- Email: [email protected]
The pair spectrum in diamagnetically doped TMMC
JOURNAL
OF MAGNETIC
RESONANCE
60,46-53
(1984)
The Pair Spectrum in Diamagnetically
Doped TMMC
S. CLEMENT AND J. P. RENARD Institut d’Electronique Fondamentale. Laboratoire asski au CNRS Universiti Paris XI, (Bit. 220) 91405Orsay, Ceder France AND
G. ABLART Laboratoire de Magndisme et d’Electronique Quan fique, Universiti Paul Sabatier, 39, Alike Jules-Guesde, 31062-Toulou.re. Cedex, France Received March 15, 1984 A symmetrical ten-line structure has been observed in the electron spin-resonance spectrum of quasi one-dimensional (CHs),NMnClr(TMMC) doped with diamagnetic Cd at 20% atomic concentration. This structure, on which is superimposed a single-ion line and a much broader finite chain line, has been attributed to Mn2+ ion pairs. It disappears when the angle 0 of the magnetic field with the chain axis exceeds 20”. Because of the rather large linewidth the hyperhne structure was not resolved. The relevant parameters of the fine structure (dipole interaction D, and single-ion anisotropy DE) are somewhat different from those measured in the “symmetrical case” of Mn2+ pairs doped in diamagnetic isomorphous TMCC. In particular it appears that the Mn-Mn distance is smaller in TMMC-Cd. The broadening of lines is related to interactions between paired Mn2+ ions and other Mn2+ ions belonging to neighboring finite chains. 0 1984 Academic Press, Inc.
Extensive studies have been made on the electron-spin-resonance spectra of exchange-coupled pairs in crystals (I, 2). In many cases the results were obtained in diamagnetic crystals doped with paramagnetic impurities. If the concentration of impurities is low, only single-ion spectra are observed, but at higher concentrations the occurrence of nearest neighbor paramagnetic ions gives rise to pirir spectra, consisting generally of complicated structures of narrow lines. From the analysis of the spectra one can get information on the Heisenberg exchange, anisotropic exchange, and dipole-dipole interactions between the ions belonging to pairs, and improve the information obtained about single ions. We present here a study of pair spectra obtained in a paramagnetic sample doped by diamagnetic impurities. Significant discrepancies with the symmetrical case (i.e., diamagnetic crystal paramagnetically doped) are noted concerning the position and width of lines. A linewidth analysis is made for the isolated and paired ion lines. The paramagnetic host crystal was tetramethylammonium trichloromanganate (CH3)4NMnC13 (TMMC) which is a quasi unidimensional (1D) Heisenberg antiferromagnet with S = 5/2 0022-2364184 $3.00 Copyright 0 1984 by Academic Prcs, Inc. All rights of reproduction in any form reserved.
46
EXCHANGE-COUPLED
PAIRS
IN
DOPEiD
47
CRYSTALS
(3). This compound consists of MnC& chains well separated from each other by the TMA ions; the Mn-Mn separation is 3.25 A within a chain (the intrachain coupling being J = -6.7 K) and 9.15 A between neighboring chains (the interchain coupling being - 1 mK). Thus TMMC can be considered as a good 1D not only for short range interactions (exchange) but also for long-range interactions (dipolar). Important consequences on spin dynamics result, which have been well verified by magnetic resonance experiments (4). The cadmium salt (CH&NCdC& (TMCC) is isomorphous to TMMC at room temperature and has very similar crystallographic parameters (5), the Cd-Cd separation being 3.36 A within a chain and 9.13 A between the chains. The replacement of Mn*+ ions in TMMC by Cd*’ ions creates linear finite chains of n spins, weakly coupled by their extremities. If impurity Cd ions are randomly placed inside the crystal, one can expect a proportion 2x2( 1 - x) of Mn*+ ions belonging to pairs, where x is the concentration of impurities. THE
SPIN
HAMILTONIAN
The ESR of single ion Mn*+ in a TMCC matrix was studied by McPherson et al. (6) and by Tazuke (7). Their results establish that the line positions are quite well described, at room temperature, by a Hamiltonian with axial symmetry: R’=gbHo*Si+AIi*Si+D,
1
t11
1) .
