- Email: [email protected]
Paramagnetic resonance of ZnO:Mn++ single crystals
J. Phys. Chem. Solids
*Pergamon Press 1968. Vol. 29, pp. 1369-I 375.
Printed in Great Britain.
PARAMAGNETIC RESONANCE OF ZnO: Mn++ SINGLE CRYSTALS A. HAUSMANN and H. HUPPERTZ II. Physikalisches Institut, TH Aachen, Germany (Received
17 January 1968; in reoisedform
2 1 February
1968)
Abstract - ZnO single crystals doped with Mn ++ have been investigated by ESR at 9.5 and 35 kMc/s. The measured spectra show minimal linewidth of 0.25 Cl. The resonances can theoretically be described by a spin Hamiltonian of axial symmetry of which the parameters have been determined with great accuracy. Forbidden transitions with AM = &l, Am = &l, . . . k5 have been observed. From these transitions the nuclear g factor can directly be calculated. An angular dependent splitting of all the lines into doublets has been detected. 1. lNTRODUCTION OXIDE crystals (ZnO) doped with Mn++ ions have been investigated by means of Electron Spin Resonance (ESR) by numerous authorsll-41. The spectrum of Mn++ ions in ZnO consists of five fine structure (fs) groups, each of which is split into six hyperfine lines. In addition to those allowed transitions with AM = +l, Am = 0 further lines for which Am # 0 can be observed. These forbidden resonances have first been observed by Bleaney and IngramlSl, detailed investigations of the spectra have been done by Bleaney and Rubins[6,7]. In the early measurements the spectra of the crystals showed lines with a halfwidth of approximately 20 G, making a detailed analysis of the signals and a proof of the theoretical predictions by Bleaney and Rubins]& 71 impossible. In this paper we can show for the first time that lines with a halfwidth of 0.25-l G can be obtained on ZnO crystals doped with Mn++ under special conditions. From the experimental data all the parameters of the crystalline field can be deduced with m-eat accuracv. Moreover we have been able to observe transitions with considerable changes in nuclear quantum number.
ZINC
2. EXPERIMENTS
The investigated crystals are transparent hexagonal needles, 1 mm in dia. and of approximately 20 mm length. They are grown from the gas phase with the Mn++ already added*. The content of 4 X 1014Mn++ ions per ccm of the crystals has been calculated from the intensity of the ESR lines. In contrast to higher doped crystals the microwave losses of the investigated samples are very small. The ESR measurements have been done at room temperature in a Varian V 4500 spectrometer at frequencies of 9.5 and 35 kMc/s. The static magnetic field, modulated with 100 kc/s, is measured by means of proton resonance with an accuracy of O-1 kc/s. The setup allows the registration of the first derivative of the absorption signal. 3. THEORY
(a) Positions ofthe lines ZnO crystallizes in the wurtzite structure C&. The added Mn++ ions replace Zn++ ions on regular lattice sites. The electron configuration of the Mn++ ions is 3d5, the electronic ground state Y?,,,. The only natural *The authors are indebted to Herrn Physik-Ingenieur K. Fischer for kindly preparing the crystals. 1369
1370
A. HAUSMANN
isotope is Mn55 which has a nuclear spin I = 5/2. Assuming that the g factor and the hfs constant are isotropic the spin-Hamiltonian can be written in the following way:
+s+
(Sit +
s;r+s;,> 1)(3Sz+3S-iZ(Z+
17A2
6H = w+
2HgJg -7$(2m-1)
+8 %(2m--I)--2P(2m-1).
For the transitions M = 3/2 + l/2 and -l/2 + -3/2 half of the lines are shifted by A to higher fields, the’ other half by A to smaller fields. For the two outer fs groups the shift is 2A. For k > 1 the central transition consists of 2Z+ 1 -k doublets of a separation k - 6H. For odd k these doublets are grouped between the lines AM = 21, Am = 0. For even k they enclose the lines with Am = 0.
