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Γ6-ground state resonance in (La , Er) B6 single crystals
Volume 95A, number 3,4
PHYSICS LETTERS
25 April 1983
F6-GROUND STATE RESONANCE IN (La, Er)B 6 SINGLE CRYSTALS H. LUFT, K. BABERSCHKE Institu t fffr A tom- und FestkOrperphysik, Freie Universitiit Berlin, Arnimallee 14, D-1000 Berlin 33, Fed. Rep. Germany
and K. WINZER L Physikalisehes Institut der Universitiit GOttingen, Bunsenstrasse 9, D-3400 GOttingen, Fed. Rep. Germany
Received 27 December 1982
The ESR on cubic (La, Er) B6 single crystals at three frequencies (4, 9 and 35 GHz) reveals unambiguously a I"6 as the Er 3+ ground state with an excited r' s at 8.5 + 1 K, equivalent to a negative cubic crystal field paxameter A 4 (r4). The gshift of Ag = 0.075 +- 0.025 implies a negative effective exchange coupling of J A g ° N(EF) = -0.075 + 0.025, whereas the thermal line broadening yields IJAH • N(EF) I = 0.029 + 0.002.
In the concentrated and dilute rare earth alloys a wide range of bulk phenomena like specific heat, susceptibility, spin-glass behaviour, resistivity or magnetoresistance are strongly influenced by the crystal field splitting (CEF) of the rare earth (RE) ions. But it remains difficult and uncertain to determine the crystal field splitting from such measurements. The magnetic resonance is a useful tool to determine unambiguously the CEF ground state for non Sstate ions. Moreover, in metallic systems the g-shift and the thermal broadening of the linewidth give further information on the exchange coupling between the RE ions and the conduction electrons. Recently, we published the ESR results on (__~_L, Gd)B 6 [1 ]. Using Gd 3+ as a probe one gets information on the exchange interaction times the conduction electron density o f states on the RE site in metallic LaB 6. The cubic CEF splits the Er 3+ ground state 4115/2 (gj = 1.2) in two doublets (V6, F7) and three quartets (FS) [2]. The effective g-values for the isotropic ['6 and ['7 are 6.0 and 6.8. An analysis o f the resonance in a F 8 in metals was recently given for (Y_, Er)A12 [3]. Including the exchange interaction the hamiltonian writes = g j t t B J - H - J S " ~ + ~CEF = gj//B J . H - (gj - 1 ) J J " ~ + ~T£CEF , 186
where J is the exchange integral between the conduction electrons and the RE ion and the crystal field hamiltonian ~fCEF is used in the notation of ref. [2]. The details of the crystal growth and sample preparation were described previously [1 ]. We used single crystals doped with 1% and 0.1% erbium of natural abundance. The ESR was measured at frequencies of 4, 9 and 35 GHz (S, X and Q band) in a temperature range between 1.3 K and 4.2 K, and for the X-band up to 10 K. At all frequencies and temperatures we observed only one resonance line of approximate dysonian shape due to the Er isotope with I = 0, in addition, at 1.3 K the 8 hyperfine lines of 167Er (I = 7/2). We determined the hyperfine constant as IAI = 75 -+ 1 G. At the S and X band no or only small variation of the field for a resonance as a function o f orientation occurs whereas in the Q band experiments an overall variation of 250 G is present (fig. 1). The angular 15 variation is proportional to p (0) = 1 5 sin20 + ~- X sin40. All fields for resonance correspond to effective g-values close to 6 (fig. 2). There is no temperature dependence for the resonance fields but a pronounced increase of the linewidth with temperature. In addition, at all frequencies the width is angular dependent with a minimum for H parallel to the [ 111 ] direction. Since we observe for all orientations no second line
(1) 0 031-9163/83/0000
0000/$ 03.00 © 1983 North-Holland
Volume 95A, number 3,4
PHYSICS LETTERS
25 April 1983
440
4.1
4.3
45
H (kGouss)
Fig. 1. ESR spectrum of (La, Er)B 6 (c = 0.1%) at T= 1.3 K and v = 34.652 GHz for two different orientations. Note the different H-scales.
