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ULTRASONIC PHONONS IN Hg0.8Mn0.2Te : DEPENDENCES OF ELASTIC MODULI ON
PRESSURE AND TEMPERATURE
M. Chao, R. Sladek
To cite this version:
M. Chao, R. Sladek. ULTRASONIC PHONONS IN Hg0.8Mn0.2Te : DEPENDENCES OF ELASTIC
MODULI ON PRESSURE AND TEMPERATURE. Journal de Physique Colloques, 1981, 42 (C6),
pp.C6-667-C6-669. �10.1051/jphyscol:19816195�. �jpa-00221280�
JOURNAL DE PHYSIQUE
CoZZoque C6, suppZ6ment au n o 12, Tome 42, ddeembre 1981 page c6-667
ULTRASONIC PHONONS I N H g o a 8 M n O s 2 T e
:
DEPENDENCES OF E L A S T I C MODULI ON PRESSURE AND TEMPERATUREM.H. Chao and R . J . Sladek
Department of Physics, &due University, West Lafayette, Indiana 47907, U.S.A.
Abstract.
-
U l t r a s o n i c t r a n s i t times have been measured f o r Hgo. 8Mno+2Te, a semimagnetic semiconductor, as a f u n c t i o n o f pressure up t o 4 kbar a t 296 K and o f temperature from 1.5 t o 296 K. They a r e used t o deduce t h e second o r d e r e l a s t i c s t i f f n e s s constants SOEC and a l s o f o r c e constants and t h i r d o r d e r e l a s t i c constants a t 296 K. The shear modulus CS = (Cll-
C12)/2 i s decreased by pressure i m p l y i n g a s t r u c t u r a l t r a n s f o r m a t i o n a t 10 kbar. No e l a s t i c e f f e c t s a t t r i b u t a b l e t o t h e magnetic moments o f t h e Mn i o n s are observed even a t low temperatures.Hgl-XMnxTe c r y s t a l s w i t h x s 0.35 have t h e c u b i c zinc-blende s t r u c t u r e . The magnetic s u s c e p t i b i l i t y ,
x,
and heat c a p a c i t y o f Hgl-xMnxTe e x h i b i t e f f e c t s a t low temperatures which depend 1 on t h e magnetic moments o f t h e Mn ions. Since t h e e l a s t i c p r o p e r t i e s o f Hgl-XMnxTe a r e unknown f o r x > 0, we have begun s t u d y i n g them i n c r y s t a l s w i t h d i f f e r e n t concentrations o f Mn and r e p o r t h e r e i n t h e e l a s t i c behavior o f semiconducting Hgo. 8Mno 2Te.The t r a n s i t times of 30 MHz l o n g i t u d i n a l and t r a n s v e r s e u l t r a s o n i c waves propagating along t h e C l l O l d i r e c t i o n were measured as a f u n c t i o n o f h y d r o s t a t i c pressure up t o 4 kbar a t 296 K and o f temperature from 1.5 t o 296 K a t 1 bar.
We o b t a i n values of Cll, C12, C44 and CS = (Cll
-
C12)/2 f o r Hgo.8Mno.,Te w i t h i n 8% o f those f o r H ~ T ~ . ~ A l l e l a s t i c s t i f f n e s s moduli o f Hgo.8Mno.2Te have l i n e a r dependences on pressure. As can be seen from Table I , t h e shear moduliC,
and C44 decrease, w h i l e C1 and C12 increase w i t h i n c r e a s i n g pressure. For Hgo. 8Mn0 .,Te t h e pressure d e r i v a t i v e s o f Cll, C12, and Cs are w i t h i n 9% of those f o r HgTe. 3 However, dCk4/dp i s much s m a l l e r i n Hg0.,Mno.,Te than i n HgTe i n which i t equals -0.12. Our r e s u l t s , along w i t h t h e f a c t t h a t HgTe transforms t o t h e cinnabar s t r u c - t u r e a t 14 kbar,4 i m p l i e s t h a t Hgo.8Mno.nTe w i l l have a s i m i l a r t r a n s f o r m a t i o n a t somewhat lower pressure which we estimate t o be 10 kbar by assuming i t occurs5 when CS/B reaches 0.17 as i n HgTe. (B i s the b u l k modulus (Cll + 2C12)/3.) E l a s t i c gammas c a l c u l a t e d from o u r data using the r e l a t i o nr i j
= 4 BT a l n Cij/aP-
1/6 a r e l i s t e d i n Table I also. The negative shear mode gammas imply t h a t t h e thermal expansion c o e f f i c i e n t o f Hgo.8Mno.2Te w i l l be negative a t low temperatures as i s t h e case f o r HgTe. 6Using equations from t h e l i t e r a t u r e : which we c o r r e c t e d f o r some e r r o r s , and o u r d a t a we deduced t h e f o r c e constants and t h i r d o r d e r e l a s t i c s t i f f n e s s constants
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19816195
JOURNAL DE. PHYSIQUE
Table I. Values and pressure d e r i v a t i v e s o f e l a s t i c s t i f f n e s s moduli and t h e anhar- m o n i c i t y parameters ( e l a s t i c gammas) o f Hgo.8Mno.zTe a t 296 K.