1 +;[
and H. HUPPERTZ
l)]
1
1) -g&z7
(ZL~= Bohr’s magneton, g = electron g factor, g, = nuclear g factor, D, F = parameters of the axial crystalline field, A = hfs coupling parameter, a = parameter of the cubic part of the crystalline field, P = quadrupole coupling parameter). For the special orientations of the magnetic field H ]Ic and H * c (c being the polar axis of the ZnO crystal) the eigenvalues of the spin Hamiltonian can be calculated using a perturbational treatment. At 9-5 kMc/s the perturbation has to be in third order of A to find the line positions for the AM = +-1, Am = 0 transitions. Therefore terms proportional to A3/H2 and A2D/H2 have to be taken into account. At 35 kMc/s these terms are negligibly small. The forbidden transitions AM& 1, Am # 0 are observed for angles 6 # 0” and 9 Z 90” (6 = angle between c axis and magnetic field H). They arise from off-diagonal terms of the form (S,S+)(S_Z+) and (SJ-)(S+Z_) with energy coefficients of the order of magnitude DA/H. The line positions of the weak and transitions ]M, m) f, ](M-l),(m-_k)) IM, (m-k)) f, I(m-l),m) can approximately be calculated, (k= IAm] = 1,. . . 5; m=+I.... -I+k). For k= 1, 0”~ 6< 3” one finds for the central electronic transition five doublets with a separation of
(b) Intensities For the resonances AM = +l, Am = 0 the relative intensities of the five fs groups (each consisting of six equally intense hfs lines) are 5 : 8 : 9 : 8 : 5. For the forbidden transitions (M,m) t* IM-l,m-1) and IM,m-1) f, IM - 1,m) Bleaney and Rubins[6,7] give for the relative intensity the expression
. Z(Z+ 1) -m*+m
1
These lines are strongest in the electronic ]+1/2) * ]-l/2) transition and their intensity decreases with increasing field due to the term proportional to 1/H2. By means of perturbation theory it can be shown that the relative intensity of the four doubletsAM=-+l,Am=%2is5:9:9:5. The intensity as a function of d has been computed by Bleaney and Rubins[6,7], too. 4. REsULls
(a) Transitions AM = + 1 Am = 0 From the special orientations H )Ic and H I c several parameters of the spin Hamiltonian can be deduced. In first order quadrupole and nuclear Zeeman-energy give no contribution to the allowed transitions.
PARAMAGNETIC
RESONANCE
Further on only la-F1 can be determined but not a and F separately. At 35 kMc/s the following data have been measured gll= 1.9984 f 0.0002 gl = 1.9998 k 0.0002 ]A,,[= 79.24 -+ 0.02 G
OF ZnO: Mn++ SINGLE
CRYSTALS
512 -+ 312
2.70 G
312 --, l/2
3.34 G
l/2 --, -l/2
2.20 G
-l/2
--, -312
-312 --+ -512
1371
8.04G 6.27 G
The increasing splitting within a group may be due to terms proportional to u/H, but is IDI = 252*18*0.04 G certainly not the reason for the other observed deviations. la-F1 = 5.83 +0.04 G. The forbidden lines do also split to the same The theory of the crystalline field splitting extent. Figure 1 shows for some resonances requires the knowledge of the cubic part of the with Am = +l, -C2 in the central electronic field expressed by a. The factor a can be transition the splitting for angles d = 14”, q = 0” and 29= 14”, q = 30”. determined separately from F in the following For measuring the line splitting into way[3,8]. In the ZnO lattice there are two doublets the crystal has been mounted in a lattice sites in the unit cell having different symmetry with respect to H. Generally the teflon rod in such a way that both angles cubic field axes of the two sites do not co- 6 and * can be varied simultaneously by means of a thread transmission. incide, giving rise to two sets of energy levels. Therefore all lines are split into doublets, the The splitting of all lines into doublets in splitting being only dependent on a. The contrast to the predictions made by Schneider splitting H of the fs lines can be calculated and Sircar[3] can only be detected on crystals by first order perturbation theory resulting in with extremely small linewidth. Otherwise the lines cannot be identified with certain ti/2 * s/2 transitions. A superhyperhne interaction with 6H = (20 d2/3) (sin3 6 cos @cos 3*]u the next-nearest neighbor Zn ions as has been reported for instance by Title[9] on Cr+ in +3/2 * &l/2 ZnS, ZnSe and ZnTe has not been observed. 