Search Results (12)

In this work, we study the magnetocaloric effect (MCE) in a working substance corresponding to a square lattice of spins with Q possible orientations, known as the “Q-state clock model”. When the Q-state clock model has $Q\ge 5$ possible configurations, it presents the famous Berezinskii–Kosterlitz–Thouless (BKT) phase associated with vortex states. We calculate the thermodynamic quantities using Monte Carlo simulations for even Q numbers, ranging from $Q=2$ to $Q=8$ spin orientations per site in a lattice. We use lattices of different sizes with $N=L\times L=8^2,{16}^2,{32}^2,{64}^2,\mathrm{and}{128}^2$ sites, considering free boundary conditions and an external magnetic field varying between $B=0$ and $B=1.0$ in natural units of the system. By obtaining the entropy, it is possible to quantify the MCE through an isothermal process in which the external magnetic field on the spin system is varied. In particular, we find the values of Q that maximize the MCE depending on the lattice size and the magnetic phase transitions linked with the process. Given the broader relevance of the Q-state clock model in areas such as percolation theory, neural networks, and biological systems, where multi-state interactions are essential, our study provides a robust framework in applied quantum mechanics, statistical physics, and related fields. Full article

We fabricated high-quality c-axis-oriented epitaxial YBa₂Cu₃O_7−x films with 15% of the yttrium atoms replaced by terbium (YTBCO) and studied their electrical properties. The Tb substitution reduced the charge carrier density, resulting in increased resistivity and decreased critical current density compared to pure YBa₂Cu₃O_7−x films. The electrical properties of the YTBCO films showed an in-plane anisotropy in both the superconducting and normal states that, together with the XRD data, provided evidence for, at least, a partially twin-free film. Unexpectedly, the resistive transition of the bridges also demonstrated the in-plane anisotropy that could be explained within the framework of Tinkham’s model of resistive transition and the Berezinskii–Kosterlitz–Thouless (BKT) model, depending on the sample parameters. Measurements of the differential resistance in the temperature range of the resistive transition confirmed the occurrence of the BKT transition in the YTBCO bridges. Therefore, we consider the YTBCO films to be a promising platform for both the fabrication of devices with high kinetic inductance and fundamental research on the BKT transition in cuprate superconductors. Full article

Superconducting nanofilms are tunable systems that can host a 3D–2D dimensional crossover leading to the Berezinskii–Kosterlitz–Thouless (BKT) superconducting transition approaching the 2D regime. Reducing the dimensionality further, from 2D to quasi-1D superconducting nanostructures with disorder, can generate quantum and thermal phase slips (PS) of the order parameter. Both BKT and PS are complex phase-fluctuation phenomena of difficult experiments. We characterized superconducting NbN nanofilms thinner than 15 nm, on different substrates, by temperature-dependent resistivity and current–voltage (I-V) characteristics. Our measurements evidence clear features related to the emergence of BKT transition and PS events. The contemporary observation in the same system of BKT transition and PS events, and their tunable evolution in temperature and thickness was explained as due to the nano-conducting paths forming in a granular NbN system. In one of the investigated samples, we were able to trace and characterize the continuous evolution in temperature from quantum to thermal PS. Our analysis established that the detected complex phase phenomena are strongly related to the interplay between the typical size of the nano-conductive paths and the superconducting coherence length. Full article

We review our theoretical results of the sound propagation in two-dimensional (2D) systems of ultracold fermionic and bosonic atoms. In the superfluid phase, characterized by the spontaneous symmetry breaking of the $U\left(1\right)$ symmetry, there is the coexistence of first and second sound. In the case of weakly-interacting repulsive bosons, we model the recent measurements of the sound velocities of ${}^{39}$K atoms in 2D obtained in the weakly-interacting regime and around the Berezinskii–Kosterlitz–Thouless (BKT) superfluid-to-normal transition temperature. In particular, we perform a quite accurate computation of the superfluid density and show that it is reasonably consistent with the experimental results. For superfluid attractive fermions, we calculate the first and second sound velocities across the whole BCS-BEC crossover. In the low-temperature regime, we reproduce the recent measurements of first-sound speed with ${}^6$Li atoms. We also predict that there is mixing between sound modes only in the finite-temperature BEC regime. Full article

