- Email: [email protected]
Electron spin resonance of Mn2+ in CdF2
Volume
i,
number
5
CHEMXAL
ELECTRON
PHYSICS
SPIN
RESONANCE
Duuglas
Corp.,
September
LETTERS
OF
Mn2+
IN
1968
CdF2
U. RANON McDonnell
Santa Monica,
California,
USA
and D. N. STAMIRES McDonnell
Douglas
Co@.,
Huntington
Received
BeucJz.
California.
USA
25 July 1968
The electron spin resonance of Mn 2+ in CdFZ was measured and the &II? - F- interaction parameters were determined. ResuIts are compared with those in other fluorides, and discussed in the light of the interplay of the fine. hyperfine. and superhyperfine interactions.
CdF2 has the fluorite structure where Cd2+ ions are located at alternate body centers of cubes of F’ ions. The lattice constant of CdF2 is slightly smaller than that of CaF2 [l]. We report here some preliminary results of an EPR study of Mn2f ions in CdF2 which were carried out at room temperature, and in the X and Ka bands. The paramagnetic Mn2+ substitutes for Cd2+ and is located at a site of. cubic symmetry. EPR of Mn2+ in fluorites has been previously reported for CaF2 [2,3], BaF2 [4] and SrF2 [5]. A striking feature of all these spectra is the observation of superhyperfine structure caused ‘by interaction with the neighboring F- nuclei (of nuclear spin I = 2 each). Since Mn2+ is an S-state ion with a ground state S = 5, the EPR spectrum can be described by a spin-Hamiltonian of the form Be= ~/3k&s+~a[s~+s_~+s$
;s(s+1)(3s2+3s-
1) +
where u is the cubic field-splitting parameter and A is the Mn hyperfine constant due to the nuclear spin Z = $ of Mn. The last term in eq. (1) represents the supernyperfine interaction with the eight nearest-neighbor fluorines and the fluorine nuclear Zeeman interaction. The tensor T has principal values T ., (= T,) and TL in a coordinate system #here z is parallel to a Mn2+ - F- axis, i.e., to a (111) direction_ For this discussion, it is more donvenient to use the parameters T, and Tp, which represent, respectively, the isotropic and anisotropic parts of the 286
.-
Mn2+ - F- interaction and are given by 7, = i( T,, + 2 TL) and Tp = i( T,, - 7-J. The general features of the EPR spectrum of Mn2+ in the S = $ state and cubic sites are well established. Since ] A ] >> ] ~11, a six-line hyperfine spectrum results; each of these lines is split into five fine-structure lines due to a (the A&1=1 transitions). In the fluorites, cf is very small (see table 1 and fig. l), and as a consequence these pentads are obscured by the superhyperfine structure caused by the surrounding fluorines. In addition, the pentad structure is complicated by the second-order term of the hyperfine interaction, which, expressed in gauss, has the form 121: - ,2
+ 2)2(2&l- l,J.
