Journal ArticleWe report the specific heat C(T) of (DMeFc)(TCNE) for temperatures 3 K < T < 50 K. We observe an anomaly at Tc-4.82 K corresponding to a transition to a three-dimensional (3D) macroscopic ferromagnet. A broad maximum at = 15 K corresponds to an exchange interaction of J = 35 K along the chain axis. We propose a generalized 1D Hubbard Hamiltonian to account for this feature. Below T (c) results are consistent with the opening up of a gap of approximately 2 meV in the spin-wave spectrum due to the anisotropy in the exchange interaction within the 1D chains

Chackraborty, A.

Miller, Joel Steven

English

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RAPID COMMU],;ICA fIO>;S PHYSICAL REVIEW B VOLUME 40. NUMBER 16 1 DECEMBER 1989 Specific heat or decamethylferrocenium tetracyanoethanide (DMeFc) (TCNE) A. Chakraborty and A. J. Epstein Department of Physics. The Ohio State University. Columbus. Ohio 43210-1106 W. N. Lawless Ceram Physics. Inc .• Westerville. Ohio 43081 Joel S. Miller Central Research and Development Department. E. I. Dupont de Nemours and Company. Inc .. Wilmington. Delaware 19880-0328 (Received 13 June 1989) We report the specific heat C(T) of (DMeFc)(TCNE) for temperatures 3 K < T < 50 K. We observe an anomaly at Tc -4.82 K corresponding to a transition to a three-dimensional (3D) macroscopic ferromagnet. A broad maximum at .... 15 K corresponds to an exchange interaction of J .... 35 K along the chain axis. We propose a generalized ID Hubbard Hamiltonian to ac-count for this feature. Below Tc results are consistent with the opening up of a gap of approxi-mately 2 meV in the spin-wave spectrum due to the anisotropy in the exchange interaction within the 1 D chains. There has been considerable experimental and theoreti-cal interest in the past decade in the physics of quasi-one-dimensional (quasi-lD) charge-transfer salts. 1 Stacks of alternate donors and acceptors are of interest particularly due to their magnetic properties. 2 Decamethylferroceni-um tetracyanoethanide. (DMeFc)(TCNE), consisting of stacks of alternate donors (DMeFc)' + and acceptors (TCNE) . -, is the first reported 3 molecular ferromagnet. Above the transition temperature Tc ==4.82 K, the system has been described 3,4 as having primarily I D ferromag-netic interactions among the spin S - t radicals along the chain axis. At Te. magnetization and neutron studies 3,4 show that (DMeFc) (TCNE) undergoes a phase transition to a macroscopic 3D ferromagnet. We report here the specific heat of (DMeFc)(TCNE) in the temperature range 3-50 K. The data show a cusp in the specific heat C(T) at the 3D ferromagnetic transi-tion temperature with a crossover to primarily ID behav-ior at higher temperatures. There is a broad maximum in C(T) at T= 15 K. in accord with a one-dimensional an-isotropic Hesienberg exchange along the chain axis with a ferromagnetic J = 35 K. For T just above Tc the magnet-ic specific heat varies as C M - (T - Te) - a with a - 0.1 ± 0.02. For T < Te. CM is proportional to exp(l!JkB T) with ..:1- 22 K. which is consistent with the opening up of a gap of = 2 meV at q -0 in the spin-wave spectrum. (DMeFc) (TCNE) crystalizes in an orthorhombic structure (space group Cmca) with stacks of alternating (DMeFc)' + and (TCNE)' - radical ions parallel to the long needle axis of the solution grown crystals. 5 Both cat-ion and anion have spin t. with the highest occupied en-ergy levels of the donor being degenerate and those of the acceptor non degenerate. 5 The presence of the partly oc-cupied degenerate orbital on the donor (DMeFc)' + has been proposed as the origin of the ferromagnetic intras-tack and interstack exchange. 5,6 The specific-heat measurements were performed in an adiabatic calorimeter. The samples were in pellet form with a mass of = 0.5 g. The measurements between 3-11 K were performed using a drift method described ear-lier. 7,8 Measurements between 10 and 50 K were per-formed by loading the samples onto copper holders and then letting them drift down in temperature. The thermal links between the holders and the reservoir were calibrat-ed separately. The drift method consisted of relating the specific heat to the time (d-temperature (T) decay of the sample temperature (dT/dt = 10-20 mK/s). The carbon-chip sample thermometers were calibrated in situ. 9 We measured the specific heat of spinless (DMeCo)(C3(CN)5) to obtain an experimental