Chemical Physics54 (1980) 109-li3 0 North-Holland Publishing Company

MAGNET~CPROPERTIESOFTHEQUASIONE-DIMENSIONALHEISENBERG LINEARCHAINANTIFERROMAGNET:MANGANOCENE

E. KijNIC;, V.P. DESAI Institut fur Physikalixhe und Theoretfxhe Chemie, Universittit Erlangen-Nihberg, 0.8520 Erlangen, West Germany

B. KANELLAKOPULOS and R. KLENZE Heis!;e Chemlc, Kern Jorschungszentnrm Karlsruhe, Da 7500 Karlsruhe, West Germany

Received 16 July 1980

Mlogne1.i~ susceptibility mcasurcmcnts on the rhombic form r)f manganoccnc, Mn(CsHs)a, arc rcporteil bctwcen 0.94 and 297.5 K. A pronouncod minimum in the l/xc,o”versus T cu:ve is located at Tmin = 141 f 1 K. The rl;sults arc well reproduce’d by the solution of Fisher tc tkc quasi one-dimensio:-al Heisenbcrg linear chain modified such as to include intcr- chain intemction for J/k = - 14 K,g = ; :/ o = -5 K. A less accurate approximation to the experimental results has been achieved i:n terms of the pair model (J/k = -22.5 K,g = 2.0). The results arc in excellent agreement with the zigzag! chain structure of CsH5 -Mn units reported for the compound.

I. Introduction

The magnetism of manganocene, Mn(cp); where cp = CsH;, was investigated as early as 1956 by Wilkinson et al. [ 1 J as well as by some other workers [2,3 1. According to these studies, the effective mag netic moment of MII(C~)~ at 294 K in ether or ben- zne solution is close to the spin-only value of 5.92 BM for a ‘A, (aI c!i:e:) ground state. Solid Mr~(cp)~ has been obtained in two crystalline forms: the rhom- bic modification (amber-brown) which is stable up to the transition temperature of 432 K, and the moni- clinic modific.ation (pink) which is formed above 432 K and up to the melting point at 445 K. The mono- clinic form as well as the melt above 445 K show essentially the spin.only moment, whereas for the rhombic form,, a more complicated temperature beha- viour was found. Thus between 77 and 432 K, the magnetic susceptibility of solid Mn(cp)l shows a maximum which was reported to be situated at 134?2K [I:/ orat 15O~lOK[3].Sinceforan8%

solid solution of Mn(cp), in Mg(cp)2 which is pink, &rr = 5.94 BM over the temperature range 77 -438 K. the anomalous behaviour of the undiluted Mr~(cp)~ was attributed to antiferromagnctism [I]. A similar situation was found shortly thereafter for the related I,]‘-dimcthyl~mangan~:nc, Mn(Mecp)o [4j.

The discussion concerning the ground state of mamganocene was taken up again when Switz:r ct al. [S] reported the measurement of the magnetism of Mn(Mecp)z in toluene solution by the NMR method of Evans. The effective magnetic moment was found to increase from an initial p?rf = 3:23 BM at 214 K to pen = 4.77 BM at 371 K with a susceptibility

maximum around 3 10 K. Based on supporting EPR results it was concluded that a thermal high-spin * low-spin equilibrium is involved, the separation between the 6A,(a,e:e$)and the *Ez(a:e:)grounJ states being estimated to 630 cm-‘. From the analy- sis of HIeI photoelectron spectra it was demonstrated [6] that, although gaseous Mn(cp)z is a high-spin species, the Mn(Mecp)Z vapour exists as a mixture ot

110 E. K6nig et al. /Magnetic properties of manganocene /-

tbk hi,&-sin and low-spin configurations. Moreover, the cryogenic range were measured using a gold/iron versus chrome1 thermocouple and checked by noting the vapour pressure of helium. The thermocouple was calibrated against a Pt or Ge resistor placed in the position of the sample.More details have been given elsewhere [ 1 I]. All measurements were performed at six different field strengths, viz. 3.50,5.55,8.60, 10.90, 12.00 and 13.10 kG. The diamagnetic correction applied to xm is -104 X 10e6 cgs mol-’ and the effective mag- netic moment was obtained according to prfr = 2.828 (~2” T)“‘, where x:,“” is the corrected molar magne- tic susceptibility in cgs mol-’ and T is the temperature in K.

