MAGNETIC PROPERTIES OF DISLOCATIONS, SPIN POLARONS

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MAGNETIC PROPERTIES OF DISLOCATIONS, SPIN POLARONS

J. Gouyet

To cite this version:

J. Gouyet. MAGNETIC PROPERTIES OF DISLOCATIONS, SPIN POLARONS. Journal de

Physique Colloques, 1979, 40 (C6), pp.C6-107-C6-109. �10.1051/jphyscol:1979622�. �jpa-00219038�

JOURNAL DE PHYSIQUE CoZZoque C6, suppZhent au n06, tome 40, j u i n 7979, page C6-107

MAGNETIC PROPERTIES OF DISLOCATIONS, SPIN POLARONS

J.F. Gouyet

Laboratoire de Physique de Za MatiOre Condensle, EcoZe PoZytechnique, 91128 PaZaiseau Cedex, France.

Resume.- Cette note examine l e s c a r a c t e r i s t i q u e s des polarons magnetiques i n d u i t s s u r l e s d i s l o c a - t i o n s du s i l i c i u m par des e l e c t r o n s photocrees.

Abstract.- We examine i n t h i s n o t e the c h a r a c t e r i s t i c s o f magnetic polarons induced on d i s l o c a t i o n s by photocreated e l e c t r o n s i n s i l i c o n .

1. I n t r o d u c t i o n . - I n a r e c e n t paper /l/, exchange i n - Ho =

-

25

1 ip .

-f ^s

t e r a c t i o n between unpaired e l e c t r o n s has been e s t i - P'q q ( 1

mated on t h e model H3Si-SiH3. The i n t e r a c t i o n , o f As f o r t h e o r b i t a l s @ ( r ) , they can be w r i t t e n D P

a n t i ferromagnetic character, was found around 3 meV i n the SiH3 case /I/ : f o r a d i s t a n c e of 3.82 between t h e dangling bonds,

= 0.4(3s)

-

0.2(2p,)p ⁺ 0.6(3p ) taken p r e c i s e l y equal t o t h e corresponding d i s t a n c e _{- .} P P P

in

c ~ ~ ~ - J

dislocations in silicon. Hence,. from this w h i l e the exchange i n t e r a c t i o n between two e l e c t r o n s i n f o r m a t i o n we proposed t h e sane value for t h e unpai- 0"wo centers S i i n SiH3-SiH3 a t a d i s t a n c e of r e d e l e c t r o n s i n these d i s l o c a t i o n s .

We showed t h a t e l e c t r o n paramagnetic resonance experiments o f Schmidt e t a l . / 2 / could be e x p l a i n e d w i t h o u t t h e assumption o f ferromagnetic coupling.

I n t h e absence o f l i g h t , we found no l a r g e s p i n value on d i s l o c a t i o n s b u t , i t i s shown i n t h i s paper t h a t photoelectrons trapped on such d i s l o c a t i o n s can induce on them magnetic polarons w i t h l a r g e spins.

3.82 i s estimated around 3 meV. The corresponding t and U i n aHubbard Hamiltonian a r e found r e s p e c t i - v e l y equal t o 3.7 meV and 9 eV.

I n t h i s note, t h e anisotrowy o f i n t e r a c t i o n present i n d i s l o c a t i o n s i s neglected. The v i r t u a l s t a t e s on each s i l i c o n c e n t e r q a r e described as qq = ( 4 ~ ) ~ ( o r qq = a(4s)

+

b(40 ) i f a n i s o t r o p y

q x q

i s present) so t h a t t h e e x c i t e d s t a t e s o f t h e chain w i t h one e x t r a - e l e c t r o n i m p l y l i n e a r combinations o f Whereas'in a one dimensional Hubbard model we qq'

do n o t expect any i n f o r m a t i o n o f s p i n polarons /3/ i t Hence a p h o t o e l e c t r o n i s suoposed t o be trapped is not the same case when the extra-electron is loca- o m d i s l o c a t i o n . I t s exchange. i n t e r a c t i o n j w i t h t h e ted on virtual orbitals of each silicon center posses- unpaired e l e c t r o n on t h e same s i l i c o n c e n t e r i s taken s i n g a d a n g l i n g bond. This e x t r a - e l e c t r o n i s coupled positive and much larger than

