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The hyperfine structure of 161Dy in dysprosium salts
J. Phys. Chem. Solids
Pergarnon Press 1967. Vol. 28, pp. 2099-2103.
THE HYPERFINE
Printed in Great Britain.
STRUCTURE
DYSPROSIUM
OF lelDy IN
SALTS
H. H. WICKMAN and I. NOWIE* Bell Telephone Laboratories, Incorporated, Murray Hill, New Jersey (Receiwed 26 April 1967)
Abstract-The MGssbauer technique was used to investigate the low temperature (4*2”K) hyperfine structure of rslDy in the following paramagnetic salts: Group 1; Dy-oxalate, Dy-acetate, DyFs.SHaO, Dy(NO&.6HaO, DyPOl.5Ha0, Dy(MoO&, DyFeOs, DyMnaOs, DyAlG; and Group 2; DyaOs, DyCls.6H,O, Dy-ethyl sulfate. In all cases the observed spectra were consistent with a collinear hyperfine magnetic field and axially symmetric EFG. This requires a ground doublet with the property gL = 0 # g,,. In Group 1 compounds the observed hfs interactions were within
4 per cent of the free ion hyperfine interaction, g,&H,, = 820 + 20 MC/S for a doublet I+ J, > with J, = 15/2. The three compounds in Group 2 had g&H,, = 727, 675 and 446 MC/S respectively. The results in Group 1 imply a ground doublet with gll N 19.6 and in Group 2 we have values for gll of 17.2, 16.0 and 10.6 for the three compounds, respectively.
THE M~SSBAUER technique has recently shown the presence of well resolved hypefine splittings in several concentrated psramagnetic dysprosium salts at low temperatures.(1-3) In the reported cases, the spectra were simply interpreted in the usual effective hyperfine field approximation. In general, however, the hyperfine interaction may contain off-diagonal elements which lead to grossly different spectra, and we have investigated a number of dysprosium salts in an effort to observe such effects. Although well resolved hfs spectra were obtained, it was found that for all the compounds investigated, the effective field approximation suffices to interpret the spectra. This result implies a somewhat restrictive magnetic character for the ground doublets of these compounds; the discussion below shows that gI is non-zero while gL vanishes in every instance. HYPERFINX STRUCTURE OF A KRAMERS DOUBLET The ground term of Dy3+ is 6H,,,2 and is split by crystalline fields of lower than cubic symmetry
into eight Kramers’ doublets (in a cubic field 2 doublets and 3 quartets are found). The ground Kramers doublet can be described by an effective spin S = 4, whenever the next Stark level is high in comparison with small perturbations such as the Zeeman interaction or in our case (zero external field) the much smaller hyperfine interactions. For such cases the hyperfme levels are given in the spin Hamiltonian representation as eigenvalues of the operator X
= S*A.I+P{31,a-I(I+l) +(V/2)(1+2
address:
Yale
University,
New
(1)
where
P = e2qQ/41(21-
l),
and A is the magnetic hyperfine tensor. In the case of axial symmetry (which exists in trigonal or higher symmetries) the Hamiltonian has the form :
(A, = A,, 71= 0) a? = A,[S,I,+x(S+I_
* Present corm.
+I-“)>,
+S_I.,)]
Haven,
+ P(31,2 -I(l+ 2099
1)).