S:,-i;si(S,+
The z axis is the line joining the two ions, here the chain axis. The g value (g = 2.00) and the hyperfine constant value (A = -87 G) are isotropic. The zerofield splitting parameter (0, = 45 G) is almost an order of magnitude smaller than the corresponding one in a CsMgQ matrix. The fourth-order terms arising from crystal fields are very small and can be neglected. We consider here the case of two neighboring ions with Si and S2 strongly coupled by an Heisenberg exchange interaction -2rSr . S2. The spectrum of the pair consists thus of spectra from different multiplets, each multiplet being characterized by a total spin S = S, + S2 taking the values S = 0, 1, 2, 3, 4, and 5. The spin Hamiltonian for the manifold of spin S becomes (I) [email protected]+D
+(2;+
1
1) +;&(I1
+I*)
[2]
where Ds = 3asDe + &D,
[31
The coupling coefficients (Yeand & take the values shown in Table 1. The term De represents the anisotropic interaction axial symmetry, including dipole-dipole interaction and a pseudo-dipolar term arising from anisotropic exchange. If the two Mn*+ ions are treated as point dipoles separated by a distance r, De can be calculated from the simple expression De = -g2/3*/r3. The allowed ESR transitions occur within the various multiple& following a selection rule AM = + 1. If the field HO is
48
CLfiMENT,
RENARD, TABLE
AND ,4BLART I
Interaction Parameters crs and OS for Pairs with S, = S, = 512 and Identification of the Observed Lines
s
5
4 3
2 1
as
0s
5
4 9
ii 4 ii 41 90
-2 41
41 42 37 ii
-20 21 -32 5
ohserved M++M
2
lines
3 ‘-+ 2
d
2 ‘-D 1
b
2 ‘+ 1
C
2*+ 1
e
1 *+ 0
a
1 -+o
C
i
parallel to the axis joining the two ions the energy differences corresponding transitions M w M - 1 (fine structure lines) are AE = E,,., - EM-, = ho, + Ds(2M - 1). EXPERIMENTAL
to
141
RESULTS AND DISCUSSION
Single crystals of TMMC-Cd were grown following the prescriptions described in (8). The ESR measurements were carried out on a conventional X-band spectrometer. Figure 1 shows a room-temperature spectrum obtained in a sample doped with cadmium concentration x = 0.20. The static magnetic field & was nearly parallel
1
4000
,
6000
\_,
000
H,(G)
FIG. I. Electron resonance spectrum of TMMC doped with Cd (x = 0.20) recorded at room temperature. The magnetic field is parallel to the chain axis.
EXCHANGE-COUPLED
PAIRS IN DOPED CRYSTALS
49
to the chain axis. The central line of this spectrum is presumably composed of a line caused by single ion resonances and a much broader line ascribed to short chains of Mn*’ ions. The symmetrical structure (ten lines) which is superimposed on it is attributed to ion pairs. Such a structure appears also, though faintly, in a sample with lower dopant concentration (X = 0.09). These dimer lines broaden and disappear when the angle between the chain axis and the magnetic field II,-, exceeds 20” (in relation probably to the increase of the nonsecular dipolar interactions). The fine-structure lines should be split into 11 equally separated lines with relative intensities of 1:2:3:4:5:6:5:4:3:2:1. In fact, this hyperfine structure is not resolved. The separation between adjacent hypertIne lines being equal to half of that of the single ion (thus about 44 G), the full linewidth at half intensity of a fine structure line must be about 300 G. The corresponding derivative peak-to-peak linewidth is about 180 G for a Lorentzian line. This value is in good agreement with the experimental result reported on Fig. 1. The components (&de) of the pair spectrum shown in Fig. 1 can be identified with six transitions, with the help of relations [3] and [4]. They are listed in Table 1. Other existing transitions are not visible in the spectrum because their shifts from the free electron resonance field are smaller than the central linewidth or greater than the magnetic field applied. The line intensities vary with temperature (I) according to this identification, the lines b and d (S = 5) vanishing first near 70 K whereas the line c (S = 2) still exists at 30 K. The resulting value of the exchange integral J which can be deduced with some inaccuracy is about 10 K. The Ds values can be obtained from the relations [3] and [4]. One sees, from Table 1, that Ds is nearly equal to the dipolar term D, for S = 3, corresponding to the lines a and e. We get then D, = -605 + 10 G and, taking this value, we obtain from the other lines DC = 75 f 25 G. Using a point-dipole model, the D, value corresponds to a distance of 3.13 f 0.02 A between the Mn2+ ions of the pair, thus about 3 or 4% smaller than the distance in pure TMMC. Such a result is not unexpected if one considers that the ionic radius of Mn*+ (0.80 A) is smaller than that of Cd*+ (0.97 A); one can conceive that the Mn’+ ions belonging to the pair are pushed toward each other by the Cd ions. On the other hand, we find a zerofield splitting parameter DC almost an order of magnitude smaller than the dipolar term, in agreement with the results of McPherson et a,!. and Tazuke from