we attribute the resonance to a doublet F 6 or 1"7. Because a g-shift of more than 10% is rather unlikely there remains only the P 6 doublet as ground state. From the LLW diagram [2] f o r J = 15/2 it comes out that this is the case only for x W < 0 and a nearby F 8 first excited state. In this case the Zeeman interaction mixes the 1"6 and ['8 states resulting in an anisotropy of the F 6-resonance. The experimental field for resonance in the S band
shows no significant angular variation. Therefore, we assume that the observed g-value o f g = 5.875 + 0.020 is the isotropic value of the Er P6 state in LaB 6. The difference from 6 is due to the conduction electron exchange and to chemical shift. We will discuss this point at the end of the paper. Including the mixing of the F 8 states into the P6 the g-value writes correct to second order as a function of orientation geff(0) = ge0ff + P2 [A + Bp(O)] ,
geff 600
i
I
i
(2)
i
where A and B contain matrix elements of J between the F 6 and P 8 states divided by the square of the energy splitting A between P6 and F 8 [4]. This angular dependence is clearly seen in the Q band results for geff (fig. 2). With g0ff = 5.875 the results fit to
5.90
580 0011
A = - ( 7 . 1 +- 2.0) × 10 - 5 GHz - 2 - ( 3 . 1 + 0.9) X 10 - 2 K - 2 ,
5.70
B --- +(16.6 -+ 1.5) X 10 -5 GHz - 2 5.60
+(7.21 + 0.60) X 10 - 2 K - 2 . o°
36 °
66 °
9b ° 0
Fig. 2. Experimental g-value as a function of orientation for (La, Er)B6 (c = 0.1%). The curves were calculated with eq. (2), A = -7.1 X 10-s GHz-2, B = +16.6 × 10-s GHz-2, squares (solid line) 34.652 GHz, triangles (dashed line) 9.367 GHz, dots (dot-dashed line) 4.053 GHz.
One yields an overall angular variation of 243 G, 5 G and 0.5 G at the Q, X and S band, respectively. In the X and S band this variation is within the error bars of the experimental fields for resonance. To determine the CEF parameters x and W, we cal187
Volume 95A, number 3,4
PHYSICS LETTERS
culate the fields for resonance within the F 6 for different parameter sets o f x and I4' with (1) and compare them with the experimental values. Unfortunately, the anisotropy of the [`6 resonance is only a second order effect and therefore not very sensitive to x. But nevertheless we get the best results for Ix l ~> 0.7 and an energy splitting of A ~ 8.5 K. For Ix l ~ 0.7 there is no problem to fit B in eq. (2) but A runs out of the experimental errors. To summarize the results, very good agreement with the experiment is given for - 0 . 6 8 K ~ x l 4 / ~ - 0 . 1 4 K and Ix l > 0.7. This means - 254 K ~ < A 4 ( r 4 > ~ < - 5 2 K ,
25 April 1983
we can follow the line over a large enough temperature interval we observe for both concentrations the same behaviour, down to T = 2 K within the limits of error a linear decrease with a slope of 12 G/K, below 2 K the curves flatten with a slope of 5 to 7 G/K. The difference of the three data sets in fig. 3 is due to differences in the residual linewidths, caused by a frequency term for the squares and triangles and a concentration dependence between the triangles and dots. The thermal broadening supports strongly the proposed level scheme. In the case of a doublet ground state (P 6 or I'7) with a low lying P8 quartet the Korringa part of the linewidth is written [5] AH K (T) = (rr/2geff/.z B) [(gj -- 1 )JA H "N(EF )] 2{ X ~ Y)
- 3 K~
~o !
with
Now we want to analyse the observed temperature dependence of the linewidth (fig. 3). In the cases where
X = [(<21Jzl2>-) 2 + ~(<21 J÷ 12> - )2 + ½( ( 2 1 J _ t 2 ) - { l l J _ 11>)2]k • T ,
g
Y=~ l[l(]lJ+li)12+l(/lJ /,i j4=i
T <]
/
60
50
z.C
30
2C
0~
/,
+ 21(/" IJz Ii>12] " 2xi//[exp(Zxi//kT) - 1] ,
/
/
/
// ~
½
3
4 T{K)
Fig. 3. Experimental linewidth of (La, Er)B6 versus temperature, HII [ 111 ] direction. The curves were calculated with eq. (3): x = +0.9, W = - 0 . 7 5 K, IJAH" N(EF) I = 0.029. squares: 34.69 GHz, 1%, triangles: 9.367 GHz, 1%, dots: 9.367 GHz, 0.1%.
