Synthetic Metals'. 12 (1985) 4 3 3  4 3 8
433
MAGNETIC PHASE TRANSITIONS IN CoC12GRAPHITE INTERCALATION COMPOUNDS
G. DRESSELHAUS, S.T. CHEN and K.Y. SZETO Massachusetts Institute of Technology, Cambridge, MA 02139 (U.S.A.)
ABSTRACT Evidence for the dominance of 2DXY behavior in a magnetic graphite intercalation compound (GIC) is presented. The strongest present support for 2DXY behavior in a magnetic GIC comes from a comparison of the high temperature series expansion calculation above Tcu with susceptibility measurements for a high stage CoCI2GIC sample and from a comparison of the experimental susceptibility results with a more general model Hamiltonian that is applicable over a broader temperature range. INTRODUCTION Recent experimental[i,2,3,4,5] and theoretical[6] activity in the study of twodimensional magnetism in magnetic graphite intercalation compounds (GICs) has focused on the role of dimensionality on the magnetic behavior near phase transitions. The Hamiltonian of CoCl2intercalated graphite can be expressed as =
+ JA
S,,S,z +
(1)
where the sums are over spin pairs, J is the intraplanar exchange coupling, JA is the anisotropy term associated with spins on the same plane, while J' is the interplanar exchange coupling constant. For the ideal 2DXY system ( J a / J ) ~ 1 and j i ~ 0. Although 2D behavior has been discussed for several magnetic GICs (including the CoC12GIC, NiClzGIC and MoClsGIC systems),[2,4,5] few studies have focused on investigating the experimental and theoretical basis for identifying the observed magnetic behavior with the 2DXY model, as is done in this paper for the CoC12GIC system.[6,7] It is well established experimentally that the CoC12GICs, NiC12GICs and MoCIsGICs all exhibit two magnetic transition temperatures Tel and Teu[2,4,5,8]. The upper critical temperature Ten is identified with the onset of short range order while the lower critical temperature Tet is identified with the onset of long range (3D) magnetic order. In the present work we focus attention on the 2DXY behavior near Tcu. Firstly we show by comparison of experimental susceptibility
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434 results for a stage 3 CoCI2GIC sample with a high temperature seriesexpansion calculationthat the 2 D  X Y model is applicable to this system for temperatures above Tc~. For T >> To,, CurieWeiss behavior is observed.181 Closer to Tcu where the high temperature series expansion breaks down, we then show that the experimental susceptibilityresults can be understood on the basis of a more complete model Hamiltonian[71 which includes the 2 D  X Y interactionas the dominant term, as well as weak perturbations due to the 6fold inplane symmetrybreaking crystal field[9] interplanar exchange coupling and finitesize effects[9]associated with the magnetic intercalate islands. Further support for the 2 D  X Y behavior comes from the magnitude of the theoretically predicted island size,[7]which is in good agreement with T E M
measurements of the intercalate
domains.[1,10]
SYNTHESIS
AND
CHARACTERIZATION
The CoCl2intercalated graphite samples were prepared from Kish graphite,pure CoCl2 powder and Cl2 gas heated to ~ 560 °C for 1 month.Ill,12,13] Controlled variation of the Cl2 pressure between 100 Torr and 2 atmospheres allows the preparation of stage 1, 2 and 3 samples with high staging fidelity. The stage index and the magnetic interplanar distance Ic are determined by (00£) xray diffractograms. The (kh0) electron diffractionpattern shows that the Co +2 ions form a two dimensional triangularlatticesandwiched between chlorine layers on either side. The inplane latticeconstant for CoCl2 in the GIC is almost the same as that for pristineCOC12 (3.56 ± 0.02 ~). The inplane structure for the CoCl2 intercalatesandwich is incommensurate with that of the adjacent graphite layers, but the latticevectors for the intercalateand the graphite are rotated with respect to one another by 3.5° for the stage 1 compound and by 30° for the stage 2 and stage 3 compounds.[1,13] A comparison between the stoichiometry (C5.sCoC12.07)for the stage 1 compound[141 and the crystal structure implies a fillingfactor of N0.71 and suggests that the COC12 forms island structures within the intercalate layers[15]. Direct observation of these island structures by transmission electron microscopy (TEM) indicates that a typical 2D island contains about 3600 spins.J7]Since the inplane latticeconstants for CoCl2 do not change upon intercalation,it is not surprising that the inplane Curie constant for the high temperature
magnetic susceptibility also is essentially unchanged upon intercalation[12,13] (C=3.36 K emu/mole for CoCI~GICs as compared with C=3.33 K emu/mole for pristine COC12[16]). On the basis of the similarity of the inplane lattice constants and Curie constants, we argue that the inplane exchange constants J=28.5K and JA=16.0K for pristine CoC12117] can be used to approximate the corresponding exchange constants for Co +2 in the CoCI2GICs.