(2)
2100
H. H. WICKMAN
where x = (J4,/2&); when x = 0 we are left with the effective field approximation. In systems having a ground doublet with A, = A, = 0 # A, there will usually be “long” relaxation times at low temperatures;(4) that is, T x v&-l where T is an effective electronic relaxation time and vr is the nuclear Larmor frequency. Mijssbauer spectra in this case are similar to spectra observed in ferrimagnets, and A, is easily derived from the Mossbauer data.c5) In the general case when the effective hyperfine tensor has more than one non-vanishing component, one still expects paramagnetic hfs at low enough temperatures and/or paramagnetic concentration. It should be remarked that low paramagnetic concentration is not a prerequisite for the appearance of hfs in the Mossbauer spectrum. For even in concentrated salts it is possible to achieve effectively long relaxation times by taking the samples to ultra low temperatures and thus depopulating spin states which are involved in relaxation. An approximate criteria for hfs is that the effective relaxation time T satisfy T B max(h/AJ for any A, # 0, i = x, y, z. Under these conditions the hyperfine interaction may be determined by comparing the experimental data with theoretical spectra computed from the Hamiltonian of equation (1). The Hamiltonians for the ground and excited nuclear levels are diagonalized and the eigenvectors used to calculate transition probabilities: typical results are given in Fig. 1. It is obvious that small values of A, (4 per cent of A,) are enough to distort the effective field Miissbauer spectrum. However, the total splitting (the separation between the two outer lines) is a measure of A, and is not sensitive to the value of A, up to AZ/A, = 0.4 (x = 0.2). The resulting Mijssbauer spectra therefore yield the value of A, even under conditions when the effective field approximation is not exactly satisfied. Neglecting interactions from higher Jmultiplets, the hyperfine tensor, A, E 2gO&Heeff, and the spectroscopic splitting factor g, for the ground doublet are proportional: go&Heft = kg,; and more generally, A, = 2kg,, i = x, y, x. The constant k has been determined in recent Miissbauer
and I. NOWIK
studie#) in DYES, DyAlG and Dy metal in which cases the g, factors are known. Using this derived value of k, 41.2 MC, the electronicg factor, g,, for a salt showing paramagnetic hfs with x M 0 is readily determined from the Mbssbauer data. It is interesting to consider the special case of a Kramers doublet in cubic symmetry: A, = A, = A,, P = 0. Here the hyperfine splitting can be described by the quantum number F = S-+1and the Miissbauer transitions will have the selection rules AF = 0, f 1. For the nuclear angular momentum involved in 16rDy (I,, = Ig( = 5/2), four transitions are allowed with relative intensities given by standard formulae of angular momentum theory.(s) The simple resulting spectra are given in Fig. 1, x = 0.5. A more complicated example is also shown in Fig. 1 and corresponds to the hfs expected for Dy-acetate, where the g factors from ESR are g, = 13.6, g, M 3 and g, w 4.‘7) The hyperfine tensor components are related to the g-tensor components as discussed above. This spectrum is useful in pointing out the complexity of Miissbauer patterns which may result from paramagnetic hfs. EXPERIMENTAL A source of lelTb,O, was used in a conventional Miissbauer apparatus. The absorbers were trivalent salts obtained from the Lindsay Division of Table 1. Magnetic and electric hyperjne interactions in several dysprosium salts
Compound Dy-oxalate Dy-acetate -4HnO DyF:, -5HaO DydCO&
DyCla.6HsO Dy(NO&*6HzO DyP01-5Ha0
DyaOa
Dy-ethyl sulfate DydMoOr)s
DyFeOs
DyMn& DyAlG
e2qQ14 575*30 625 525 550 375 500 575 290 -158 500 436 540 370
-&iH,, (4*2”K)
“&”
787klO 796 785 780 675 734 795 727 446 799 830 780 769
18.6 18.9 18.6 18.6 16.0 17.4 18.8 17.2 10.6 18.9 19.7 18.5 18.2
the American Potash and Chemical Corporation, and contained 99.9 per cent dysprosium of natural
THE
HYPERFINE
STRUCTURE
OF
relDg
IN
DYSPROSIUM
”
-If
I
x=0=05
I
SALTS
2101
”
XSO?5 PI0
FIG. 1. Theoretical lexDy paramagnetic hyperfine structure, assuming an isolated ground IGarners doublet, long relaxationtimes, and the hyperfine tensor parameters indicated in the figure.
abundance. Hyperfine structure was expected only at temperatures G 20°K and all reported measurements were made at 4~2°K. A few typica spectra are given in Fig. 2. For comparison and completeness we have summarized in Table 1 the present results in the paramagnetic salts: Dy-oxalate, Dy-acetate 4Ha0, DyF,. 05Hs0, DyCI,. 6Hs0, D~stCOs)s, Dy(n’Os)s*6HaO, DyPO,*SHaO, with similar measurements in the remaining compounds listed in the Table. By comparing the typical spectral of Fig. 2 with those in Fig. 1, it is seen that in all the
experimental data (A,/&) is less than OG4. The data may therefore be described by the Dy-161 ground state magnetic and electric hype&me constants, together with the “ga” factors for the ground Kramers doublets in the various systems. DISCUSSION
From the data of Table 1 it is seen that in the majority of cases a value of g, close to the maximum 19.6, expected for a ]Jz = rt: E/2> doublet is found. In DyCls+6HaO, Dy-ethyl sulfate, and DysOs the g, values are lower; they are 16.0,
2102
H.
