Ferromagnetism is typically discussed in terms of the exchange interaction and magnetic anisotropies. Yet real samples are inevitably affected by the magnetostatic dipole-dipole interaction. Because of this interaction, a theorem [R.B. Griffiths, Free Energy of interacting magnetic dipoles, Phys. Rev. 176, 655 (1968)] forbids a spontaneous magnetization in, nota bene, three-dimensional bodies. Here we discuss perpendicularly and in-plane magnetized ferromagnetic bodies in the shape of a slab of finite thickness. In perpendicularly magnetized slabs, magnetic domains are energetically favored when the lateral size is sufficiently large, i.e., there is no spontaneous magnetization. For in-plane magnetization, instead, spontaneous magnetization is possible below a critical thickness which, in very thin films, could be as small as few monolayers. At this critical thickness, we predict a genuine phase transition to a multi-domain state. These results have implications for two-dimensional ferromagnetism.

Magnetic materials interfaced with superconductors may reveal new physical phenomena with potential for quantum technologies. The use of molecules as magnetic components has already shown great promise, but the diversity of properties offered by the molecular realm remains largely unexplored. Here we investigate a submonolayer of tetrairon( iii ) propeller-shaped single molecule magnets deposited on a superconducting lead surface. This material combination reveals a strong influence of the superconductor on the spin dynamics of the single molecule magnet. It is shown that the superconducting transition to the condensate state switches the single molecule magnet from a blocked magnetization state to a resonant quantum tunnelling regime. Our results open perspectives to control single molecule magnetism via superconductors and to use single molecule magnets as local probes of the superconducting state.

The possibility to operate on magnetic materials through the application of electric rather than magnetic fields-promising faster, more compact and energy efficient circuits-continues to spur the investigation of magnetoelectric effects. Symmetry considerations, in particular the lack of an inversion centre, characterize the magnetoelectric effect. In addition, spin-orbit coupling is generally considered necessary to make a spin system sensitive to a charge distribution. However, a magnetoelectric effect not relying on spin-orbit coupling is appealing for spin-based quantum technologies. Here, we report the detection of a magnetoelectric effect that we attribute to an electric field modulation of the magnetic exchange interaction without atomic displacement. The effect is visible in electron paramagnetic resonance absorption of molecular helices under electric field modulation and confirmed by specific symmetry properties and spectral simulation.

In real magnets the tendency towards ferromagnetism, promoted by exchange coupling, is usually frustrated by dipolar interaction. As a result, the uniformly ordered phase is replaced by modulated (multi-domain) phases, characterized by different order parameters rather than the global magnetization. The transitions occurring within those modulated phases and towards the disordered phase are generally not of second-order type. Nevertheless, strong experimental evidence indicates that a standard critical behavior is recovered when comparatively small fields are applied that stabilize the uniform phase. The resulting power laws are observed with respect to a putative critical point that falls in the portion of the phase diagram occupied by modulated phases, in line with an avoided-criticality scenario. Here we propose a generalization of the scaling hypothesis for ferromagnets, which explains this observation assuming that the dipolar interaction acts as a relevant field, in the sense of renormalization group.

Secondary electrons emitted from a scanning field-emission microscope are spin analyzed with a Mott detector. Spin polarization up to 15% is observed with a lateral resolution of less than 5 nm, with a potential resolution of even less than 1 nm. In this paper the proof of principle is conducted by comparing this method with a well-established method of spin mapping and with reference samples examined by these two microscopes.

Nature Communications 7: Article number: 13611 (2016); Published 5 December 2016; Updated 17 January 2017 The original version of this Article contained a typographical error in the spelling of the author S.A. Cannas, which was incorrectly given as S. Cannas. This has now been corrected in both the PDF and HTML versions of the Article.

The current flowing through a Mott spin junction depends on the relative spin orientation of the two ferromagnetic layers comprising the "source" and "drain" sides of the junction. The resulting current asymmetry is detected as giant or tunnelling magnetoresistance depending on whether the two ferromagnets are separated by a metal or an insulator. Based on the fundamental principles of reciprocity for spin-dependent electron scattering, one can envisage a one-magnet-only spin junction in which the source is non-magnetic, and the spin information is encoded by the spin polarisation of the electrons that have crossed or are backscattered from the drain magnetic layer. The practical significance of using an unpolarised source is that the state of the magnetic layer can be modified without affecting the process of probing it. Whether this reciprocity is realised in the actual junctions is not yet known. Here, we demonstrate a nano-sized, one-magnet-only Mott spin junction by measuring the finite spin polarisation of the backscattered electrons. Based on this finding, we conclude that since the junction acts as a spin filter, the magnetic layer must experience a spin transfer that could become detectable in view of the high current densities achievable in this technology.

Nature Communications 7: Article number: 13611 (2016); Published 5 December 2016; Updated 17 January 2017 The original version of this Article contained a typographical error in the spelling of the author S.A. Cannas, which was incorrectly given as S. Cannas. This has now been corrected in both the PDF and HTML versions of the Article.

Nature Communications 7: Article number: 13611 (2016); Published 5 December 2016; Updated 17 January 2017 The original version of this Article contained a typographical error in the spelling of the author S.A. Cannas, which was incorrectly given as S. Cannas. This has now been corrected in both the PDF and HTML versions of the Article.