I J I .

t o t h e unpaired e l e c t r o n on t h e same center by a s t r o n g exchange i n t e r a c t i o n . T h i s i n t e r a c t i o n i s f e r - romagnetic s i n c e Hund's r u l e applies. I t seems t h a t t h e magnetic polaron cannot e x p l a i n t h e s p i n depen- dent recombination o f photocreated e l e c t r o n s / 4 , 5 / i n s p i t e o f models proposed by Lepine e t a l . /6/ and by R.M. White and J.'F. Gouyet (unpublished).

However,the e x i s t e n c e of a superparamegnetism

j = <9p U J~l H l q p O~ > ; j >,

IJI

b u t we a l s o suppose t h a t t h e ground s t a t e on a s i n g l e S i c e n t e r i s

I @

^a q0 a> and n o t a

mp B>

which i s found l a r g e r by 9' eV. P

The i n t e r a c t i o n between t h e p h o t o e l e c t r o n and the chain i s w r i t t e n :

Xint

=

-

^2j

1

^fp

.

^{3 aptap}

P (2)

on d i s l o c a t i o n s i s o f g r e a t physical i n t e r e s t . where a +a i s t h e occupation number o p e r a t o r on o r - P P

2. D e s c r i p t i o n o f a spin-polaron i n one dimension.- b i t a l i) and

f

t h e s p i n o p e r a t o r o f t h e supplemen- We consider a chain o f broken bonds, t h e o r b i t a l s o f t a r y e l e c t r o n . P

which, a p ( r p ) a r e occupied, each one .by an Unpaired Yoreover :

e l e c t r o n . This i s t h e case f o r d i s l o c a t i o n s i n s i l i - =

-

^t*

1

a a

⁺

con, f o r which i t has been shown t h e Hamiltonian was P q (3)

Pq proper1 y represented by an Heisenberg Hami 1 to n i a n n e i ghbour

8

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979622

C6- 108 J O l l R N A L DE PHYSIQUE

represents the i n t e r a c t i o n between two neighbouring w h i l e a t h i g h temperature kT >>

JJI

o r b i t a l s q0 and

+

( t * i s t h e t r a n s f e r m a t r i x e l e -

q n

=

2 n 2 v 2 t*

ment). _PO'

(2 ⁺

l n 2 (kT - 25)

Approximated s o l u t i o n s o f ke = $ 0

+

^$1

+

^J&,-+

l l l L

are given i n the framework o f t h e polaron model / 7 / . The p o l a r o n spectrum i s a l i n e a r f u n c t i o n o f The f r e e energy F, per s p i n o f an Heisenberg i n - "01 :

-

finite chain has been c a l c u l a t e d by Johnson and Yc Epol = Eo

-

(31n2 J

+ 2

^{t ) n DO 1}

Coy / 8 / . As a consequence we note t h a t a t h i g h temperature t h e

In absence O f magnetic at low

r e l a t i v e number o f trapped e l e c t r o n s decreases as T-'/~.

t u r e :

The f i g u r e shows t h e v a r i a t i o n of n and F ] = EO

- mt + . . .

^{with^,, =}

( - 7

¹ + 2 l n 2 ) J Epol as a f u n c t i o n o f T f o r a reasonable s e t o f para- ^{PO 1}

3

IJI

(4) meters. To t h i s spectrum o f s t a b l e oolarons we can m i l e a t h i g h temperature imagine t o add a l l p o s s i b l e e x c i t a t i o n w i t h

n

v '

F =

-

T 2

- - $ + ...

( 5 ) k

=-(17

n v

'

where v

'

⁼ 1,2.

.v , . . .