the single ion spectrum in TMCC-Mn. Recently, however, Heming et al. (9) were able to produce Mn*+ pairs in doped TMCC, and obtained singular results. First, the magnitude of D, inferred from the S = 3 lines corresponded to a large distance between the Mn*+ ions of 3.58 A (using a pointdipole calculation), thus about 7% greater than the undistorted Cd distance. Second, it appeared that either D, or DC, or both, were S dependent. The authors explained these results by the respective hypothesis of spin transfer to the ligands and exchange striction effects (10). Our measurements are too limited and inaccurate to confirm a variation of interaction parameters with S. If it does exist it is probably, however, smaller than that deduced in TMCC-Mn. On the other hand, the spin transfer hypothesis can be hardly invoked in our case. One may imagine other explanations for the anomalous effects observed in TMCC-Mn, such as anisotropic exchange interaction (but the g value is isotropic) or, more plausibly, suppose that the Mn*+ ions are not on the
50
CLBMENT,
RENARD,
AND
ABLART
Cd-Cd axis. It is known furthermore that the zero-field parameter is very much sensitive to distortions in the environment geometry. Whatever the exact reason be, it appears that the situation for Mn” pairs in TMMC-Cd is not similar to that in TMCC-Cd. STUDY
OF
THE
LINEWIDTHS
We focus now on the linewidths of the lines resulting from isolated ions or pair ions in TMMCCd. The observed lines are in fact composed of unresolved hyperhne lines. Consequently, the linewidth of an individual hpf line must exceed the hyperfme constant A (expressed in comparable units). On the contrary, in TMCC:Mn, the linewidth of hpf lines is about 10 G (6) and thus is less than A. We performed a calculation for the angle B = 0”. The broadening of the lines is expected to be caused by the interaction of the corresponding Mn2+ ions with their neighbors across the Cd ions: the secular part of the dipolar interaction and a possible superexchange Heisenberg interaction with the nearest neighbors. The predominant interaction is not known and we consider the two cases. As we want only an evaluation of the linewidth, we suppose that the lineshape is Lorentzian. It is expected that the resulting error does not exceed 20%. Furthermore, we neglect the interchain couplings. (a) Isolated Ion Linewidth Let us consider first the case of an Mn ion with spin & surrounded by two diamagnetic Cd ions. Its interaction with the neighboring spins Si can be written (so+s; -k s&y X’ = D’ + c.Te, = - 2 bi S6 Sf - -4 [ i
1+2J’So
(S2 + S-2)
[5]
with bi = wDlilP3, wg = hyQc3, ye being the electronic gyromagnetic ratio and c the separation between nearest neighbors ions in the chain (c = 3.25 A). The index i run from 2 to co and from -2 to -co. The relevant function to be calculated is the so-called torque-spin-torque (TST) function (4, 11): $@) = ([S,+,t), WI (S,‘S,) the time evolution of Z’ being given by X’(t) = eiHtPIiHr where the Hamiltonian Z? (in rads-‘) is composed of the Heisenberg exchange interaction and the Zeeman term. We calculate tirst the linewidth by considering only the dipolar interaction, to verify if this interaction alone can be responsible for the lack of hpf resolution:
+ ; sgt)sy(t) (( Si$f+ ; s&s:)(S,@)S$) 1) +dt)= C bbi ij
(S&i)
The next step consists of factorizing the four-spin correlation functions into a product of two-spin correlation functions. We neglect correlation between S, and
EXCHANGE-COUPLED
51
PAIRS IN DOPED CRYSTALS
Sj, since the coupling between these spins is quite small compared to the exchange interaction J. We have (S&S;(t)) = (So+Sij)e-AWr (S&!?;(t)) = (S&.Yf$e-tfT1
171
with Aw the half linewidth at half power (to be calculated) and T, the electronic spin-lattice relaxation time. Then +o(t) = 2 b,b,EemAwf(S:S;(t)) + i e+“(S:S;(t))] ki
.
PI
In this summation, it is clear that the spins Si and Sj must be on the same side of the spin &. In fact, they belong to a finite chain composed of n spins coupled by an Heisenberg interaction and a dipolar interaction. If n is not too great (n Q lo), the correlation functions (SfSi’
The quantity
+D(t)
(srqt))
=
SW + 1) ,-& 3n
(s:sjlt>)
=
2s(s + l) e-u:j . 3n
is related to the linewidth Aw through the relation Aw =
s0
m #&)dt.
[lOI
The problem is now to compare the different parameters Aw, T;‘, wf, and w,‘. The last two are related to the magnetic resonance spectrum of the n-spin chain (1 I). The cut-off frequency w5 corresponds to the electronilc spin-lattice-relaxation rate, and it is known from NMR (12) and ESR (13) experiments that its value is very small (w: - lo8 rad s-’ 4 Aw). On the other hand, w: is related to the ESR linewidth, the value of which is greater than the one measured in pure TMMC: w: > 2 X 10” rad s-’ (see Fig. 1). w: is of course much greater than Aw and T;’ and in the integral we can safely neglect the term containing (S~S;(t)). Finally, we obtain the self consistent relation Aw _s(s+
3n 1) (0.07wQ 2;.
