Intensities of allowed hyperfine transitions and intensities and doublet separations of forbidden hyperfine transitions in the EPR of Mn2+: Zn(CH3COO)2 · 2H2O single crystals

JOURNAL

OF MAGNETIC

RESONANCE

l&281-292

(1975)

Intensities of Allowed Hyperfine Transitions and Intensities and Doublet Separations of Forbidden Hyperfine Transitions in the EPR of Mn’+ : Zn(CH, COO), -2H, 0 Single Crystals G. C. UPRETI* Physics

Department,

Indian Institute o.f’Technology, Kanpur-208016, India

1.1.7’. Post

Ofice,

Received September 16,1974 Forbidden hyperfine transitions (Am = +l, Am =z +2) in the EPR of Mn*+ doped in single crystals of zinc acetate dihydrate have been investigated at room temperature (-300 K) and X-band microwave frequency. The values of the axial and rhombic components of the n&ear quadrupole coupling constant obtained from the doublet separations of the forbidden transitions are Q’ = 0.18 G, Q” = 5.00 G, respectively. The observed angular variation of the intensities of allowed and forhidden transitions is found to be in good agreement with that obtained from Sir’s theory. The intensity of the forbidden transitions due to cross terms (ES,&) (AS, I+) is found to obey a (sin 2# dependence in agreement with theory. INTRODUCTION

In anearlier note (I) we reported the spin-Hamiltonian analysis and some preliminary results on forbidden hyperfine (hf) transitions in the electron paramagnetic resonance of Mn2+ doped in zinc acetate dihydrate crystals. The system is suitable for the study of forbidden hyperfine transitions because of the relatively smaller width of resonance lines and because of the presence of a single paramagnetic complex. In this paper we

report the observations and analyses of forbidden hf transitions Am = +I - ,- +2 2 in the fine structure transition M = +1/2 tt - l/2 and Am = k 1 in the fine structure transitions M = +3/2 t--t k l/2 and A4 = +5/2 f-) *3/2. We also report our studies on the angular variation of the intensities of allowed and forbidden hf transitions in the X.2 and XY planes and compare these observations with theory. THEORY

spin Hamiltonian the form (I): The

for MnZ+ substituting for Zn*+ in zinc acetate dihydrate is of

.# = fl(gz H, S, + g, Hx S, + sv Hy S,) + D{S; - $S(S + 1)) + E(S: - S,“) + A,S,I,

+ Ax&Z,

+ A,S,Z, - y&H.I+

Q’{Z: - +Z(Z+ I)} + Q”(Z; - If),

where the symbols have their usual meaning and S = 512, Z = 512. For isotropic hyperfine constant and isotropic g-value and under the approximation g/?H $ IDI, IEI, /Al, * Present address : Physikalische tjarmstadt, West Germany.

Chemie III, Technische Hochschule,

Copyright 0 1975 by Academic Press. Inc. All rights of reproduction in any form reserved. Printed m Great Rritom

287

Petersenstrasse 15, D-61

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G. C. UPREII

the perturbation theoretic expressions for doublet separations of forbidden hyperfine transitions in various fine structure transitions have already been reported (2). Both of the above conditions, isotropy of A and g and gj?H 9 /D I,] E 1, IA /, are satisfied for the system Mn2+:Zn(CH,COO),*2H,0. Hence these expressions are used for small angles away from the principal axes in discussing the doublet separations of forbidden hyperfine transitions in this system. Angles 8 and r$ used in the discussion below are the usual polar angles defining the direction of the magnetic field relative to the principal X, Y and 2 axes. The intensities of EPR hyperfine lines of ions in sufficiently strong crystalline fields exhibit strong angular variations when the external magnetic field direction is varied with respect to the crystal field directions. A comprehensive theory explaining the intensity variations of the allowed and forbidden hf lines was developed by Bir (3). Bir’s theory gives expressions for the transition probabilities of the allowed and forbidden lines in terms of the spin-Hamiltonian parameters. In calculating the intensities of allowed and forbidden hf transitions we have made use of Eqs. [25], [26], [48] and [50] of Ref. (3). EXPERIMENTAL

Single crystals of Zn(CH,COO),.2H,O doped with MnZ+ were grown by slow evaporation of a saturated distilled water solution of zinc acetate dihydrate containing about 2% manganese acetate by weight. The crystals grew in the form of thin plates parallel to the bc plane. The spectra were recorded with a Varian V-4502 EPR spectrometer operating at X-band microwave frequency (-9.5 GHz). It has a 9-inch rotatable magnet and is provided with lOO-kHz field modulation. DPPH with g = 2.0036 was used as the standard field marker. The magnetic field at DPPH resonance was measured by proton resonance using a Varian Model F-8A fluxmeter and a Hewlett-Packard 524-c counter. RtSULTS