188
li>[2
w h e r e / = 1,2 and i = 1,2, ..., 6 label the eigenstates of ['6 and P 8 and Aii = E i - E~ is the energy splitting between the states i and/. J A H is the effective exchange integral and N(EF) the density of states of the conduction electrons at the Fermi level. Eq. (3) holds for all orientations of H with respect to the crystal axes. With the parameter sets for x and W determined above eq. (3) predicts indeed a temperature dependence of the relaxation as observed in our experiments. The {/IJli> in eq. (3) are not very sensitive to x, the experiment yields I JzxH • N(EF)I = 0.029 -+ 0.002. The solid lines in fig. 3 were calculated with x = +0.9, I4/ = - 0 . 7 5 K, IJAr4 " N(EF)[ = 0.029 and a residual width of 20 G (Q band, 1%), 7.5 G (X band, 1%) and 5 G (X band, 0.1%). Our ESR results on single crystals were in rough agreement with previously published polycrystalline data [6]. However, as shown in the previous paragraphs details of the resonance (anisotropy, narrow lines etc.) are masked if one averages over all orientations in a polycrystalline sample.
Volume 95A, number 3,4
PHYSICS LETTERS
Now we comment on the residual width "a" observed in the experiments. It is largest in the [001 ] direction (a -~ 24 G), reduces to an absolute minimum in the [111] direction (a ~ 5 G), and increases again in the [110] direction (a ~ 12 G). The numbers are given for 9 GHz and 0.1%, they can be fitted to [A'(3 cos 20 1) 2 + B'] 1/2 with positive A ' and B' and A ' > B ' . A ' and B' exhibit a frequency and concentration dependence. Qualitatively this is in agreement with the "random strain model" proposed in refs. [4] and [7], but our experimental values for A ' and B' do not scale with the square of the frequency as the "strain model" predicts. This might indicate that for the full analysis of the residual width not only strain terms but also terms depending on concentration and concentration times frequency have to be considered [8], although in (La, Er)B 6 the strain terms seem to be dominant. From the previous analysis one can conclude, that at temperatures of T ~ 7 K one should in principle detect the P8 resonance lines as well. In our experiment we were not successful in doing so, we believe because of the following reasons: (i) We have shown that random strain in our samples is very likely. This splits the P8 into two doublets [9], (ii)because of the large linewidth (fig. 3) we could follow the ESR signal to higher temperatures only for the 1% sample. Such a high concentration causes cluster resonances, forbidden transitions etc. (see fig. 11 in ref. [3]). Now let us discuss the exchange coupling between the conduction electrons and Er 3+. The electron density of states at the Fermi surface in LaB 6 at the La site is 0.5 states/eV and spin direction [1 ]. So the -
25 April 1983
linewidth data give an effective exchange constant for Er3+ [ J a n l = 0.058 eV, a value one third larger than for Gd3+ [1]. More difficult to determine is the exchange constant JAg from the g-shift. To our knowledge the only case where the g-value of a Er F 6 state is measured in a non-metallic host, is (Zn, Er)Se [10] with gr6 = 5.950 --- 0.005. Using this value as reference and under the assumption that the chemical shift is not larger in LaB 6 we get in (La, Er)B 6 a shift due to the conduction electrons of Ag = - 0 . 0 7 5 -+ 0.025. With Ag = geff [(gJ -- 1)/gj ][JAg"N(EF)] this yields [JAg • N ( E F ) ] = -(0.075 + 0.025) and JAg = --(0.150 -+ 0.050) eV, a value roughly three times larger than J/,H" This value is clearly negative but relative large compared to other values of JAg for Er [3,8]. Surprising is the negative sign of Jag. Two explanations are possible: (i) It has been shown [8] that positive and negative exchange contributions may cancel each other for Er. Perhaps in our case the negative con. tribution overcomes the atomic exchange. (ii) In the analysis of (Y, Er)A12 it has been pointed out [3], that contributions of the orbital suceptibility may become relevant. In addition, the negative value for Xexp in LaB 6 [1] is not understood yet. A detailed analysis goes beyond this letter. In the discussion of the crystal field parameters we want to focus on the A4(r4 )value only since this is the dominant one in the most cubic substances. Assuming that the value o f A 4 is mostly effected by the host ligands the sign o f A 4 (r 4 )should not change for different RE ions in the same matrix. This is fulfilled in insulators [10] and metals [11], too. As far as the
Table 1 Crystal field parameters for REB 6. A 4(r 4 ) CeB 6 (La, Ce) B 6
A 6(r 6 )
Method
Ref.
