Table of contents

Undoped bilayer graphene is a two-dimensional semimetal with a low-energy excitation spectrum that is parabolic in the momentum. As a result, the screening of an arbitrary external charge Ze is accompanied by a reconstruction of the ground state: valence band electrons (for Z  >  0) are promoted to form a space charge around the charge while the holes leave the physical picture. The outcome is a flat neutral object resembling the regular atom except that for $Z\gg 1$ it is described by a strictly linear Thomas–Fermi theory. This theory also predicts that the bilayer's static dielectric constant is the same as that of a two-dimensional electron gas in the long-wavelength limit.

In this Letter, we study the magnetic transport in AA-stacked bilayer honeycomb chiral magnets coupled either ferromagnetically or antiferromagnetically. For both couplings, we observe chirality-induced gaps, chiral protected edge states, magnon Hall and magnon spin Nernst effects of magnetic spin excitations. For ferromagnetically coupled layers, thermal Hall and spin Nernst conductivities do not change sign as function of magnetic field or temperature similar to single-layer honeycomb ferromagnetic insulator. In contrast, for antiferromagnetically coupled layers, we observe a sign change in the thermal Hall and spin Nernst conductivities as the magnetic field is reversed. We discuss possible experimental accessible honeycomb bilayer quantum materials in which these effects can be observed.

Using density functional theory, we study the structure, electronic properties and partial charges of a new carbon allotrope—penta-graphene (PG)—substitutionally doped by Si, B and N. We found that the electronic bandgap of PG can be tuned down to 0.2 eV due to carbon substitutions. However, the value of the band gap depends on the type and location of the dopants. For example, the strongest reduction of the band gap is obtained for Si substitutions on the top (bottom) plane of PG, whereas the substitution in the middle plane of PG has a smaller effect on the band gap of the material. Surface termination with fluorine and hydroxyl groups results in an increase of the band gap together with considerable changes in electronic and atomic partial charge distribution in the system. Our findings, which are robust against the use of different exchange-correlation functionals, indicate the possibility of tuning the bandgap of the material to make it suitable for optoelectronic and photovoltaic applications.

We have measured the time-of-flight of ortho-positronium emitted from Cs-, Na- and Li-coated single-crystal tungsten surfaces. The data obtained after the coating show a new positronium energy component with a specific energy loss in addition to the component whose emission energy is simply determined by the positron and the electron work functions. We suggest that this new component is attributed to the formation of positronium accompanied by inter-band transition and/or surface plasmon excitation at the surfaces.

The growth of 3, 4, 9, 10-perylene tetracarboxylic dianhydride (PTCDA) on the Ga-polar GaN(0 0 0 1) surface has been studied by x-ray photoelectron spectroscopy (XPS), spot profile analysis low-energy electron diffraction (SPA-LEED), near edge x-ray absorption fine structure (NEXAFS), and scanning tunneling microscopy (STM). The stoichiometric ratios derived from XPS indicate that the molecules remain intact upon adsorption on the surface. Furthermore, no chemical shifts can be observed in the C 1s and O 1s core levels with progressing deposition of PTCDA, suggesting none or only weak interactions between the molecules and the substrate. NEXAFS data indicate the PTCDA molecules being oriented with their molecular plane parallel to the surface. High-resolution STM shows PTCDA islands of irregular shape on the sub-micron scale, and together with corresponding SPA-LEED data reveals a lateral ordering of the molecules that is compatible with the presence of (1 0 2) oriented PTCDA nano-crystals. SPA-LEED moreover clearly shows the presence of homogeneously distributed rotational domains of two-dimensionally isotropic PTCDA.

We have investigated an alternative to the standard periodic boundary conditions for simulating the diffusion of tracer particles in a polymer gel by performing Brownian dynamics simulations using spherical boundary conditions. The gel network is constructed by randomly distributing tetravalent cross-linking nodes and connecting nearest pairs. The final gel structure is characterised by the radial distribution functions, chain lengths and end-to-end distances, and the pore size distribution. We have looked at the diffusion of tracer particles with a wide range of sizes, diffusing in both static and dynamic networks of two different volume fractions. It is quantitatively shown that the dynamical effect of the network becomes more important in facilitating the diffusional transport for larger particle sizes, and that one obtains a finite diffusion also for particle sizes well above the maximum in the pore size distribution.