6H = (25 d/2/3) / sin3 Q cos 29cos 3*\Irlu This hfs splitting characterizes an interaction -l/2 c-+1/2 between the nuclear magnetic moment of 6ff=O Zna7 (4 per cent abundant) and the magnetic for the different electronic transitions. field produced at these sites by the Mn++ ion. (d = angle between c axis and field H, \I’= If an interaction of this sort exists it may be angle of rotation around c). It can easily be estimated that the resulting hfs splitting is seen that there is a maximum splitting for smaller than O-5 G. 6 = 60”, T = O”, 60”, 120”. . . Splitting of the (b) Transitions AM = +l , Am = 21, central fs group should only occur if factors 22,...* of higher order in a are taken into account. Figure 2 shows the spectrum of Mn++ in Our data support the angular dependence given earlier by Schneider and Sircar[3]. On ZnO for 29= ll”, Y = 30”. Besides the five the other hand the observed splittings do not fs groups Am = 0 three groups with Am = +l agree in any case with those predicted by the each consisting of five doublets can be seen. theory. For d = 10.5”, W = 0” 6H has the Moreover four doublets Am = %2 are grouped around H,. The intensities do well agree with following values (A~1= 78.73 f 0.02 G
1372
A. HAUSMANN
and H. HUPPERTZ
ZnO . Mn++
9,5 GHt 300’ K
8=14”
y=O”
I
I
1OOG Fig. 1. ZnO: Mn++, splitting of the forbidden transitions
-
H Am = *1,&2 in the central fs group.
ZnO : Mn++ 11’
9,5 GHz 300’ K
a-
3f5
4!0
4.5 kG
Fig. 2. Three groups of transitions Am = 21, one group Am = k2 for 6 = 11”.
PARAMAGNETIC
RESONANCE
OF ZnO:Mn++
those predicted by Bleaney and Rubins [61, especially the influence of the factor l/W can be noticed. Transitions Am = 0, r+l, Sz, . . . H are shown in Fig. 3. There are doublets grouped around Ho each with a k-times larger splitting than for the Am = al transitions. The lines have been registered at angles 8 = 24”, q = 30”. At these angles the observed intensities of the signals Am = &2 are already more intense than those with Am = O,+l. For a single fs group the overall intensity is constant. Therefore the transitions with Am = O,lml being large, lose less in intensity than the inner lines, because of the intensity distribution of the forbidden resonances. This can be seen in Fig. 4 for the central transition&I= +1/2 + -l/2. For the forbidden doublets a,decrease ofthe splitting with increasing field has ibeen found, partly caused by the quadrupole interaction of the Mn55 nucleus with the axial component
SINGLE
CRYSTALS
1373
of the crystalline field gradient. From the data measured at 35 kMc/s a quadrupole coupling parameter of P = O-15 + 0.01 G can be calculated. The line position of the transition M = l/2 4 -l/2, m = l/2 +-l/2 is given by H 1,2,1,2= Ho+ g,/gHo. The value g,/g can be calculated from the separation of the central doublet 6H = (17A2/2) - H,,+ (g,/g) -H,,, by measuring the field values of 6H and H,,2,1,2. The result is g,/g = O+IOO3762 ONKIOO3. The value taken from nuclear magnetic resonance is gr/g = O$lOO377. Both values agree very well. From the spectrum H 11c follows: sign A = sign D = - sign (a-F). For determination of the signs of the other parameters it is necessary to take the forbidden transitions into account. From the distance between the doublets M = l/2 + -l/2, m = +1/2 --, ~1/2
95 GHz 300°K
ZnO : Mn++
4 t 24” y-30”
k
k I
I
I
u
L-l
4
Am=+5
1
4
,
,
,
1
-
k. Fig. 3. ZnO: Mn++, resonances with Am = 0,+-l,. . . 5 near H,.
H
1374
A. HAUSMANN
and H. HUPPERTZ
9,s GHz 300* K
1000
ii
Fig. 4. Overall intensity distribution in the central fs group.
we have: sign g, = sign g, P > 0. The sign of A relative to grlg can be determined by finding out whether the shift A in the outer fs groups has to be added to or subtracted from the shift caused by H, *gJg. If only terms of first order in A are taken into account one has to know whether the transitions with M > 0 lie at higher or lower field than H,,. That means sign D has to be known. The absolute sign of D can be taken from susceptibility The great accuracy with measurements. which the ESR lines have been observed in this paper allows, however, to determine sign A directly by considering terms of higher order in A. The result is: sign A = sign g{Jg. Thus all parameters relative to g are known.