[Ill
For the sample doped with a concentration of impurities x = 0.20 we can take a mean value n N 5. The relation [ 1 l] gives a linewidth Aw I: 2 X lo9 rad s-l corresponding to AH = 115 G. This is really greater than the hypertine constant of the isolated ion (A = 87 G). In the less doped sample (x = 0.09) the single-ion line was not visible.
52
CLi?MENT,
RENARD,
AND
ABLART
We consider then the influence of an exchange interaction between & and its nearest neighbors. The existence of such a term can be suspected, considering the relatively great width of the central single-ion line in Fig. 1 (the peak to peak linewidth being 560 G). If we perform the calculation, following the same arguments as before, we obtain the relation
The linewidth of the central line sets the upper limit of the exchange constant J’:J’ 6 0.05 K. (b) Pair Linewidth The principal lines of reasoning are the same as before. We consider now two spins S, and Sz coupled by an Heisenberg exchange interaction and a dipolar interaction. The secular part of this latter interaction gives rise to theJine structure studied in the first part of this paper. Again we consider that the source of broadening is the dipolar interaction D’ of SI and SZ with the neighboring spins, D’ = -C,b,i[(SfSf - 1/4(S:ST + &‘;St)] + bzi[S$Sf - 1/4(S:ST + s,st)] with bli = wDli - 11m3and i < 0 or > 3. The TST function becomes
qdt) = (IS: + S:, D’lP’(O, S; + Gl) ((S + s:w; + ST)) We have now (S:S;(t))
z (S:S,(t))
N 3y
(SfSf(t))
3! (S$S;(t)) N “p
emAof e-‘lTI
so that W)
=
‘(’
+
6n
‘)
e-Awte-w;t
+
i
+b1b2i> 1(Z Uhiblj
e-f/T,p:t
4
With the same considerations relation
concerning the cut-off frequency values we get the
pw=
w+l)
112
6n
(0.085)
[
1
tog.
For n = 5 we obtain a linewidth AH = 90 G an’d for n = 12, AH = 58 G, in any case a value greater than the hypcrhne constant for the pair (44 G). Here again, we calculate the value of the exchange constant J’ compatible with a maximum value of the linewidth (a peak-to-peak value of 180 G). With the same arguments as before, we get A0
=
[s(sg;
1’l”2
J’
which gives J’ 6 0.04 K, a result similar to the one obtained ion case.
for the isolated
EXCHANGECOUPLED
PAIRS IN DOPED CRYSTALS
53
CONCLUSION
TMMC is considered as a reference material concerning one-dimensional magnetic properties. In this context, a good knowledge of anisotropic interactions (dipolar, zero-field splitting) is highly desirable. These parameters can be obtained, in principle, from an analysis of the ESR spectrum of isolated pairs. We show here that the features of pair spectra differ somewhat, according to whether one studies Mn2+ pairs in doped isomorphous TMCC or in diamagnetically doped IMMC. In the latter case, the linewidths are of course relatively much larger, limiting the accuracy. The interactions between a Mn ion and its neighbors across the diamagnetic ion are responsible for the broadening of the lines. There can be inferred from the linewidth a maximum value for the Heisenberg exchange interaction: J' < 0.04 K. REFERENCES 1. J. OWEN, J. Appl. Phys. Suppi. 32, 2 13 (1961). 2. A. ABRAGAM AND B. BLEANEY, “Electron Paramagnetic Resonance of Transition Metal Ions,” Oxford Univ. Press (Clarendon), Oxford, 1970. 3. M. STEINER, J. VILLAIN, AND C. G. WINDSOR, Adv. Phys. 25, 87 (1976). 4. P. M. RICHARDS, in “Local Properties at Phase Transitions,” p. 539, Editrice Compositori, Bologna, 1975. 5. B. MOROSIN Ada Crystaiiogr. B 2ll, 2303 (1972). 6. G. L. MCPHERSON, L. M. HENLING, R. C. KOCH, AND H. F. QUARLS, Phys. Rev. B 16, 1893 (1977). 7. Y. TAZUKE, .I. Phys. Sm. Jpn. 42, 1617 (1977). 8. C. DUPAS AND J. P. RENARD, Phys. Rev. B 18,401 (1978). 9. M. HEMING, G. LEHMANN, H. MOSEBACH, AND E. SIEGEL, Solid State Commun. 44, 543 (1982). 10. E. A. HARRIS, J. Phys. C 5, 338 (1972). il. J. P. BOUCHER, M. AHMED BAKHEIT, M. NECHTSCHEIN, M. VILLA, G. BONERA, AND F. BORSA,
Phys. Rev. B 13,4098 (1976). 12. S. CLEMENT, 13. D. BOURDEL,
TRAN VAN HIEP, AND J. P. RENARD, Solid State Comm. 31, 967 (198 I). G. ABLART, J. PESCIA, S. CLEMENT, AND J. P. WNARD, Phys. Rev. B 23,
1339 (1981).