We use time dependent perturbation theory to study the terahertz nonlinear response of gapped intrinsic and extrinsic nearly-metallic armchair graphene nanoribbons of finite length under an applied electric field. Generally, the nonlinear conductances exhibit contributions due to single-photon, two-photon, and three-photon processes. The interference between each of these processes results in remarkably complex behavior for the third-order conductances, including quantum dot signatures that should be measurable with a relatively simple experimental configuration. Notably, we observe sharp resonances in the isotropic third-order response due to the Van Hove singularities in the density of states at one-, two-, and three-photon resonances. However, these resonances are absent in the anisotropic third-order response; a result of the overall symmetry of the system.

Electrical devices based on suspended multi-wall carbon nanotubes were constructed and studied. The chiral structure of each shell in a particular nanotube was determined using nanobeam electron diffraction in a transmission electron microscope. The transport properties of the carbon nanotube were also measured. The nanotube device length was short enough that the transport was nearly ballistic, and multiple subbands contributed to the conductance. Thermal excitation of carriers significantly affected nanotube resistance at room temperature.

Indium phosphide nanowires with a single crystalline zinc-blend core and polycrystalline/amorphous shell were grown from a reliable route without the use of hazardous precursors. The nanowires are composed by a crystalline core covered by a polycrystalline shell, presenting typical lengths larger than 10 μm and diameters of 80–90 nm. Raman spectra taken from as-grown nanowires exhibited asymmetric line shapes with broadening towards higher wave numbers which can be attributed to phonon localization effects. It was found that optical phonons in the nanowires are localized in regions with average size of 3 nm, which seems to have the same order of magnitude of grain sizes in the polycrystalline shell. Regardless of the fact that the nanowires exhibit a crystalline core, any considerable degree of disorder can lead to a localized behaviour of carriers. In consequence, the variable range hopping was observed as the main transport instead of the usual thermal excitation mechanisms. Furthermore the hopping length was ten times smaller than nanowire cross-sections, confirming that the nanostructures do behave as a 3D system. Accordingly, the V-shape observed in PL spectra clearly demonstrates a very strong influence of the potential fluctuations on the exciton optical recombination. Such fluctuations can still be observed at low temperature regime, confirming that the amorphous/polycrystalline shell of the nanowires affects the exciton recombination in every laser power regime tested.

In this study, we have carried out a detailed theoretical investigation on the binding energy of an exciton in type-II CdTe/CdSe core/shell/well/shell (CSWS) nanocrystal quantum dot (NCQD) in the strong confinement region. The calculations are based on the effective mass approximation, and the coulombic interaction between electron and hole is introduced using Hartree approximation. With these theoretical basis, the coupled Poisson–Schrodinger equations are solved in a self consistent iterative manner. In strong confinement regime, the binding energy variation with core radius in type-II NCQD shows a peak. And this peak widens for larger well width and inner shell thickness. Our study suggests that, this anomalous behavior of exciton binding energy is due to an effect called 'positional flip of exciton', caused by the faster tunneling of hole to the inner layer in comparison with electron. Our results can be applied in laser and optoelectronic engineering for designing more efficient optoelectronic devices.

A systematic dynamic theory is established to deal with the optical collective resonance in metamaterial arrays. As a reference model, we consider an infinite split ring resonator (SRR) array illuminated by a linearly polarized wave and introduce an N-degree-of-freedom forced oscillator equation to simplify the coupled-mode vibration problem. We derive a strict formula of resonance frequency (RF) and its adjustable range from the steady-state response. Unlike a single SRR possesses invariant RF, it successfully explains the mechanism of RF shift effect in the SRR array when the incident angle changes. Instead of full wave analysis, only one or two adjacent resonance modes can give an accurate response line shape. Our approach is applicable for metallic arrays with any N-particle cell at all incident angles and well matched with numerical results. It provides a versatile way to study the vibration dynamics in optical periodic many-body systems.

Through first-principles calculations, we predict a new superhard carbon allotrope named C₂₀  −  T, which possesses a cubic T symmetry with space group No.198(P2₁3). This new carbon allotrope has an all-sp³ hybridized bonding network with 20 atoms in its primitive unit cell. The dynamic, mechanical, and thermal stabilities of this new carbon phase at zero pressure are confirmed by using a variety of state-of-the-art theoretical calculations. Interestingly, despite the fact that C₂₀  −  T carbon has a porous structure with large cavities, our calculations identify its superhard properties with the Vickers hardness of 72.76 Gpa. The ideal tensile and shear strength of C₂₀  −  T carbon are calculated to be 71.1 and 55.2 GPa respectively, comparable to that of c-BN. Electronic band calculations reveal that this new carbon allotrope is a transparent insulator with an indirect band gap of 5.44 eV. These results broaden our understanding of superhard carbon allotropes.