(TOEC) f o r our Hgo.8Mno.2Te sample as shown i n Table I 1
--
u and y are bond- s t r e t c h i n g w h i l e B and 6 are bond-bending constants, whereas E i s a mixed bond stretching-bending constant.Table 11. Harmonic f o r c e constants a and B ( i n
l o 4
dyn/cm), anharmonic f o r c e constants y, 6, and E , and t h i r d o r d e r e l a s t i c s t i f f n e s s constants C i j k ( i n 1012 dyn/cm2) o f Hgo-8Mno-2Te a t 296 K.Our value o f @/a f o r Hgo.8Mno.zTe i s equal t o t h a t found f o r H ~ i m p l y i n g T ~ ~ t h a t both m a t e r i a l s have the same P h i l l i p s i o n i c i t y (0.65) i n view o f Ref. 8. Our values o f 6/y and ~ / y f o r Hgo.8Mno.2Te a r e c o n s i s t e n t w i t h how these r a t i o s depend on fi f o r v a r i o u s 111-V and 11-VI compounds.7 The SOEC, t h e f o r c e constants, and t h r e e o f t h e TOEC are s m a l l e r i n Hgo.8Mno.2Te than i n HgTe. This seems c o n s i s t e n t w i t h t h e lower t r a n s i t i o n pressure we have deduced f o r Hgo.8Mno.2Te compared t o HgTe.
The SOEC o f Hgo.8Mno.2Te increase smoothly i n t h e usual manner as temperature i s decreased from 296 K t o 1.5 K. The o v e r a l l temperature dependences o f the SOEC are somewhat s m a l l e r than i n HgTe. This may be due t o the r i j and TOEC' having d i f f e r e n t values i n t h e two m a t e r i a l s . To l o o k more c l o s e l y f o r p o s s i b l e e f f e c t s associated w i t h the increase o f magnetic s u s c e p t i b i l i t y 1 a t low temperatures we show i n F i g . 1 data o n l y f o r 100 K and below. From Fig. 1 t h e r e seems t o be no evidence f o r e f f e c t s which m i g h t be associated w i t h t h e magnetic moments o f t h e Mn ions. The absence o f anomalies i n the SOEC i s c o n s i s t e n t w i t h t h e r e being no cusp i n
x
and no s p i n glass t r a n s i t i o n f o r x = 0.20 a t low temperatures. 1I n sununary, from our u l t r a s o n i c measurements on Hgo.$n0.,Te we conclude t h a t i t s bonding i s weaker and t r a n s i t i o n pressure s m a l l e r than i n HgTe and t h a t t h e SOEC a r e n o t a f f e c t e d appreciably by the magnetic moments of the Mn ions.
F i g . 1. Temperature dependences o f normalized second o r d e r e l a s t i c constants. A t 100 K, Cll = 5.503, C12 = 3.845, and CQ4 = 2.027, a l l i n u n i t s o f 1011 dyn/crn2.
0 20 40 60 80 100
Acknowledgments.- This work was supported by the N a t i o n a l Science Foundation
M a t e r i a l s Research Laboratory Program Grant No. DMR77-23798 and DMR80-20249. Thanks a r e due t o Professor J. K. Furdyna f o r t h e samples and f o r a number o f discussions.
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