OF MAGNETIC
RESONANCE
60,46-53
(1984)
The Pair Spectrum in Diamagnetically
Doped TMMC
S. CLEMENT AND J. P. RENARD Institut d’Electronique Fondamentale. Laboratoire asski au CNRS Universiti Paris XI, (Bit. 220) 91405Orsay, Ceder France AND
G. ABLART Laboratoire de Magndisme et d’Electronique Quan fique, Universiti Paul Sabatier, 39, Alike Jules-Guesde, 31062-Toulou.re. Cedex, France Received March 15, 1984 A symmetrical ten-line structure has been observed in the electron spin-resonance spectrum of quasi one-dimensional (CHs),NMnClr(TMMC) doped with diamagnetic Cd at 20% atomic concentration. This structure, on which is superimposed a single-ion line and a much broader finite chain line, has been attributed to Mn2+ ion pairs. It disappears when the angle 0 of the magnetic field with the chain axis exceeds 20”. Because of the rather large linewidth the hyperhne structure was not resolved. The relevant parameters of the fine structure (dipole interaction D, and single-ion anisotropy DE) are somewhat different from those measured in the “symmetrical case” of Mn2+ pairs doped in diamagnetic isomorphous TMCC. In particular it appears that the Mn-Mn distance is smaller in TMMC-Cd. The broadening of lines is related to interactions between paired Mn2+ ions and other Mn2+ ions belonging to neighboring finite chains. 0 1984 Academic Press, Inc.
Extensive studies have been made on the electron-spin-resonance spectra of exchange-coupled pairs in crystals (I, 2). In many cases the results were obtained in diamagnetic crystals doped with paramagnetic impurities. If the concentration of impurities is low, only single-ion spectra are observed, but at higher concentrations the occurrence of nearest neighbor paramagnetic ions gives rise to pirir spectra, consisting generally of complicated structures of narrow lines. From the analysis of the spectra one can get information on the Heisenberg exchange, anisotropic exchange, and dipole-dipole interactions between the ions belonging to pairs, and improve the information obtained about single ions. We present here a study of pair spectra obtained in a paramagnetic sample doped by diamagnetic impurities. Significant discrepancies with the symmetrical case (i.e., diamagnetic crystal paramagnetically doped) are noted concerning the position and width of lines. A linewidth analysis is made for the isolated and paired ion lines. The paramagnetic host crystal was tetramethylammonium trichloromanganate (CH3)4NMnC13 (TMMC) which is a quasi unidimensional (1D) Heisenberg antiferromagnet with S = 5/2 0022-2364184 $3.00 Copyright 0 1984 by Academic Prcs, Inc. All rights of reproduction in any form reserved.
46
EXCHANGE-COUPLED
PAIRS
IN
DOPEiD
47
CRYSTALS
(3). This compound consists of MnC& chains well separated from each other by the TMA ions; the Mn-Mn separation is 3.25 A within a chain (the intrachain coupling being J = -6.7 K) and 9.15 A between neighboring chains (the interchain coupling being - 1 mK). Thus TMMC can be considered as a good 1D not only for short range interactions (exchange) but also for long-range interactions (dipolar). Important consequences on spin dynamics result, which have been well verified by magnetic resonance experiments (4). The cadmium salt (CH&NCdC& (TMCC) is isomorphous to TMMC at room temperature and has very similar crystallographic parameters (5), the Cd-Cd separation being 3.36 A within a chain and 9.13 A between the chains. The replacement of Mn*+ ions in TMMC by Cd*’ ions creates linear finite chains of n spins, weakly coupled by their extremities. If impurity Cd ions are randomly placed inside the crystal, one can expect a proportion 2x2( 1 - x) of Mn*+ ions belonging to pairs, where x is the concentration of impurities. THE
SPIN
HAMILTONIAN
The ESR of single ion Mn*+ in a TMCC matrix was studied by McPherson et al. (6) and by Tazuke (7). Their results establish that the line positions are quite well described, at room temperature, by a Hamiltonian with axial symmetry: R’=gbHo*Si+AIi*Si+D,
1
t11
1) .