This study reports the experimental characterization of the hydrostatic properties of arsenolite (As₄O₆), a molecular solid which is one of the softest minerals in the absence of hydrogen bonding. The high compressibility of arsenolite and its stability up to 15 GPa have been proved by x-ray diffraction measurements, and the progressive loss of hydrostaticity with increasing pressure up to 20 GPa has been monitored by ruby photoluminescence. Arsenolite has been found to exhibit hydrostatic behavior up to 2.5 GPa and a quasi-hydrostatic behavior up to 10 GPa at room temperature. This result opens the way to explore other molecular solids as possible quasi-hydrostatic pressure-transmitting media. The validity of arsenolite as an insulating, stable, non-penetrating and quasi-hydrostatic medium is explored by the study of the x-ray diffraction of zeolite ITQ-29 at high pressure.

The electrical transport properties of undoped and yttrium-doped strontium titanate (Sr(Ti_{1 – x}Y_x)O_{3 – δ}, x  =  0, 0.02) under high pressure were investigated with in situ impedance spectroscopy measurements. A pressure-induced conductivity switching for undoped and 2 mole% Y-doped strontium titanate is observed at around ~10.0 and 7.0 GPa respectively, which are caused by a cubic to tetragonal I4/mcm phase transition. The decrease of the phase transition point of 2 mole% Y-doped strontium titanate can be attributed to larger Y³⁺ atoms occupying the B-site and the creation of more oxygen vacancies, which lead to octahedra tilting and symmetry breaking. The results of the voltage-bias dependence of grain-boundary impedance of undoped and 2 mole% Y-doped strontium titanate at different pressures revealed that Schottky-type potential barriers formed at grain boundaries are the key factor for the accumulation of oxygen vacancy at the interface under pressure.

Low temperature thermal and magnetic measurements performed on ferro-magneticl (FM) alloys of composition Ce_2.15(Pd_1−xAg_x)_1.95In_0.9 are presented. Pd substitution by Ag depresses ${{T}_{\text{C}}}(x)$ from 4.1 K down to 1.1 K for x  =  0.5, which is related to the increase of band electrons, with a critical concentration extrapolated to ${{x}_{\text{cr}}}\approx 0.6$. The ${{T}_{\text{C}}}(x)$ decrease is accompanied by a weakening of the magnetization of the FM phase. At high temperature (T  >  30 K) the inverse magnetic susceptibility reveals the presence of robust magnetic moments ($2.56\geqslant ~{{\mu}_{\text{eff}}}\geqslant 2.4$${{\mu}_{\text{B}}}$), whereas the low value of the Curie–Weiss temperature ${{\theta}_{P}}\approx -10$ K excludes any relevant effect from Kondo screening. The specific heat jump at ${{T}_{\text{C}}}(x)$ decreases accordingly, while an anomaly emerges at a fixed temperature ${{T}^{\ast}}\approx 1$ K. This unexpected anomaly does not show any associated sign of magnetism checked by AC-susceptibility measurements. Since the total magnetic entropy (evaluated around $T={{T}_{\text{C}}}(x=0)$) practically does not change with Ag concentration, the transference of degrees of freedom from the FM component to the non-magnetic T^* anomaly is deduced. The origin of this anomaly is attributed to an arising magnetic frustration of the ground state and the consequent entropy bottleneck produced by the divergent increasing of density of excitations at low temperature.

We investigate the superconducting phases and boundary modes for a quasi-1D system formed by up to three Fe chains on an s-wave superconductor, motivated by a recent experiment. While the Rashba type spin–orbit coupling together with a magnetic ordering is necessary to drive the system to be of nontrivial topology, we show that the onsite $\vec{l}\centerdot \vec{s}$ spin–orbit term, inter-chain diagonal hopping couplings, and magnetic disorders in the Fe chains are crucial in determining the symmetry classes of superconducting phases, which can be topologically trivial or nontrivial in different parameter regimes. In general multiple low-energy Andreev bound states, as well as a single Majorana zero mode if the phase is topological, are obtained in the ends of Fe chains. The nontrivial symmetry reduction mechanism is uncovered to provide an understanding of the present results, and may explain the zero-bias peak observed in the experiment. The present study can be applied to generic multiple-chain system.