AND

DISCUSSION

At room temperature a spectrum with a single group of 30 allowed lines (dm = 0) has been observed for all orientations of the crystal with respect to the static magnetic field. This suggests the existence of only one kind of paramagnetic complex with Mn2+ substituting for Zn2+ in zinc acetate dihydrate single crystals (I). The principal Y axis is found to be along the b axis by studying the angular variation of the spectrum in the flat bc plane of the crystal. Then fixing the crystal with the b axis vertical, the angular variation study of the spectrum in the ac plane yielded the 2 and X axes of the complex. Complete angular variation study has been carried out in the XZ and XY planes. The spin-Hamiltonian parameters obtained from the analysis of the allowed hf transitions are (I): g, = 2.0014 f 0.001,

g, = 2.0024 + 0.001,

g, = 2.0013 + 0.001,

A,=-89.9

A,=-89.3

A,=-89.6f0.5G,

*OSG,

D = 248 f 0.5 G,

+0.5G,

E = -25.5 f 1.5 G.

We shall now discuss the results on allowed and forbidden

hf transitions separately.

MANGANOUS

ION

IN ZINC

289

ACETATE

Allowed Transitions The angular variation of the intensities of allowed transitions 1l/2, 512) --f /3/2, 512) and 1I/2, I/2) + 13/2, l/2) in the XZ plane are shown in Figs. I(a) (b), respectively. The experimental results are represented by dotted circles; the solid curves are those

(b)

Cd)

CC)

FIG. I. Angular variation of the intensities of allowed hf transitions, (a) [l/2, 5!2) --f 1312. Z/2>, (b) /l/2,1/2> --jr /3/2,1,% and forbidden hf transitions, (c) )-l/2,1/2) -+ ]I12,312i,(d) ]-l/2,-1/2) + ) 112, l/2>, in the EPR of Mn2+:Zn(CH&00)2.2Hz0. The experimental points are marked 0 and the solid lines are based on calculations from Bir’s theory.

21 22 I 1’

23 24 IIII 2’ 3’

25 26 OII 4’ 5’

27 28 II II 6’ 7’

29 II

30

I

8’

FIG. 2. Allowed and forbidden hf lines in the EPR of Mn ‘+.ZII(CH~COO)~.~H,,O . for the transition M = l/2 c--t-l/2 with H at an angle 0 = 14” from the Z axis in the XZ plane. The lines numbered from 21 through 30 correspond to Am=+1 transitions and those numbered from 1’ through 8’ to Am = +2 transitions.

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obtained from the theoretical expressions given above for transition probabilities. The agreement between theoretical and experimental results is seen to be quite good. Forbidden Transitions Figure 2 shows the EPR spectrum of Mn *+.Zn(CH,COO),.2H,O . for transition M = +1/Z f+ -l/2 with H at an angle B = 14” from the Z axis in the XZ plane. The forbidden hf transitions corresponding to Am = &I are numbered from 21 through 30 and those corresponding to Am = +2 from 1’ through 8’. We now discuss separately the results on intensities and doublet separations of forbidden hf transitions. Intensities of Forbidden Transitions Figures l(c) and (d), respectively, show the angular variations of the intensities of forbidden transitions \--l/2, l/2) -+ )1/2, 312) and I-112, -l/2) --f \1/2, l/2), in the XZ plane. Experimental results are represented by dotted circles. The solid curves are those obtained from the expressions for transition probabilities given in Ref. (3). The agreement between calculated and observed intensity variations is fairly good. An interesting and intriguing observation is the larger relative intensity of forbidden transitions in the group M= -3/2 *-l/2 compared to that in the group

1 rCI .4x e 0 d I= E 0 ldY!zi

0

b

0 10 20 30 40 50 60 70 80 9( X-AXIS V-AXIS ANGLE ($,

IN DEGREES---c

FIG. 3. Angular variation of the relative intensity of forbidden rransition I-l/?, -l/2> -+ 11/2, l/2> to the allowed transition \-l/2. t/2> -+ )1/2, lj2> in the XY plane. Open circles correspond to experimentally observed relative intensity and the solid line to the theoretical relative intensity 0.134 (sin2#.