5. SIJhmARY ZnO is a suitable substance for investigations of paramagnetic centers in a crystalline field with axial symmetry, In well grown in0
single crystals for which the addition of Mn++ is not too high spectra with extraordinary small tinewidth can be found. Thus it is possible to determine the parameters of the crystalline field with great accuracy. In contrast to earlier measurements a slight anisotropy of g and A has been detected, the anisotropy being 7 x 10e4 and 6 X 10e3 respectively. The nuclear g factor can directly be taken from the ESR data. The accuracy in gr is comparable to the one obtained from NMR. At 35 kMc/s an exact value for the quadrupole couphng parameter can be given. Besides the splitting predicted by Schneider a splitting of all lines has been observed. The line positions for H L c can be calculated with the data taken from the spectrum H 11c within an accuracy of 0-t kc/s. We have been able to prove also quantitatively the theoretical predictions of Bleaney and
PARAMAGNETIC
RESONANCE
Rubins[6] to a far extent. The positions and splittings of the forbidden lines, their relative intensities and the functional dependence of intensity and an angle 19can be described with the given formulas in good approximation. Note
added in proof: Meanwhile the splitting of the central fs transition has been understood. A paper concerning this fact is to be published.
Acknowledgements-The advice and encouragement of Professor Dr. W. Sander has been highly appreciated in all phases of this work. We are indebted to Dr. E. Wassermann for valuable suggestions. The authors would like to express their gratitude to the Deutsche Forschungsgemeinschaft for providing the apparatus.
OF ZnO:Mn++
SINGLE
CRYSTALS
1375
REFERENCES 1. DORAIN P. B.,Phys. Rev. 112,1058 (1958). 2. HALL T. P. P., HAYES W. and WILLIAMS F. I. B.,Proc.phys. Sot. 78,883 (1961). 3. SCHNEIDER J. and SIRCAR S. R., Z. Naturf. 17a, 570 (1962). 4. SCHNEIDER J. and SIRCAR S. R., Z. Naturf. 17a, 651(1962). B. and INGRAM D. J. E., Proc. R. 5. BLEANEY Sot. A205,336 (1951). 6. BLEANEY B. and RUBINS R. S., Proc. phys. Sot. 77, 103 (1961). 7. BLEANEY B. and RUBINS R. S., Proc. phys. Sot. 78,778 (1961). 8. MCCONNELL H. M.,J. them. Phys. 24,904 (1956). 9. TITLE R. S., Phys. Rev. 133A, 1614 (1964).
*Pergamon Press 1968. Vol. 29, pp. 1369-I 375.
Printed in Great Britain.
PARAMAGNETIC RESONANCE OF ZnO: Mn++ SINGLE CRYSTALS A. HAUSMANN and H. HUPPERTZ II. Physikalisches Institut, TH Aachen, Germany (Received
17 January 1968; in reoisedform
2 1 February
1968)
Abstract - ZnO single crystals doped with Mn ++ have been investigated by ESR at 9.5 and 35 kMc/s. The measured spectra show minimal linewidth of 0.25 Cl. The resonances can theoretically be described by a spin Hamiltonian of axial symmetry of which the parameters have been determined with great accuracy. Forbidden transitions with AM = &l, Am = &l, . . . k5 have been observed. From these transitions the nuclear g factor can directly be calculated. An angular dependent splitting of all the lines into doublets has been detected. 1. lNTRODUCTION OXIDE crystals (ZnO) doped with Mn++ ions have been investigated by means of Electron Spin Resonance (ESR) by numerous authorsll-41. The spectrum of Mn++ ions in ZnO consists of five fine structure (fs) groups, each of which is split into six hyperfine lines. In addition to those allowed transitions with AM = +l, Am = 0 further lines for which Am # 0 can be observed. These forbidden resonances have first been observed by Bleaney and IngramlSl, detailed investigations of the spectra have been done by Bleaney and Rubins[6,7]. In the early measurements the spectra of the crystals showed lines with a halfwidth of approximately 20 G, making a detailed analysis of the signals and a proof of the theoretical predictions by Bleaney and Rubins]& 71 impossible. In this paper we can show for the first time that lines with a halfwidth of 0.25-l G can be obtained on ZnO crystals doped with Mn++ under special conditions. From the experimental data all the parameters of the crystalline field can be deduced with m-eat accuracv. Moreover we have been able to observe transitions with considerable changes in nuclear quantum number.
