Static and dynamic properties of Single-Chain Magnets with sharp and broad domain walls

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 anisotropy 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.Comment: 18 pages, 13 figures, to be published in Phys. Rev.

Critical exponents and scaling invariance in the absence of a critical point

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 length -- 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.Comment: 10 pages, added figure 1, rearranged section

One-dimensional Ising ferromagnet frustrated by long-range interactions at finite temperatures

We consider a one-dimensional lattice of Ising-type variables where the ferromagnetic exchange interaction J between neighboring sites is frustrated by a long-ranged anti-ferromagnetic interaction of strength g between the sites i and j, decaying as |i-j|^-alpha, with alpha>1. For alpha smaller than a certain threshold alpha_0, which is larger than 2 and depends on the ratio J/g, the ground state consists of an ordered sequence of segments with equal length and alternating magnetization. The width of the segments depends on both alpha and the ratio J/g. Our Monte Carlo study shows that the on-site magnetization vanishes at finite temperatures and finds no indication of any phase transition. Yet, the modulation present in the ground state is recovered at finite temperatures in the two-point correlation function, which oscillates in space with a characteristic spatial period: The latter depends on alpha and J/g and decreases smoothly from the ground-state value as the temperature is increased. Such an oscillation of the correlation function is exponentially damped over a characteristic spatial scale, the correlation length, which asymptotically diverges roughly as the inverse of the temperature as T=0 is approached. This suggests that the long-range interaction causes the Ising chain to fall into a universality class consistent with an underlying continuous symmetry. The e^(Delta/T)-temperature dependence of the correlation length and the uniform ferromagnetic ground state, characteristic of the g=0 discrete Ising symmetry, are recovered for alpha > alpha_0.Comment: 12 pages, 7 figure

NetKet 3: Machine Learning Toolbox for Many-Body Quantum Systems

We introduce version 3 of NetKet, the machine learning toolbox for many-body quantum physics. NetKet is built around neural-network quantum states and provides efficient algorithms for their evaluation and optimization. This new version is built on top of JAX, a differentiable programming and accelerated linear algebra framework for the Python programming language. The most significant new feature is the possibility to define arbitrary neural network ansätze in pure Python code using the concise notation of machine-learning frameworks, which allows for just-in-time compilation as well as the implicit generation of gradients thanks to automatic differentiation. NetKet 3 also comes with support for GPU and TPU accelerators, advanced support for discrete symmetry groups, chunking to scale up to thousands of degrees of freedom, drivers for quantum dynamics applications, and improved modularity, allowing users to use only parts of the toolbox as a foundation for their own code

Scale invariance of a diodelike tunnel junction

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.Comment: 6 pages, 6 figures. Accepted for publication in Physical Review

Magnetic susceptibility of EuTe/PbTe Heisenberg superlattices: experimental and theoretical studies

We report results on the temperature dependence of the susceptibilities of a set of MBE-grown short-period EuTe/PbTe antiferromagnetic superlattices having different EuTe layer thicknesses. In-plane and orthogonal susceptibilities have been measured and display a strong anisotropy at low temperature, confirming the occurrence of a magnetic phase transition in the thicker samples, as seen also in neutron diffraction studies. We suggest that dipolar interactions stabilize antiferromagnetic long-range order in an otherwise isotropic system and we present numerical and analytical results for the low-temperature orthogonal susceptibility.Comment: 30 pages, 8 ps figures, RevTe

Electron spin-lattice relaxation of Yb3+ and Gd3+ ions in glasses

The electron spin-lattice relaxation rate (T1 -1) was measured in two glass samples: (i) a phosphate glass doped with 1 wt% Yb2O3 and (ii) a Li2Si4O9 glass sample doped with 0.2 wt% Gd2O3. In the Yb3+-doped glass sample, T1, was measured by an electron-spin-echo technique from 4.2 to 6 K, by the modulation method from 10 to 26 K and by the EPR linewidth from 30 to 100 K. It was found that (T1 -1) ∝ Tn with n = 9 in the range 4.2-6 K. n decreased gradually as the temperature was increased and tended towards 2 above 40 K. Over the entire temperature range 4.2-100 K, (T1 -1) was fitted to AT + BT9J8 (ΘD/T) (where A and B are two temperature-independent constants, J8 is the well-known Van Vleck integral and ΘD is the Debye temperature). The value of ΘD (= 46.3±0.9 K) so determined is in good agreement with that of Stevens and Stapleton from their T1, measurements in the range 1.5 to 7 K. In the Gd3+-doped glass, it was observed that (T1 -1) ∝ T over the range 50-150 K. The data for Ye3+-doped glass sample were accounted for by assuming that the phonon modulation of the ligand field is the dominant mechanism, associated with a low Debye temperature in accordance with the published data obtained by using other techniques to study lattice dynamics. On the other hand, the data on the Gd3+-doped glass sample were explained to be predominantly due to a mechanism involving Two-Level-Systems (TLS). © Springer-Verlag 1996 Printed in Austria

Ferromagnetism and Temperature-Driven Reorientation Transition in Thin Itinerant-Electron Films

The temperature-driven reorientation transition which, up to now, has been studied by use of Heisenberg-type models only, is investigated within an itinerant-electron model. We consider the Hubbard model for a thin fcc(100) film together with the dipole interaction and a layer-dependent anisotropy field. The isotropic part of the model is treated by use of a generalization of the spectral-density approach to the film geometry. The magnetic properties of the film are investigated as a function of temperature and film thickness and are analyzed in detail with help of the spin- and layer-dependent quasiparticle density of states. By calculating the temperature dependence of the second-order anisotropy constants we find that both types of reorientation transitions, from out-of-plane to in-plane (``Fe-type'') and from in-plane to out-of-plane (``Ni-type'') magnetization are possible within our model. In the latter case the inclusion of a positive volume anisotropy is vital. The reorientation transition is mediated by a strong reduction of the surface magnetization with respect to the inner layers as a function of temperature and is found to depend significantly on the total band occupation.Comment: 10 pages, 8 figures included (eps), Phys Rev B in pres

A Scaling Hypothesis for Modulated Systems

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 distance. 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.Comment: 13 pages, 6 figures, expanded versio