^{n (-4)}

A spin polaron is then a stable of the Dhoto- as w e l l as e x c i t a t i o n s o f t h e remaining soins on t h e e l e c t r o n i n the p o t e n t i a l o f n p a r a l l e l spins. This chain.

? o t e n t i a l i s l i m i t e d a t each end by cwo a n t i p a r a l l c l ^'O' spins producing a p o t e n t i a l b a r r i e r 2j ,which i s pro- bably very l a r g e .

The e x c i t a t i o n energy o f a chain w i t h a s e t o f ^{3 5 -} n p a r a l l e l spins i s

t* = 0.6 ev

-;J-nee=-2ln2nJ

^{IJI = 3 mev}

v : I The s t a t e s o f t h e e x t r a - e l e c t r o n a r e

n o - l + n

= n ¹

'nk n

p=no ⁸ -

n v

w i t h k = - n d

,

v

-

^{1, 2}

^...,

ⁿ 50 100 150 ZOO 250 TIKI

and t h e i r energy spectrum i s : Fig. 1 : Energy and number of a l i g n e d spins o f a po-

=

-

2 t X cos kd l a r o n as a f u n c t i o n o f temperature f o r a reasonable

'nk s e t o f parameters.

The polaron energy i s then, except an a d d i t i v e

constant E?tlmation-of

-the-effe~~i_!!e~mas_s_-fer-!h_es_c-ee!~r~~s. -

E =

-

2 t f cos kd

-

21n2 n J ( 7 ) The t r a n s f e r m a t r i x element can be s i m p l y c a l c u l a t e d t

-

- ? c o s ( k d ) n J

Moreover, t h e e n t r o p y o f the n para1 l e l spins i s zero PO1 Pol

so t h a t t h e f r e e energy o f t h e p o l a r o n i s g i v i n g an e f f e c t i v e mass decreasing w i t h t h e i n v e r s e

- ~

E p o l ⁼

-

2 t X cos kd

-

21n2 n J

-

nF1 of t h e l e n g t h o f t h e polaron.

3. Conclusion.- As t h e conclusion, i t would be i n t e - T h i s polaron i s i n a s t a b l e e q u i l i b r i u m a t

T

r e s t i n g t o perform magnetic resonance experiment when 6F = 0 t h a t i s t o say under h i g h i n t e n s i t y l i g h t i r r a d i a t i o n . The e f f e c t ,

po 1

-

21n2 J

-

F1

+

2 t X s i n (kd)

.

^(T) -kd ^{= 0} b o t h on t h e resonance l i n e i n t e n s i t y and shape c o u l d o r when kd<<n, has an e q u i l i b r i u m l e n g t h (npolx d) g i v e an experimental c o n f i r m a t i o n of t h i s superpara-

w i t h magnetism. I n p a r t i c u l a r , an increase i n t h e c r e a t i o n

At 1 ow temperature kTcc LJ

I

^:

r a t e o f photoelectrons wdlrld s a t u r a t e t h e number o f ( 8 ) polarons i n each d i s l o c a t i o n .

References

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16

(1977) 3596.

Schmidt, U., Weber, E., Alexander, H. and Sander, W . , S o l i d S t a t e Commun

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Brinkman, W. F. and Rice, T.M.

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Phys. Rev. B

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Lepine, D., Phys. Rev. B

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Kaplan, D., Solomon, I . and Mott, N.F., J. Phys- sique L e t t . - 39 (1978) L 51.

Lgpine, D.

,

Grazhulis, V. and Kaplan, D., Pro- ceedings o f t h e T h i r t e e n t h I n t e r n a t i o n a l Con- ference on t h e Physics o f Semiconductors, Rome, 1976. See a1 so a r e c e n t paper by L'vov

,

V.S.

,

Tretyak, O.V. and Kolomiets, I.A., Sov. Phys.

Semicond.

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Johnson, J.D., and McCoy, B.Y., Phys. Rev.

5

(1972) 1613.