Temperature-dependent hyperfine coupling constants of Mn2+ in flourides

Temperature-dependent hyperfine coupling constants of Mn2+ in flourides

Volume 26A, number 6 PHYSICS LETTERS TEMPERATURE-DEPENDENT OF 12 February 1968 HYPERFINE COUPLING M n 2+ IN F L U O R I D E S CONSTANTS CHAO-YUA...

140KB Sizes 2 Downloads 39 Views

Volume 26A, number 6

PHYSICS LETTERS

TEMPERATURE-DEPENDENT OF

12 February 1968

HYPERFINE COUPLING M n 2+ IN F L U O R I D E S

CONSTANTS

CHAO-YUAN HUANG, J. F. REICHERT and J. GIGANTE

Department of Physics and Condensed State Center, Case Western Reserve University, Cleveland, Ohio, USA Received 8 January 1968

The temperature dependence of hyperfine coupling constants of Mn2. in CaF 2 and BaF 2 were measured. Agreement between theory and experiment is excellent.

In a r e c e n t p a p e r [1], Huang calculated the t e m p e r a t u r e dependence of the e l e c t r o n - n u c l e a r h y p e r fine coupling constant of Mn2+ in the octahedral coordination, u s i n g the m e c h a n i s m proposed by Sim~mek and Orbach [2]. In o r d e r to f u r t h e r test the theory, it i s d e s i r a b l e to study the case in which the Mn2+ ion sits in a cubal e n v i r o n m e n t . We have m e a s u r e d the hyperfine coupling cons t a n t s A(T) of Mn 2+ in CaF2 and BaF2 as a f u n c tion of t e m p e r a t u r e . The data a r e shown in fig. 1. The hyperfine coupling c o n s t a n t s A(T) w e r e obtained f r o m an a n a l y s i s of the e l e c t r o n spin r e s onance s p e c t r u m b a s e d on Low's theory [3]. A b a l a n c e d b o l o m e t e r s p e c t r o m e t e r at 13.5 GHz ,vas u s e d to obtain the e l e c t r o n spin r e s o n a n c e s p e c t r u m . The s a m p l e t e m p e r a t u r e was v a r i e d by m e a n s of a "hot-cold f i n g e r " i n s e r t e d into the m i c r o w a v e cavity [4]. As d e r i v e d in ref. 1 the t e m p e r a t u r e dependence of A(T) for Mn2+ ion can be w r i t t e n as

A(T) = A(O) { 1 - [C(0) + C(T)} ,

(1)

103r

[

~

o

Mn z+ in CaF2



Mn2+ in BoF2

(CoF2)

~

Theory

---

Theory (BoF2)

I01' .

99

"~

b,

I)5

0

I

I 200

I

I 400

I

r 600

I

800

TEMPERATURE ( ' K )

with

C(O) = KL(2~VD2/p)(vl-3 + 2vt-3) , C(T)

=

(2)

K L ( 8 y / p ) ( v l - 3 + 2vt-3)(kB T/h)2 x X

×

f

x{exp(x)-l} (ix,

(3)

0

L = {27~/(36 x 5)} (eeeff/R4)2 .

(4)

All the quantities in the above equations are as defined in ref. 1. L was calculated, for the cubal

Fig. 1. The hyperfine coupling constant A(T) of Mn2~ in CaF 2 and BaF 2. e n v i r o n m e n t , by u s i n g the a p p r o p r i a t e e l e c t r o n i c o p e r a t o r s [5]. The following independently d e t e r m i n e d p a r a m e t e r s were u s e d to calculate the phonon-induced hyperfine coupling c o n s t a n t s A(O)C(T) for Mn2+ in CaF2: eeff = e , p = 3.21g/cm 3, R = I . 3 8 3 × 10"8cm, vt = 3.34 x 1 0 - ~ c m / s e c , v l = 7.36 x 1 0 5 c m / s e c , and TD = 474OK [6,7]. The t h e o r e t i c a l c u r v e shown in fig. 1 was obtained by m u l t i p l y i n g the t h e o r e t i c a l e s t i m a t e by a scale factor of 2.4. The t e m p e r a t u r e dependence, as p r e d i c t e d by the theory, i s in good a g r e e m e n t with the e x p e r i m e n t a l r e s u l t s . The "rigid lattice" 219

Volume 26A, number 6

PHYSICS LETTERS

~D/(n)~, w h e r e n is the n u m b e r of a t o m s p e r unit cell [9] and eq. (2), we find that Cac(O)/Cop(O) ~ 1. T h e r e f o r e the optical phonons a r e as i m p o r t a n t as the a c o u s t i c a l phonons in z e r o - p o i n t phonon contribution to the h y p e r f i n e coupling constant in f l u o r i d e s .

