Journal ArticleWe have systematically introduced spinless defects in the quasi-one-dimensional ferromagnetic system decamethylferrocenium tetracyanoethanide, [FeCp(2*)] [TCNE]. The three-dimensional ordering temperature  Tc decreases rapidly with the concentration of spinless sites. The rate of decrease of Tc with concentrate is in the order of the exchange spatial anisotropy (i.e., J interchain /J intrachain) of the parent system in accordance with long-standing theoretical predictions

Miller, Joel Steven

Narayan, K. S.

English

The University of Utah: J. Willard Marriott Digital Library

PHYSICAL REVIEW B VOLUME 46, NUMBER 10 1 SEPTEMBER 1992-11 Spin dilution in a ferromagnetic chain K. S. Narayan and B. G. Morin Department of Physics, The Ohio State University, Columbus, Ohio 43210-1106 Joel S. Miller The Du Pont Company, Wilmington, Delaware 19880-0328 A. J. Epstein Department of Physics and Department of Chemistry, The Ohio State University, Columbus, Ohio 43210-1106 (Received 4 February 1992; revised manuscript received 5 May 1992) We have systematically introduced spinless defects in the quasi-one-dimensional ferromagnetic system decamethylferrocenium tetracyanoethanide, [FeCp: J[TCNEj. The three-dimensional ordering tempera-ture Tc decreases rapidly with the concentration of spinless sites. The rate of decrease of Tc with con-centrate is in the order of the exchange spatial anisotropy (i.e., Jinterch,in / Jintrachain) of the parent system in accordance with long-standing theoretical predictions. Despite the apparent simplicity of the problem of a site-diluted one-dimensional (ID) ferromagnet, i.e., a magnetic system in which some magnetic spin sites are replaced by nonmagnetic spinless sites in increasing amounts, little experimental information is available. This may be attributed in part to the difficulty in finding magnetic compounds that can be diluted without drastic changes in the lattice symmetry or in the lattice parame-ters, leading to strong variations in the magnetic ex-change interactions. The magnetic dilution problem is a particularly simple form of the more general percolation or connectivity problem, which encompasses widely different phenomena such as branching processes, electri-cal networks, polymerization of chemical monomer units, clustering of lattice defects, etc. 1 Since the magnetic sys-tems can be investigated by a variety of different experi-ments, the various aspects of th percolation problem, in principle, can be advantageously studied in diluted mag-nets. In parallel, there is increasing interest in ID mag-netic chains, especially molecular-based systems. 2 Molecular electron transfer salts based on alternating metallocene donors and planar organic acceptors form a convenient system to study the effects of magnetic and nonmagnetic defects in a quasi-ID system. A variety of isomorphous donors with differing spin configurations are available enabling a parent compound to be doped through donor substitutions, thus making possible a sys-tematic study of changes in the magnetic phenomena. Using the molecular ferromagnetic compound [FeCpiHTCNE) as the parent compound, we have deter-mined the effects of dilution in a low-dimensional mag-netic system. We find that the three-dimensional order-ing temperature decreases with increasing defect concen-tration at a rate that is of the order of the spatial anisot-ropy of the system. Though site dilution has been studied for quasi-ID ferromagnetic systems where the interchain interaction is antiferromagnetic,3 here we study the site dilution in a quasi-ID ferromagnetic system where the in-terchain interaction is ferromagnetic. 46 [FeCPiHTCNE), which consists of S =+ [FeCpi )+. donors and S =+ [TCNE)-· acceptors, crystallizes with stacks of alternating cations and anions parallel to the long needle axis of the solution-grown crystals. 4 The donor [FeCpi) +. consists of two C5(CH3)5 rings 11" bond-ed to a FellI ion. The acceptor [TCNE)-· is essentially planar. The Lande g factors for [FeCPi)+· are gll-4.0 and g 1 - 1. 