S:,-i;si(S,+
The z axis is the line joining the two ions, here the chain axis. The g value (g = 2.00) and the hyperfine constant value (A = -87 G) are isotropic. The zerofield splitting parameter (0, = 45 G) is almost an order of magnitude smaller than the corresponding one in a CsMgQ matrix. The fourth-order terms arising from crystal fields are very small and can be neglected. We consider here the case of two neighboring ions with Si and S2 strongly coupled by an Heisenberg exchange interaction -2rSr . S2. The spectrum of the pair consists thus of spectra from different multiplets, each multiplet being characterized by a total spin S = S, + S2 taking the values S = 0, 1, 2, 3, 4, and 5. The spin Hamiltonian for the manifold of spin S becomes (I) [email protected]+D
+(2;+
1
1) +;&(I1
+I*)
[2]
where Ds = 3asDe + &D,
[31
The coupling coefficients (Yeand & take the values shown in Table 1. The term De represents the anisotropic interaction axial symmetry, including dipole-dipole interaction and a pseudo-dipolar term arising from anisotropic exchange. If the two Mn*+ ions are treated as point dipoles separated by a distance r, De can be calculated from the simple expression De = -g2/3*/r3. The allowed ESR transitions occur within the various multiple& following a selection rule AM = + 1. If the field HO is
48
CLfiMENT,
RENARD, TABLE
AND ,4BLART I
Interaction Parameters crs and OS for Pairs with S, = S, = 512 and Identification of the Observed Lines
s
5
4 3
2 1
as
0s
5
4 9
ii 4 ii 41 90
-2 41
41 42 37 ii
-20 21 -32 5
ohserved M++M
2
lines
3 ‘-+ 2
d
2 ‘-D 1
b
2 ‘+ 1
C
2*+ 1
e
1 *+ 0
a
1 -+o
C
i
parallel to the axis joining the two ions the energy differences corresponding transitions M w M - 1 (fine structure lines) are AE = E,,., - EM-, = ho, + Ds(2M - 1). EXPERIMENTAL
to
141
RESULTS AND DISCUSSION
Single crystals of TMMC-Cd were grown following the prescriptions described in (8). The ESR measurements were carried out on a conventional X-band spectrometer. Figure 1 shows a room-temperature spectrum obtained in a sample doped with cadmium concentration x = 0.20. The static magnetic field & was nearly parallel
1
4000
,
6000
\_,
000
H,(G)
FIG. I. Electron resonance spectrum of TMMC doped with Cd (x = 0.20) recorded at room temperature. The magnetic field is parallel to the chain axis.
EXCHANGE-COUPLED
PAIRS IN DOPED CRYSTALS
49
to the chain axis. The central line of this spectrum is presumably composed of a line caused by single ion resonances and a much broader line ascribed to short chains of Mn*’ ions. The symmetrical structure (ten lines) which is superimposed on it is attributed to ion pairs. Such a structure appears also, though faintly, in a sample with lower dopant concentration (X = 0.09). These dimer lines broaden and disappear when the angle between the chain axis and the magnetic field II,-, exceeds 20” (in relation probably to the increase of the nonsecular dipolar interactions). The fine-structure lines should be split into 11 equally separated lines with relative intensities of 1:2:3:4:5:6:5:4:3:2:1. In fact, this hyperfine structure is not resolved. The separation between adjacent hypertIne lines being equal to half of that of the single ion (thus about 44 G), the full linewidth at half intensity of a fine structure line must be about 300 G. The corresponding derivative peak-to-peak linewidth is about 180 G for a Lorentzian line. This value is in good agreement with the experimental result reported on Fig. 1. The components (&de) of the pair spectrum shown in Fig. 1 can be identified with six transitions, with the help of relations [3] and [4]. They are listed in Table 1. Other existing transitions are not visible in the spectrum because their shifts from the free electron resonance field are smaller than the central linewidth or greater than the magnetic field applied. The line intensities vary with temperature (I) according to this identification, the lines b and d (S = 5) vanishing first near 70 K whereas the line c (S = 2) still exists at 30 K. The resulting value of the exchange integral J which can be deduced with some inaccuracy is about 10 K. The Ds values can be obtained from the relations [3] and [4]. One sees, from Table 1, that Ds is nearly equal to the dipolar term D, for S = 3, corresponding to the lines a and e. We get then D, = -605 + 10 G and, taking this value, we obtain from the other lines DC = 75 f 25 G. Using a point-dipole model, the D, value corresponds to a distance of 3.13 f 0.02 A between the Mn2+ ions of the pair, thus about 3 or 4% smaller than the distance in pure TMMC. Such a result is not unexpected if one considers that the ionic radius of Mn*+ (0.80 A) is smaller than that of Cd*+ (0.97 A); one can conceive that the Mn’+ ions belonging to the pair are pushed toward each other by the Cd ions. On the other hand, we find a zerofield splitting parameter DC almost an order of magnitude smaller than the dipolar term, in agreement with the results of McPherson et a,!. and Tazuke from