XI.
WICKMAN
10.6 and 17.2, respectively. In all cases g,_ 2: 0. Thus the composition of the wavefunctions of the ground doublet is somewhat variable, as evidenced by the low g, value salts, while the dipole-like magnetic character is retained in all the compounds. &?*a1
and
I.
NOWfK
It has been suggested that rare earth ions often find themselves in icosahedral semen in which case a possible ground doublet derived from a I’s quartet has g, = 12-24, and g, = g, = 0. EIowever, this value of g, was not observed-
FIG. 2. Some experimkntaI MSssbauer spectra of zslDy in pammagnetic compounds. The upper single line spectrum for DyCls-6Ha0 shows the collapse of hfs due to enhanced relaxation times at 20°K.
THE
HYPERFINE
STRUCTURE
OF
The Miissbauer spectrum observed in dysprosium acetate (Fig. 3) is in disagreement with the theoretical spectrum shown in Fig. 1 (A, = 1125, A, = 249, A, = 331 MC/S) which was derived from ESR work.@) Since the MGSSbauer results show the ground doublet to have
2 z
5.7
I -20
I -10
i 0
I 10
I
20
:: 2mO
2.165
2.130
c
II
tb)
-20
I
I
I
0
-10 VELOCITY
IO
I
20
(CM/SEC)
FIG. 3. Mijssbauer spectra of ‘s’Dy in dysprosium acetate at 4*2”K. Note the expanded scale of the lower spectrum. gl z 0 (and hence be non-resonant) it follows that if the crystalline material were completely homogeneous the ESR results may arise from an excited doublet. This possibility is not supported by the fact that both ESR and ME experiments were performed at 4.2”K and the Mijssbauer spectrum, Fig. 3, showed no evidence of distortion from the effective field approximation which would be expected from a superposition of spectra from two doublets or perhaps an increased relaxation time due to Orbach relaxation to the first excited doublet. A second possibility that seems more likely is that a small minority of the Dy3+ in the metal organic compound are present in an
ialDy
IN
DYSPROSIUM
SALTS
2103
environment which leaves a lowest lying ESR resonant doublet, and which contributes a negligible absorption in the ME spectrum. Support for this argument also comes from the results of DWECK’~) who has recently observed ESR from minority Dy3+ sites in DyES where the majority ground doublet is well known to be nonresonant and where the ME hyperfine structure is in excellent agreement with that expected for the majority sites.(3) In conclusion, the basic experimental results may be summarized by the statement that, in all the compounds reported here, the relations N 0 are satisfied in the ground A, > 0; A,, A, Kramers doublet of Dy3 +. While it is tempting to conclude that this may be a general property of Dy salts, there is in fact no ready theoretical justification for such a conjecture. As noted above, we expect far different behavior in the event of a cubic ligand field about the Dy3+. Relaxation times are expected to be faster in the cubic case and may complicate matters somewhat; however, an isotropic hyperfme tensor should be found. There are doubtless other special cases in which the ground doublet possesses rather different hyperfine tensors than have been observed thus far. REFERENCES OFER S. et al., Phys Lett. 11, 205 (1964). 2. NOWIK I. and WICKMAN H. H., Phys. Rew. 140,869
1.
(1965). 3. WICKMAN H. H. and NOWIK I., Phys. Reo. 142, 115 (1966). 4. NOWIK I., Phys. Lett. 15, 219 (1965). Effect Methodology, 5. WICKMAN H. H., Miisbauer p. 39, Vol. 2, Plenum Press, New York (1966). 6. EDMONDS A. R., Angular Momentum in Quantum Mechanics, p. 111, Princeton (1957). 7. PARK J. G., Proc. R. Sot. AZ45, 118 (1958). 8. JUDD B. R., Proc. R. Sot. A241, 122 (1957). 9. DWECK J. and SEIDEL G., Phys. Rev. 155,267 (1967).