Usually an inverse square relation between the optical energy gap and the size of crystallites is observed for semiconducting materials due to the strong quantum localization effect. Coulomb attraction that may lead to a proportional dependence is often ignored or considered less important to the optical energy gap when the crystallite size or the thickness of a thin film changes. Here we report a proportional dependence between the optical energy gap and the thickness of ALD-grown CuO thin films due to a strong Coulomb attraction. The ultrathin films deposited in the thickness range of 9–81 nm show a p-type semiconducting behavior when analyzed by Seebeck coefficient and electrical resistivity measurements. The indirect optical energy gap nature of the films is verified from UV–vis spectrophotometric measurements. A progressive increase in the indirect optical energy gap from 1.06 to 1.24 eV is observed with the increase in the thickness of the films. The data are analyzed in the presence of Coulomb attractions using the Brus model. The optical energy gap when plotted against the cubic root of the thickness of the films shows a linear dependence.

Nanocrystalline tungsten trioxide (WO₃) thin films prepared by DC magnetron sputtering have been studied using soft x-ray spectroscopy and optical spectrophotometry. Resonant inelastic x-ray scattering (RIXS) measurements reveal band gap states in sub-stoichiometric γ-WO_3−x with x  =  0.001–0.005. The energy positions of these states are in good agreement with recently reported density functional calculations. The results were compared with optical absorption measurements in the near infrared spectral region. An optical absorption peak at 0.74 eV is assigned to intervalence transfer of polarons between W sites. A less prominent peak at energies between 0.96 and 1.16 eV is assigned to electron excitation of oxygen vacancies. The latter results are supported by RIXS measurements, where an energy loss in this energy range was observed, and this suggests that electron transfer processes involving transitions from oxygen vacancy states can be observed in RIXS. Our results have implications for the interpretation of optical properties of WO₃, and the optical transitions close to the band gap, which are important in photocatalytic and photoelectrochemical applications.

Special quasirandom structures (SQS) are presently generated for disordered (A'_1−x${{\text{A}}^{\prime \prime}}$_x)BX₃ and A(B'_1−x${{\text{B}}^{\prime \prime}}$_x)X₃ perovskite solid solutions, with x  =  1/2 as well as 1/3 and 2/3. These SQS configurations are obtained by imposing that the so-called Cowley parameters are as close to zero as possible for the three nearest neighboring shells. Moreover, these SQS configurations are slightly larger in size than those available in the literature for x  =  1/2, mostly because of the current capabilities of atomistic techniques. They are used here within effective Hamiltonian schemes to predict various properties, which are then compared to those associated with large random supercells, in a variety of compounds, namely (Ba_1−xSr_x)TiO₃, Pb(Zr_1−xTi_x)O₃, Pb(Sc_0.5Nb_0.5)O₃, Ba(Zr_1−xTi_x)O₃, Pb(Mg_1/3Nb_2/3)O₃ and (Bi_1−xNd_x)FeO₃. It is found that these SQS configurations can reproduce many properties of large random supercells of most of these disordered perovskite alloys, below some finite material-dependent temperature. Examples of these properties are electrical polarization, anti-phase and in-phase octahedral tiltings, antipolar motions, antiferromagnetism, strain, piezoelectric coefficients, dielectric response, specific heat and even the formation of polar nanoregions (PNRs) in some relaxors. Some limitations of these SQS configurations are also pointed out and explained.

