Single .. crystal ac susceptibility measurements on [Co(NH 3 )s][CuCls], a 3D, S=1/2 Heisenberg antiferromagnet

Single-crystal ac magnetic susceptibilities of [Co(NH 3 )..,] [CuCls l along the three crystallographic axes in the temperature range from 1.1 to 90 K are presented, The magnetic behavior is characteristic of a three-dimensional antiferromagnet, its ordering temperature being at Tc = 3.8 K. Susceptibilty data can be fit to a Heisenberg S = 1/2 simple cubic model using high-temperature series expansions extrapolated with Pade approximants. Good agreement is found for an exchange constant J / kB = - 3.13 K and values of g factor go = 2.09, gb = gc = 2.04, G,b, and c being the crystallographic axes. This result makes [Co(NH 3)6] [CuCI s) one of the few examples ofa 3D antiferromagnetic Heisenberg S = 1/2 model. The magnetic behavior below Tc indicates the existence of crystallographic domains due to the structural transition from cubic to tetragonal symmetry that the system has at about 280K.


I. INTRODUCTION
Bimetallic compounds have been shown to exhibit very interesting magnetic properties. 1 ,2 Moreover, coordination compounds of copper(II) have been of continuing interest for several reasons. Copper (II) possesses one unpaired electron irrespective of the local geometry and therefore always has spin S = 1/2. Since the ground state in an octahedral complex is 2 E g , the orbital degeneracy is usually resolved by the Jahn-Teller effect and, as a consequence, the coordina~ tion sphere around the copper ion is generaily distorted.
Although many copper(H) compounds exhibit such structural anisotropy, they nevertheless display relatively little magnetic anisotropy. The orbital contribution is largely quenched, the g-value anisotropy is typically not large, about 5% or 10% (g always of the order of 2.0-2.3), and being a S = 112 system there is no zero-field splitting to complicate the situation. This leads copper(H) to be one of the best ions, after manganese(II) and iron on), in providing magnetically ordered compounds with only weak anisotropy. 3 Another feature of copper magnetochemistry is the high tendency the ion exhibits for ferromagnetic interactions. Moreover, there are few copper compounds which order three-dimensionally and copper is better known as a source of dimers, linear chain, and planar magnets. 4 It is therefore of some interest to report here on the mea- Both single-crystal x-ray and neutron diffrac~ion data 5 show that the substance crystallizes at room temperature in the cubic space group Fd 3c with a = 21. 992 A. The environment of the cobalt ion is octahedral and the copper ion is situated in the center of an axially compressed trigonal bipyramid with Cu-Cl(ax) = 2.301 A and Cu-Cl(eq) = 2.409 A.
At about 7' ., = 280 K the system undergoes a structural phase transition as deduced from differential scanning calorimetry measurements. 6 Powder diffraction patterns in the temperature range from 300 to 12 K have been recorded. 7 They indicate the existence of a tetragonal splitting of the cubic refiexions below the transition temperature. In the low-temperature phase a tetragonal unit cell, presumably belonging to space group 14 1 /acd and with lattice parameters at 14 K of a = 15.507( 1) A, c = 22.018 (2) A, and c/ (2 112 a) = 1.004, is found.
Analysis of EPR spectra measured? in the temperature range between 300 and 4 K shows that the g tensor changes from cubic to tetragonal at about 280 K. The g anisotropy still increases with decreasing temperature below Ts and reaches its final value only at 120 K. This experimental result and the fact of the strongly anomalous temperature ellipsoids of the equatorial chlorine ligands has suggested that the stable static geometry of the CuCI~polyhedra is a square pyramid. In the high-temperature phase the axially compressed trigonal bipyramid exists as the dynamic average of three square-pyramidal conformations. In the lowtemperature phase the stable geometry of the CuCl~ -polyhedra, a static one, is a square pyramid, in which the apical bond is appreciably longer than the equatorial distances. The cooling procedure from 298 K to temperatures below Ts leads to extensive twinning and hence to a three-domain pattern in the EPR spectra.
In order to verify the structural transition, differential scanning calorimetric measurements were made with a Perkin-Elmer DSC-2 instrument in the range 105-310 K. They show a phase transition at Ts = 278.0 K when heating and a T" = 277.8 K when cooling, in reasonable agreement with Ts = 280 K previously reported. 6 Magnetic ac susceptibility measurements in the range 4.2-90 K were conducted in a computer-controlled susceptometer already described,9 on a single crystal of 56.70 mg. Data between 1.1 and 4.2 K were taken in another ac susceptometer. 10