3, where the g II and g 1 refer to the g factor ob-tained for magnetic fields (H) parallel and perpendicular to the molecular axis. 6, 7 In contrast, the [TCNE) -. has g = 2 and is isotropic. The dc susceptibility (X), magneti-zation (M), specific heat (C), and neutron diffraction stud-ies show that the system is a three-dimensional ferromag-net below the transition temperature Tc ::::::4.8 K. 5- 7 The M-vs-H hysteresis curves at 2.0 K indicate that the ma-terial is a hard ferromagnet with a coercive field of - I kG. 6 The temperature-dependent specific heat has a cusp at the 3D ferromagnetic transition temperature with a crossover to primarily ID behavior at higher tempera-tures. 7 The magnetic properties of the individual chains have been described by a Heisenberg form spin Hamiltonian with a near-neighbor interaction and an orientational dependence of the [FeCpi )+. moment:6,7 H = -J 'f;.' [gDgAS iSi+l+gDgA(SiSi+I+SiSi+I») ~ II zz 1 xx yy , i where g[TCNE1=2.0 and is isotropic, and g~FeCP~l =3.9 and g ~Fecp: 1 = 1. 3. Substituting these values, the Hamil-tonian can be rewritten as H - 2J 'f;.' [SiSi+l+ (SiSi+I+SiSi+I») - - intrachain ~ z z r x x y y , i where r -0. 35. Hence even though Jintrachain is isotropic in spin space, the final Hamiltonian is anisotropic. Utiliz-ing Jintrachain = 25 K from fits of T> 50 K data to ID Heisenberg models,8 we estimate the value of Jinterchain' which is responsible for 3D ferromagnetic ordering, using 6195 © 1992 The American Physical Society 6196 NARAYAN, MORIN, MILLER, AND EPSTEIN 46 a simplified mean-field-theory resu1t:9 Tc - 1.5 (JintrachainJinterchain )1/2, i.e., Jinterchain IJintrachain -1 160. The replacement of some S = + [FeCp! ] +. sites by S =0 [CoCp!]+ sites in a chain causes sub-stantial changes in the magnetic properties. [FeCp!]x [CoCp!](! ~x)[TCNE] forms an isostructural di-lution series. Samples with compositions ( 1 - x) =0,0.045,0.077,0.085,0.145 were obtained in form of needlelike crystals. 1O The ratios of the Fe and Co in these samples were further verified using the Rutherford backscattering technique. The dc susceptibility and magnetization measurements were performed using a modified version of the Faraday technique where the field gradient varies between +(dB Idz) and -(dB Idz) and the change in force is monitored for cycles typically of 40-sec duration. The magnetometer has an absolute sensitivity of 10 ~ 11 emu. The measurements were carried out from 2.2 to 300 K. In order to confirm our experimental observations, we measured the ac susceptibility of these compounds using a mutual inductance bridge technique. For these experi-ments an alternating magnetic field is applied to a sample by means of a primary coil. Two oppositely wound secondary coils connected in series are used to detect a flux variation created when the sample is positioned in one of the secondary coils. A phase-sensitive detector an-alyzes the resulting signal obtained via a highly sensitive mutual inductance bridge, and produces an output volt-age proportional to the susceptibility of the sample. The mutual inductance bridge employs operational amplifiers and a Kelvin-Varley divider in a configuration providing high precision and low noise. The experimental setup was modified in order to be accommodated in a dilution refrigerator to achieve low temperatures down to 25 mK. That ferromagnetic interactions dominate at low tem-peratures for all the doped samples is demonstrated by the magnetic moment, which grows larger as the temper-ature decreases. The reciprocal of the experimentally measured spin susceptibility X·pin, for the highest and lowest doped samples, is plotted vs T in Fig. 1. To esti-mate a value for the intrachain exchange integral Jintrachain we fit the high-temperature data (T> 30 K) to the high-temperature Pade series expansion for the S = + Heisenberg model. 