Pergarnon Press 1967. Vol. 28, pp. 2099-2103.
THE HYPERFINE
Printed in Great Britain.
STRUCTURE
DYSPROSIUM
OF lelDy IN
SALTS
H. H. WICKMAN and I. NOWIE* Bell Telephone Laboratories, Incorporated, Murray Hill, New Jersey (Receiwed 26 April 1967)
Abstract-The MGssbauer technique was used to investigate the low temperature (4*2”K) hyperfine structure of rslDy in the following paramagnetic salts: Group 1; Dy-oxalate, Dy-acetate, DyFs.SHaO, Dy(NO&.6HaO, DyPOl.5Ha0, Dy(MoO&, DyFeOs, DyMnaOs, DyAlG; and Group 2; DyaOs, DyCls.6H,O, Dy-ethyl sulfate. In all cases the observed spectra were consistent with a collinear hyperfine magnetic field and axially symmetric EFG. This requires a ground doublet with the property gL = 0 # g,,. In Group 1 compounds the observed hfs interactions were within
4 per cent of the free ion hyperfine interaction, g,&H,, = 820 + 20 MC/S for a doublet I+ J, > with J, = 15/2. The three compounds in Group 2 had g&H,, = 727, 675 and 446 MC/S respectively. The results in Group 1 imply a ground doublet with gll N 19.6 and in Group 2 we have values for gll of 17.2, 16.0 and 10.6 for the three compounds, respectively.
THE M~SSBAUER technique has recently shown the presence of well resolved hypefine splittings in several concentrated psramagnetic dysprosium salts at low temperatures.(1-3) In the reported cases, the spectra were simply interpreted in the usual effective hyperfine field approximation. In general, however, the hyperfine interaction may contain off-diagonal elements which lead to grossly different spectra, and we have investigated a number of dysprosium salts in an effort to observe such effects. Although well resolved hfs spectra were obtained, it was found that for all the compounds investigated, the effective field approximation suffices to interpret the spectra. This result implies a somewhat restrictive magnetic character for the ground doublets of these compounds; the discussion below shows that gI is non-zero while gL vanishes in every instance. HYPERFINX STRUCTURE OF A KRAMERS DOUBLET The ground term of Dy3+ is 6H,,,2 and is split by crystalline fields of lower than cubic symmetry
into eight Kramers’ doublets (in a cubic field 2 doublets and 3 quartets are found). The ground Kramers doublet can be described by an effective spin S = 4, whenever the next Stark level is high in comparison with small perturbations such as the Zeeman interaction or in our case (zero external field) the much smaller hyperfine interactions. For such cases the hyperfme levels are given in the spin Hamiltonian representation as eigenvalues of the operator X
= S*A.I+P{31,a-I(I+l) +(V/2)(1+2
address:
Yale
University,
New
(1)
where
P = e2qQ/41(21-
l),
and A is the magnetic hyperfine tensor. In the case of axial symmetry (which exists in trigonal or higher symmetries) the Hamiltonian has the form :
(A, = A,, 71= 0) a? = A,[S,I,+x(S+I_
* Present corm.
+I-“)>,
+S_I.,)]
Haven,
+ P(31,2 -I(l+ 2099
1)).
