Coupling Matrix Representation of Nonreciprocal Filters Based on Time Modulated Resonators

This paper addresses the analysis and design of non-reciprocal filters based on time modulated resonators. We analytically show that time modulating a resonator leads to a set of harmonic resonators composed of the unmodulated lumped elements plus a frequency invariant element that accounts for differences in the resonant frequencies. We then demonstrate that harmonic resonators of different order are coupled through non-reciprocal admittance inverters whereas harmonic resonators of the same order couple with the admittance inverter coming from the unmodulated filter network. This coupling topology provides useful insights to understand and quickly design non-reciprocal filters and permits their characterization using an asynchronously tuned coupled resonators network together with the coupling matrix formalism. Two designed filters, of orders three and four, are experimentally demonstrated using quarter wavelength resonators implemented in microstrip technology and terminated by a varactor on one side. The varactors are biased using coplanar waveguides integrated in the ground plane of the device. Measured results are found to be in good agreement with numerical results, validating the proposed theory

Magnetic transitions in Pr2NiO4 single crystal

The magnetic properties of a stoichiometric Pr2NiO4 single crystal have been examined by means of the temperature dependence of the complex ac susceptibility and the isothermal magnetization in fields up to 200 kOe at T=4.2 K. Three separate phases have been identified and their anisotropic character has been analyzed. A collinear antiferromagnetic phase appears first between TN = 325 K and Tc1 = 115 K, where the Pr ions are polarized by an internal magnetic field. At Tc1 a first modification of the magnetic structure occurs in parallel with a structural phase transition (Bmab to P42/ncm). This magnetic transition has a first‐order character and involves both the out‐of‐plane and the in‐plane spin components (magnetic modes gx and gxcyfz, respectively). A second magnetic transition having also a first‐order character is also clearly identified at Tc2 = 90 K which corresponds to a spin reorientation process (gxcyfz to cxgyaz magnetic modes). It should be noted as well that the out‐of‐phase component of χac shows a peak around 30 K which reflects the coexistence of both magnetic configurations in a wide temperature interval. Finally, two field‐induced transitions have been observed at 4.2 K when the field is directed along the c axis. We propose that the high‐field anomaly arises from a metamagnetic transition of the weak ferromagnetic component, similarly to La2CuO4

Effect of the spin-orbit interaction on the thermodynamic properties of crystals: The specific heat of bismuth

In recent years, there has been increasing interest in the specific heat $C$ of insulators and semiconductors because of the availability of samples with different isotopic masses and the possibility of performing \textit{ab initio} calculations of its temperature dependence $C(T)$ using as a starting point the electronic band structure. Most of the crystals investigated are elemental (e.g., germanium) or binary (e.g., gallium nitride) semiconductors. The initial electronic calculations were performed in the local density approximation and did not include spin-orbit interaction. Agreement between experimental and calculated results was usually found to be good, except for crystals containing heavy atoms (e.g., PbS) for which discrepancies of the order of 20% existed at the low temperature maximum found for $C/T^3$. It has been conjectured that this discrepancies result from the neglect of spin-orbit interaction which is large for heavy atoms ($\Delta_0\sim$1.3eV for the $p$ valence electrons of atomic lead). Here we discuss measurements and \textit{ab initio} calculations of $C(T)$ for crystalline bismuth ($\Delta_0\sim$1.7 eV), strictly speaking a semimetal but in the temperature region accessible to us ($T >$ 2K) acting as a semiconductor. We extend experimental data available in the literature and notice that the \textit{ab initio} calculations without spin-orbit interaction exhibit a maximum at $\sim$8K, about 20% lower than the measured one. Inclusion of spin-orbit interaction decreases the discrepancy markedly: The maximum of $C(T)$ is now only 7% larger than the measured one. Exact agreement is obtained if the spin-orbit hamiltonian is reduced by a factor of $\sim$0.8.Comment: 4 pages, 3 figure

Nonreciprocal Wavefront Engineering with Time-Modulated Gradient Metasurfaces

We propose a paradigm to realize nonreciprocal wavefront engineering using time-modulated gradient metasurfaces. The essential building block of these surfaces is a subwavelength unit cell whose reflection coefficient oscillates at low frequency. We demonstrate theoretically and experimentally that such modulation permits tailoring the phase and amplitude of any desired nonlinear harmonic and determines the behavior of all other emerging fields. By appropriately adjusting the phase delay applied to the modulation of each unit cell, we realize time-modulated gradient metasurfaces that provide efficient conversion between two desired frequencies and enable nonreciprocity by (i) imposing drastically different phase gradients during the up/down conversion processes and (ii) exploiting the interplay between the generation of certain nonlinear surface and propagative waves. To demonstrate the performance and broad reach of the proposed platform, we design and analyze metasurfaces able to implement various functionalities, including beam steering and focusing, while exhibiting strong and angle-insensitive nonreciprocal responses. Our findings open an alternative direction in the field of gradient metasurfaces, in which wavefront control and magnetic-free nonreciprocity are locally merged to manipulate the scattered fields