The properties of two molecular-based magnetic helices, composed of 3$d$ metal Co and Mn ions bridged by Nitronyl Nitroxide radicals, are investigated by density functional calculations. Their peculiar and distinctive magnetic behavior is here elucid
ated by a thorough description of their magnetic, electronic, and anisotropy properties. Metal ions are antiferromagnetically coupled with the radicals, leading to a ferrimagnetically ordered ground state. A strong metal-radical exchange coupling is found, about 44 meV and 48 meV for Co- and Mn-helices, respectively. The latter have also relevant next-nearest-neighbor Mn-Mn antiferromagnetic interactions (of $sim$ 6 meV). Co-sites are characterized by non-collinear uniaxial anisotropies, whereas Mn-sites are rather isotropic. A key result pertains to the Co-helix: the microscopic picture resulting from density-functional calculations allows us to propose a spin Hamiltonian of increased complexity with respect to the commonly employed Ising Hamiltonian, suitable for the study of finite-temperature behavior, and that seems to clarify the puzzling scenario of multiple characteristic energy scales observed in experiments.
The paramagnetic-to-ferromagnetic phase transition is believed to proceed through a critical point, at which power laws and scaling invariance, associated with the existence of one diverging characteristic length scale -- the so called correlation le
ngth -- appear. We indeed observe power laws and scaling behavior over extraordinarily many decades of the suitable scaling variables at the paramagnetic-to-ferromagnetic phase transition in ultrathin Fe films. However, we find that, when the putative critical point is approached, the singular behavior of thermodynamic quantities transforms into an analytic one: the critical point does not exist, it is replaced by a more complex phase involving domains of opposite magnetization, below as well as $above$ the putative critical temperature. All essential experimental results are reproduced by Monte-Carlo simulations in which, alongside the familiar exchange coupling, the competing dipole-dipole interaction is taken into account. Our results imply that a scaling behavior of macroscopic thermodynamic quantities is not necessarily a signature for an underlying second-order phase transition and that the paramagnetic-to-ferromagnetic phase transition proceeds, very likely, in the presence of at least two long spatial scales: the correlation length and the size of magnetic domains.
We consider Gaussian fluctuations about domain walls embedded in one- or two-dimensional spin lattices. Analytic expressions for the free energy of one domain wall are obtained. From these, the temperature dependence of experimentally relevant spatia
l scales -- i.e., the correlation length for spin chains and the size of magnetic domains for thin films magnetized out of plane -- are deduced. Stability of chiral order inside domain walls against thermal fluctuations is also discussed.
We measure the current vs voltage (I-V) characteristics of a diodelike tunnel junction consisting of a sharp metallic tip placed at a variable distance d from a planar collector and emitting electrons via electric-field assisted emission. All curves
collapse onto one single graph when I is plotted as a function of the single scaling variable Vd^{-lambda}, d being varied from a few mm to a few nm, i.e., by about six orders of magnitude. We provide an argument that finds the exponent {lambda} within the singular behavior inherent to the electrostatics of a sharp tip. A simulation of the tunneling barrier for a realistic tip reproduces both the scaling behavior and the small but significant deviations from scaling observed experimentally.
Single-chain magnets are molecular spin chains displaying slow relaxation of the magnetisation on a macroscopic time scale. To this similarity with single-molecule magnets they own their name. In this chapter the distinctive features of single-chain
magnets as opposed to their precursors will be pinpointed. In particular, we will show how their behaviour is dictated by the physics of thermally-excited domain walls. The basic concepts needed to understand and model single-chain magnets will also be reviewed.
We discuss time-quantified Monte-Carlo simulations on classical spin chains with uniaxial anisotropy in relation to static calculations. Depending on the thickness of domain walls, controlled by the relative strength of the exchange and magnetic anis
otropy energy, we found two distinct regimes in which both the static and dynamic behavior are different. For broad domain walls, the interplay between localized excitations and spin waves turns out to be crucial at finite temperature. As a consequence, a different protocol should be followed in the experimental characterization of slow-relaxing spin chains with broad domain walls with respect to the usual Ising limit.
We propose a scaling hypothesis for pattern-forming systems in which modulation of the order parameter results from the competition between a short-ranged interaction and a long-ranged interaction decaying with some power $alpha$ of the inverse dista
nce. With L being a spatial length characterizing the modulated phase, all thermodynamic quantities are predicted to scale like some power of L. The scaling dimensions with respect to L only depend on the dimensionality of the system d and the exponent alpha. Scaling predictions are in agreement with experiments on ultra-thin ferromagnetic films and computational results. Finally, our scaling hypothesis implies that, for some range of values alpha>d, Inverse-Symmetry-Breaking transitions may appear systematically in the considered class of frustrated systems.
We investigate the details of pattern formation and transitions between different modulated phases in ultra-thin Fe films on Cu(001). At high temperature, the transitions between the uniform saturated state, the bubble state and the striped state are
completely reversible, while at low temperature the bubble phase is avoided. The observed non-equilibrium behavior can be qualitatively explained by considering the intrinsic energy barriers appearing in the system due to the competition between the short-ranged exchange and the long-ranged dipolar interactions. Our experiments suggest that the height of these energy barriers is related to the domain size and is therefore strongly temperature dependent.