HIGH
TEMPERATURE
SERIES
EXPANSION
W e show here using a high temperature seriesexpansion that for the various possible 2D spin models, the 2 D  X Y model provides the best fitto the susceptibilitymeasurements for the highest stage (3) sample of CoCI2GICs for which reliablemeasurements are available. The high stage. limit provides the best approximation for a 2D system.
435
The model Hamiltonian to be tested in the high temperature expansions are all of the form
=J, ss ~ ~," ~i
~
(2)
where ISI = 1 and Jef! =
Js2
for the classical spin model. Here
(i,j)
refers to the sum over
nearest neighbor spins on the two dimensional planar triangular lattice and S is an n component spin vector ( n = l , 2, 3 for the Ising, XY, and Heisenberg models, respectively), and the effective exchange coupling
Jeff
is defined so that the spin magnitude s is absorbed. Using the arguments
given above, the magnitude of J e l l in Eq. (2) is taken as that for pristine CoCl2, namely JeI! ~ 7.125 K. Thus, by comparing the high temperature series expansion with susceptibility measurements for the stage 3 CoC13GICs, we are able to determine unambiguously the number of spin components a and to find the best fit value of Jeff For this comparison (see Fig. 1), we believe that other effects such as the finite size of the intercalate islands[Ill, symmetrybreaking fields[Ill, and the interplanar correlation[7,19] are more important then quantum effects.J20]
2OO
._.
:
I
(.9 IX
150 
.¢..
Stage 3

c~
.m .i.,
I00
(D C.} (D
l'
_
(D

"E} (D
ac
0 1.00
\
:
o 50 _,, (D
~ 2DIsing
2Dlteisenberg
\
,
]
\\.
"4
%%
I

"'I"I:'~~:~I~.=:'I'#'~,,=I
1.75 2.50 3.25 Reduced tempereture (T/Jeff)
4.00
Fig. 1. Comparison of the high temperature series expansion magnetic susceptibility results for the classical 2DHeisenberg, 2DXY and 2DIsing models with the experimental measurements for a stage 3 CoC12GIC sample. The value of JeYI is 7.125 K and C is 3.36 K emu/mole.
We see from Fig. 1 t h a t the experimental data are well fit by the classical 2DXY model with
Jell
= 7.125 K, from which we conclude t h a t the classical 2DXY term is the dominant term
in the magnetic Hamiltonian of CoC12GICs for temperatures below 20 K.[7] Attempts to fit the experimental data with the 2DHeisenberg model and the 2DIsing model using JelI as a totally free parameter were significantly less successful.J7] Furthermore, the good fit obtained for T > Tcu with the JelI 7.125 K value for pristine CoCI2 is consistent with the close similarity of the planar lattice constants and Curie constants for the pristine and intercalated CoCl2 compounds, as well
436 as the finding t h a t for magnetic interplanar separations as large as for stage 3, the interplanar magnetic coupling is dominated by dipoledipole interactions with little contribution from the RKKY mechanism.[7] If the RKKY interaction were important, perturbation of the Je/I value would be expected, arising from the interaction of the cobalt spins with the conduction electrons. Since the RKKY interaction becomes increasingly important for the stage 2 and stage 1 CoC12GICs[7] a determination of Jeff for these lower stage compounds would be of considerable interest.