(2)
2100
H. H. WICKMAN
where x = (J4,/2&); when x = 0 we are left with the effective field approximation. In systems having a ground doublet with A, = A, = 0 # A, there will usually be “long” relaxation times at low temperatures;(4) that is, T x v&-l where T is an effective electronic relaxation time and vr is the nuclear Larmor frequency. Mijssbauer spectra in this case are similar to spectra observed in ferrimagnets, and A, is easily derived from the Mossbauer data.c5) In the general case when the effective hyperfine tensor has more than one non-vanishing component, one still expects paramagnetic hfs at low enough temperatures and/or paramagnetic concentration. It should be remarked that low paramagnetic concentration is not a prerequisite for the appearance of hfs in the Mossbauer spectrum. For even in concentrated salts it is possible to achieve effectively long relaxation times by taking the samples to ultra low temperatures and thus depopulating spin states which are involved in relaxation. An approximate criteria for hfs is that the effective relaxation time T satisfy T B max(h/AJ for any A, # 0, i = x, y, z. Under these conditions the hyperfine interaction may be determined by comparing the experimental data with theoretical spectra computed from the Hamiltonian of equation (1). The Hamiltonians for the ground and excited nuclear levels are diagonalized and the eigenvectors used to calculate transition probabilities: typical results are given in Fig. 1. It is obvious that small values of A, (4 per cent of A,) are enough to distort the effective field Miissbauer spectrum. However, the total splitting (the separation between the two outer lines) is a measure of A, and is not sensitive to the value of A, up to AZ/A, = 0.4 (x = 0.2). The resulting Mijssbauer spectra therefore yield the value of A, even under conditions when the effective field approximation is not exactly satisfied. Neglecting interactions from higher Jmultiplets, the hyperfine tensor, A, E 2gO&Heeff, and the spectroscopic splitting factor g, for the ground doublet are proportional: go&Heft = kg,; and more generally, A, = 2kg,, i = x, y, x. The constant k has been determined in recent Miissbauer
and I. NOWIK
studie#) in DYES, DyAlG and Dy metal in which cases the g, factors are known. Using this derived value of k, 41.2 MC, the electronicg factor, g,, for a salt showing paramagnetic hfs with x M 0 is readily determined from the Mbssbauer data. It is interesting to consider the special case of a Kramers doublet in cubic symmetry: A, = A, = A,, P = 0. Here the hyperfine splitting can be described by the quantum number F = S-+1and the Miissbauer transitions will have the selection rules AF = 0, f 1. For the nuclear angular momentum involved in 16rDy (I,, = Ig( = 5/2), four transitions are allowed with relative intensities given by standard formulae of angular momentum theory.(s) The simple resulting spectra are given in Fig. 1, x = 0.5. A more complicated example is also shown in Fig. 1 and corresponds to the hfs expected for Dy-acetate, where the g factors from ESR are g, = 13.6, g, M 3 and g, w 4.‘7) The hyperfine tensor components are related to the g-tensor components as discussed above. This spectrum is useful in pointing out the complexity of Miissbauer patterns which may result from paramagnetic hfs. EXPERIMENTAL A source of lelTb,O, was used in a conventional Miissbauer apparatus. The absorbers were trivalent salts obtained from the Lindsay Division of Table 1. Magnetic and electric hyperjne interactions in several dysprosium salts
Compound Dy-oxalate Dy-acetate -4HnO DyF:, -5HaO DydCO&
DyCla.6HsO Dy(NO&*6HzO DyP01-5Ha0
DyaOa
Dy-ethyl sulfate DydMoOr)s
DyFeOs
DyMn& DyAlG
e2qQ14 575*30 625 525 550 375 500 575 290 -158 500 436 540 370
-&iH,, (4*2”K)
“&”
787klO 796 785 780 675 734 795 727 446 799 830 780 769
18.6 18.9 18.6 18.6 16.0 17.4 18.8 17.2 10.6 18.9 19.7 18.5 18.2
the American Potash and Chemical Corporation, and contained 99.9 per cent dysprosium of natural
THE
HYPERFINE
STRUCTURE
OF
relDg
IN
DYSPROSIUM
”
-If
I
x=0=05
I
SALTS
2101
”
XSO?5 PI0
FIG. 1. Theoretical lexDy paramagnetic hyperfine structure, assuming an isolated ground IGarners doublet, long relaxationtimes, and the hyperfine tensor parameters indicated in the figure.
abundance. Hyperfine structure was expected only at temperatures G 20°K and all reported measurements were made at 4~2°K. A few typica spectra are given in Fig. 2. For comparison and completeness we have summarized in Table 1 the present results in the paramagnetic salts: Dy-oxalate, Dy-acetate 4Ha0, DyF,. 05Hs0, DyCI,. 6Hs0, D~stCOs)s, Dy(n’Os)s*6HaO, DyPO,*SHaO, with similar measurements in the remaining compounds listed in the Table. By comparing the typical spectral of Fig. 2 with those in Fig. 1, it is seen that in all the
experimental data (A,/&) is less than OG4. The data may therefore be described by the Dy-161 ground state magnetic and electric hype&me constants, together with the “ga” factors for the ground Kramers doublets in the various systems. DISCUSSION
From the data of Table 1 it is seen that in the majority of cases a value of g, close to the maximum 19.6, expected for a ]Jz = rt: E/2> doublet is found. In DyCls+6HaO, Dy-ethyl sulfate, and DysOs the g, values are lower; they are 16.0,
2102
H.