ZINC
2. EXPERIMENTS
The investigated crystals are transparent hexagonal needles, 1 mm in dia. and of approximately 20 mm length. They are grown from the gas phase with the Mn++ already added*. The content of 4 X 1014Mn++ ions per ccm of the crystals has been calculated from the intensity of the ESR lines. In contrast to higher doped crystals the microwave losses of the investigated samples are very small. The ESR measurements have been done at room temperature in a Varian V 4500 spectrometer at frequencies of 9.5 and 35 kMc/s. The static magnetic field, modulated with 100 kc/s, is measured by means of proton resonance with an accuracy of O-1 kc/s. The setup allows the registration of the first derivative of the absorption signal. 3. THEORY
(a) Positions ofthe lines ZnO crystallizes in the wurtzite structure C&. The added Mn++ ions replace Zn++ ions on regular lattice sites. The electron configuration of the Mn++ ions is 3d5, the electronic ground state Y?,,,. The only natural *The authors are indebted to Herrn Physik-Ingenieur K. Fischer for kindly preparing the crystals. 1369
1370
A. HAUSMANN
isotope is Mn55 which has a nuclear spin I = 5/2. Assuming that the g factor and the hfs constant are isotropic the spin-Hamiltonian can be written in the following way:
+s+
(Sit +
s;r+s;,> 1)(3Sz+3S-iZ(Z+
17A2
6H = w+
2HgJg -7$(2m-1)
+8 %(2m--I)--2P(2m-1).
For the transitions M = 3/2 + l/2 and -l/2 + -3/2 half of the lines are shifted by A to higher fields, the’ other half by A to smaller fields. For the two outer fs groups the shift is 2A. For k > 1 the central transition consists of 2Z+ 1 -k doublets of a separation k - 6H. For odd k these doublets are grouped between the lines AM = 21, Am = 0. For even k they enclose the lines with Am = 0.
1 +;[
and H. HUPPERTZ
l)]
1
1) -g&z7
(ZL~= Bohr’s magneton, g = electron g factor, g, = nuclear g factor, D, F = parameters of the axial crystalline field, A = hfs coupling parameter, a = parameter of the cubic part of the crystalline field, P = quadrupole coupling parameter). For the special orientations of the magnetic field H ]Ic and H * c (c being the polar axis of the ZnO crystal) the eigenvalues of the spin Hamiltonian can be calculated using a perturbational treatment. At 9-5 kMc/s the perturbation has to be in third order of A to find the line positions for the AM = +-1, Am = 0 transitions. Therefore terms proportional to A3/H2 and A2D/H2 have to be taken into account. At 35 kMc/s these terms are negligibly small. The forbidden transitions AM& 1, Am # 0 are observed for angles 6 # 0” and 9 Z 90” (6 = angle between c axis and magnetic field H). They arise from off-diagonal terms of the form (S,S+)(S_Z+) and (SJ-)(S+Z_) with energy coefficients of the order of magnitude DA/H. The line positions of the weak and transitions ]M, m) f, ](M-l),(m-_k)) IM, (m-k)) f, I(m-l),m) can approximately be calculated, (k= IAm] = 1,. . . 5; m=+I.... -I+k). For k= 1, 0”~ 6< 3” one finds for the central electronic transition five doublets with a separation of
(b) Intensities For the resonances AM = +l, Am = 0 the relative intensities of the five fs groups (each consisting of six equally intense hfs lines) are 5 : 8 : 9 : 8 : 5. For the forbidden transitions (M,m) t* IM-l,m-1) and IM,m-1) f, IM - 1,m) Bleaney and Rubins[6,7] give for the relative intensity the expression
. Z(Z+ 1) -m*+m
1
These lines are strongest in the electronic ]+1/2) * ]-l/2) transition and their intensity decreases with increasing field due to the term proportional to 1/H2. By means of perturbation theory it can be shown that the relative intensity of the four doubletsAM=-+l,Am=%2is5:9:9:5. The intensity as a function of d has been computed by Bleaney and Rubins[6,7], too. 4. REsULls
(a) Transitions AM = + 1 Am = 0 From the special orientations H )Ic and H I c several parameters of the spin Hamiltonian can be deduced. In first order quadrupole and nuclear Zeeman-energy give no contribution to the allowed transitions.