+139 K +160 K
0 0
x x
[12] [13]
<0 -200 K
0 0
c x
[14] [14]
o ESR
[151 this work
ESR
"-"
c<5% PrB 6 (La, Pr) B 6
c = 1.8% NdB 6 (La, Er)B 6
c = 1%, 0.1% (La, Dy)B 6
+349 K > 254 K, ~< 52K P8 ground state
0 ~>-3 K, ~<2K
c = 0.5%
189
Volume 95A, number 3,4
PHYSICS LETTERS
CEF in REB 6 is known, the measured A 4 (r 4 ) changes in sign (table 1). Our ESR experiments show unambiguously that the ground state of Er in LaB 6 is 1"6 and this is only possible for negative A 4 (r 4 ). We measured a single crystal of LaB 6 doped with 0.5% Dy. Two anisotropic ESR lines were detected. This preliminary result indicates a F 8 ground state for (La, Dy)B 6. Since the Stevens factors of Er and Dy have different sign, this is in agreement with the Er results: P6 for Er forces I"8 for Dy if one assumes the same x value. We are convinced that A 4 < 0 holds for the other REB6, too. As far as we know there is no physical argument why the sign o f A 4 (r4) should change for different RE ions in the same host. Under these aspects the proposed CEF parameters for Ce 3+ and Nd 3+ in LaB 6 seem rather inconsistent to us. This work was supported by the Deutsche Forschungsgemeinschaft (DEG). Special Research Funds Sfb 126 and 161.
190
25 April 1983
Reference [1] H. Luft, K. Baberschke and K. Winzer, Z. Phys. B47 (1982) 195. [2] K.R. Lea, M.J.M. Leask and W.P. Wolf, J. Phys. Chem. Solids 23 (1962) 1381. [3] U. DSbler, K. Baberschke and S.E. Barnes, Phys. Rev. B, submitted for publication. [4] S.B. Oseroffand R. Calvo, Phys. Rev. B18 (1978) 3041. [5] L.L. Hirst, Phys. Rev. 181 (1969) 597. [6] D. Davidov, E. Bucher, L.W. Rupp, L.D. Longinotti and C. Rettori, Phys. Rev. B9 (1974) 2879. [7] J.M. Bloch, D. Davidov and C. Rettori, J. Magn. Magn. Mat. 25 (1982) 271. [8] Y. von Spalden and K. Baberschke, J. Magn. Magn. Mat. 23 (1981) 183. [9] A. Abragam and B. Bleaney, Electron paramagnetic resonance of transition ions (Clarendon, Oxford, 1970). [101 J.D. Kingsley and M. Aven, Phys. Rev. 155 (1967) 235. [11] P. Touborg, Phys. Rev. B16 (1977) 1201. [12] J.C. Nickerson and R.M. White, J. Appl. Phys. 40 (1969) 1011. [13] W. Felsch, Z. Phys. B29 (1978) 211. [14] Z. Fisk and D.C. Johnston, Solid State Commun. 22 (1977) 359. [15] Z. Fisk, Solid State Commun. 18 (1976) 221.
PHYSICS LETTERS
25 April 1983
F6-GROUND STATE RESONANCE IN (La, Er)B 6 SINGLE CRYSTALS H. LUFT, K. BABERSCHKE Institu t fffr A tom- und FestkOrperphysik, Freie Universitiit Berlin, Arnimallee 14, D-1000 Berlin 33, Fed. Rep. Germany
and K. WINZER L Physikalisehes Institut der Universitiit GOttingen, Bunsenstrasse 9, D-3400 GOttingen, Fed. Rep. Germany
Received 27 December 1982
The ESR on cubic (La, Er) B6 single crystals at three frequencies (4, 9 and 35 GHz) reveals unambiguously a I"6 as the Er 3+ ground state with an excited r' s at 8.5 + 1 K, equivalent to a negative cubic crystal field paxameter A 4 (r4). The gshift of Ag = 0.075 +- 0.025 implies a negative effective exchange coupling of J A g ° N(EF) = -0.075 + 0.025, whereas the thermal line broadening yields IJAH • N(EF) I = 0.029 + 0.002.