XI.
WICKMAN
10.6 and 17.2, respectively. In all cases g,_ 2: 0. Thus the composition of the wavefunctions of the ground doublet is somewhat variable, as evidenced by the low g, value salts, while the dipole-like magnetic character is retained in all the compounds. &?*a1
and
I.
NOWfK
It has been suggested that rare earth ions often find themselves in icosahedral semen in which case a possible ground doublet derived from a I’s quartet has g, = 12-24, and g, = g, = 0. EIowever, this value of g, was not observed-
FIG. 2. Some experimkntaI MSssbauer spectra of zslDy in pammagnetic compounds. The upper single line spectrum for DyCls-6Ha0 shows the collapse of hfs due to enhanced relaxation times at 20°K.
THE
HYPERFINE
STRUCTURE
OF
The Miissbauer spectrum observed in dysprosium acetate (Fig. 3) is in disagreement with the theoretical spectrum shown in Fig. 1 (A, = 1125, A, = 249, A, = 331 MC/S) which was derived from ESR work.@) Since the MGSSbauer results show the ground doublet to have
2 z
5.7
I -20
I -10
i 0
I 10
I
20
:: 2mO
2.165
2.130
c
II
tb)
-20
I
I
I
0
-10 VELOCITY
IO
I
20
(CM/SEC)
FIG. 3. Mijssbauer spectra of ‘s’Dy in dysprosium acetate at 4*2”K. Note the expanded scale of the lower spectrum. gl z 0 (and hence be non-resonant) it follows that if the crystalline material were completely homogeneous the ESR results may arise from an excited doublet. This possibility is not supported by the fact that both ESR and ME experiments were performed at 4.2”K and the Mijssbauer spectrum, Fig. 3, showed no evidence of distortion from the effective field approximation which would be expected from a superposition of spectra from two doublets or perhaps an increased relaxation time due to Orbach relaxation to the first excited doublet. A second possibility that seems more likely is that a small minority of the Dy3+ in the metal organic compound are present in an
ialDy
IN
DYSPROSIUM
SALTS
2103
environment which leaves a lowest lying ESR resonant doublet, and which contributes a negligible absorption in the ME spectrum. Support for this argument also comes from the results of DWECK’~) who has recently observed ESR from minority Dy3+ sites in DyES where the majority ground doublet is well known to be nonresonant and where the ME hyperfine structure is in excellent agreement with that expected for the majority sites.(3) In conclusion, the basic experimental results may be summarized by the statement that, in all the compounds reported here, the relations N 0 are satisfied in the ground A, > 0; A,, A, Kramers doublet of Dy3 +. While it is tempting to conclude that this may be a general property of Dy salts, there is in fact no ready theoretical justification for such a conjecture. As noted above, we expect far different behavior in the event of a cubic ligand field about the Dy3+. Relaxation times are expected to be faster in the cubic case and may complicate matters somewhat; however, an isotropic hyperfme tensor should be found. There are doubtless other special cases in which the ground doublet possesses rather different hyperfine tensors than have been observed thus far. REFERENCES OFER S. et al., Phys Lett. 11, 205 (1964). 2. NOWIK I. and WICKMAN H. H., Phys. Rew. 140,869
1.
(1965). 3. WICKMAN H. H. and NOWIK I., Phys. Reo. 142, 115 (1966). 4. NOWIK I., Phys. Lett. 15, 219 (1965). Effect Methodology, 5. WICKMAN H. H., Miisbauer p. 39, Vol. 2, Plenum Press, New York (1966). 6. EDMONDS A. R., Angular Momentum in Quantum Mechanics, p. 111, Princeton (1957). 7. PARK J. G., Proc. R. Sot. AZ45, 118 (1958). 8. JUDD B. R., Proc. R. Sot. A241, 122 (1957). 9. DWECK J. and SEIDEL G., Phys. Rev. 155,267 (1967).