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COMPARISON OF ELECTRON SPIN-LATTICE
RELAXATION IN AMORPHOUS AND
CRYSTALLINE MATERIALS
A. Deville, B. Gaillard, C. Blanchard, J. Livage
To cite this version:
JOURNAL DE PHYSIQUE
CoZZoque C6, suppZe'ment au n o 12, Tome 42, de'cembre 1981 page C6-465
COMPARISON OF ELECTRON S P I N - L A T T I C E R E L A X A T I O N I N AMORPHOUS AND C R Y S T A L L I N E M A T E R I A L S
A. Deville, B. Gaillard, C. Blanchard and J . ~iva~e'
De'pmtement d'EZectronique (E.R.A. 3751 Universite' de Provenee, Centre de Saint-Je'rhe, Rue Henri Poincare', 13397 MarseiZZe Cedex 1 3, France.
"Spectrochimie du SoZide (L.A. 3021, Universite' Pierre e t Marie Curie, (Paris V I ) , 75000 Paris, France.
Abstract
-
A quadratic law i s observed f o r the f i r s t time i n a trueamorphous %S%%ZT w i t h d i l u t e electron spins. He i n t e r p r e t i t as due t o a coupling of the spins t o the phonons via T.L.S. w i t h a cbnstant density of s t a t e s up t o 2Emax = 56 K.1. Introduction.- Mechanisms and processes describing s n i n - l a t t i c e relaxation of electron paramagnetic centers diluted i n a c r y s t a l l i n e diamagnetic s o l i d a r e well- known. The s i t u a t i o n i s somewhat d i f f e r e n t i n amorohous s o l i d s , where t h e existencd of Two-Level Systems (T.L.S.) 111 121 strongly coupled t o the phonons 131 i s well established. One can then imagine t h a t t h e i n d i r e c t t r a n s f e r of energy from the spins t o t h e phonons via the T.L.S. will by oass t h e usual d i r e c t t r a n s f e r from spins t o phonons. This will then lead t o new relaxation laws. This prob7em has been recently examined by S . 9 . Kurtz and H.J. S t a ~ l e t o n 141 f o r an amornhous-like system ($-Alumina doped w i t h ~ a + .
. .
and i r r a d i a t e d ) . A similar s i t u a t i o n has been found by J . Szeftel and H . Alloul ("B i n B2O3.. .). We hereafter present r e s u l t s obtained f o r a t r u e amorphous material and f o r the correspondinq c r y s t a l l i n e material.2.
1
We studied paramagnetic defects i n V205..
-=+
V (3d0) has no permanent magnetic moment. We used non-stochiometric oxide where paramagnetic defects were associated with oxygen vacancies. This non-stochiometry appears because V205 heated above i t s meltinq point (650" C ) loses oxygen. The amorphous material was obtained by s p l a t cooling.
In c r y s t a l l i n e V205, we have an E.P.R. spectrum consisting of 15 l i n e s caused by an additional electron (S = 1/2) delocalized over two vanadium ( I = 7/2), the electron spin being coupled t o both nuclear moments.
In amorphous V205, t h e E.P.R. spectrum consists of 8 l i n e s ; t h e additional electron i s localized on a s i n g l e vanadium (v4+3dl), the electron spin being
coupled t o t h e nuclear moment of t h e vanadium ion. Although V2O5 i s a semiconductor, i n these experiments the electron may be considered bound t o a given paramagnetic center (very low mobility)
.
3 . Experimental r e s u l t s . - We measured T1 by t h e saturating pulse method. For the c r y s t a l l i n e sample, i n the temperature-range 1.4
-
50 K ( f i g . 1 ) :15.5
T,-' = 12.5 T
+
3.1.103/sh -T (1) (T s , TK)C6-466 JOURNAL DE PHYSIQUE
For T > 30 K i t i s d i f f i c u l t t o s a t u r a t e t h e system because we have a broad inho- mogeneous 1 i ne.
For the amorphous sample ( f i g . Z ) , in the temperature-range 1.4
-
100 K :Fig. 1 : Temperature variation of the Fig. 2 : Temperature variation of the s p i n - l a t t i c e re1 axation time of m a t t i c e relaxation time of amor- c r y s t a l l i n e V2O5. o pulse s a t u r a t i o n , phous V2O5. pulse saturation. o progressive saturation. The s o l i d Experimental variation corresponds curve corresponds t o eq. ( 1 ) . t o the s o l i d curve, dashed curve
corresponds t o eq. ( 2 ) .
4. Interpretation.- In c r y s t a l l i n e V2O5, f o r T < 2 K, we have t h e usual d i r e c t process. For T > 5 K , the dominant process i s characterized by an energy Er =15.5 K and i s a l s o a one-phonon process since TI-'
-
T when T > 20 K. According t o Murphy model 151, the spin i s coupled t o the phonons via a system having two energy l e v e l s(PA
,
QB separated by Er. The e f f i c i e n t t r a n s i t i o n s a r e1%
1/2, @A><--> 13112, @B>and use phonons w i t h an energy c Er. The origin of these two energy levels i s s t i l l uncertain. An explanation i s t o consider t h a t the electron i s submitted t o a symmetrical double well potential l 6 l t then each vibrational s t a t e i s s p l i t i n two l e v e l s by tunnel e f f e c t . The energy s p l i t t i n g difference i s much l e s s than the vibrational energy fin. A t low temperature we have t o consider only t h e vibrational
-
1process. He i n t e r p r e t t h i s behaviour supposing t h a t the spins a r e coupled t o the phonons via the T.L.S. The T.L.S.-phonon coupling i s strong ; i t s hamiltonian, with usual notations, i s 131 :
E
JA
XTePh
=F(a)
[-AoYx+
AoZ] where ox and oZ a r e Pauli matrices acting on the eigen- s t a t e s of the T.L.S. The spin-T.L.S. coupling i s l e s s known ; our r e s u l t s suggest i t is e f f i c i e n t in our case ; a general expression f o r i t s hamiltonian i s :Following S.R. Kurtz and H.J. Stapleton 141, the t r a n s i t i o n probability f o r a d e f i n i t e spin t o f l i p through the coup1 ing with a T.L. S. and the phonons (Debye model)
A2 A:
i r f - 7
.
Averaging over A and A. w i t h Philips d i s t r i b u t i o n , one f i r p l l y getsE 3 Sh(rn)
expression ( 2 ) , the cutoff value f o r the energy of t h e T.L.S. being 2Emax = 56 K.
In t h e t r a n s i t i o n probability we have omitted an additional term leading t o a T4 dependence unobserved in the present case.
The e f f i c i e n t Drocess i s pictured i n fioure 3 :
s p i ~ s T. L.S. PHONONS
Fig. 3 : Indirect spin phonon coupling
References
-
111 W.A. Philips. J . of Low-Temp. Sol.,
7
(1972), 351.121 P.M. Anderson, B.I. Halperin, C.M. Varma. Phil. Mag.,
25
(1972), 1. 131 P. Doussineau, C. Frenois, R.G. Leisure, A. Levelut, J.Y. Prieur.J . Phys.,
41
(1980), 1193.141 S.R. Kurtz, H.J. Stapleton. Phys. Rev. B ,