In the concentrated and dilute rare earth alloys a wide range of bulk phenomena like specific heat, susceptibility, spin-glass behaviour, resistivity or magnetoresistance are strongly influenced by the crystal field splitting (CEF) of the rare earth (RE) ions. But it remains difficult and uncertain to determine the crystal field splitting from such measurements. The magnetic resonance is a useful tool to determine unambiguously the CEF ground state for non Sstate ions. Moreover, in metallic systems the g-shift and the thermal broadening of the linewidth give further information on the exchange coupling between the RE ions and the conduction electrons. Recently, we published the ESR results on (__~_L, Gd)B 6 [1 ]. Using Gd 3+ as a probe one gets information on the exchange interaction times the conduction electron density o f states on the RE site in metallic LaB 6. The cubic CEF splits the Er 3+ ground state 4115/2 (gj = 1.2) in two doublets (V6, F7) and three quartets (FS) [2]. The effective g-values for the isotropic ['6 and ['7 are 6.0 and 6.8. An analysis o f the resonance in a F 8 in metals was recently given for (Y_, Er)A12 [3]. Including the exchange interaction the hamiltonian writes = g j t t B J - H - J S " ~ + ~CEF = gj//B J . H - (gj - 1 ) J J " ~ + ~T£CEF , 186
where J is the exchange integral between the conduction electrons and the RE ion and the crystal field hamiltonian ~fCEF is used in the notation of ref. [2]. The details of the crystal growth and sample preparation were described previously [1 ]. We used single crystals doped with 1% and 0.1% erbium of natural abundance. The ESR was measured at frequencies of 4, 9 and 35 GHz (S, X and Q band) in a temperature range between 1.3 K and 4.2 K, and for the X-band up to 10 K. At all frequencies and temperatures we observed only one resonance line of approximate dysonian shape due to the Er isotope with I = 0, in addition, at 1.3 K the 8 hyperfine lines of 167Er (I = 7/2). We determined the hyperfine constant as IAI = 75 -+ 1 G. At the S and X band no or only small variation of the field for a resonance as a function o f orientation occurs whereas in the Q band experiments an overall variation of 250 G is present (fig. 1). The angular 15 variation is proportional to p (0) = 1 5 sin20 + ~- X sin40. All fields for resonance correspond to effective g-values close to 6 (fig. 2). There is no temperature dependence for the resonance fields but a pronounced increase of the linewidth with temperature. In addition, at all frequencies the width is angular dependent with a minimum for H parallel to the [ 111 ] direction. Since we observe for all orientations no second line
(1) 0 031-9163/83/0000
0000/$ 03.00 © 1983 North-Holland
Volume 95A, number 3,4
PHYSICS LETTERS
25 April 1983
440
4.1
4.3
45
H (kGouss)
Fig. 1. ESR spectrum of (La, Er)B 6 (c = 0.1%) at T= 1.3 K and v = 34.652 GHz for two different orientations. Note the different H-scales.
we attribute the resonance to a doublet F 6 or 1"7. Because a g-shift of more than 10% is rather unlikely there remains only the P 6 doublet as ground state. From the LLW diagram [2] f o r J = 15/2 it comes out that this is the case only for x W < 0 and a nearby F 8 first excited state. In this case the Zeeman interaction mixes the 1"6 and ['8 states resulting in an anisotropy of the F 6-resonance. The experimental field for resonance in the S band
shows no significant angular variation. Therefore, we assume that the observed g-value o f g = 5.875 + 0.020 is the isotropic value of the Er P6 state in LaB 6. The difference from 6 is due to the conduction electron exchange and to chemical shift. We will discuss this point at the end of the paper. Including the mixing of the F 8 states into the P6 the g-value writes correct to second order as a function of orientation geff(0) = ge0ff + P2 [A + Bp(O)] ,
geff 600
i
I
i
(2)
i
where A and B contain matrix elements of J between the F 6 and P 8 states divided by the square of the energy splitting A between P6 and F 8 [4]. This angular dependence is clearly seen in the Q band results for geff (fig. 2). With g0ff = 5.875 the results fit to
5.90
580 0011
A = - ( 7 . 1 +- 2.0) × 10 - 5 GHz - 2 - ( 3 . 1 + 0.9) X 10 - 2 K - 2 ,
5.70
B --- +(16.6 -+ 1.5) X 10 -5 GHz - 2 5.60
+(7.21 + 0.60) X 10 - 2 K - 2 . o°
36 °
66 °
9b ° 0
Fig. 2. Experimental g-value as a function of orientation for (La, Er)B6 (c = 0.1%). The curves were calculated with eq. (2), A = -7.1 X 10-s GHz-2, B = +16.6 × 10-s GHz-2, squares (solid line) 34.652 GHz, triangles (dashed line) 9.367 GHz, dots (dot-dashed line) 4.053 GHz.