PARAMAGNETIC
RESONANCE
Further on only la-F1 can be determined but not a and F separately. At 35 kMc/s the following data have been measured gll= 1.9984 f 0.0002 gl = 1.9998 k 0.0002 ]A,,[= 79.24 -+ 0.02 G
OF ZnO: Mn++ SINGLE
CRYSTALS
512 -+ 312
2.70 G
312 --, l/2
3.34 G
l/2 --, -l/2
2.20 G
-l/2
--, -312
-312 --+ -512
1371
8.04G 6.27 G
The increasing splitting within a group may be due to terms proportional to u/H, but is IDI = 252*18*0.04 G certainly not the reason for the other observed deviations. la-F1 = 5.83 +0.04 G. The forbidden lines do also split to the same The theory of the crystalline field splitting extent. Figure 1 shows for some resonances requires the knowledge of the cubic part of the with Am = +l, -C2 in the central electronic field expressed by a. The factor a can be transition the splitting for angles d = 14”, q = 0” and 29= 14”, q = 30”. determined separately from F in the following For measuring the line splitting into way[3,8]. In the ZnO lattice there are two doublets the crystal has been mounted in a lattice sites in the unit cell having different symmetry with respect to H. Generally the teflon rod in such a way that both angles cubic field axes of the two sites do not co- 6 and * can be varied simultaneously by means of a thread transmission. incide, giving rise to two sets of energy levels. Therefore all lines are split into doublets, the The splitting of all lines into doublets in splitting being only dependent on a. The contrast to the predictions made by Schneider splitting H of the fs lines can be calculated and Sircar[3] can only be detected on crystals by first order perturbation theory resulting in with extremely small linewidth. Otherwise the lines cannot be identified with certain ti/2 * s/2 transitions. A superhyperhne interaction with 6H = (20 d2/3) (sin3 6 cos @cos 3*]u the next-nearest neighbor Zn ions as has been reported for instance by Title[9] on Cr+ in +3/2 * &l/2 ZnS, ZnSe and ZnTe has not been observed. 6H = (25 d/2/3) / sin3 Q cos 29cos 3*\Irlu This hfs splitting characterizes an interaction -l/2 c-+1/2 between the nuclear magnetic moment of 6ff=O Zna7 (4 per cent abundant) and the magnetic for the different electronic transitions. field produced at these sites by the Mn++ ion. (d = angle between c axis and field H, \I’= If an interaction of this sort exists it may be angle of rotation around c). It can easily be estimated that the resulting hfs splitting is seen that there is a maximum splitting for smaller than O-5 G. 6 = 60”, T = O”, 60”, 120”. . . Splitting of the (b) Transitions AM = +l , Am = 21, central fs group should only occur if factors 22,...* of higher order in a are taken into account. Figure 2 shows the spectrum of Mn++ in Our data support the angular dependence given earlier by Schneider and Sircar[3]. On ZnO for 29= ll”, Y = 30”. Besides the five the other hand the observed splittings do not fs groups Am = 0 three groups with Am = +l agree in any case with those predicted by the each consisting of five doublets can be seen. theory. For d = 10.5”, W = 0” 6H has the Moreover four doublets Am = %2 are grouped around H,. The intensities do well agree with following values (A~1= 78.73 f 0.02 G
1372
A. HAUSMANN
and H. HUPPERTZ
ZnO . Mn++
9,5 GHt 300’ K
8=14”
y=O”
I
I
1OOG Fig. 1. ZnO: Mn++, splitting of the forbidden transitions
-
H Am = *1,&2 in the central fs group.
ZnO : Mn++ 11’
9,5 GHz 300’ K
a-
3f5
4!0
4.5 kG
Fig. 2. Three groups of transitions Am = 21, one group Am = k2 for 6 = 11”.