(2)
Since this term is linear in m, it affects each fine-structure pentad in a different way. On the other hand, the fine-structure splitting due to a is independent of m, and gives rise to a symmetrical pentad which is the same for every nz. Both the fine and hyperfine structure splittings have been treated in detail before [2,6]. From this, it is clear that if the second-order hyperfine term ._ prevails, a rather complicated spectrum will result, in which each hyperfine line will have a different fine-structure splitting. Adding to this the -superhyperfine splitting from the fluorines results in a distinct superhyperfine pattern for each hy- . -; -.I perfine transition. This is seen in the X-band ’ spectrum, fig. lk On the other hand, in the Ka --:T band spectrum along (loo), fig. lB, five groups are very similar to each other while the sixth one.::.-:i is broadened We have measured the parameters- ‘_s
Volume 2, number 6
CHEMICAL
PHYSICS Table
LETTERS
1
Comparison of spin-Hamiltonian parameters of Mn2+ in various fluorides
September
a.cd the amount of fluorine
1968
2s character
of
the 3d electrons Host Crystal
Mn2+ _ F- (A)
Temperature
A (G)
-L1.0
BaF2
2.67
LX
102
SrF2
2.49
Room
101.9 + 1.0
CaF2 CdF2
2.36 2.33
Room Room
102 99
ZnF2
2.026 2.042
Room Room
* 1 * 0.5
97.1 i; 0.3 98.8 rt 0.5
Ts (G)
5.7 * 0.5
Tp (G)
Q2s
1.5
8.4 f 1.0 9.4 It 0.5 10 f 0.3
2.9 f 0.5 3.3 ‘- 0.3
16.16 P 0.17 3.23 i 3.32 17.72 5 0.20 3.72 + 0.18
g and A which are given in table 1. The pentad splitting due to the CI term, which is maximum along 100 [Z, 61, is 5 cr. At X-band, the maximum splitting of a pentad due to the second-order hyperfine term is 29 gauss; at Ka band it is about 8 gauss. The distinct superhyperfine pattern at X band can be attributed to a prevailing secondorder hyperfine term; the similarity between the lines at Ka band indicates that the cubic field splitting is the prevailing factor at Ka band From this, we get 6 1 1u 1 > 1.5 gauss. If sign a f sign A , and a =: 1.5 gauss, separation between the external lines in the high field pentad along 000) at Ka band is expected to be about twice as large as in the other pentads. This is in qualitative agreement with fig. 1. The opposite signs for a and A are in agreement with results in other fluorites [2.4]. Turning now to the superhyperfine interaction parameters TS and Tp, we must be careful in obtaining them from a spectrum as complex as the one at X band (fig. 1A). It has been shown before [‘I, 81 that whenever the fluorine nuclear Zeeman interaction is of the same magnitude as the superhyperfine interaction, a breakdown in selection rules may occur, allowing “forbidden” transitions which involve fluorine nuclear flips to take place. One feature of this breakdown in $election rules is that the splittings between the superhyperfine lines becomes fieid-dependent [‘i’, 81. Another is the number of superhyperfine lines which may be observed along a high symmetry orientation in the crystal such as the (100) direction. For this orientation, the fluorines should give rise to 2(cIF) + 1 = 9 lines of the “allowed” type (AuzF = 0). However, if the “forbidden” transitions become allowed, there would be four superhyperfine transitions for each F’ nucleus, resulting in twenty-five superhyperfine lines. A priori, therefore, we cannot attribute the
character
g
0.18
2.009
0.26
2.0015
Refs.
E4I
0.30 0.35
E51 2.0013 12,31 2.0022 This work
0.53
2.002
f?l
complex spectrum at X band (fig. IA) to the cubic field splitting and second-order hyperfine shifts alone. Comparison with the Ka band spectrum is important in determining the overall character of the superhyperfine interaction. Comparison of figs. 1A and 1B shows that the splitting between sink?ar lines does not change appreciably by going from X band to Ka band The Ka band spectrum shows nine distinct superhyperfine lines on each hyperfine transitions. This indicates that the main superhyperfine transitions are indeed of the “allowed” type. These transitions are described in terms of T, and Tp by Ts+
f
Tp~"z~(3COS2%F-
1).
(3)
Along (loo), kos28F - 1 = 0 for all eight fhtorines, and the splitting is a measure of T,, giving IT,! = lOiO.3 gauss. Along (110), the fluorines split into two groups of four each, with 3~0~28 - 1 = 1 and -1, respectively. The superhyperfine splittings between lines in each group are then ( T,+ Tp) and ( Ts - T ), respectively. Along this direction, a pattern o? thirteen superhyperfine lines was observed at Ka band with a separation of 6 gauss between adjacent Lines. Assuming ( T,+ Tp) = 2( TS- T 1, we get lTpl = 3.3 f 0.3 gauss and a thirteen Pme spectrum. The pitfalls of using superhyperfine data alone for calculating superhyperfine tensor parameters without doing ENDOR measurements have been stressed before [8], but in the present case they may be justified by the close agreement of our values with those obtained in other fluorites, as shown in the table. Ligand ENDOR experiments in this system are under way and will be reported elsewhere. Assuming that all the magnetic electrons occupy 2s orb&&, the time they spent in the s orbitals of the F- ions can be estimated [S]. A value of 0.35% for the 2s character of,the magnetic 3d 28’7
Volume
2, number
5
CHEMICAL
PHYSICS
September
LETTERS
1968
electrons of Mn2+ at each F’ nucleus is obtained. This value is in accord with values reported for other crystals and is shown in the table for comparison. A trend is observed for the Mn2+ 3d electrons to occupy fluorine 2s orbitals for longer periods as the Mi12+ - F’ separation decreases. This indicates an increase in the covalent character of the Mn2+ - F- bond as the interatomic distance decreases. The increase in Tp is mainly due to the increase in the contribution of the direct dipole-dipole interaction AD with decreasing interatomic distance, since Tp = ( .4p+ A ); A is the interaction of the 36 electrons of Mn% l Wl %I the F- p orbitals. As one would expect, there is no noticeable change in theg factor among the various crystals, since the crystalline field splitting is small.