8 The value of Jintrachain obtained from the fit (Fig. 1) is approximately 23 K for the (l - x) = O. 045 compound, essentially the same as that of the undoped sample. The high-temperature series-expansion results for the infinite chain become less valid for the higher doping levels, and deviation from the pre-dicted behavior is observed. The values obtained for Jintrachain is not substantially different from that of the pure system. As the temperature is decreased the onset of spontane-ous magnetization, i.e., magnetization at zero applied magnetic field, is observed for ( 1 - x) =0.045,0.077,0.085 at temperatures 4.4, 3.8, and 2.75 K, respectively; see Fig. 2. The zero-field magnetization for (I-x)=0.045 is fit well to a curve M=(Tc-T)P, where {3 is the critical exponent. It is noted that the value of {3".,0.35±0.015 obtained for a Tc of 4.4 K lies between 150 "'" ;:j S Q) "-Q) 100 ..... o S >< 50 "-"" o o 50 100 150 200 250 T (K) FIG. 1. Inverse molar spin susceptibility of [FeCpi lx [CoCpi 10 -xl [TCNEl as a function of temperature, for (1- x)=O.045 t:,. and (1-x)=O.145 •. The solid curve is a fit to the high-temperature series expansion (Ref. 8) for FeCp· (1- x)=O.045 using gil 2 =3.9 and g TCNE=2.0. the 3D Heisenberg value of 0.37 and the 3D Ising value of 0.31. The deviation of M (T) below 0.9 Tc is not pro-portional to a simple T 3/2 behavior as predicted by spin-wave theory for a classical ferromagnet with lattice im-purities. 11 The different anisotropies and internal fields in the system have to be taken into account to predict the 2.0XI0· I I Abo ""' Q) .... 4 • (1 ~ x) = a 0 1.5XIO· S 4 t::. (1 ~ x) = 0.045 "-4 .. • (1 - x) = 0.077 rn tP" rn 4 ;l ~ 0(1 - x) = 0.085 (U 1.0X10· .. 4 0 ;l .\. S 'l!. • Q) 5.0XIO' r ~ 0 4 • ~ 4 0.0 L-.,-'ao-'C..1 • ..J. .. _~ • .... LA-.. ................................ --'---'--"---l 2 4 6 8 T (K) FIG. 2. Spontaneous magnetization of [FeCpi lx[Cocpi l(l-xl [TCNEl as a function of temperature. 46 SPIN DILUTION IN A FERROMAGNETIC CHAIN 6197 correct behavior. The M(H) curves for (1-x)=0.045,0.077,0.085 samples show substantial hysteresis at 2.3 K, characteristic of a hard ferromagnet. Hysteresis was not observed for the (1 - x) = O. 145 sam-ple at 2.3 K. The ac x( 100 Hz) for (1-x)=0,0.045, and 0.145 has a maximum at the ferromagnetic transition at 4.9, 4.4, and 0.75 K, respectively; see Fig. 3. The decrease in the dy-namic susceptibility below Tc is attributed to the hard-ness of the ferromagnet. These results are in agreement with the results of the dc susceptibility experiment. The dependence of Tc on the defect concentration is directly related to the dependence of the correlation lengths on temperature and the defect concentration. It follows that in such quasi-10 systems the nonmagnetic ions will break up the chains in finite segments and effectively reduce the correlation length, thereby reducing Tc' The variation of Tc with x has been studied for different lattice models and interaction Hamiltonians by such methods as Monte Carlo simulations, closed-form approximations (cluster methods), series expansions, and renormalization-group techniques. 12 These theories have a similar quantitative estimation of the decrease in the transition temperature at low impurity concentration lev-els. The common features of these theories are as fol-lows. \3 (i) For low concentration levels the Tc(x) curve de-pends on the spatial anisotropy (10, 20, or 30) as well as the spin dimensionality (Ising, XY, or Heisenberg). (ii) The initial decrease of Tc with increasing x is linear in x with the slope ~(Jintra/Jinter)' (iii) The critical concentration for xc' where Tc =0 is independent of the anisotropy and spin dimensionality, in contrast to feature (i), for 30 lattices coincides with the percolation limit, which is a purely geometric quantity, .. . 12 ..... • . ""' f/l • >< ... .", I:: "'", • : 6e 6 . .. ;:l 8 " • 0.0 0.3 0.6 0.9 1.2 ..0 I. T (K) III '-' • " >< CJ 4 -( " " • • "'4' " "If • • • •• •• \ •• 4 6 8 10 T (K) FIG. 3. ac susceptibility of [FeCp~ lx [CoCp~ 1(1-x)[TCNEl vs temperature for (1 - x ) = o. 0 ., 0.045 /:::,., and (1 - x ) = O. 145 • (inset). and the value of Xc is thus determined by the topology of the underlying lattice only. A typical phase diagram of Tc(x) using position-space renormalization-group technique for an Ising-like chain system shows that the Tc drops drastically to a small value as one approaches one dimensionality, i.e., as JinterchainlJintrachain tends to 0. 12,14 Tc(X) eventually van-ishes at the percolation concentration x: for the dimen-sionality corresponding to that of the coupled chains. In other words, the transition temperature decreases rapidly with increasing defect concentration when 10 correla-tions dominate, crossing over to a lesser variation with x at higher concentration of defects when the 30 couplings dominate. 