.. detail& EPR measurements by &meter et al. 173 showed that both Mn(cp)s and Mn(Mecp)a may be found in the high-spin (‘Ar) or the low-spin (ZEa) ground state, depending on the molecular environ- ment. It was suggested that the anomalous magnetic behaviour of undiluted Mn(cp)* should be attributed to a temperature dependent high-spin + low-spin equi- librium [7]. This interpretation seemed reasonable since ligand field calculations.indicated that Mn(cp)a should be c!ose to the cross-over point between the 6Ar and *b ground states [8].

However, a very recent X-ray structure investiga- tion of the rhombic modification of Mn(cp)* clearly shows that this species forms a polymeric chain struc- ture with a zigzag arrangement of CsHsMn units which are bridged by additional CsHs-rings [9,10]. In view of this result it seemed worthwhile to reinves- tigate the magnetism of solid Mn(cp)a over a range of temperatures.

In the present s:udy, we have therefore carefully remeasured the magnetism of Mn(cp)s. through the region of abnormal behaviour, the range of measured susceptibilities being extended down to 0.94 K. The results were compared with calculations for a one- dimensional (1-D) Heisenberg linear chain as well as for some other models of antiferromagnetic type interactions and the values of the exchange constants J were determined.

3. Results of magnetic measurements

A representative selection of the experimental mag- netic data is presented in table 1. Between 0.94 and 3.39 K, the data obtained for six different strengths (H= 3.50 to 13.10 kC) are listed individually. At and

130

120

2. Experimental 110

The preparation of manganocene was accomplished according to methods published in the literature [l]. The product was purified by extraction with benzene, its identity and purity were checked by chemical ana- lyses and by routine physical measurements..

Magnetic susceptibilities were measured over the range 0.94-297.5 K by the Faraday method. The equipment employs a 10 inch electromagnet (Bruker- Physik) with Henry-type pole caps, an electrical micro- balance (Sartorius type 4102) and the required cryo- genic equipment. Temperatures below 4.2 K were achieved by pumping on the helium reservoir with a Roots pump (Leybold-Heraeus type WS-250, suction power 324 m3/h), all connecting pipes and flanges being of 65 mm diameter or larger. Temperatures in

100

90

80

0 100 200 T.K 300 Fig. 1. Inverse molar magnetic SusceptibiIity for hIn(cp)a as a function of temperature. Esperimental data, indicated by squares, CUN~S are ukuhted. Solid curve: Heisenbcr_e linear cbnin [LT. (6), J/k = -14 K,g = 2.0.0 = -S K]. Dashed curve: Qme with 0 = 0. Dotdash curve: Pair model [eq. (4). J/k = -23.5 K,g = 2.01. Dotted cu:ve: Correlated effective field method {eq. (5),J/k = -14.5 K.g= 2.01.

E. K&zig et al. /Magnetic properties of manganocene 111

Table’ 1 Magnetic susce tibilities xg and x” a) and effective mwnetic

bti for Mn(cp);! c) * 5

moment pefr

Table 1 (continued)

H T 106xg 106Xc,D” &ff (W (U (ckssh) (cgslmolc) (BM)

3.50 5.55 8.60

10.90 12.00 13.10 3.50 5.55 8.60

10.90 12.00 13.10 3.50 5.55 8.60

10.90 12.00 13.10 3.50 5.55 8.60

10.90 12.00 13.10 3.50 5.55 8.60

10.90 12.00 13.10 3.50 5.55 8.60

10.90 12.00 13.10

0.94

1.26 1.30 1.34 1.38 1.42 1.48 1.62 1.64 1.66 1.68 1.70 1.72 2.01 2.02 2.03 2.04 2.05 2.06 2.89 2.90 2.92 2.94 2.96 2.98 3.33 3.34 3.35 3.36 3.37

3.39

4.20

4.5 1 4.98

5.64

6.69 7.47

10.22 19.90 33.05 44.90 54.30 65.30 71.45 81.38 88.40

32.486 32.072 31.750 31.634 31581 31.489 32.283 32.720 31.978 31.7?0 31.664 31.521 32540 31.972 3 1.668 31.576 31.594

31.509

32581 31.961 31.709 31.673 31.638 31.577 32.608 32.050 31.825 3 1.802 31.773 31.757 32.689 32.095 31.900 31.910 31.960 31.906 37.277 37.065 37.470 37.161 36.855 36.612 37.412 39.587 42578 45.115 46.971 48.885 50.789 51.362 52.312