III. RESULTS AND DISCUSSION
Susceptibility data made with the alternating magnetic field paranel to the three four-fold axes are shown in Fig. 1. Measurements performed along two of the three axes (named band c) overlap each other within experimental error. The data show a smooth increase in the susceptibility as temperature decreases, present a maximum at about 7.5 K, and then drop more rapidly. The out-of-phase component of the susceptibility is negligible over the whole range of temperature. The behavior is characteristic of that of a threedimensional antiferromagnet, its ordering temperature being Tc = 3.8 K as calculated from the maximum value of (aX I aT). Susceptibility data can be fit by a Heisenberg S = 112 simple cubic model using high-temperature series expansions extrapolated with a [515} Pade approximant, II as shown in Fig. 2. Good agreement is found for an exchange constantJ IkB = -3.13 Kand values ofg factor ga = 2.09, gb = gc = 2.04, a, b, and c being four-fold crystallographic axes. These results are compared with related systems in Table I. .. A striking feature in the data represented in Fig. 1 is that no easy axis for antiferromagnetic alignment is observed. However, the experimental decrease in X is so large that it is not consistent with the behavior expected for Xl' For instance, we may estimate the value for Xl at T = 0 expected on the basis of spin-wave theory from the relation 15 In this expression z = 6 for a simple cubic lattice; AS and e denote the zero-point spin reduction and the ground-state energy shift, respectively. Values for these quantities have been given by Semura and Huber l6 for the simple cubic Heisenbergmodel, namely, AS = 0.078 ande = 0.58. TakingJ I kll = -3.13 one calculates Xl (T= 0) = 0.0155 for g" = 2.09 and 0.0163 for gl, = gc = 2.04, wen above experimental values of 0.011 for the a axis and 0.008 for the h,c axes. However, susceptibility values are not far from those expected for a powdered sample, for X( T = 0) ~2/ 3X ( T = T max) in both sets of data. A logical explanation is that tetragonal distortions could lead to a three-domain structure which prevents the establishment of a macroscopic easy axis and thus a weighted average of XII and Xl is ob- tained. The conclusion corroborates above mentioned results obtained from EPR measurements. 7 A simple analysis of the calorimetric data of the compound also supports a model in which degrees offreedom in the position of the CuCl~unit change from 3 to 1. The entropy content of the structural transition can be roughly estimated as ASjR2!O.96, as calculated from the ratio aHsIT" a value reasonably close to in 3. Therefore, the g values calculated from the fitting of the susceptibility measurements along directions parallel to the (room-temperature) crystallographic axis have to be understood as an average over a distribution of crystallographic domains. That would explain the apparent discrepancy between the g values calculated here and those measured by EPR at 120 K, gil = 2.28 and gl = 2.07. The effects of crystallographic domains on the susceptibilty data have also been observed in [Cu(C s H s NO)6](BF 4 h. 17 The fact that the susceptibility along the direction parallel to the a axis of [Co(NH 3 )6] [CuCI 5 J slightly diifers from the data along the two other directions, band c, could indicate that the proportions of the three domains were not the same, as found in the cubic perovskite NH 4 MnC1 3 . 18 At this point, more structural data at low temperature would be necessary in order to have a better understanding of the tetragonal phase. Heat capacity measurements of the magnetic phase and susceptibility-field dependence studies in the antiferromagnetic phase are in progress. 19 search in Chicago has been supported by Grant No. DMR· 8515224 from the Solid State Chemistry Program, Division of Materials Research of the National Science Foundation. Cooperative work has been supported by grant CCB-8504/ 001 from the American-Spain Joint Committee for Technical and Scientific Cooperation. One of us (M. C. M.) wants also to acknowledge a student fellowship from the Ministerio de Educacion y Ciencia.