PARAMAGNETIC
RESONANCE
OF ZnO:Mn++
those predicted by Bleaney and Rubins [61, especially the influence of the factor l/W can be noticed. Transitions Am = 0, r+l, Sz, . . . H are shown in Fig. 3. There are doublets grouped around Ho each with a k-times larger splitting than for the Am = al transitions. The lines have been registered at angles 8 = 24”, q = 30”. At these angles the observed intensities of the signals Am = &2 are already more intense than those with Am = O,+l. For a single fs group the overall intensity is constant. Therefore the transitions with Am = O,lml being large, lose less in intensity than the inner lines, because of the intensity distribution of the forbidden resonances. This can be seen in Fig. 4 for the central transition&I= +1/2 + -l/2. For the forbidden doublets a,decrease ofthe splitting with increasing field has ibeen found, partly caused by the quadrupole interaction of the Mn55 nucleus with the axial component
SINGLE
CRYSTALS
1373
of the crystalline field gradient. From the data measured at 35 kMc/s a quadrupole coupling parameter of P = O-15 + 0.01 G can be calculated. The line position of the transition M = l/2 4 -l/2, m = l/2 +-l/2 is given by H 1,2,1,2= Ho+ g,/gHo. The value g,/g can be calculated from the separation of the central doublet 6H = (17A2/2) - H,,+ (g,/g) -H,,, by measuring the field values of 6H and H,,2,1,2. The result is g,/g = O+IOO3762 ONKIOO3. The value taken from nuclear magnetic resonance is gr/g = O$lOO377. Both values agree very well. From the spectrum H 11c follows: sign A = sign D = - sign (a-F). For determination of the signs of the other parameters it is necessary to take the forbidden transitions into account. From the distance between the doublets M = l/2 + -l/2, m = +1/2 --, ~1/2
95 GHz 300°K
ZnO : Mn++
4 t 24” y-30”
k
k I
I
I
u
L-l
4
Am=+5
1
4
,
,
,
1
-
k. Fig. 3. ZnO: Mn++, resonances with Am = 0,+-l,. . . 5 near H,.
H
1374
A. HAUSMANN
and H. HUPPERTZ
9,s GHz 300* K
1000
ii
Fig. 4. Overall intensity distribution in the central fs group.
we have: sign g, = sign g, P > 0. The sign of A relative to grlg can be determined by finding out whether the shift A in the outer fs groups has to be added to or subtracted from the shift caused by H, *gJg. If only terms of first order in A are taken into account one has to know whether the transitions with M > 0 lie at higher or lower field than H,,. That means sign D has to be known. The absolute sign of D can be taken from susceptibility The great accuracy with measurements. which the ESR lines have been observed in this paper allows, however, to determine sign A directly by considering terms of higher order in A. The result is: sign A = sign g{Jg. Thus all parameters relative to g are known.
5. SIJhmARY ZnO is a suitable substance for investigations of paramagnetic centers in a crystalline field with axial symmetry, In well grown in0
single crystals for which the addition of Mn++ is not too high spectra with extraordinary small tinewidth can be found. Thus it is possible to determine the parameters of the crystalline field with great accuracy. In contrast to earlier measurements a slight anisotropy of g and A has been detected, the anisotropy being 7 x 10e4 and 6 X 10e3 respectively. The nuclear g factor can directly be taken from the ESR data. The accuracy in gr is comparable to the one obtained from NMR. At 35 kMc/s an exact value for the quadrupole couphng parameter can be given. Besides the splitting predicted by Schneider a splitting of all lines has been observed. The line positions for H L c can be calculated with the data taken from the spectrum H 11c within an accuracy of 0-t kc/s. We have been able to prove also quantitatively the theoretical predictions of Bleaney and
PARAMAGNETIC
RESONANCE
Rubins[6] to a far extent. The positions and splittings of the forbidden lines, their relative intensities and the functional dependence of intensity and an angle 19can be described with the given formulas in good approximation. Note
added in proof: Meanwhile the splitting of the central fs transition has been understood. A paper concerning this fact is to be published.
Acknowledgements-The advice and encouragement of Professor Dr. W. Sander has been highly appreciated in all phases of this work. We are indebted to Dr. E. Wassermann for valuable suggestions. The authors would like to express their gratitude to the Deutsche Forschungsgemeinschaft for providing the apparatus.
OF ZnO:Mn++
SINGLE
CRYSTALS
1375
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