One yields an overall angular variation of 243 G, 5 G and 0.5 G at the Q, X and S band, respectively. In the X and S band this variation is within the error bars of the experimental fields for resonance. To determine the CEF parameters x and W, we cal187
Volume 95A, number 3,4
PHYSICS LETTERS
culate the fields for resonance within the F 6 for different parameter sets o f x and I4' with (1) and compare them with the experimental values. Unfortunately, the anisotropy of the [`6 resonance is only a second order effect and therefore not very sensitive to x. But nevertheless we get the best results for Ix l ~> 0.7 and an energy splitting of A ~ 8.5 K. For Ix l ~ 0.7 there is no problem to fit B in eq. (2) but A runs out of the experimental errors. To summarize the results, very good agreement with the experiment is given for - 0 . 6 8 K ~ x l 4 / ~ - 0 . 1 4 K and Ix l > 0.7. This means - 254 K ~ < A 4 ( r 4 > ~ < - 5 2 K ,
25 April 1983
we can follow the line over a large enough temperature interval we observe for both concentrations the same behaviour, down to T = 2 K within the limits of error a linear decrease with a slope of 12 G/K, below 2 K the curves flatten with a slope of 5 to 7 G/K. The difference of the three data sets in fig. 3 is due to differences in the residual linewidths, caused by a frequency term for the squares and triangles and a concentration dependence between the triangles and dots. The thermal broadening supports strongly the proposed level scheme. In the case of a doublet ground state (P 6 or I'7) with a low lying P8 quartet the Korringa part of the linewidth is written [5] AH K (T) = (rr/2geff/.z B) [(gj -- 1 )JA H "N(EF )] 2{ X ~ Y)
- 3 K~
~o !
with
Now we want to analyse the observed temperature dependence of the linewidth (fig. 3). In the cases where
X = [(<21Jzl2>-
g
Y=~ l[l(]lJ+li)12+l(/lJ /,i j4=i
T <]
/
60
50
z.C
30
2C
0~
/,
+ 21(/" IJz Ii>12] " 2xi//[exp(Zxi//kT) - 1] ,
/
/
/
// ~
½
3
4 T{K)
Fig. 3. Experimental linewidth of (La, Er)B6 versus temperature, HII [ 111 ] direction. The curves were calculated with eq. (3): x = +0.9, W = - 0 . 7 5 K, IJAH" N(EF) I = 0.029. squares: 34.69 GHz, 1%, triangles: 9.367 GHz, 1%, dots: 9.367 GHz, 0.1%.
188
li>[2
w h e r e / = 1,2 and i = 1,2, ..., 6 label the eigenstates of ['6 and P 8 and Aii = E i - E~ is the energy splitting between the states i and/. J A H is the effective exchange integral and N(EF) the density of states of the conduction electrons at the Fermi level. Eq. (3) holds for all orientations of H with respect to the crystal axes. With the parameter sets for x and W determined above eq. (3) predicts indeed a temperature dependence of the relaxation as observed in our experiments. The {/IJli> in eq. (3) are not very sensitive to x, the experiment yields I JzxH • N(EF)I = 0.029 -+ 0.002. The solid lines in fig. 3 were calculated with x = +0.9, I4/ = - 0 . 7 5 K, IJAr4 " N(EF)[ = 0.029 and a residual width of 20 G (Q band, 1%), 7.5 G (X band, 1%) and 5 G (X band, 0.1%). Our ESR results on single crystals were in rough agreement with previously published polycrystalline data [6]. However, as shown in the previous paragraphs details of the resonance (anisotropy, narrow lines etc.) are masked if one averages over all orientations in a polycrystalline sample.