We investigate the effects of higher-order quantum fluctuations on the bulk properties of self-bound droplets in three-, two- and one-dimensional binary Bose mixtures using the Hartree–Fock–Bogoliubov theory. We calculate higher-order corrections to the equation of state of the droplet at both zero and finite temperatures. We show that our results for the ground-state energy are in a good agreement with recent quantum Monte Carlo simulations in any dimension. Our study extends to the finite temperature case where it is found that thermal fluctuations may destabilize the droplet state and eventually destroy it. In two dimensions, we reveal that the droplet occurs at temperatures well below the Berezinskii–Kosterlitz–Thouless transition temperature. Full article

This present work explores the performance of a thermal–magnetic engine of Otto type, considering as a working substance an effective interacting spin model corresponding to the $q-$ state clock model. We obtain all the thermodynamic quantities for the q = 2, 4, 6, and 8 cases in a small lattice size ($3\times 3$ with free boundary conditions) by using the exact partition function calculated from the energies of all the accessible microstates of the system. The extension to bigger lattices was performed using the mean-field approximation. Our results indicate that the total work extraction of the cycle is highest for the $q=4$ case, while the performance for the Ising model ($q=2$) is the lowest of all cases studied. These results are strongly linked with the phase diagram of the working substance and the location of the cycle in the different magnetic phases present, where we find that the transition from a ferromagnetic to a paramagnetic phase extracts more work than one of the Berezinskii–Kosterlitz–Thouless to paramagnetic type. Additionally, as the size of the lattice increases, the extraction work is lower than smaller lattices for all values of q presented in this study. Full article

In this study, we measure the in-plane transport properties of high-quality Ba(Fe_0.914Co_0.086)₂As₂ single crystals. Signatures of vortex unbinding Berezinskii–Kosterlitz–Thouless (BKT) transition are shown from both the conventional approach and the Fisher–Fisher–Huse dynamic scaling analysis, in which a characteristic Nelson–Kosterlitz jump is demonstrated. We also observe a non-Hall transverse signal exactly at the superconducting transition, which is explained in terms of guided motion of unbound vortices. Full article

Beyond the usual ferromagnetic and paramagnetic phases present in spin systems, the usual q-state clock model presents an intermediate vortex state when the number of possible orientations q for the system is greater than or equal to 5. Such vortex states give rise to the Berezinskii-Kosterlitz-Thouless (BKT) phase present up to the XY model in the limit $q\to \infty$. Based on information theory, we present here an analysis of the classical order parameters plus new short-range parameters defined here. Thus, we show that even using the first nearest neighbors spin-spin correlations only, it is possible to distinguish the two transitions presented by this system for q greater than or equal to 5. Moreover, the appearance at relatively low temperature and disappearance of the BKT phase at a rather fix higher temperature is univocally determined by the short-range interactions recognized by the information content of classical and new parameters. Full article

Octacyanometallate-based compounds displaying a rich pallet of interesting physical and chemical properties, are key materials in the field of molecular magnetism. The [M(CN)₈]ⁿ⁻ complexes, (M = W^V, Mo^V, Nb^IV), are universal building blocks as they lead to various spatial structures, depending on the surrounding ligands and the choice of the metal ion. One of the functionalities of the octacyanometallate-based coordination polymers or clusters is the magnetocaloric effect (MCE), consisting in a change of the material temperature upon the application of a magnetic field. In this review, we focus on different approaches to MCE investigation. We present examples of magnetic entropy change ΔS_m and adiabatic temperature change ΔT_ad, determined using calorimetric measurements supplemented with the algebraic extrapolation of the data down to 0 K. At the field change of 5T, the compound built of high spin clusters Ni₉[W(CN)₈]₆ showed a maximum value of −ΔS_m equal to 18.38 J·K⁻¹ mol⁻¹ at 4.3 K, while the corresponding maximum ΔT_ad = 4.6 K was attained at 2.2 K. These values revealed that this molecular material may be treated as a possible candidate for cryogenic magnetic cooling. Values obtained for ferrimagnetic polymers at temperatures close to their magnetic ordering temperatures, T_c, were lower, i.e., −ΔS_m = 6.83 J·K⁻¹ mol⁻¹ (ΔT_ad = 1.42 K) and −ΔS_m = 4.9 J·K⁻¹ mol⁻¹ (ΔT_ad = 2 K) for {[Mn^II(pyrazole)₄]₂[Nb^IV(CN)₈]·4H₂O}_n and{[Fe^II(pyrazole)₄]₂[Nb^IV(CN)₈]·4H₂O}_n, respectively. MCE results have been obtained also for other -[Nb(CN)₈]-based manganese polymers, showing significant T_c dependence on pressure or the remarkable magnetic sponge behaviour. Using the data obtained for compounds with different T_c, due to dissimilar ligands or other phase of the material, the ΔS_m ~ T_c^−2/3 relation stemming from the molecular field theory was confirmed. The characteristic index n in the ΔS_m ~ ΔHⁿ dependence, and the critical exponents, related to n, were determined, pointing to the 3D Heisenberg model as the most adequate for the description of these particular compounds. At last, results of the rotating magnetocaloric effect (RMCE), which is a new technique efficient in the case of layered magnetic systems, are presented. Data have been obtained and discussed for single crystals of two 2D molecular magnets: ferrimagnetic {Mn^II(R-mpm)₂]₂[Nb^IV(CN)₈]}∙4H₂O (mpm = α-methyl-2-pyridinemethanol) and a strongly anisotropic (tetren)Cu₄[W(CN)₈]₄ bilayered magnet showing the topological Berezinskii-Kosterlitz-Thouless transition. Full article