6118.1 0.214 6041.4 0.213 5981.8 0.212 5960.3 0.212 5950.5 0.212 5933.5 0.211 6080.5 0.248 6161.4 0.253 6024.0 0.254 5985.5 0.257 5965.9 0.260 5939.4 0.265 6128.1 0.282 6022.9 0.281 5966.6 0.28 1 5949.6 0.283 5952.9 0.284 5937.2 0.286 6135.7 0.314 6020.9 0.312 5974.2 0.311 5967.6 0.312 5961.1 0.313 5949.8 0.313 6 140.7 0.377 6037.4 0.374 5995.7 0.374 5991.4 0.37s 5986.1 0.376 5983.1 0.377 6155.6 0.405 6045.7 0.402 6009.6 0.401 6011.4 0.402 6020.7 0.403 6010.7 0.404 7005.0 0.485 6965.8 0.501 7040.7 0.530 69835 0.56: 6926.9 0.609 6881.9 0.641 7030.0 0.758 7432.7 1.088 7986.4 1.453 8456.0 1.743 8799.6 1.955 9 154.0 2.186 9506.5 2.427 9612.5 2.501 9788.4 2.631

H T

(kc) (Q ~-

106xg 1 06Xgrr lwf (csk) (c&mole) (BM!

98.70 53.526 10013 2.811 107.8 54.406 10176 2.962 118.2 55.002 10286 3.119 122.3 55.127 10310 3.176 129.8 55.283 10338 3.276 136.5 55.364 10353 3.362 143.4 55.387 10358 3.447 150.2 55.279 10338 3.524 155.8 55.157 1031s 3585

165.1 54.893 10266 3.682

172.8 54.591 10210 3.756

184.4 54.025 10106 3.861

199.2 53.241 9960.4 3.983

220.5 51.819 9697.1 4.13s

236.5 50.565 9465.0 4.231

249.4 49.754 9314.9 4.310

271.2 48.102 9009.0 4.420

279.8 47.423 8883.3 4.459 280.5 47.399 8878.9 4.463

295.0 46.317 8678.6 4.525

297.5 46.201 8657.1 4.538 -

‘) Molecular weight dl= 185.128 au. diamagnetic correction

xm dirr = -104 X lo+ c&mole, experimental uncertainty between 0.2 and 0.970, dependent on temperature.

b).~eff= 2.828 (xz’r T)"', experimental uncertainty approsimately kO.005 BM.

‘) Between 0.94 and 3.39 R, the values listed apply to the field strengths H = 3.50 to H = 13.10 kG individually (sample weight 82.359 mg). At and above 4.20 K, the average values for the sis fields arc given (umple weight 19.102 mg).

above 4.2 K, the average values for the six fields are given. The resuIts up to 3.39 K are part of data set 1 for a sample of 82.359 mg which sample was mea- sured up to 289.8 K (higher temperature data not listed), whereas the data at and above 4.2 K are from set 2 for a sample of 19.102 mg. The data are also dis- played, as far as possible, in fig. 1 iri terms of the inverse molar magnetic susceptibility, l/xEX’.

From fig. 1 it is seen that a broad minimum appears in the l/xm “lT versus T curve which has been previously attributed [l] to an antiferromagnetic type of interaction. On the basis of the present dat;, this minimum is at Tmin = 141 f 1 K. There is prac- ticaliy no detectable field dependence down to 0.94 K, as is evident from the data of table 1.

112 E. KGnig et al. /Magnetic properties of manganocene

4. Theoretical calculatio as

From the available Y-ray structure of tf.e rhombic form of Mn(cp), [9] it is known that the manganese ions form a zigzag chain with bridging CsFIs-rings. In addition, based on soluti m magnetic studies, EPR and photoelectron spectra, the Mn2+ ions may be assumed to be in the high-spin “AI (a, ezej) ground state. The hamiltonian for the present problem may then be written as

(1)

As is well known, a general solution for the hamilto- nian of eq. (I) is not available. Therefore, in what follows, we will consider the results of calculations for a few special models and compare these with the experimental magnetic data for Mn(cp)z. In addition, we assume g = 2.0, since this is a very good approxi- mation for the S = 4 Mn2* ion.

4.1. Tk isolatd puir model

We consider the chain to be approximated by an assczmbly of isolated pairs with the hamiltonian

‘31” --w&s, ’ ,s2 -g&Jl(Sf + s,“)l . (2)

nx resulting isusceptibility irgiven by [I:!]

li:m = (N@cT)

C sS’(S t 1)(2S’ t I) exp[JS’(S’ + i.)/kT] , (3) x ._,_^.. _--* “.._..7‘r--

C (2; + 1) exp[JS (S -t l)/kT]

whcrc the summations extend over S’ = 0, I, 2, . . . . 5. For the case of S = $ one derives readilly

XIII =I (pis2.Il@T)

x x + 5x3 t 14x” + 3ox’O + 55X’S ------- I +3x+5x3+7x6 +9.Xx’“+ 11X’S’ (4)

where x = 2]J]/kT. The best approximation to the map netic data for Mn(cp)a hos been achieved for J/k = --X.5 K and g = 2.0 (cf. fig. 1).

