RESONANT CROSS-RELAXATION TO Cr4+ IN RUBY

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RESONANT CROSS-RELAXATION TO Cr4+ IN RUBY

Aime Vasson, C. Bates

To cite this version:

Aime Vasson, C. Bates. RESONANT CROSS-RELAXATION TO Cr4+ IN RUBY. Journal de

Physique Colloques, 1978, 39 (C6), pp.C6-1005-C6-1006. �10.1051/jphyscol:19786444�. �jpa-00217922�

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JOURNAL DE PHYSIQUE Colloque C6, supplément au n° 8, Tome 39, août 1978, page C6-1005

RESONANT CROSS-RELAXATION TO Cr + IN RUBY

A.M. Vasson , A. Vasson and C.A. Bates

* Laboratoire de RadioelectricitS et ThSorie du Solide, Universite de Clermont- Ferrand II, 63170 Aubiere, France.

** Department of Physios, University of Nottingham, Nottingham NG7 2RD, England

Résumé.- Des mesures sur la relaxation croisée résonnante entre l'ion C r3 +, choisi comme sonde, et l'ion Jahn-Teller Cr1*"1", dans des monocristaux de rubis, sont décri- tes. Les valeurs de g., et D pour Cr + sont déduites et comparées à celles obtenues par d'autres méthodes.

Abstract.- Measurements on the resonant cross-relaxation between the monitored C r3 +

ion and a Jahn-Teller Cr1*-1- ion in ruby crystals are described. Values for g„ and D for Cr4"1" are deduced and compared to other measurements and calculations.

1. EXPERIMENTAL MEASUREMENTS.- The effects of various trace Jahn-Teller (JT) impurities on the spin-lattice relaxation time Ti (Cr3-1-: Al 0 )

2 3_

have been reported /1-3/. Marked reductions in the measured value Tj of Tj occur whenever the energy

level separation in the non-monitored ion exactly matches that in the monitored ion. This process is called resonant cross-relaxation (RCR).

We now consider RCR involving the Cr1*"1"

ion. Crystals have been obtained by either adding Mg to the initial ruby powders or by Y"irra<iiating a pure ruby crystal.

The energy-level diagrams of the two ions are shown in figure 1(a) as the magnetic field H is varied. Standard pulse saturation Tj measurements are carried out at 11.472 GHz.

Fig. 1 (a): The energy levels of C r3 + and Cr1*"1" in A12C>3 as a function of H along the c-axis (not to

scale);

(b): and (c) Schematic EPR line shapes of Cr3 + and Cr1*"1" when the peaks coincide (b) and at maximum overlap (c) (Not to scale).

Figure 2 shows the isofrequency curves for the various C r3 + transitions and the upper

doublet transition in Cr1** as a function of x.

the angle between H and the crystal c-axis.

Fig. 2 : Isofrequency curves of Cr3 ( ) and CJ-'H- ( ) a t n.472 GHz.

The experimental values of Ti were measured in the region of the three intersections of the C r4 + and Cr3 + curves and the results are shown in Figure 3. While some of the dips are explained in terms of multiple spin processes in the C r3 + sys- tem only /3/, pronounced dips in Tj occur due to Cr1*"1- but at an angle slightly larger than that expected (indicated by I in Figure 3) .

The temperature dependence of T. at the positions of the dips has also been investigated for 1.3<T<_4.2 K for all samples. We have previously shown that /1-3/ ^ 'Tl ^c r i t- ^ lr^% e n

= Wxf(T) + c (1)

with

f(T) = 2cosh(c/T){2cosh(o7T) + exp [(D + n) / T ] } "1 ,

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19786444

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where

20 = hv and n = 1 .5D (gLB~sin~) { ~ 2

- ( g 1 1 ~ ~ ~ ~ ~ ~ ) 2 1 - 1 .

"crit" refers to the value at the dip on Tlm while

"gen" refers to a value of Tlm just outside the dip.