h y p e r f i n e coupling constant of Mn 2+ in C a F 2 at T = 0 as obtained f r o m eq. (1) and the e x p e r i m e n t a l data, is -102.8 gauss. S i m i l a r l y we computed A(O)C(T) f o r Mn 2+ in B a F 2 u s i n g the p a r a m e t e r s : p = 4 . 8 9 g / c m 3, R -= 1.545 × 1 0 - 8 c m , vt = 2.28 × 1 0 5 c m / s e c , Vl = = 4.27 × 1 0 5 c m / s e c and TD = 282°K [8]. H e r e a s c a l e f a c t o r of 9.0 was u s e d to obtain the t h e o r e t i c a l c u r v e . F r o m the fitted c u r v e we find the " r i g i d l a t t i c e " h y p e r f i n e coupling constant at T = 0 to be -101.6 gauss. Again the t e m p e r a t u r e d e p e n d e n c e is well d e s c r i b e d by the t h e o r y . T h e r e l a t i v e c o n t r i b u t i o n s to C(0) f r o m the a c o u s t i c a l phonons C ac(0) and the o p t i c a l phonons Cop(0) can be obtained in the following way. Using the " m o d i fi ed Debye f r e q u e n c y " (which only a c c o u n t s f o r the a c o u s t i c a l phonons), v D' : *

EFFECTS IMPURITY

*

12 February 1968

1. 2. 3. 4. 5. 6. 7.

Chao-Yuan Huang, Phys. Rev. 158 (1967) 280. E. ~im~nek and R. Orbach. Phys. Rev. 145 (1966) 191. W. Low, Phys. Rev. 105 (1957) 793. J. F. Reichert and J. Gigante, to be published. Chao-Yuan ttuang, Phys. Rev. 139 (1965) A241. H.B. Huntington, Solid State Physics 7 (1957) 793. M. Born and K. Huang, Dynamical theory of crystal lattices (Oxford University Press, Oxford, 1954). 8. D. Gerlich, Phys. Rev. 135 (1964) A1331. 9. Chao-Yuan Huang, to be published.

*

*

*

OF OPTICAL PHOTOCONDUCTIVITY

PHONONS

IN OF

THE ZnTe

*

V. J. M A Z U R C ZY K and H. Y. FAN

Depart nlent of Physics, Purdue University, Lafayette, Indiana, USA Received

5 January

1968

The effects of phonon assisted transitions and longitudinal optical phonon emission by excited c a r r i e r s are observed in the impurity photoconductivity of ZnTe at low temperatures.

Two e f f e c t s involving longitudinal optical p h o nons h a v e b e e n o b s e r v e d in the i m p u r i t y p h o t o conductivity s p e c t r u m of p - t y p e ZnTe. T h e f i r s t e f f e c t is o p t i cal t r a n s i t i o n s with the e m i s s i o n of longitudinal o p t i cal phonons, and the s e c o n d effect is the l o s s of e n e r g y by e x c i t e d h o l e s through longitudinal o p ti c a l phonon e m i s s i o n . C o n s i d e r f i r s t the f o r m e r effect. T h e a b s o r p tion s p e c t r u m shows a s t e p - l i k e s t r u c t u r e with s h a r p p eak s at the beginning of each step; c o r r e s p o n d i n g p e a k s a r e s e p a r a t e d by an e n e r g y equal to a longitudinal o p t ic a l phonon e n e r g y . T h i s effect in the a b s o r p t i o n h a s b e e n p r e v i o u s l y r e p o r t e d [1]. Th e i n t e r p r e t a t i o n is that the p e a k s at the beginning of each step r e p r e s e n t e x c i t a t i o n s of the i m p u r i t y with the e m i s s i o n of z e r o , one, two, e t c . , longitudinal o p t ic a l phonons. The e x c i t a t i o n l i n e s of each group g r a d u a l l y b e c o m e u n r e s o l v a b l e and finally m e r g e with the i o n i z a * Work supported in part by an ONR contract. 220

tion continuum. T h e e x c i t a t i o n s do not p r o d u c e f r e e holes. Being a c o m p e t i t i v e p r o c e s s f o r photon ab so r p t i o n , t h e i r p r e s e n c e r e d u c e s the ionization that is e f f e c t i v e f o r photoconductivity. Fig. 1 shows that dips in the photoconductivity a r e o b s e r v e d which c o r r e s p o n d to the 2rid, 3rd. 4th and 5th s t r o n g p e a k s in absorption. T h i s e f fect has been o b s e r v e d in s a m p l e s f r o m two d i f f e r e n t ingots. In the 2nd effect, the e x c i t e d c a r r i e r s l o s e e n e r g y ef f i ci en t l y through o p t i cal phonon e m i s s i o n leading to a v a r i a t i o n of c a r r i e r e n e r g y between z e r o and one longitudinal phonon e n e r g y , with inc r e a s i n g photon e n e r g y . O s c i l l a t i o n s o c c u r in the photoconductivity s p e c t r u m when the c a r r i e r s r e c o m b i n e b e f o r e b e c o m i n g t h e r m a l i z e d and the l i f e t i m e o r m o b i l i t y o r both depend on the c a r r i e r e n e r g y [2]. T h i s effect has been r e p o r t e d f o r a n u m b e r of m a t e r i a l s . In ZnTe this effect r e v e a l s the p r e s e n c e of d i f f e r e n t i m p u r i t i e s . VCith a single type of i m p u r i t y the e n e r g i e s of the m i n i m a