Resonance Raman spectroscopy was applied to doped PbSc_0.5Ta_0.5O₃ and PbSc_0.5Nb_0.5O₃ relaxor ferroelectrics, to better understand the effect of composition disorder on the mesoscopic-scale polar order in complex perovskite-type (ABO₃) ferroelectrics. The excitation photon energy used was 3.8 eV, which is slightly above the energy gap and corresponds to the maximum of the optical dielectric permittivity. Group-theory analysis reveals that the resonance Raman scattering (RRS) observed under these conditions is allowed only in polar crystal classes. Therefore, RRS is dominated by the atomic dynamics of nanoregions with coherent polar distortions, which considerably facilitates the comparison of polar order in various compounds. The results show that A-site doping (Ba²⁺, Sr²⁺, La³⁺, Bi³⁺) has significantly stronger effect on the structural polarity than the introduction of a third element at the B site (Nb⁵⁺ or Sn⁴⁺ doped in PbSc_0.5Ta_0.5O₃). The A-site substitution by cations that in contrast to Pb²⁺ have isotropic outermost electron shells disturbs the system of lone-pair electrons, thus reducing the correlation length of coupled polar distortions and the strength of the electric field associated with the mean polarization of polar nanoregions. A-site doping with larger cations (Ba²⁺) augments the polar deformation of the individual BO₆ octahedra due to local elastic fields. As a result, such A-site doping intensifies the initial structural polarity at high temperatures and prevails the enlargement of the polar fraction at low temperatures. A-site doping with smaller cations (Sr²⁺, La³⁺), regardless if they are isovalent or aliovalent to Pb²⁺, increases the correlation length of antiferrodistortive order (BO₆ tilts), which in turn assists the development of double-perovskite structure with coherent local polar distortions. A-site doping with aliovalent cations (Bi³⁺) having the same outermost electron shell and ionic radius as the host A-site Pb²⁺ cations leads to stronger coupling along the –B–O–B– bond linkages due to enhanced random local electric fields.

We report a comprehensive specific heat and inelastic neutron scattering study to explore the possible origin of multiferroicity in HoCrO₃. We have performed specific heat measurements in the temperature range 100 mK–290 K and inelastic neutron scattering measurements were performed in the temperature range 1.5–200 K. From the specific heat data we determined hyperfine splitting at 22.5(2) μeV and crystal field transitions at 1.379(5) meV, 10.37(4) meV, 15.49(9) meV and 23.44(9) meV, indicating the existence of strong hyperfine and crystal field interactions in HoCrO₃. Further, an effective hyperfine field is determined to be 600(3) T. The quasielastic scattering observed in the inelastic scattering data and a large linear term $\gamma =6.3(8)$ mJ mol⁻¹  K⁻² in the specific heat is attributed to the presence of short range exchange interactions, which is understood to be contributing to the observed ferroelectricity. Further the nuclear and magnetic entropies were computed to be, ∼17.2 Jmol⁻¹ K⁻¹ and  ∼34 Jmol⁻¹ K⁻¹, respectively. The entropy values are in excellent agreement with the limiting theoretical values. An anomaly is observed in the peak position of the temperature dependent crystal field spectra around 60 K, at the same temperature an anomaly in the pyroelectric current is reported. From this we could elucidate a direct correlation between the crystal electric field excitations of Ho³⁺ and ferroelectricity in HoCrO₃. Our present study, along with recent reports, confirm that HoCrO₃, and RCrO₃ (R  =  rare earth) in general, possess more than one driving force for the ferroelectricity and multiferroicity.

Fe₂MnSi fails to follow the Slater–Pauling rule. This phenomenon is thought to originate from either: (i) an antiferromagnetic arrangement of Mn ions at low temperature and/or (ii) chemical disorder. An important insight on this issue could be achieved by considering Fe₂MnSi_1−xGa_x compounds, thoroughly studied here by means of magnetization, neutron diffraction and density functional calculations (DFT). Our results indicate that chemical disorder (and not the antiferromagnetic arrangement) is responsible for the deviation of the Slater–Pauling rule on Fe₂MnSi-based Heusler alloys. Furthermore, evidences suggest that Ga substitution into Si site favors the Fe/Mn disorder, further enhancing the observed deviation.

In this work, we have performed Monte Carlo simulations in a classical model for RFe_1−xCr_xO₃ with R  =  Y and Lu, comparing the numerical simulations with experiments and mean field calculations. In the analyzed compounds, the antisymmetric exchange or Dzyaloshinskii–Moriya (DM) interaction induced a weak ferromagnetism due to a canting of the antiferromagnetically ordered spins. This model is able to reproduce the magnetization reversal (MR) observed experimentally in a field cooling process for intermediate x values and the dependence with x of the critical temperatures. We also analyzed the conditions for the existence of MR in terms of the strength of DM interactions between Fe³⁺ and Cr³⁺ ions with the x values variations.