REFERENCES [I] R. W. G. Wyckoff, Crystal Structures, Vol. 1 (John Wiley and Sons, New York, 1963) p, 241.
100 GAUSS I
I
[2] W. Low, Phys. Rev. 105 (1957) 793. [3] 3. M. Baker, B. BIeaney ans W.Hayes, Proc. Roy. Sot. (London) 247A (1958) 141. [4] J. E. Drumheller. J. Chem. Phys. 38 (1963) 970. [5] V. IX Vinokurov and V. G. Stepanov, Soviet Phys. Solid State 6 (1964) 303. (English transl. of Fizika Tverdogo Tela 6 (1964) 380.) [6] R. De L.Kronig and C. J. Bouwkamp, Physica 6 (1939) 290. [7] A. AM.Clogston. J.P. Gordon, V. Jaccarino. M. Peter and R. L.Walker. Phys. Rev. 117 (1960) 1222. fS] U. Ranon and J.S. Hyde. Phys. Rev. 141 (1966) 259.
100 ,
GAUSS 4
-Fig.- 1. ESR spectrum of CdF : X band; B :%a
. .
Mi2+ al&g-(100). A : band.
__,__I.
:.
,
.
-.
_
i,
number
5
CHEMXAL
ELECTRON
PHYSICS
SPIN
RESONANCE
Duuglas
Corp.,
September
LETTERS
OF
Mn2+
IN
1968
CdF2
U. RANON McDonnell
Santa Monica,
California,
USA
and D. N. STAMIRES McDonnell
Douglas
Co@.,
Huntington
Received
BeucJz.
California.
USA
25 July 1968
The electron spin resonance of Mn 2+ in CdFZ was measured and the &II? - F- interaction parameters were determined. ResuIts are compared with those in other fluorides, and discussed in the light of the interplay of the fine. hyperfine. and superhyperfine interactions.
CdF2 has the fluorite structure where Cd2+ ions are located at alternate body centers of cubes of F’ ions. The lattice constant of CdF2 is slightly smaller than that of CaF2 [l]. We report here some preliminary results of an EPR study of Mn2f ions in CdF2 which were carried out at room temperature, and in the X and Ka bands. The paramagnetic Mn2+ substitutes for Cd2+ and is located at a site of. cubic symmetry. EPR of Mn2+ in fluorites has been previously reported for CaF2 [2,3], BaF2 [4] and SrF2 [5]. A striking feature of all these spectra is the observation of superhyperfine structure caused ‘by interaction with the neighboring F- nuclei (of nuclear spin I = 2 each). Since Mn2+ is an S-state ion with a ground state S = 5, the EPR spectrum can be described by a spin-Hamiltonian of the form Be= ~/3k&s+~a[s~+s_~+s$
;s(s+1)(3s2+3s-
1) +
where u is the cubic field-splitting parameter and A is the Mn hyperfine constant due to the nuclear spin Z = $ of Mn. The last term in eq. (1) represents the supernyperfine interaction with the eight nearest-neighbor fluorines and the fluorine nuclear Zeeman interaction. The tensor T has principal values T ., (= T,) and TL in a coordinate system #here z is parallel to a Mn2+ - F- axis, i.e., to a (111) direction_ For this discussion, it is more donvenient to use the parameters T, and Tp, which represent, respectively, the isotropic and anisotropic parts of the 286
.-
Mn2+ - F- interaction and are given by 7, = i( T,, + 2 TL) and Tp = i( T,, - 7-J. The general features of the EPR spectrum of Mn2+ in the S = $ state and cubic sites are well established. Since ] A ] >> ] ~11, a six-line hyperfine spectrum results; each of these lines is split into five fine-structure lines due to a (the A&1=1 transitions). In the fluorites, cf is very small (see table 1 and fig. l), and as a consequence these pentads are obscured by the superhyperfine structure caused by the surrounding fluorines. In addition, the pentad structure is complicated by the second-order term of the hyperfine interaction, which, expressed in gauss, has the form 121: - ,2
+ 2)2(2&l- l,J.