measure-ment of the background lattice contribution and hence the magnetic contribution to the specific heat (CM) in (DMeFc)(TCNE). Figure 1 shows the specific heat of both (DMeFc)-(TCNE) and (DMeCo)(C3(CNh) in the range 3-11 K. A cusp in the specific heat is clearly seen at T -4.82 K for (DMeFc)(TCNE). This confirms previous magnetiza-tion,3 - 5 neutron diffraction,4 and Mossbauer results 5 that the system becomes a ferromagnet below 4.82 K. Careful examination of the data also reveals a small anomaly at T = 6.1 K. The inset in Fig. 1 shows the specific heat of the above compounds in the range 10-50 K. The magnet-ic contribution to the specific heat of (DMeFc)(TCNE). CM, obtained by subtracting the lattice term is plotted in Fig. 2 in units of (C/3NkB) vs (kBT/J), with J-35 K. Also depicted in Fig. 2 are the exact solutions for the 1 D Ising and isotropic Heisenberg chains 10 with ferromagnet-ic exchange. The magnetic entropy. Sm(T) = fnCM(T)/T]dT, is plotted in Fig. 3. The entropy saturates to 3R In2. (DMeFc) (TCNE) consists of two spin t's, one each on the donor and the acceptor. Hence it is expected that the entropy would saturate to 2R In2 instead of 3R In2. We plotted eM in units of C/3NkB in Fig. 2, to facilitate com-11422 © 1989 The American Physical Society fl \1'11) (O!\t\tll"ICATlONS ~ SPECIFIC HEAT OF OECAMETHYLFERROCENIUM ... 11423 35 30 25 ::.::: (5 20 E ....... ~ 15 U 10 5. 0 2 3 4 5 6 7 8 T(K) (DMeFc)( TeNE)-::." 9..~~ r:P~~~ ~ ~ 9 10 II 12 13 FIG. 1. Specific heat vs T for (OMeFc)(TCNE) and (OMeCo)(C3(CN)s) from 3 to 11 K. Inset shows specific heat from 10 to 50 K. parison with the model-Ising and the Heisenberg-chain predictions. We consider these data in the context of a generalized Hubbard Hamiltonian with only near-neighbor interac-tions along the stack and accounting for the orientational dependence of the (DMeFc)' + moment: H .... -J' 1: [(gfg A)S1s1+ 1 + (gfgA)(S~S~+1 +S~S~+I») , i J'>O. Here J' is the ferromagnetic exchange expected in a Hub-bard model for sites with a partially occupied degenerate level. 6 Using gpMeFc = 4.0, g£MeFc = 1.3 (Ref. I I) and gTCNE_2.0: H'" -2J1: [S1s1+ 1 + y(S~S~+I+S~S~+1 »), i J>O, y=0.35, where J-4J'. It is emphasized that the anisotropy in the Hamiltonian arises from the fact that g is anisotropic at the (DMeFc)' + site. Hence, even though the intrachain 0.6 0.6 0.5 0.5 0.4 ,.- ...... ~ID Ising-0.4 .....--...... C .....--...... el::'::: 0.3 EI::.::: u~ I ... """" 0.3 U Z ----....- " -0 EXPto Data~ -- 0- _ ----....-0.2 0.2 0.1 I ~ID Heisenberg --- 0.1 I 0 1.4 FIG. 2. Magnetic specific heat (eM) vs (kBTIJ) of (OMeFc)(TCNE) (x). The experimental data are plotted with J-35 K. Also shown are 10 Ising and Heisenberg (isotropic) results. 18 ~ "0 12 E "-.3 E 6 if) 0 0 _~lD.(~ ____ __ .~ 2 '#~" ,xxx' xxX; 4.5[2j x>f."" "0 30 T ..... .... xxx E . c ..... · ./ ~ 1.5 I .. ······· E .. ·· If) 0 .... 0.5 0.7 0.9 1.1 1.3 1.5 (T ITc) 4 6 8 (T fTc) 10 FIG. 3. Entropy vs reduced temperature TIT. for (OMeFc)(TCNE). Inset shows entropy vs TIT. in the vicinity of T •. coupling J is isotropic (spin space) the final Hamiltonain is anis6tropic. The above Hamiltonian does not distin-guish between g and J anisotropy. Comparison of the ex-erimental CM(T), Fig. 2, with the limiting model predic-tions, indeed shows that the specific-heat data are between y-OCisotropic Heisenberg) and y-I (Ising) limits, for T> Te. The entropy (Sm) as a function of the reduced temperature TITe, Fig. 3, shows little change at Te, in contrast with other I D systems like CoCh' 2H20 which is an Ising chain with Tc -3.15 K. IO The inset in Fig. 3 shows the entropy gained in the vicinity of Te. Approxi-mately only 4% of the total entropy is involved in the 3D ordering, in accord with the specific-heat peak being so small. The vast majority of the spin entropy is involved in the I D correlations evident in the broad peak at - 15 K, Fig. 2. At Te when the system undergoes a phase transition, C= IEI-a.