We perform scanning tunnelling microscopy (STM) in a regime where primary electrons are field-emitted from the tip and excite secondary electrons out of the target-the scanning field-emission microscopy regime (SFM). In the SFM mode, a secondary-electron contrast as high as 30% is observed when imaging a monoatomic step between a clean W(110)-and an Fe-covered W(110)-terrace. This is a figure of contrast comparable to STM. The apparent width of the monoatomic step attains the 1 nm mark, i.e. it is only marginally worse than the corresponding width observed in STM. The origin of the unexpected strong contrast in SFM is the material dependence of the secondary-electron yield and not the dependence of the transported current on the tip-target distance, typical of STM: accordingly, we expect that a technology combining STM and SFM will highlight complementary aspects of a surface while simultaneously making electrons, selected with nanometre spatial precision, available to a macroscopic environment for further processing.

The paramagnetic-to-ferromagnetic phase transition is classified as a critical phenomenon due to the power-law behaviour shown by thermodynamic observables when the Curie point is approached. Here we report the observation of such a behaviour over extraordinarily many decades of suitable scaling variables in ultrathin Fe films, for certain ranges of temperature T and applied field B. This despite the fact that the underlying critical point is practically unreachable because protected by a phase with a modulated domain structure, induced by the dipole-dipole interaction. The modulated structure has a well-defined spatial period and is realized in a portion of the (T, B) plane that extends above the putative critical temperature, where thermodynamic quantities do not display any singularity. Our results imply that scaling behaviour of macroscopic observables is compatible with an avoided critical point.

The recently developed technique Scanning Tunneling Microscopy in the Field Emission regime (STM FE) is based on the Russell Young's topografiner technology [1]. The set-up is a no contacting device consisting of a sharp tip approached vertically to a conducting surface at variable distances and biased with a small voltage with respect to the surface (Figure 1). The system builds a junction across which electrons can be transferred from the tip apex to the surface by direct quantum mechanical tunneling if the distance is in the sub nanometer region. In this case the surface topography can be imaged with atomic spatial resolution using the STM technique. In the STM FE mode, the distance between tip and collector is increased and the current is dominated by electrons emitted from the tip into the vacuum region via electric field assisted tunneling. In the experiment, secondary electrons carrying chemical and magnetic information are produced via diverse mechanisms on the surface of the sample and form a cloud in the vicinity around the interaction region in a macroscopic environment. Some of them are attracted by an electric potential to the entrance of a lens system designed for focusing the electrons into a counter and a Mott detector. The imaging of the sample with a resolution in the nanoscale depends on the amount of secondary electrons that effectively reach the detectors. We use COMSOL Multiphysics® to optimize the electrostatic and geometric parameters by calculating the trajectories of the secondary electrons from the sample to the final position on the detectors. The set of results achieved on the physical characterization of the instrument refers to a situation where a nanoscale quantum process, comprising field emission, secondary electron production and electron transport in the presence of strongest electric fields is shown to couple efficiently to a macroscopic environment. An accurate modeling of this multiscale process requires the solution of the Laplace and movement equations in two separate subsystems with different space scales. In the first component, the system consists of a tungsten tip in front of a silicon surface in a subspace of some hundreds of nanometers [2]. In the second component, the geometry is generated by importing a simplified version of the CAD-construction files of the instrument (in a scale of centimeters) (Figure 2). In both cases the electrostatic problem is solved using the AC/DC Module and the trajectories of the electrons are calculated with the Particle Tracing Module. For coupling the two simulations, in analogy to the model "Syngas Combustion in a Round-Jet Burner" (Model Library), the final positions and velocities on the walls of the first Component are used as initial values in the second Component (Figure 3). Most of the calculations are performed on a cluster. First results shown that only a few electrons can escape from the interaction region if their energies are about 70 eV. From the escaped electrons, a 10% can reach the Mott detector (Figure 4).

The properties of two molecular-based magnetic helices, composed of 3d metal Co and Mn ions bridged by nitronyl nitroxide radicals, are investigated by density-functional calculations. Their peculiar and distinctive magnetic behavior is here elucidated 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 and 48 meV for Co and Mn helices, respectively. The latter have also relevant next-nearest-neighbor Mn-Mn antiferromagnetic interactions (of similar to 6 meV). Co sites are characterized by noncollinear 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 possibility of resolving magnetic-textures in real space at atomic scale may trigger novel fundamental and applicative perspectives. We report on energy-resolved surface imaging with a new technique called Near Field-Emission SEM, which confirms the feasibility of electron spectroscopy and magnetic-domain mapping with nanometer spatial resolution.

Recent experiments report the current (I) versus voltage (V) characteristics of a tunnel junction consisting of a metallic tip placed at a distance d from a planar electrode, d varying over six orders of magnitude, from few nanometres to few millimetres. In the 'electric-field-assisted' (or 'field emission') regime, as opposed to the direct tunnelling regime used in conventional scanning tunnelling microscopy, all I-V curves are found to collapse onto one single graph when d is suitably rescaled, suggesting that the current I=I(V,d) is in reality a generalized homogeneous function of one single variable, i.e. [Formula: see text], where λ being some characteristic exponent and [Formula: see text] being a scaling function. In this paper, we provide a comprehensive explanation-based on analytical arguments, numerical simulations and further experimental results-for the scaling behaviour that we show to emerge for a variety of tip-plane geometries and thus seems to be a general feature of electric-field-assisted tunnelling.

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 spatial 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.

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.