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The effective mass of Abrikosov vortices in superconductors remains a challenging problem with limited experimental verification. In this paper, we present a method based on observation of the vortex mass in magnetic circular dichroism at terahertz frequencies. We demonstrate the emergence of dichroism with decreasing temperature in two YBa$_2$Cu$_3$O$_{7-\delta}$ thin films of different doping. The experimental results can be explained within a theoretical model that takes into account the vortex mass and provides an expression for the optical complex conductivity. We discuss the model parameters and show how they are obtained from the supporting experiments., Comment: 5 pages, 3 figures

The complex conductivity of underdoped and optimally doped YBa$_2$Cu$_3$O$_{7-\delta}$ samples and overdoped similar compound Y$_{0.7}$Ca$_{0.3}$Ba$_2$Cu$_3$O$_{7-\delta}$ was measured using time-domain terahertz spectroscopy. In the normal state, the frequency dependence is described by the Drude model. Below the critical temperature $T_\mathrm{c}$, the two-fluid model was successfully employed to fit all the spectra, from 5 K up to $T_\mathrm{c}$. The temperature behaviour of fundamental parameters such as the scattering rate $1/\tau$, the superfluid (normal) fraction $f_\mathrm{s}$ ($f_\mathrm{n}$) and the conductivity $\sigma$ was investigated at given frequencies. For the optimally doped and the overdoped samples, even at 5 K, a fifth of the electrons do not condense to the superfluid fraction. We observed that a substantial fraction of electrons do not condense to the superfluid fraction even at 5 K for optimally doped and overdoped samples. The real part of the conductivity $\sigma_1(T)$ exhibits a peak at low frequencies. It can be observed for all three stoichiometries and its exact shape depends on the quality of the sample. A further analysis shows that this peak is a consequence of the competition between the scattering time $\tau(T)$ and the superfluid fraction $f_\mathrm{s}(T)$., Comment: 8 pages, 6 figures + Supplemental material 2pages, 3 figures

Type-II multiferroics, where spin interactions induce a ferroelectric polarization, are interesting for new device functionalities due to large magnetoelectric coupling. We report on a new type of multiferroicity in the quadruple-perovskite $\text{BiMn}_{\text{3}}\text{Cr}_{\text{4}}\text{O}_{\text{12}}$, where an antiferromagnetic phase is induced by the structural change at the ferroelectric phase transition. The displacive nature of the ferroelectric phase transition at 125 K, with a crossover to an order-disorder mechanism, is evidenced by a polar soft phonon in the THz range and a central mode. Dielectric and pyroelectric studies show that the ferroelectric critical temperature corresponds to the previously reported N\'eel temperature of the $\text{Cr}^{\text{3+}}$ spins. An increase in ferroelectric polarization is observed below 48 K, coinciding with the N\'eel temperature of the $\text{Mn}^{\text{3+}}$ spins. This increase in polarization is attributed to an enhanced magnetoelectric coupling, as no change in the crystal symmetry below 48 K is detected from infrared and Raman spectra.

We use the synergy of infrared, terahertz, and Raman spectroscopies with DFT calculations to shed light on the magnetic and lattice properties of VI3. The structural transition at TS1 = 79 K is accompanied by a large splitting of polar phonon modes. Below TS1, strong ferromagnetic fluctuations are observed. The variations of phonon frequencies at 55 K induced by magnetoelastic coupling enhanced by spin-orbit interaction indicate the proximity of long-range ferromagnetic order. Below TC = 50 K, two Raman modes simultaneously appear and show dramatic softening in the narrow interval around the temperature TS2 of the second structural transition associated with the order-order magnetic phase transition. Below TS2, a magnon in the THz range appears in Raman spectra. The THz magnon observed in VI3 indicates the application potential of 2D van der Waals ferromagnets in ultrafast THz spintronics, which has previously been considered an exclusive domain of antiferromagnets., Comment: Accepted in Journal of Physical Chemistry Letters