-a', where E-(T-Te)/Te and a,a' are the critical exponents above and below Te. To determine a, In(CM) vs In(T-Te ) is plotted in Fig. 4, for T between 4.82 and 5.12 K which corresponds to 0 < E < 0.06. The small magnitude of the peak makes a good determination of the critical exponent difficult. Noting that our data spans a little more than one decade in E, we obtain a -0.10 ± 0.02, close to the value predicted for an Ising system,I2 as might be expected in a material with aniso-tropicJ. Below Tc we were unable to determine the exponent a'. The plot of In(CM) vs In(Tc - T) did not yield a straight line. Instead CM varies as exp(!::JkBT) below Te from our lowest temperature to the transition temperature of 4.82 K. The failure to obtain a' below Te is likely due to the fact that the specific heat below Tc shows an activation behavior all the way up to Te. Attempts to force a fit to the data below Te as a power law yielded an exponent of = 5 which is unrealistic. One should note that for a 3D Heisenberg ferromagnet CM = T 3/ 2 for T below Te. In-stead In(CM) V8 liT, Fig. 5, yields a gap .6-22 K in the spin-wave spectrum. The likely origin of .6 lies in the presence of I D chains in this material. The anisotropy in the exchange interaction along the chains causes a gap to open up at q -0, for T below Te. It is conceivable that multimagnon states as well as nonlinear excitations (soli-RAPID COMMl'i\lICA IIO'\s 11424 CHAKRABORTY, EPSTEIN, LAWLESS, AND MILLER 2.3 r----r--,-I---,---,-I--,--'I---, _ 2.1-E U 1.9f-T>TC O<E<O.06 --I I I 1.7 L-_"'--_-,'-_....J......_--L.._--'-_----'._----' -4 -3 -2 -I In (T -Tc ) FIG. 4. In (eM) vs In (T - Te) for T> Te. The data are plot-ted for 0 < e<0.06, where e-(T- Te)/Te. tons) exist in this system. Soliton pairs created in the form of a pair of spin flips along the length of a chain, are depicted in the inset of Fig. 5. One should note that both multimagnon states as well as solitons have been known to exist in ID ferromagnetic chains. 13•14 Further experi-ments like far-infrared spectroscopy and inelastic neutron diffraction may elucidate these features. The origin of the small 6.1 K anomaly in CM(T) is elusive. The limiting value of 3R In2 for Sm (T), instead of the expected 2R In2, may lie in an additional degree of freedom in (DMeFc)-(TCNE). In summary, we have reported the specific heat of (DMeFc)(TCNE). This system exhibits one dimen-IFor recent results, see Proceedings of the International Confer-ence on Science and Technology of Synthetic Metals. Santa Fe, NM, 1988 [Synth. Met. 27 (1988); ibid. 28-29 (1989)]. 2Z. G. 8008, in The Physics and Chemistry of Low Dimensional Solids, edited by L. Alcacer (Reidel, Dordrecht, Holland, 1980), p. 143; J. S. Miller, A. J. Epstein, and W. M. Reiff, Chem. Rev. 88, 201 (1988). 3S. Chittipeddi, K. R. Cromack, J. S. Miller, and A. J. Epstein, Phys. Rev. Lett. 58, 2695 (1987). 4S. Chittepeddi, M. A. Selover, A. J. Epstein, D. M. O'Hare, J. Manriquez, and Joel S. Miller, Synth. Met. 27, B417 (1988). 5J. S. Miller, J. C. Calabrese, H. Rommelmann, S. Chittipeddi, J. H. Zhang, W. M. Reiff, and A. J. Epstein, J. Am. Chem. Soc. 109,769(1987). 6J. S. Miller and A. J. Epstein, J. Am. Chem. Soc. 109, 3850 (1987). E 1 -U 01-1 1 1 ----I~--~--~I~--~--~I=---~--~I=-~ 0.21 0.25 0.29 0.33 --L (K- ' ) T FIG. 5. In (eM ) vs l/T; T < Te for (1/4.82 K) < I/T < (1/3.0 K). Inset shows a soliton/antisoliton pair along the chain. sionality both below and above Tc in its magnetic proper-ties. We confirm that the system undergoes a phase tran-sition at Tc to a long-range ferromagnetic ordered state. The spin-wave spectrum below Tc is dominated by the one-dimensional chains. This is the first known molecular ferromagnet to illustrate these features. We thank C. Jayaprakash for useful discussions and comments. A.C. and A.J.E. were supported in part by the U.S. Department of Energy, Division of Materials Sci-ence, Grant No. DE-FG02-86ER45271.AOOO. 'W. N. Lawless, C. F. Clark, and R. W. Arenz, Rev. Sci. In-strum. 53, 1647 (1982). SA. Chakraborty, A. J. Epstein, D. L. Cox, E. M. McCarron, and W. E. Farneth, Phys. Rev. B 39, 12267 (1989). 9W. N. Lawless, S. K. Hampton, and C. F. Clark, Rev. Sci. In-strum. 59, 2505 (1988). . IOL. J. De Jongh and A. R. Miedema, Adv. Phys. 23, 1 (1974). "D. N. Hendrickson, Y. S. Sohn, and H. B. Gray, Inorg. Chem. 10, 1559 (1971). 12H. E. Stanley, Introduction to Phase Transitions and Critical Phenomena (Oxford Univ. Press, Oxford, 1971). 13J, B. Torrance and M. Tinkham, Phys. Rev. 187, 595 (1969). 14M. Steiner, K. Kakurai, and W. Knop, Solid State Commun. 41,329 (1982). 

Specific heat of decamethylferrocenium tetracyanoethanide (DMeFc)(TCNE)

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Specific heat of decamethylferrocenium tetracyanoethanide (DMeFc)(TCNE)

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