Volume 95A, number 3,4
PHYSICS LETTERS
Now we comment on the residual width "a" observed in the experiments. It is largest in the [001 ] direction (a -~ 24 G), reduces to an absolute minimum in the [111] direction (a ~ 5 G), and increases again in the [110] direction (a ~ 12 G). The numbers are given for 9 GHz and 0.1%, they can be fitted to [A'(3 cos 20 1) 2 + B'] 1/2 with positive A ' and B' and A ' > B ' . A ' and B' exhibit a frequency and concentration dependence. Qualitatively this is in agreement with the "random strain model" proposed in refs. [4] and [7], but our experimental values for A ' and B' do not scale with the square of the frequency as the "strain model" predicts. This might indicate that for the full analysis of the residual width not only strain terms but also terms depending on concentration and concentration times frequency have to be considered [8], although in (La, Er)B 6 the strain terms seem to be dominant. From the previous analysis one can conclude, that at temperatures of T ~ 7 K one should in principle detect the P8 resonance lines as well. In our experiment we were not successful in doing so, we believe because of the following reasons: (i) We have shown that random strain in our samples is very likely. This splits the P8 into two doublets [9], (ii)because of the large linewidth (fig. 3) we could follow the ESR signal to higher temperatures only for the 1% sample. Such a high concentration causes cluster resonances, forbidden transitions etc. (see fig. 11 in ref. [3]). Now let us discuss the exchange coupling between the conduction electrons and Er 3+. The electron density of states at the Fermi surface in LaB 6 at the La site is 0.5 states/eV and spin direction [1 ]. So the -
25 April 1983
linewidth data give an effective exchange constant for Er3+ [ J a n l = 0.058 eV, a value one third larger than for Gd3+ [1]. More difficult to determine is the exchange constant JAg from the g-shift. To our knowledge the only case where the g-value of a Er F 6 state is measured in a non-metallic host, is (Zn, Er)Se [10] with gr6 = 5.950 --- 0.005. Using this value as reference and under the assumption that the chemical shift is not larger in LaB 6 we get in (La, Er)B 6 a shift due to the conduction electrons of Ag = - 0 . 0 7 5 -+ 0.025. With Ag = geff [(gJ -- 1)/gj ][JAg"N(EF)] this yields [JAg • N ( E F ) ] = -(0.075 + 0.025) and JAg = --(0.150 -+ 0.050) eV, a value roughly three times larger than J/,H" This value is clearly negative but relative large compared to other values of JAg for Er [3,8]. Surprising is the negative sign of Jag. Two explanations are possible: (i) It has been shown [8] that positive and negative exchange contributions may cancel each other for Er. Perhaps in our case the negative con. tribution overcomes the atomic exchange. (ii) In the analysis of (Y, Er)A12 it has been pointed out [3], that contributions of the orbital suceptibility may become relevant. In addition, the negative value for Xexp in LaB 6 [1] is not understood yet. A detailed analysis goes beyond this letter. In the discussion of the crystal field parameters we want to focus on the A4(r4 )value only since this is the dominant one in the most cubic substances. Assuming that the value o f A 4 is mostly effected by the host ligands the sign o f A 4 (r 4 )should not change for different RE ions in the same matrix. This is fulfilled in insulators [10] and metals [11], too. As far as the
Table 1 Crystal field parameters for REB 6. A 4(r 4 ) CeB 6 (La, Ce) B 6
A 6(r 6 )
Method
Ref.
+139 K +160 K
0 0
x x
[12] [13]
<0 -200 K
0 0
c x
[14] [14]
o ESR
[151 this work
ESR
"-"
c<5% PrB 6 (La, Pr) B 6
c = 1.8% NdB 6 (La, Er)B 6
c = 1%, 0.1% (La, Dy)B 6
+349 K > 254 K, ~< 52K P8 ground state
0 ~>-3 K, ~<2K
c = 0.5%
189
Volume 95A, number 3,4
PHYSICS LETTERS
CEF in REB 6 is known, the measured A 4 (r 4 ) changes in sign (table 1). Our ESR experiments show unambiguously that the ground state of Er in LaB 6 is 1"6 and this is only possible for negative A 4 (r 4 ). We measured a single crystal of LaB 6 doped with 0.5% Dy. Two anisotropic ESR lines were detected. This preliminary result indicates a F 8 ground state for (La, Dy)B 6. Since the Stevens factors of Er and Dy have different sign, this is in agreement with the Er results: P6 for Er forces I"8 for Dy if one assumes the same x value. We are convinced that A 4 < 0 holds for the other REB6, too. As far as we know there is no physical argument why the sign o f A 4 (r4) should change for different RE ions in the same host. Under these aspects the proposed CEF parameters for Ce 3+ and Nd 3+ in LaB 6 seem rather inconsistent to us. This work was supported by the Deutsche Forschungsgemeinschaft (DEG). Special Research Funds Sfb 126 and 161.
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25 April 1983
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