The first family of rare-earth-based single chain magnets is presented. Compounds of general formula [M(hfac)3(NITPhOPh)], where M = Eu, Gd, Tb, Dy, Ho, Er, or Yb, and PhOPh is the nitronyl-nitroxide radical (2,4'-benzoxo-4,4,5,5-tetramethylimidazoline-1-oxyl-3-oxide), have been structurally characterized and found to be isostructural. The characterization of both static and dynamic magnetic properties of the whole family is reported. Dy, Tb, and Ho compounds display slow relaxation of the magnetization, and ac susceptibility shows a thermally activated regime with energy barriers of 69, 45, and 34 K for Dy, Tb, and Ho compounds, respectively, while only a frequency-dependent susceptibility is observed for Er below 2.0 K. In Gd and Yb derivatives, antiferromagnetic interactions dominate. The pre-exponential factors differ by about 4 orders of magnitude. Finite size effects, due to naturally occurring defects, affect the static and dynamic properties of the compounds differently.

A Family of Rare-Earth-Based Single Chain Magnets: Playing with Anisotropy

Molecular engineering for single-chain-magnet behavior in a one-dimensional dysprosium-nitronyl nitroxide compound.

The cyano-bridged trinuclear compound, (NEt(4))[Mn(2)(salmen)(2)(MeOH)(2)Fe(CN)(6)] (1) (salmen(2)(-) = rac-N,N'-(1-methylethylene)bis(salicylideneiminate)), reported previously by Miyasaka et al. (ref 19d) has been reinvestigated using combined ac and dc susceptibility measurements. The strong frequency dependence of the ac susceptibility and the slow relaxation of the magnetization show that 1 behaves as a single-molecule magnet with an S(T) = (9)/(2) spin ground state. Its relaxation time (tau) follows an Arrhenius law with tau(0) = 2.5 x 10(-)(7) s and Delta(eff)/k(B) = 14 K. Moreover, below 0.3 K, tau saturates around 470 s, indicating that quantum tunneling of the magnetization becomes the dominant process of relaxation. (NEt(4))[Mn(2) (5-MeOsalen)(2)Fe(CN)(6)] (2) (5-MeOsalen(2)(-) = N,N'-ethylenebis(5-methoxysalicylideneiminate)) is a heterometallic one-dimensional assembly made of the trinuclear [Mn(III)(SB)-NC-Fe(III)-CN-Mn(III)(SB)] (SB is a salen-type Schiff-base ligand) motif similar to 1. Compound 2 has two types of bridges, a cyano bridge (-NC-) and a biphenolate bridge (-(O)(2)-), connecting Mn(III) and Fe(III) ions and the two Mn(III) ions, respectively. Both bridges mediate ferromagnetic interactions, as shown by modeling the magnetic susceptibility above 10 K with g(av) = 2.03, J(Mn)(-)(Fe)/k(B) = +6.5 K, and J'/k(B) = +0.07 K, where J' is the exchange coupling between the trimer units. The dc magnetic measurements of a single crystal using micro-SQUID and Hall-probe magnetometers revealed a uniaxial anisotropy (D(T)/k(B) = -0.94 K) with an easy axis lying along the chain direction. Frequency dependence of the ac susceptibility and time dependence of the dc magnetization have been performed to study the slow relaxation of the magnetization. A mean relaxation time has been found, and its temperature dependence has been studied. Above 1.4 K, both magnetic susceptibility and relaxation time are in agreement with the dynamics described in the 1960s by R. J. Glauber for one-dimensional systems with ferromagnetically coupled Ising spins (tau(0) = 3.7 x 10(-)(10) s and Delta(1)/k(B) = 31 K). As expected, at lower temperatures below 1.4 K, the relaxation process is dominated by the finite-size chain effects (tau'(0) = 3 x 10(-)(8) s and Delta(2)/k(B) = 25 K). The detailed analysis of this single-chain magnet behavior and its two regimes is consistent with magnetic parameters independently estimated (J'and D(T)) and allows the determination of the average chain length of 60 nm (or 44 trimer units). This work illustrates nicely a new strategy to design single-chain magnets by coupling ferromagnetically single-molecule magnets in one dimension.

Single-Chain Magnet (NEt4)[Mn2(5-MeOsalen)2Fe(CN)6] Made of MnIII−FeIII−MnIII Trinuclear Single-Molecule Magnet with an ST = 9/2 Spin Ground State

Single chain magnets (SCMs) are an interesting class of molecular polymeric materials displaying slow relaxation of the magnetization. They provide, at low temperatures, a magnetic hysteretic behaviour for a single polymeric chain. Although their behaviour evokes better-known magnetic nanoparticles and single-molecule magnets (SMMs), the similarity is mainly apparent. The fundamental differences in the physical origin of the magnetic behaviour offer perspectives that are still largely unexplored. Here we review the progress made in the synthesis, characterization and theoretical understanding of SCMs, highlighting differences and similarities with SMMs. For each of the points we then present a perspective of the advantages offered by this class of materials and we point out the main aspects that remain to be developed in the field.

Single chain magnets: where to from here?

A note on the q-deformation-theoretic aspect of the generalized entropies in nonextensive physics

A new type effective field approach is used to derive the thermodynamical properties of the transverse Ising model. The method is based on an exact formal identity for the two-state transverse Ising model and utilizes an exponential operator technique. The lines of critical points in the Ω-T plane are derived and the critical transverse fields ΩC are obtained analytically, for lattices with coordination numbers z = 2, 4 and 6. This simple method yields results which represent a remarkable improvement on the usual mean field approximation. Our results are also compared with those from series expansion method.

New effective field theory for the transverse Ising model

Within the framework of the recently introduced nonextensive statistical mechanics, we generalize the Planck law for the blackbody radiation. The generalized thermal spectrum contains an additional parameter q, for which q=1 in the Planck limit. For the cosmic microwave background radiation, we find a 95% confidence limit of \ensuremath{\Vert}q-1\ensuremath{\Vert}3.6\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}5}$ from the data of Mather et al. [Astrophys. J. 420, 439 (1994)] that were obtained with the Cosmic Background Explorer satellite, under the assumption that the internal reference of the apparatus has a Planck spectrum.

Generalization of the Planck radiation law and application to the cosmic microwave background radiation.

An effective-field theory study of trilayer Ising nanostructure: Thermodynamic and magnetic properties

Critical dynamics of the open Ising chain

Using the Finite Size Scaling Renormalisation Group we obtain the two-dimensional flow diagram of the Blume-Capel model, for S = 1 and S = 3/2. In the first case our results are similar to those of Mean Field Theory, which predicts the existence of first and second order transitions whith a tricritical point. In the second case, however, our results are different. While we obtain, as in the S = 1 case, a phase diagram presenting a multicritical point, the Mean Field approach predicts only a second order transition and a critical end point.

F. C. Sá Barreto

Papers

New effective field theory for the transverse Ising model

Generalization of the Planck radiation law and application to the cosmic microwave background radiation.

An effective-field theory study of trilayer Ising nanostructure: Thermodynamic and magnetic properties

Critical dynamics of the open Ising chain

The spin-s blume-capel rg flow diagram