the single ion spectrum in TMCC-Mn. Recently, however, Heming et al. (9) were able to produce Mn*+ pairs in doped TMCC, and obtained singular results. First, the magnitude of D, inferred from the S = 3 lines corresponded to a large distance between the Mn*+ ions of 3.58 A (using a pointdipole calculation), thus about 7% greater than the undistorted Cd distance. Second, it appeared that either D, or DC, or both, were S dependent. The authors explained these results by the respective hypothesis of spin transfer to the ligands and exchange striction effects (10). Our measurements are too limited and inaccurate to confirm a variation of interaction parameters with S. If it does exist it is probably, however, smaller than that deduced in TMCC-Mn. On the other hand, the spin transfer hypothesis can be hardly invoked in our case. One may imagine other explanations for the anomalous effects observed in TMCC-Mn, such as anisotropic exchange interaction (but the g value is isotropic) or, more plausibly, suppose that the Mn*+ ions are not on the
50
CLBMENT,
RENARD,
AND
ABLART
Cd-Cd axis. It is known furthermore that the zero-field parameter is very much sensitive to distortions in the environment geometry. Whatever the exact reason be, it appears that the situation for Mn” pairs in TMMC-Cd is not similar to that in TMCC-Cd. STUDY
OF
THE
LINEWIDTHS
We focus now on the linewidths of the lines resulting from isolated ions or pair ions in TMMCCd. The observed lines are in fact composed of unresolved hyperhne lines. Consequently, the linewidth of an individual hpf line must exceed the hyperfme constant A (expressed in comparable units). On the contrary, in TMCC:Mn, the linewidth of hpf lines is about 10 G (6) and thus is less than A. We performed a calculation for the angle B = 0”. The broadening of the lines is expected to be caused by the interaction of the corresponding Mn2+ ions with their neighbors across the Cd ions: the secular part of the dipolar interaction and a possible superexchange Heisenberg interaction with the nearest neighbors. The predominant interaction is not known and we consider the two cases. As we want only an evaluation of the linewidth, we suppose that the lineshape is Lorentzian. It is expected that the resulting error does not exceed 20%. Furthermore, we neglect the interchain couplings. (a) Isolated Ion Linewidth Let us consider first the case of an Mn ion with spin & surrounded by two diamagnetic Cd ions. Its interaction with the neighboring spins Si can be written (so+s; -k s&y X’ = D’ + c.Te, = - 2 bi S6 Sf - -4 [ i
1+2J’So
(S2 + S-2)
[5]
with bi = wDlilP3, wg = hyQc3, ye being the electronic gyromagnetic ratio and c the separation between nearest neighbors ions in the chain (c = 3.25 A). The index i run from 2 to co and from -2 to -co. The relevant function to be calculated is the so-called torque-spin-torque (TST) function (4, 11): $@) = ([S,+,t), WI (S,‘S,) the time evolution of Z’ being given by X’(t) = eiHtPIiHr where the Hamiltonian Z? (in rads-‘) is composed of the Heisenberg exchange interaction and the Zeeman term. We calculate tirst the linewidth by considering only the dipolar interaction, to verify if this interaction alone can be responsible for the lack of hpf resolution:
+ ; sgt)sy(t) (( Si$f+ ; s&s:)(S,@)S$) 1) +dt)= C bbi ij
(S&i)
The next step consists of factorizing the four-spin correlation functions into a product of two-spin correlation functions. We neglect correlation between S, and
EXCHANGE-COUPLED
51
PAIRS IN DOPED CRYSTALS
Sj, since the coupling between these spins is quite small compared to the exchange interaction J. We have (S&S;(t)) = (So+Sij)e-AWr (S&!?;(t)) = (S&.Yf$e-tfT1
171
with Aw the half linewidth at half power (to be calculated) and T, the electronic spin-lattice relaxation time. Then +o(t) = 2 b,b,EemAwf(S:S;(t)) + i e+“(S:S;(t))] ki
.
PI
In this summation, it is clear that the spins Si and Sj must be on the same side of the spin &. In fact, they belong to a finite chain composed of n spins coupled by an Heisenberg interaction and a dipolar interaction. If n is not too great (n Q lo), the correlation functions (SfSi’
The quantity
+D(t)
(srqt))
=
SW + 1) ,-& 3n
(s:sjlt>)
=
2s(s + l) e-u:j . 3n
is related to the linewidth Aw through the relation Aw =
s0
m #&)dt.
[lOI
The problem is now to compare the different parameters Aw, T;‘, wf, and w,‘. The last two are related to the magnetic resonance spectrum of the n-spin chain (1 I). The cut-off frequency w5 corresponds to the electronilc spin-lattice-relaxation rate, and it is known from NMR (12) and ESR (13) experiments that its value is very small (w: - lo8 rad s-’ 4 Aw). On the other hand, w: is related to the ESR linewidth, the value of which is greater than the one measured in pure TMMC: w: > 2 X 10” rad s-’ (see Fig. 1). w: is of course much greater than Aw and T;’ and in the integral we can safely neglect the term containing (S~S;(t)). Finally, we obtain the self consistent relation Aw _s(s+
3n 1) (0.07wQ 2;.
