposed tha t the insulating layer is to be identified with a region in the material which is not spontaneously magnetized, such a region occurring presumably at the surface of each crystal grain. The surface layer has been estimated s) to have an effective thickness of the order of a few atomic diameters.

Results of measurements on a manganite of composition Lao.9Sr0.1MnO 3 can now be considered in relation to this hypothesis. The linear extrapolat ion of the log 0, lIT results s), from well above the Curie point, suggests tha t if the ferromagnetic ordering could be destroyed at 77°K, the resulting value of ~ would be 7 × I07 ~2 cm. The resist ivity of the barrier layer of a similar material at this temperature has been est imated as 14.5 × 10 7 Q cm from dispersion measurements. In view of ' the reported variations in ~ from one specimen to the n e x t , the simplifying assumptions in calculating the dispersion constants, and the extrapolat ion from 0 ~ 2 -Q cm, the agreement between the two results may b.e considered as satisfactory.

Magneto-resistance measurements on a specimen of composition La0.gCa0AMnO3 will now be considered. At 10 s c/s the magneto-resistance curve resembles, both in shape and in magnitude, tha t of an ordinary unsaturated ferromagnetic material undergoing technical magnetization. The D.C. magneto-resistance, on the other hand, exhibits a strictly linear decrease of AQ/0 with the applied field H. I t is well known tha t this la t ter phenomenon is characteristic of all ferromagnetics 4) when the applied field causes an increase in the intrinsic magnetization, either above or below the Curie point.

These apparent ly complex results are exact ly those expected from the proposed

*) The notation of references 1) and 2) is used unless otherwise defined.

- - 1 3 1 4 - -

INSULATING LAYERS IN FERROMAG'NETIC SEMICONDUCTORS 1315

model . At high f requencies the magneto- res i s tance , l ike the res is t iv i ty , is readi ly shown to be charac te r i s t i c of the bulk of the mater ia l . The D.C. magneto- res i s tance , however , depends a lmos t en t i re ly upon the induced intr insic magne t i za t i on in t he p a r a m a g n e t i c barriers , since x01 >~ 02-

I t is t e m p t i n g to e s t ima te the ef fec t ive suscept ib i l i ty f rom the ava i lab le magne to - res is tance data . This can be done most s imply by assuming t h a t the induced magne t - i za t ion in these layers is due to a r educ t ion in the i r e f fec t ive thickness. "With the aid of the above assumpt ion it is readi ly shewn t h a t

d(Ao/~)/dH = 0 -1 (~0/~Is ) (d l s /dH ) (I)

where 60 denotes the difference be tween the ac tua l and ex t r apo l a t ed res is t iv i ty , cor responding to the appea rance of t he intr insic magne t i za t i on ~I s a t the t emper - a tu re under considera t ion. W i t h the aid of equa t ion (1) one f inds t h a t a reduc t ion in t he ef fec t ive v o l u m e of the barr ie r layers a t 90°K is 4% wi th H = 5.000 O; the v o l u m e suscept ib i l i ty of the layers t hen t akes the plausible va lue of 3"5 × 10 -3. I t should be stressed t h a t owing to the s o m e w h a t ar t i f icial a s sumpt ion under ly ing this ca lcu la t ion , the l a t t e r va lue can only be t a k e n as an indica t ion of the order of magn i tude .

F ina l ly it is o f in te res t to consider the occurrence of insu la t ing layers in re la t ion to o the r phys ica l proper t ies of these mater ia ls . A pa r amagne t i c surface layer should be fo rmed in mater ia l s where the exchange in te rac t ion be tween the ind iv idua l ionic m o m e n t s is on ly jus t s t rong enough to ma in t a in fe r romagne t i c order in the bu lk of the mater ia l . One would expect , therefore , to observe dispersion p h e n o m e n a in mater ia l s which fall wi th in a compos i t ion range close to the cr i t ical compos i t ion for which f e r romagne t i sm disappears comple te ly . This seems to be the case for t he mangan i t e s discussed here. I t has been shewn 5) t h a t s t rong fe r romagne t ic in ter- act ion, (i.e. h igh Curie t empera tu res ) occurs for va lues of ~ be tween 0"2 and 0-45, while pure LaMnO 3 is pa r amagne t i c down to the lowest t empera tu res . The on ly o the r ma te r i a l for which s imilar dispersion proper t ies have been repor t ed 1) is Ni0.4Zn0.sFe20 4. This ferr i te has a Curie point , Q, near room t empera tu re , and Q drops rap id ly to zero wi th increas ing zinc concen t r a t ion e). F r o m a compar i son of t he theore t i ca l and expe r imen ta l Bohr Magne ton number s of the mater ia l s considered here s) s) i t m a y be conc luded t h a t only a par t ia l a l i gnmen t of the ionic m o m e n t s is ach ieved in eve ry case. F r o m these cons idera t ions i t appears v e r y l ikely t h a t dis- pers ion p h e n o m e n a will be found a m o n g o the r ferr i tes of the ' f e r roxcube ' t ype v).

Received 2-9-54. R. PARKER.

University College of North Wales, Bangor

REFERENCES

1) K o o p s , C. G., Phys. Rev. 83 (1951) 121. 2) V o l g e r , J., Physica 30 (1954) 49. 3) J o n k e r , G.H. and V a n S a n t e n , J.H.,Physica16(1950) 599. 4) B e c k e r, R. and D 5 r i n g, W., Ferromagnetismus (Berlin: Springer), ch. 4 (1939). 5) J o n k e r , G. H. and V a i l S a n t e n , J. H., Physical6(1950) 337. 6) G u i l l a u d , C.,J. Phys. Rad.,12 (1950) 239. 7) S n o e k, J. L., New Developmeuts in Ferromagnetic Materials (Elsevier Publ. Co.), ch. 22 {1949).