(2)
Since this term is linear in m, it affects each fine-structure pentad in a different way. On the other hand, the fine-structure splitting due to a is independent of m, and gives rise to a symmetrical pentad which is the same for every nz. Both the fine and hyperfine structure splittings have been treated in detail before [2,6]. From this, it is clear that if the second-order hyperfine term ._ prevails, a rather complicated spectrum will result, in which each hyperfine line will have a different fine-structure splitting. Adding to this the -superhyperfine splitting from the fluorines results in a distinct superhyperfine pattern for each hy- . -; -.I perfine transition. This is seen in the X-band ’ spectrum, fig. lk On the other hand, in the Ka --:T band spectrum along (loo), fig. lB, five groups are very similar to each other while the sixth one.::.-:i is broadened We have measured the parameters- ‘_s
Volume 2, number 6
CHEMICAL
PHYSICS Table
LETTERS
1
Comparison of spin-Hamiltonian parameters of Mn2+ in various fluorides
September
a.cd the amount of fluorine
1968
2s character
of
the 3d electrons Host Crystal
Mn2+ _ F- (A)
Temperature
A (G)
-L1.0
BaF2
2.67
LX
102
SrF2
2.49
Room
101.9 + 1.0
CaF2 CdF2
2.36 2.33
Room Room
102 99
ZnF2
2.026 2.042
Room Room
* 1 * 0.5
97.1 i; 0.3 98.8 rt 0.5
Ts (G)
5.7 * 0.5
Tp (G)
Q2s
1.5
8.4 f 1.0 9.4 It 0.5 10 f 0.3
2.9 f 0.5 3.3 ‘- 0.3
16.16 P 0.17 3.23 i 3.32 17.72 5 0.20 3.72 + 0.18
g and A which are given in table 1. The pentad splitting due to the CI term, which is maximum along 100 [Z, 61, is 5 cr. At X-band, the maximum splitting of a pentad due to the second-order hyperfine term is 29 gauss; at Ka band it is about 8 gauss. The distinct superhyperfine pattern at X band can be attributed to a prevailing secondorder hyperfine term; the similarity between the lines at Ka band indicates that the cubic field splitting is the prevailing factor at Ka band From this, we get 6 1 1u 1 > 1.5 gauss. If sign a f sign A , and a =: 1.5 gauss, separation between the external lines in the high field pentad along 000) at Ka band is expected to be about twice as large as in the other pentads. This is in qualitative agreement with fig. 1. The opposite signs for a and A are in agreement with results in other fluorites [2.4]. Turning now to the superhyperfine interaction parameters TS and Tp, we must be careful in obtaining them from a spectrum as complex as the one at X band (fig. 1A). It has been shown before [‘I, 81 that whenever the fluorine nuclear Zeeman interaction is of the same magnitude as the superhyperfine interaction, a breakdown in selection rules may occur, allowing “forbidden” transitions which involve fluorine nuclear flips to take place. One feature of this breakdown in $election rules is that the splittings between the superhyperfine lines becomes fieid-dependent [‘i’, 81. Another is the number of superhyperfine lines which may be observed along a high symmetry orientation in the crystal such as the (100) direction. For this orientation, the fluorines should give rise to 2(cIF) + 1 = 9 lines of the “allowed” type (AuzF = 0). However, if the “forbidden” transitions become allowed, there would be four superhyperfine transitions for each F’ nucleus, resulting in twenty-five superhyperfine lines. A priori, therefore, we cannot attribute the
character
g
0.18
2.009
0.26
2.0015
Refs.