Fig. 3 : Angular dependence of Tlm for the ~ r j + transitions showing RCR to Cr'++, at 4.2 K and 11.472 GHz in two rubies (I and 111) doped with magnesium.

The experimental results were fitted to (I) and its best fit gave D = 7.0 2 0.4 cm-l.

2. THEORY AND INTERPRETATION.- The three lowest states of cr4+ : A1203 are described by the spin Hamiltonian (S = I) :

2 -

^gllBH,S,⁺^gfi(%SX ⁺^%Si) ⁺

p

I ^(3s:

-

²⁾

+gstrain (2)

is the Hamiltonian for E-type random where 'strain

strains E+ and E-. Sharp features in an EPR spec- trum are then obtained when the splitting A between two of the cr4+ levels satisfies aA/aa, = 0.

For

x

= 0, this gives maxima when for AMS = f2 for AM = tl

S

where Hz0 and Hi0 are the corresponding fields.

The table above gives the previously observed values of gll and D together with those deduced from our results and equations ( 1 ) and (3).

(Note that the expressions in (3) are different from those used previously /4/ but the departures from (3) are small.).

METHOD ¹I _I glt

i

^D(cm-')

-

I I

EPR (X-band) /5/ 1.90

+

^0.02

:

⁷²^0.7

I

I 0.01

:

I 1

APR (9.375 GHz) /6/ 1.93 2 0.05

: -

1 I

EPR (140 GHz) 141

:

^1.913ⁱ0.005: 7.562

+

^0.016

I I

Optical 141 ^I

-

I

:

^7.55

*

^0.02

I 1

APR (8.9 GHz) /7/ 1.86 f 0.05

: ^-

1 I

Phonon spectroscopy

: - :

^7.17^f^0.33

181

:

¹^I

I I

Present Value I I 1.97

:

^7.0(RCR)

I

1

:

^7.16(NCR)

I I

To explain the discrepancy between our values of g,, (1.97) and that by direct EPR 141. we consider figures l(b, c) which show sketches of the cr3+ and cr4+ EPR lines. The cr4+ line has a sharp edge on the high-field side of the line, while the cr3+ line is very broad. Thus maximum

cross-relaxation occurs when the peak and edge are displaced (

x

=

xm)

as shown in figure I (c) rather than when they coincide (

x

=

x

) as in figure I(b). Thus the minimum in T l m occurs for H = H m which is less than the expected value H

.

^This

effect thus reduces g,, from 1.97 to 1.91 as observed by direct EPR /4/.

Our value of D is in good agreement with that measured by phonon spectroscopy /8/ but lower than that obtained by others (e.g. /4/). It is also in good agreement with that obtained b y w i from an analysis of non-resonant cross-relaxation (NCR). The reasons for this discrepancy are not clear.

References

/I/ Bates,C.A., Gavaix,A., Steggles,P., Vasson,A.

and Vasson,A.M., J. Phys. C.

8

(1975) 2300 /2/ Gavaix,A., Vasson,A., Vasson,A.M., Bates,C.A.

and Steggles,P., J. Phys. Chem. Solids

2

⁽¹⁹⁷⁶⁾

1051

/3/ Bates,C.A., Steggles,P., Gavaix,A., Vasson,A.M.

and Vasson,A., J. Physique

2

(1978) 315 /4/ Pontnau,J. and Adde,R., J. Phys. Chem. Solids

36 (1975) 1023 ; C.R. Acad. Sci. Paris, 280

-

(1975) 301 ; and J. Physiquex (1976) 4 1 /5/ Hosking,R.H. and Soffer,B.H., Phys. Rev.

133

(1964) A490

161 Penne,J., ThZse d1Etat, Universits de Paris ( 1968)

171 Abou-Ghantous,M., Bates,C.A. and Goodfellow,L.

C., J. Phys. Chem. Solids

2

(1976) 1059 181 Guyot,G. and ~ocatelli,M., private couununica-

tion