[Ill
For the sample doped with a concentration of impurities x = 0.20 we can take a mean value n N 5. The relation [ 1 l] gives a linewidth Aw I: 2 X lo9 rad s-l corresponding to AH = 115 G. This is really greater than the hypertine constant of the isolated ion (A = 87 G). In the less doped sample (x = 0.09) the single-ion line was not visible.
52
CLi?MENT,
RENARD,
AND
ABLART
We consider then the influence of an exchange interaction between & and its nearest neighbors. The existence of such a term can be suspected, considering the relatively great width of the central single-ion line in Fig. 1 (the peak to peak linewidth being 560 G). If we perform the calculation, following the same arguments as before, we obtain the relation
The linewidth of the central line sets the upper limit of the exchange constant J’:J’ 6 0.05 K. (b) Pair Linewidth The principal lines of reasoning are the same as before. We consider now two spins S, and Sz coupled by an Heisenberg exchange interaction and a dipolar interaction. The secular part of this latter interaction gives rise to theJine structure studied in the first part of this paper. Again we consider that the source of broadening is the dipolar interaction D’ of SI and SZ with the neighboring spins, D’ = -C,b,i[(SfSf - 1/4(S:ST + &‘;St)] + bzi[S$Sf - 1/4(S:ST + s,st)] with bli = wDli - 11m3and i < 0 or > 3. The TST function becomes
qdt) = (IS: + S:, D’lP’(O, S; + Gl) ((S + s:w; + ST)) We have now (S:S;(t))
z (S:S,(t))
N 3y
(SfSf(t))
3! (S$S;(t)) N “p
emAof e-‘lTI
so that W)
=
‘(’
+
6n
‘)
e-Awte-w;t
+
i
+b1b2i> 1(Z Uhiblj
e-f/T,p:t
4
With the same considerations relation
concerning the cut-off frequency values we get the
pw=
w+l)
112
6n
(0.085)
[
1
tog.
For n = 5 we obtain a linewidth AH = 90 G an’d for n = 12, AH = 58 G, in any case a value greater than the hypcrhne constant for the pair (44 G). Here again, we calculate the value of the exchange constant J’ compatible with a maximum value of the linewidth (a peak-to-peak value of 180 G). With the same arguments as before, we get A0
=
[s(sg;
1’l”2
J’
which gives J’ 6 0.04 K, a result similar to the one obtained ion case.
for the isolated
EXCHANGECOUPLED
PAIRS IN DOPED CRYSTALS
53
CONCLUSION
TMMC is considered as a reference material concerning one-dimensional magnetic properties. In this context, a good knowledge of anisotropic interactions (dipolar, zero-field splitting) is highly desirable. These parameters can be obtained, in principle, from an analysis of the ESR spectrum of isolated pairs. We show here that the features of pair spectra differ somewhat, according to whether one studies Mn2+ pairs in doped isomorphous TMCC or in diamagnetically doped IMMC. In the latter case, the linewidths are of course relatively much larger, limiting the accuracy. The interactions between a Mn ion and its neighbors across the diamagnetic ion are responsible for the broadening of the lines. There can be inferred from the linewidth a maximum value for the Heisenberg exchange interaction: J' < 0.04 K. REFERENCES 1. J. OWEN, J. Appl. Phys. Suppi. 32, 2 13 (1961). 2. A. ABRAGAM AND B. BLEANEY, “Electron Paramagnetic Resonance of Transition Metal Ions,” Oxford Univ. Press (Clarendon), Oxford, 1970. 3. M. STEINER, J. VILLAIN, AND C. G. WINDSOR, Adv. Phys. 25, 87 (1976). 4. P. M. RICHARDS, in “Local Properties at Phase Transitions,” p. 539, Editrice Compositori, Bologna, 1975. 5. B. MOROSIN Ada Crystaiiogr. B 2ll, 2303 (1972). 6. G. L. MCPHERSON, L. M. HENLING, R. C. KOCH, AND H. F. QUARLS, Phys. Rev. B 16, 1893 (1977). 7. Y. TAZUKE, .I. Phys. Sm. Jpn. 42, 1617 (1977). 8. C. DUPAS AND J. P. RENARD, Phys. Rev. B 18,401 (1978). 9. M. HEMING, G. LEHMANN, H. MOSEBACH, AND E. SIEGEL, Solid State Commun. 44, 543 (1982). 10. E. A. HARRIS, J. Phys. C 5, 338 (1972). il. J. P. BOUCHER, M. AHMED BAKHEIT, M. NECHTSCHEIN, M. VILLA, G. BONERA, AND F. BORSA,
Phys. Rev. B 13,4098 (1976). 12. S. CLEMENT, 13. D. BOURDEL,
TRAN VAN HIEP, AND J. P. RENARD, Solid State Comm. 31, 967 (198 I). G. ABLART, J. PESCIA, S. CLEMENT, AND J. P. WNARD, Phys. Rev. B 23,
1339 (1981).