Various experimental measurements were performed to complete the phase diagram of a weakly distorted triangular lattice system, Sr₃NiNb₂O₉ with Ni²⁺ , spin-1 magnetic ions. This compound possesses an isosceles triangular lattice with two shorter bonds and one longer bond. It shows a two-step magnetic phase transition at ${{T}_{\text{N}1}}\sim 5.1$ K and ${{T}_{\text{N}2}}\sim 5.5$ K at zero magnetic field, characteristic of an easy-axis anisotropy. In the magnetization curves, a series of magnetic phase transitions was observed such as an up-up-down phase at ${{\mu}_{0}}{{H}_{c1}}\sim 10.5$ T with 1/3 of the saturation magnetization (M_sat) and an oblique phase at ${{\mu}_{0}}{{H}_{c2}}\sim 16$ T with $\sqrt{3}$/3 M_sat. Intriguingly, the magnetic phase transition below T_N2 is in tandem with the ferroelectricity, which demonstrates multiferroic behaviors. Moreover, the multiferroic phase persists in all magnetically ordered phases regardless of the spin structure. The comparison between the phase diagrams of Sr₃NiNb₂O₉ and its sister compound with an equilateral triangular lattice antiferromagnet Ba₃NiNb₂O₉ (Hwang et al 2012 Phys. Rev. Lett. 109 257205), illustrates how a small imbalance among exchange interactions change the magnetic ground states of the TLAFs.

The thermodynamic and magnetocaloric properties of a generalized spin-(1/2,  s) Fisher's super-exchange antiferromagnet are investigated precisely by using the decoration-iteration mapping transformation. Besides the critical temperature, sublattice magnetization, total magnetization, entropy and specific heat, the isothermal entropy change and adiabatic temperature change are also rigorously calculated in order to examine the cooling efficiency of the model in the vicinity of the first- and second-order phase transitions. It is shown that an enhanced inverse magnetocaloric effect occurs around the temperature interval ${{T}_{\text{c}}}(B\ne 0)\lesssim T<{{T}_{\text{c}}}(B=0)$ for any magnetic-field change $\Delta B:0\to B$. The most pronounced inverse magnetocaloric effect can be found nearby the critical field, which corresponds to the zero-temperature phase transition from the long-range ordered ground state to the paramagnetic one. The observed phenomenon increases with an increasing value of decorating spins. Furthermore, sufficiently high values of decorating spins have also been linked to the possibility of observing reentrant phase transitions at finite temperatures.

We have investigated the temperature and the Pt layer thickness dependence of the magnetoresistances (MRs) in Co₂FeSi/Pt thin films. Based on the field dependent measurements, it can be seen that the spin-current-induced spin Hall magnetoresistance (SMR) plays the dominant role in the MRs in the Co₂FeSi/Pt bilayers in the whole temperature range. Meanwhile, a quite small part of anisotropic magnetoresistance (AMR) existed in the MRs. It proved to be originated from magnetic proximity effect (MPE) by measuring the Pt thickness and temperature dependence of the AMR. Moreover, the Co₂FeSi layer thickness has much weaker effect on the SMR and AMR compared to the Pt layer thickness. These results indicate that the Co₂FeSi/Pt interface is beneficial to be used in the spin-current-induced physical phenomena.

We study theoretically the light-induced magnetization switching in a binary ferrimagnet of the type ${{A}_{p}}\,{{B}_{1-p}}$, randomly occupied by two different species of magnetic ions. The localized spins are coupled with spins of itinerant electrons via s-d exchange interaction. Model parameters are chosen so that to achieve similarity between magnetic characteristics of the model and those of ferrimagnetic rare-earth-transition metal GdFeCo alloys. The switching is triggered by heating of the itinerant electrons by a laser pulse. The spin dynamics is governed by the cooling of itinerant electrons, exchange scattering, induced by the s-d exchange interaction and spin-lattice relaxation of the itinerant spins with a characteristic time ${{\tau}_{s}}$. The dynamics of the localized and itinerant spins is described by coupled rate equations. The main conclusion of this study is that the switching occurs only in a certain temperature range depending on ${{\tau}_{s}}$. For long ${{\tau}_{s}}$ the switching occurs only below the magnetisation compensation temperature T_K. For physically reasonable values of ${{\tau}_{s}}$ this temperature range extends from 0 K to ${{T}_{f}}\,\left({{\tau}_{s}}\right)$, where ${{T}_{f}}\,\left({{\tau}_{s}}\right)$ is slightly higher than the compensation temperature T_K. With further decrease of ${{\tau}_{s}}$ this temperature range shifts to temperatures higher than T_K.