Keccntly, an Improved molecular field method, known as the correlated effective field, has been pro. ,I bscd 1 I,!. Wcn upplied to an antifcrromagnetically

coupled chain, the method gives the magnetic suscep- tibility as

Xm = (N&/k)g%(S + I)(3 [#SCS + 1)lJI

+ [($g%(S + 1)]5])2 + T2]“2]}-r. (5)

The calculated inverse molar magnetic susceptibility does not reproduce the observed minimum of the UXEm versus T curve. In the Iimit of high tempera- ture, the best approximation has been achieved for J/k = -14.5 Kandg = 2.0 (cf. fig. I),

4.3. The Heisenberg linear chain

The solution of Fisher to the hamiltonian eq. (1) for the Heisenberg linear chain for an antiferromag netic nearest neighbour interat 1 may be shown to follow, in the classical limit (i.e. for S + a), as [ 141,

Xm _ ~s2/J$(S + 1) [I - &)I 3k(T-- II+ ’

(6)

where

U(Y) = coth($-‘) - $v

and

(7)

y = 3kT/g2S(S + 1)lJl . (8)

In eq. (6) a correction factor 0 has been introduced in order to empirically account for any possible inter- chain interaction. In the present study, the closest approximation to the observed magnetic data on Mn(cp)2 has been achieved with ;n this model if ,1/k = - 14.0 K, B = -5 K and g = 2 .O are used. The result is far less adequate if the interaction between chains is neglected by setting 0 = 0 (cf. fig. 1).

5. Discussion

The experimental data of thi:; investigation differ somewhat, although not considerably, from those reported by Wilkinson et al. [ 1 J. In contrast to the earlier measurements, no field dependence was datec- ted for the samples of the present study. Presumably, the differences are due to some unidentified impurity which may have slightly affectc d the previously obtained magnetic data. ‘The essential feature, the minimum in the temperature curve for l/x:,““, is well

E Kiinig et al. /Magnetic properties of munganocerw 113

reproduced, although now 7’min = 141 F- 1 K. It should been found only for sample 2 but not l‘sr sample I be noted that the present data extend well below the

‘77 K of the first study [ 11, in fact down to 0.94 K. and, therefore, it does not extend into the magnetic data collected below 4.2 K (cf. table 1). @paJeIldy .

However, the low-temperature data do not provide the observed deviation from the calculated values is any additional information with respect to the mag- a spurious effe;t which will not be considered any netic interaction discussed here. further.

In view of the observed polymeric chain structure of rhombic Mr~(cp)~, the close reprod:l;!ion of the measured magnetic data by the quasi oae-dimensional Hrisenberg linear chain is most gratifying. In eq. (6), a correction term 0 = -5 K is required which demon- strates the limited applicability of the simple linear chain model and the importance of the interaction between the chains. Even after applyir,.i- ‘“me correction. a slight difference between experimem, Id calcula- ted values remains, cf. fig. 1. This deviation may be tentatively attributed to the very apprriximate treat- ment of the three-dimensional problem which is rele- vant for the actual Mn(cp)n crystal and for which a genera! solution is not known.

Acknowledgement

The authors appreciate fin:!ncis! support hy the Deutsche Forschungsgemeinschaft i,nb the Fontis J~I

Chemischen Industrie.

Refereaces

[ 1 I (i. Wilkinson, I:./\. Cotton and J.M. Ilirming! ,tim. I. 111~~:. Nucl. Chcm. 2 (I 956) 95.

[ 2 1 13.0. I:ischcr and H. Lcil~lin~er, %. Naturfur~_%. IIII~

An alternate interpretation of the experimental data has been achieved by applicalit:? of the indepen- dent pair model, viz. eq. (4). The result displafld in fig. 1 is not that surprising when it is appreciated that the arrangement of the individual chains in rhombic Mn(cp)2 is zigzag rather than strictly linear. The inde- pendent: pair model can be applied if one considers sach a chain as being built up of dimers, and if one assumes a strong exchange Interaction within a dimer and a negligible interaction between the dimers. In fact, chainlike compounds well approximated by the pair model have been reported in literature, viz., e.g. CU(NO~)~ - 2.5 Hz0 [ 151 and certain methylpyrazine *:omplexes of copper (II j [I 61.

(1955) 353.

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