Quantum Heisenberg chain and square lattices are important paradigms of a low-dimensional magnetism. Their ground states are determined by the strength of quantum fluctuations. Correspondingly, the ground state of a rectangular lattice interpolates between the spin liquid and the ordered collinear Néel state with the partially reduced order parameter. The diversity of additional exchange interactions offers variety of quantum models derived from the aforementioned paradigms. Besides the spatial anisotropy of the exchange coupling, controlling the lattice dimensionality and ground-state properties, the spin anisotropy (intrinsic or induced by the magnetic field) represents another important effect disturbing a rotational symmetry of the spin system. The S = 1/2 easy-axis and easy-plane XXZ models on the square lattice even for extremely weak spin anisotropies undergo Heisenberg-Ising and Heisenberg-XY crossovers, respectively, acting as precursors to the onset of the finite-temperature phase transitions within the two-dimensional Ising universality class (for the easy axis anisotropy) and a topological Berezinskii–Kosterlitz–Thouless phase transition (for the easy-plane anisotropy). Experimental realizations of the S = 1/2 two-dimensional XXZ models in bulk quantum magnets appeared only recently. Partial solutions of the problems associated with their experimental identifications are discussed and some possibilities of future investigations in quantum magnets on the square and rectangular lattice are outlined. Full article

In this paper, we revisit the q-state clock model for small systems. We present results for the thermodynamics of the q-state clock model for values from $q=2$ to $q=20$ for small square lattices of $L\times L$ , with L ranging from $L=3$ to $L=64$ with free-boundary conditions. Energy, specific heat, entropy, and magnetization were measured. We found that the Berezinskii–Kosterlitz–Thouless (BKT)-like transition appears for $q>5$, regardless of lattice size, while this transition at $q=5$ is lost for $L<10$; for $q\le 4$, the BKT transition is never present. We present the phase diagram in terms of q that shows the transition from the ferromagnetic (FM) to the paramagnetic (PM) phases at the critical temperature $T_1$ for small systems, and the transition changes such that it is from the FM to the BKT phase for larger systems, while a second phase transition between the BKT and the PM phases occurs at $T_2$. We also show that the magnetic phases are well characterized by the two-dimensional (2D) distribution of the magnetization values. We made use of this opportunity to carry out an information theory analysis of the time series obtained from Monte Carlo simulations. In particular, we calculated the phenomenological mutability and diversity functions. Diversity characterizes the phase transitions, but the phases are less detectable as q increases. Free boundary conditions were used to better mimic the reality of small systems (far from any thermodynamic limit). The role of size is discussed. Full article

The correct detection of the Berezinskii-Kosterlitz-Thouless (BKT) transition in quasi-two-dimensional superconductors still remains a controversial issue. Its main signatures, indeed, are often at odds with the theoretical expectations. In a recent work (Maccari, I.; Benfatto, L.; Castellani, C. Phys. Rev. B 2017, 96, 060508), we have shown that the presence of spatially correlated disorder plays a key role in this sense because it is the reason underlying the experimentally-observed smearing of the universal superfluid-density jump. In the present paper we closely investigate the effects of correlated disorder on the BKT transition, specifically addressing the issue of whether or not it changes the BKT universality class. Full article