M = +3/2 c-f +1/2. Both Bleaney-Rubins’ (4) and Bir’s (3) expressions for the intensity involve quadratic terms of H in the denominator indicating that the intensities of the forbidden lines in the high-field transition must be smaller than those in the corresponding low-field transition. Our observations, as mentioned above, however, are exactly the opposite. At present we do not have any explanation for this apparent contradiction between theory and experimental observation. We have also studied the angular variation of the intensity of forbidden hf transitions in the XY plane. Figure 3 shows the relative intensity variation of the forbidden transition ]-l/2, -l/2) -+ 1l/2, l/2) in the XY plane. These transitions occur through the mixing of neighboring hyperfine levels by cross terms (ES,S,)(AS-,Zi). The relative intensity of forbidden hf transitions due to such cross terms can be shown to be

MANGANOUS

ION

IN ZINC

291

ACETATE

The experimental observations plotted in Fig. 3, along with the solid curve obtained from Eq. [I 1, do show the (sin24)2 dependence of the intensity of forbidden transitions in the XY plane. Further, because of the smaller value of E compared with that of D, the observed relative intensity of forbidden transitions in the XY plane is much smaller than that in the X2 plane. Doublet Separations of Forbidden Transitions The observed angular variation in the XZ plane of the five forbidden doublet separations for the group M = +I/2 c+ -I /2 is shown in Fig. 4 using different symbols. For the isotropic hyperfine interaction, as in our case, according to the perturbation expression the doublet separation varies as (3~0~~0 - 1) and is independent of the

26

24

T

22

2 2

20

4 ;

a

18

16

m

0 12

Z zAxi:O

I

q

+ 312

I

I

I

I

I

I

I

20

30

40

1

50

60

70

80

90

X-Axis 8O-

Angular dependence of the hyperfine forbidden (Am = 21) doublet separations of transition M= +1/2 c-)-l/2 in the X2 plane. FIG.

4.

the

angle for the central (m = -l/2) doublet. Both of these predictions are at variance with the experimental results, except at angles very near the axes. The conventional perturbation theory is known to be quantitatively unsatisfactory except for quite small 0 between H and the symmetry axis, i.e., for angles for which Zf < Z,. Thus the observed doublet separations fit reasonably well to those calculated from perturbation expressions only at small angles away from the symmetry axes. The doublet separations at all angles

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G. C. UPRETI

obtained theoretically by a complete diagonalization of the 36 x 36 matrix (5) are shown by solid lines in Fig. 4 and are seen to agree very well with the observed doublet separations at all angles. By fitting the observed forbidden doublet separations for the various groups (A4 ttM - 1) we have obtained the following values of Q’ and Q” which are, respectively, the axial and rhombic components of the quadrupole coupling constants of MrP nucleus: Q’ = 0.18 G,

Q” = 5.00 G.

Here (ypN/g/?) is taken to be 0.37 x 10e3 (6). CONCLUSION

Forbidden hyperfine transitions (AM = _~l, Am = +l, _+2)have been observed and analyzed in the electron paramagnetic resonance of Mn’+ doped in single crystals of zinc acetate dihydrate. The observed angular variations of the intensities of allowed and forbidden hyperfine transitions in the XZ plane have been found to agree with the results of Bir’s theory. However, the observation of larger intensity of forbidden transitions for high field transition compared with those of the corresponding low field transition, in contradiction to the theory, remains unexplained. The intensity variation of the forbidden transitions due to cross terms (ES,S,)(AS,II) has been investigated against the angle between the external magnetic field and a symmetry axis in the plane perpendicular to the principal axis of the axial field. The variation is found to agree remarkably well with the perturbation expression [l]. This is not unexpected, as the condition for the applicability of the perturbation theory, viz., /El/H < 1 is satisfied in the present case (]E[ = 25.5 G). The doublet separations calculated from perturbation expressions with Q’ = 0.18 G and Q” = 5.00 G are found to agree very well with the observed doublet separations only for small angles away from the symmetry axes. However, for larger angles off the symmetry axes the perturbation calculations are no longer valid and the complete diagonalization of the 36 x 36 matrix has been carried out to obtain the exact doublet separations from theory. REFERENCES 1. R. JANKIRAMAN

AND G. C. UPRETI,

J. P/zJ~s. Chem.

So/ids

2. G. C. UPRETI, J. Mugn. Resonance 13,336 (1974). 3. G. L. BIR, Sot. Phys. So/id Sfate 5,1628 (1964). 4. B. BLEANEY AND R. S. RUBINS, Proc. Phys. Sot. London 5. D. H. 6. Varian

LYONS AND R. W. KEDZIE, Associates “NMR Table

31, 1419 (1970).

77,103 P&s. Rev. 145,148 (1966). ” Fourth edition, 1964.

(1961).