12 The experimental curve of Tc(x) obtained for [FeCpilx [CoCpi ](I-x) [TCNE], Fig. 4, follows the trend predicted for diluted quasi-10 magnets. (For compar-ison, the inset of Fig. 4 shows the typical predictions 14 for Ising systems of different spatial anisotropies.) We obtain an average slope of ~ 7.0 for the experimental curve, im-plying (noting that there are two spins per [FeCPiHTCNE] repeat unit) JinterchainlJintrachain -1/14. This value is in good agreement with the value of Jinterchain 1 Jintrachain obtained from the knowledge of Tc and Jintrachain of the undoped [FeCpiHTCNE]. The re-duced value obtained from the slope of Tc(x)/Tc(O) is ex-pected in accord with the calculations. 14 A dimensionali-ty crossover to a 30 percolation behavior is not observed as the [FeCpi ] +. ion concentration is decreased to x =0.855. A higher spinless site concentration may be ~ .-< E1 -:g: e-:' 1.0 0.8 0.0 x 0.6 0.4 0.2 ,/' , ? , , t , , , , · · , ~ · , · · · , · · · , · · , , I . , . o O. 0 LLL..L..JLl...J'-'--l---<-l....L-l--'--l....L..LJ-J.--L..l.--'---L--'---L...L..1.....LJ 0.0 0.2 0.4 0.6 0.8 1.0 x FIG. 4. Tc(x)/Tc( 1) vs x for [FeCpnx [CoCp~ 1o-x)[TCNE1. The inset shows the typical theoretical calculation assuming Ising-spin nature for different spatial anisotropies and values of 'Y. The ratio of interchain to intrachain coupling is 1 (A), 0.1 (B), 0.02 (C), and 0.005 (D) (Ref. 14). 6198 NARAYAN, MORIN, MILLER, AND EPSTEIN 46 necessary to observe the onset of the crossover, which will be indicated by a change of slope in Tc (x ). These experiments illustrate and confirm the long-standing theoretical predictions concerning effects of spin dilution in quasi-ID molecular ferromagnets. These re-sults are in accord with the absence of 3D magnetism in high spin-oligomeric systems. IS Systems with small (JinterchainIJintrachain) need to have long chains and few IL. J. de Jongh, Magnetic Phase Transitions, edited by R. J. Elli-ot and M. Ausloos (Springer-Verlag, New York, 1983). 2M. Takahashi, P. Turek, Y. Nakazawa, M. Tamura, K. No-zawa, D. Shiomi, M. Ishikawa, and M. Kinoshita, Phys. Rev. Lett. 67, 746 (1991); J. L. Pailaud, M. Drillon, A. De Cian, J. Fischer, R. Weiss, and G. Villeneuve, ibid. 67, 244 (1991); S. H. Glarum, S. Geschwind, K. M. Lee, M. L. Kaplan, and J. Michel, ibid. 67, 1614 (1991). 3K. Takeda and J. C. Schouten, J. Phys. Soc. Jpn. 50, 2554 (1981). 4J. S. Miller, J. C. Calabrese, H. Rommelmann, S. Chittipeddi, J. H. Zhang, W. M. Reiff, and A. J. Epstein, J. Am. Chern. Soc. 109,769 (1987). 5J. S. Miller, A. J. Epstein, and W. M. Reiff, Science 240, 40 (1988). 6S. Chittipeddi, K. R. Cromack, J. S. Miller, and A. J. Epstein, Phys. Rev. Lett. 58, 2695 (1987). 7 A. Chakraborty, A. J. Epstein, W. N. Lawless, and J. S. Miller, spinless defects to observe intrinsic Tc' We thank K. M. Chi for assistance with the synthesis. K.S.N. acknowledges M. Kaycheck for Rutherford back-scattering analysis and H. Baddar for very-Iow-temperature ac susceptibility measurements. This work was supported in part by DOE DMS Grant No. DE-FG02-86BR45271. Phys. Rev. B 40, 11422 (1989). 8G. A. Baker, Jr., H. E. Gilbert, J. Eve, and G. S. Rushbrooke, Phys. Lett. 25, 207 (1967); T. Obokata, I. Ono, and T. Oguchi, J. Phys. Soc. Jpn. 3, 516 (1967). 9S. H. Liu, J. Magn. Magn. Mater. 82,294 (1989). IOElemental analyses were performed at Oneida Research Labo-ratory, Whitesboro, New York 13492. lIF. Keffer, in Handbuch der Physik, edited by S. Flugge (Springer, Berlin, 1966), Vol. 18, Part 2. 12R. B. Stinchcombe, in Phase Transitions and Critical Phenom-ena, edited by C. Domb and J. L. Lebowitz (Academic, Lon-don, 1983), Vol. 7. 13R. Burriel, A. Lambrecht, R. L. Carlin, and L. J. de Jongh, Phys. Rev. B 36,8641 (1987). 14A. Mujeeb and R. B. Stinchcombe, J. Phys. CIS, 3163 (1982). 15See, for example, Magnetic Molecular Materials, edited by D. Gatteschi, O. Kahn, and J. S. Miller (Kliever Academic, Bos-ton, 1991). 

Spin dilution in a ferromagnetic chain

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Spin dilution in a ferromagnetic chain

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