MODEL
HAMILTONIAN
APPROACH
The high temperature series expansion approach breaks down as T * Tcu from above for two reasons: (i) the high temperature series expansion is not a good approximation for the model Hamiltonian of Eq. (2) in the limit T , T~u; (ii) the model Hamiltonian of Eq. (2) itself breaks down as T + Tc, since small perturbations become important near To,. For example, the susceptibility for an ideM KosterlitzThouless system diverges at the transition temperature.J21] Since experimentally X remains finite for the CoCI2GIC system, additional phenomena must be considered as T * Wcu.
To treat the magnetic susceptibility for the CoC12GIC system over a wider temperature range than is possible with the high temperature series expansion approach, we have constructed a more general Hamiltonian[7] including interactions that become important as T * Tcu as well as temperatures below Tcu: z r = ~xy + us + v where
~IY
(3)
is the dominant 2DXY Hamiltonian discussed above and the remaining terms are
perturbations. Here Us is the 6fold symmetrybreaking crystal field perturbation discussed by Jos~, Kadanoff, Kirkpatrick and Nelson,[22]
u~ = MoH~ ~ cos[6¢(~]
(4)
where )d0 is the magnetization, Hs is the 6fold inplane crystal field and ¢ ( ~ is the angle betweer the spin at position F and a reference direction, and the sum is over all spins in the plane. The interplanar exchange coupling perturbation V is written as
v =  J ' ~ &C~ &+,C¢)
(5)
k
where J' is the interplanar exchange interaction ( J ' / J ~ 10 4 for a stage 2 CoC12GIC[13 D and the sum is over spins on adjacent layers. In the explicit calculation of the model Harniltonian ~ r of Eq. (3) for the CoC12GIC system, finite size effects were also included[7], by treating the size (L x L spins) as a fitting parameter. The comparison between the model calculation and the experimental susceptibility results for stage 1, 2 and 3 CoClzGIOs[1] is shown in Fig. 2 for the case of no interplanar coupling (J' = 0) for several sizes of the magnetic domains.J7] In the calculation the magnitude of the symmetrybreaking field is fixed at He = 10Oe, consistent with the magnetic field dependent susceptibility measurements[7], neutron scattering measurements[13! and other estimates[8]. Over the broad temperature range as well as near Tcu (where T / J e l ! N 1.41
437
1200
~ 6 0
(.9
~0 1
I j, 0
I,¢,,._
"
(D
600
F/!\
500
V."............
(i) (1)
'o (D ¢)
,
".
.
0 1.00
.
.
.
\ ; .~...:
.....
I. 25 I. 50 I. 75 Reduced temperoture (T/Jeff)
2.00
Fig. 2. Comparison of the finite size generalized JKKN model calculation for the magnetic susceptibility with experimental measurements for stage 1, 2, and 3 CoCl2GIC samples. In the calculation, the sixfold field is set at 10 Oe, the probing field at 0.3 Oe, and JeI! = 7.125K. The value of J'/J is set at 0. Results are shown for sizes ranging from 50x50 to 70×70.
