G. Mennenga

Specific heat and susceptibility of the 1-dimensional S = 12 Heisenberg antiferromagnet Cu(Pyrazine) (NO3)2. evidence for random exchange effects at low temperatures

Abstract Magnetic susceptibility and specific heat data are presented on the S = 1 2 antiferromagnetic Heisenberg chain Cu(pyrazine) (NO 3 ) 2 in the range 0.05 K T The intrachain exchange is obtained as J / k B = -5.20(5) K by a theoretical fit to data. No evidence for a transition to a 3-d ordered state could be detected down to the lowest temperatures (corresponding to k B T /| J | ≈ 0.01). The specific heat data provide a beautiful demonstration of the predicted linear chain low-temperature behaviour, c / R = k B T /3| J |, over one decade in temperature. Superimposed upon the behaviour for the uniform antiferromagnetic chain, the data show contributions that can be interpreted in terms of a random exchange model. It is argued that these arise from random lattice imperfections (defects) which apparently break up the chains into weakly coupled finite segments with an average length of about 200 lattice sites. The segments with an odd number of spins act as a system of highly diluted, weakly interacting, spins 1 2 . The contributions due to defects may predominate the behaviour of the susceptibility and (to a lesser extent) the specific heat at very low temperatures, in case the interchain interactions are sufficiently small. In particular, the random defects will suppress the occurence of 3-d ordering between the chains. Furthermore, they lead to random exchange phenomena similar as observed in other quasi 1-d antiferromagnetic systems. It is suggested that many of the known examples of random exchange antiferromagnets can be explained in terms of the random defect model.

Field dependent specific heat study of the dipolar Ising ferromagnet LiHoF4

Abstract We present specific heat measurements on a spherically shaped single crystal of the dipolar Ising ferromagnet LiHoF4 for various values of a magnetic field applied along the c-axis (easy axis). The measurements in zero field cover the range 0.06– K, enabling the separation of the contributions to the specific heat due to the hyperfine interactions, to the T2 singlet state at about 10 K, and to the phonons, from the longe-range magnetic anomaly at Tc = 1.530(5) K. The zero-field specific heat anomaly is analysed assuming both dipolar and exchange interactions between Ho3+ ions to be present. The zero-field specific heat appears to have the same value when measured for different sample shapes, in agreement with the theoretical prediction by R.B. Griffiths that the free energy in zero field of dipolar magnets should be independent of the shape of the sample in the thermodynamic limit. The shape of the specific heat curve is discussed, and a comparison with the dipolar Ising ferromagnet LiTbF4 is made. The in-field specific heat measurements show that upon increasing the applied field Ha the ordering temperature Tc(Ha) decreases, as does the height of the specific heat anomaly. Above a critical field Hc = Hdem, where Hdem is the demagnetizing field, magnetic ordering can no longer be discerned. Below Tc(Ha) the specific heat appears to be independent of the applied field Ha up to Ha = Hc, confirming another prediction by Griffiths.

Low temperature magnetic properties of the bimetallic compounds [Co(C5H5NO)6](MX4) (M = Co2+, Zn2+; X = Cl-, Br-)

Abstract We have measured the specific heat and suceptibility of the compounds [Co(C 5 H 5 NO) 6 ] (MX 4 ) (M = Co, Zn; X = Cl, Br), which are all isostructural and monoclinic. The data show that two magnetic subsystems are present in the Co/Co compounds. The Co 2+ ions on the octahedral positions of the chlorine compounds exhibit antiferromagnetic ordering at T c = 0.95(1) K, the Co 2+ ions on the tetrahedral positions remaining paramagnetic down to at least 0.04 K. The paramagnetic ions appear to experience two different molecular fields from the ordered Co 2+ ions. The behaviour of the bromine compounds is similar, the ordering temperature being about 0.65 K. Both chlorine compounds are apparently canted antiferromagnets. The bromine compounds show compensated antiferromagnetism.

A comparative study of the magnetic ordering specific heats of four S = 12 dipolar magnets: LiRF4 (R = Er, Dy, Ho, Tb)

Abstract Low temperature specific heat data are presented on LiRF 4 with R = Er, Dy, Ho, and compared with published results for LiTbF 4 . The compounds LiHoF 4 and LiTbF 4 are dipolar Ising ferromagnets, ordering at T c = 1.530 and 2.885 K, respectively, whereas LiErF 4 and LiDyF 4 are dipolar XY antiferromagnets, with T c = 0.380 and 0.605 K. The shapes of the specific heat anomalies are compared. The different types of dipolar ordering can be understood on the basis of the crystal field anisotropy for the rare earth electronic ground state, which is a doublet (or pseudo-doublet) in all four cases, with g ∥ ⪢ g ⊥ for R = Ho, Tb, and g ⊥ ⪢ g ∥ for R = Er, Dy. The energies involved in the magnetic ordering as obtained from integration of the specific heat curves are found to be in good agreement with the lowest-energy configurations predicted by Misra and Felsteiner for these dipolar systems.