E4I
0.30 0.35
E51 2.0013 12,31 2.0022 This work
0.53
2.002
f?l
complex spectrum at X band (fig. IA) to the cubic field splitting and second-order hyperfine shifts alone. Comparison with the Ka band spectrum is important in determining the overall character of the superhyperfine interaction. Comparison of figs. 1A and 1B shows that the splitting between sink?ar lines does not change appreciably by going from X band to Ka band The Ka band spectrum shows nine distinct superhyperfine lines on each hyperfine transitions. This indicates that the main superhyperfine transitions are indeed of the “allowed” type. These transitions are described in terms of T, and Tp by Ts+
f
Tp~"z~(3COS2%F-
1).
(3)
Along (loo), kos28F - 1 = 0 for all eight fhtorines, and the splitting is a measure of T,, giving IT,! = lOiO.3 gauss. Along (110), the fluorines split into two groups of four each, with 3~0~28 - 1 = 1 and -1, respectively. The superhyperfine splittings between lines in each group are then ( T,+ Tp) and ( Ts - T ), respectively. Along this direction, a pattern o? thirteen superhyperfine lines was observed at Ka band with a separation of 6 gauss between adjacent Lines. Assuming ( T,+ Tp) = 2( TS- T 1, we get lTpl = 3.3 f 0.3 gauss and a thirteen Pme spectrum. The pitfalls of using superhyperfine data alone for calculating superhyperfine tensor parameters without doing ENDOR measurements have been stressed before [8], but in the present case they may be justified by the close agreement of our values with those obtained in other fluorites, as shown in the table. Ligand ENDOR experiments in this system are under way and will be reported elsewhere. Assuming that all the magnetic electrons occupy 2s orb&&, the time they spent in the s orbitals of the F- ions can be estimated [S]. A value of 0.35% for the 2s character of,the magnetic 3d 28’7
Volume
2, number
5
CHEMICAL
PHYSICS
September
LETTERS
1968
electrons of Mn2+ at each F’ nucleus is obtained. This value is in accord with values reported for other crystals and is shown in the table for comparison. A trend is observed for the Mn2+ 3d electrons to occupy fluorine 2s orbitals for longer periods as the Mi12+ - F’ separation decreases. This indicates an increase in the covalent character of the Mn2+ - F- bond as the interatomic distance decreases. The increase in Tp is mainly due to the increase in the contribution of the direct dipole-dipole interaction AD with decreasing interatomic distance, since Tp = ( .4p+ A ); A is the interaction of the 36 electrons of Mn% l Wl %I the F- p orbitals. As one would expect, there is no noticeable change in theg factor among the various crystals, since the crystalline field splitting is small.
REFERENCES [I] R. W. G. Wyckoff, Crystal Structures, Vol. 1 (John Wiley and Sons, New York, 1963) p, 241.
100 GAUSS I
I
[2] W. Low, Phys. Rev. 105 (1957) 793. [3] 3. M. Baker, B. BIeaney ans W.Hayes, Proc. Roy. Sot. (London) 247A (1958) 141. [4] J. E. Drumheller. J. Chem. Phys. 38 (1963) 970. [5] V. IX Vinokurov and V. G. Stepanov, Soviet Phys. Solid State 6 (1964) 303. (English transl. of Fizika Tverdogo Tela 6 (1964) 380.) [6] R. De L.Kronig and C. J. Bouwkamp, Physica 6 (1939) 290. [7] A. AM.Clogston. J.P. Gordon, V. Jaccarino. M. Peter and R. L.Walker. Phys. Rev. 117 (1960) 1222. fS] U. Ranon and J.S. Hyde. Phys. Rev. 141 (1966) 259.
100 ,
GAUSS 4
-Fig.- 1. ESR spectrum of CdF : X band; B :%a
. .
Mi2+ al&g-(100). A : band.
__,__I.
:.
,
.
-.
_