the results of Fig. 2 show that the model Hamiltonian of Eq. (3) provides a much better fit than the
~2DXY term
alone to the high stage susceptibility measurements. The results further show
that the magnitude of the susceptibility peak near Tel (where
T/Jeff
~ 1.25) is strongly dependent
on the island size, with the best fit achieved for L x L ~ 3300 spins.[7] This is to be compared with the island size of ~3600 spins estimated from the TEM observations.J1] The good agreement between the island size estimated from the model calculation and the TEM observations provides further confirmation for the relevance of the 2DXY description of the magnetic behavior observed in CoClzGICs near Tcu. For an ideal KosterlitzThouless system below Tcu, the spins would be arranged in a bound vortex phase with strong short range correlation but no long range order.J21] Preliminary inelastic neutron scattering results[2] indicate that there is no long range order between Tot and Tcu, but the nature of the magnetic spin arrangement has not yet been identified. Since the magnetic domains contain only a few thousand spins, Monte Carlo simulations of the magnetic behavior between T~z and Tcu should provide an especially fruitful technique for studying the spin arrangement of the CoC12GIC system in this most interesting temperature range. Based on these simulated spin arrangements, model calculations of physical observable should be carried out to suggest sensitive experimental probes of this interesting temperature range. Since small magnetic fields ( ~ 100 Oe) have been shown to strongly suppress the large magnitude of the susceptibility peak,J7] Monte Carlo calculations as a function of weak magnetic fields would be especially interesting in showing how long range spin order is established above T~z by the applied magnetic field.
438 ACKNOWLEDGMENTS W e are grateful to Profs. M.S. Dresselhaus, P.A. Lee, A.N. Berker, J.V. Josd and H. Suematsu for their helpful comments. W e are especially thankful to Prof. H. Suematsu for the Kish graphite samples. This work was supported by A F O S R
contract #F4962083C0011.
K Y S gratefully
acknowledges the support of N S E R C of Canada by the award of a graduate research fellowship and S T C acknowledges support from an IBM graduate fellowship. The permanent address for K Y S is now Department of Physics, University of Toronto, Toronto, Canada. REFERENCES 1 S.T. Chen, K.Y. Szeto, M. Elahy and G. Dresselhaus, Journal de Chimie Physique 81, 863 (1984). 2 M. Suzuki, A. Furukawa, H. Ikeda and H. Nagano, Intercalated Graphite edited by S. Tanuma and H. Kamimura, March 1984, p. 91. 3 M. Elahy and G. Dresselhaus, Phys. Res. B32, 7225 (1984). 4 Proceedings of the Third Conference on Intercalation Compounds of Graphite, Pont ~ Mousson, France, A. H6rold and D. Gu6rard (eds.), Synthetic Metals Vol. 8, (1983). 5 Eztended Abstracts of the 198~ MRS Symposium on Graphite Intercalation Compounds, edited by P.C. Eklund, M.S. Dresselhaus and G. Dresselhaus, p. 88, 91 (1984). 6 K.Y. Szeto, PhD. Thesis M.I.T. (1985). 7 K.Y. Szeto, S.T. Chen and G. Dresselhaus, (to be published). 8 Yu.S. Karimov, Sos. Phys. JETP 39, 547 (1974). 9 K.Y. Szeto and G. Dresselhaus, Phys. Rev. B (in press). 10 M. Elahy, M. Shayegan, K.Y. Szeto and G. Dresselhaus, Synthetic Metals 8, 35 (1983). 11 M. Suzuki, H. Ikeda and Y. Endoh, Synthetic Metals 8, 43 (1983). 12 M. Suzuki and H. Ikeda, J. Phys. C14, L923 (1981). 13 S.T. Chen (private communication). 14 W. Riidorff, E. Stumpp, W. Spriessler and F.W. Siecke, Anyew. Chem. 75, 130 (1963). 15 F. Baron, S. Flandrois, C. Hauw and J. Gaultier, Solid State Commun. 42, 759 (1982). 16 H. Bezette, C. Terrier and B. Tsai, Compt. Rend. 243 (1956). 17 M.T. Hutchings, J. Phys. C: Solid State Phys. 6, 3143 (1973). 18 L.L. Liu and H.E. Stanley, Phys. Res. BS_, 2279 (1973). 1316, 1217 (1977). 19 E. Loh, Jr., D.J. Scalapino and P.M. Grant (to be published). 20 J.M. Kosterlitz and D.J. Thouless, Progress in Low Temp. Physics, vol.VIIB, 373 (1978). 21 J.V. Josd, L.P. Kadanoff, S. Kirkpatrick, and D.R. Nelson, Phys. Rer. B16, 1217 (1977); ibid B17, 1477 (1979).