Two magnetic subsystems in bimetallic [Co(C5H5NO6)][COCl4]

The specific heat and susceptibility of the title compound and of [Co(C5H5NO)6][ZnCl4], which are isostructural and monoclinic, have been measured. Two magnetic subsystems are present in the Co/Co compound, the Co2+ ions on octahedral positions exhibiting antiferromagnetic ordering at Tc = 0.95(1) K, the Co2+ ions on tetrahedral positions remaining paramagnetic down to at least 0.04 K. The paramagnetic ions experience two different molecular fields from the ordered Co2+ ions.

Specific heat measurements on the site-diluted dipolar ising ferromagnet LiTbpY1−pF4

Abstract Specific heat measurements on the diluted dipolar ferromagnet LiTb p Y 1− p F 4 are presented for 0.2⩽ p ⩽1.0. The measured critical temperatures T c ( p ) agree with those obtained from previous susceptibility and magnetization measurement. The shape of the specific heat curve is found to be largely influenced by the singlet-singlet separation in the ground state pseudo-doublet, which may explain why below p ≈ 0.325 a λ-anomaly in the specific heat curve can no longer be discerned. For a sample with p = 0.20 we find no evidence of an enhanced nuclear spin ordering, as was suggested by Folkins et al.

Specific heat studies of randomly diluted magnets evidence for fractal properties of the infinite percolation cluster

Abstract We present specific heat data on the system Fe p Zn 1- p L 6 (ClO 4 ) 2 , which is an experimental realization of the sc, S = 1 2 , diluted Ising antiferromagnet. Here L = C 5 H 5 NO . The results are compared with earlier data on the diluted sc, S = 1 2 , XY antiferromagnet Co p Zn 1- p L 6 (Cl) 4 ) 2 and the diluted bcc, S = 1 2 , Ising antiferromagnet Co p Zn 1- p Cs 3 Cl 5 . The specific heat behaviour of the diluted Ising systems is found to be completely different from that of the diluted XY magnet, for which very strong short-range order effects have been observed. An explanation is given in terms of the fractal properties of the infinite percolation cluster in the temperature range above T c ( p ). It is shown that there exists a strong analogy between the specific heat behaviour of a diluted magnet and that of a system of weakly coupled magnetic chains. In this picture a decrease of p corresponds with a decrease of the coupling between the chains. The differences in behaviour observed between the Ising systems on the one hand, and the (isotropic) XY or Heisenberg systems on the other, can then be explained by the fact that the intrachain correlation length depends exponentially on temperature for the Ising chain, whereas it depends much less strongly on temperature (∝ 1/ T ) for the XY and Heisenberg chains.

Decoupled magnetic subsystems in the random mixture FepCo1-p(C5H5NO)6(ClO4)2

Abstract Specific heat data on the random mixtures FepCo1-pL6(ClO4)2, where L = C5H5NO, are presented. The Fe and Co magnetic atoms have competing anisotropies since the pure Fe and Co compounds are known to be good examples of the simple cubic, S = 1 2 , Ising and XY magnet, respectively. The experimental data show the two magnetic subsystems in the mixtures to be almost completely decoupled, which is a consequence of the fact that the crystal field anisotropies of the Fe2+ and Co2+ ions, yielding g∥ ≫ g⊥ and g⊥ ≫ g∥, respectively, are very strong compared to the magnetic exchange interactions. Consequently the two magnetic subsystems experience one another as nonmagnetic impurities. A model is presented which explains these results, as well as those previously found for related random mixtures, in terms of two interpenetrating percolation clusters.

Experimental evidence for fractal properties of the infinite percolation cluster in randomly diluted magnets. Comparison with the “nodes-links-blobs” model

The structure of the infinite percolation cluster (IPC) of percolation theory is studied in a physical realization of this problem, the site-random diluted magnet. Specific heat data on diluted magnets are successfully explained in terms of the “nodes-links-blobs” model for the backbone structure of the IPC, which is shown to behave as a fractal object for ξT < ξp, where ξT is the thermal correlation length and ξp the connectedness length associated with the percolation transition. The analogy between the diluted magnet and the quasi 1-dimensional magnet is discussed.

Antiferromagnetic salts of [Gd(C5H5NO)8]3+ (abstract)

The first studies at low temperatures on pyridine N‐oxide complexes of the rare earths are reported. Susceptibility and specific heat measurements show that both [Gd(C5H5NO)8](ClO4)3 and [Gd(C5H5NO)8]I3 order antiferromagnetically at 70 mK. The perchlorate salt exhibits in the specific heat the high temperature T −2 behavior anticipated for dipole‐dipole interaction.