The collective dynamics of topological structures have been of great interest from both fundamental and applied perspectives. For example, the studies of dynamical properties of magnetic vortices and skyrmions not only deepened the understanding of many-body physics but also led to potential applications in data processing and storage. Topological structures constructed from electrical polarization rather than spin have recently been realized in ferroelectric superlattices, promising for ultrafast electric-field control of topological orders. However, little is known about the dynamics of such complex extended nanostructures which in turn underlies their functionalities. Using terahertz-field excitation and femtosecond x-ray diffraction measurements, we observe ultrafast collective polarization dynamics that are unique to polar vortices, with orders of magnitude higher frequencies and smaller lateral size than those of experimentally realized magnetic vortices. A previously unseen soft mode, hereafter referred to as a vortexon, emerges as transient arrays of nanoscale circular patterns of atomic displacements, which reverse their vorticity on picosecond time scales. Its frequency is significantly reduced at a critical strain, indicating a condensation of structural dynamics. First-principles-based atomistic calculations and phase-field modeling reveal the microscopic atomic arrangements and frequencies of the vortex modes. The discovery of subterahertz collective dynamics in polar vortices opens up opportunities for applications of electric-field driven data processing in topological structures with ultrahigh speed and density.

Mass of Abrikosov vortices defied experimental observation for more than four decades. We demonstrate a method of its detection in high-temperature superconductors. Similarly to electrons, fluxons circulate in the direction given by the magnetic field, causing circular dichroism. We report the magneto-transmittance of a nearly optimally doped thin YBaCuO film, measured using circularly polarized submillimeter waves. The circular dichroism emerges in the superconducting state and increases with dropping temperature. Our results confirm the dominant role of quasiparticle states in the vortex core and yield the diagonal fluxon mass of 2.2 x 10^8 electron masses per centimeter at 45 K and zero-frequency limit and even larger off-diagonal mass of 4.9 x 10^8 electron masses per centimeter., Comment: 5 pages 3 figures + Supplemental material 3 pages

We investigated static and dynamic magnetoelectric properties of single crystalline BaSrCoZnFe$_{11}$AlO$_{22}$ which is a room-temperature multiferroic with Y-type hexaferrite crystal structure. Below $300\,\rm K$, a purely electric-dipole-active electromagnon at $\approx 1.2\,\rm THz$ with the electric polarization oscillating along the hexagonal axis was observed by THz and Raman spectroscopies. We investigated the behavior of the electromagnon with applied DC magnetic field and linked its properties to static measurements of the magnetic structure. Our analytical calculations determined selection rules for electromagnons activated by the magnetostriction mechanism in various magnetic structures of Y-type hexaferrite. Comparison with our experiment supports that the electromagnon is indeed activated by the magnetostriction mechanism involving spin vibrations along the hexagonal axis.

The structural phase transition in hexagonal BaMnO$_3$ occurring at $T_c$=130 K was studied in ceramic samples using electron and X-ray diffraction, second harmonic generation as well as by dielectric and lattice dynamic spectroscopies. The low-temperature phase (space group $P6_{3}cm$) is ferroelectric with a triplicated unit cell. The phase transition is driven by an optical soft mode from the Brillouin-zone boundary [$q = (\frac{1}{3},\frac{1}{3},0)$]; this mode activates in infrared and Raman spectra below $T_c$ and it hardens according to the Cochran law. Upon cooling below $T_c$, the permittivity exhibits an unusual linear increase with temperature; below 60 K, in turn, a frequency-dependent decrease is observed, which can be explained by slowing-down of ferroelectric domain wall motions. Based on our data we could not distinguish whether the high-temperature phase is paraelectric or polar (space groups $P6_{3}/mmc$ or $P6_{3}mc$, respectively). Both variants of the phase transition to the ferroelectric phase are discussed based on the Landau theory. Electron paramagnetic resonance and magnetic susceptibility measurements reveal an onset of one-dimensional antiferromagnetic ordering below $\approx220\,\rm K$ which develops fully near 140 K and, below $T_{n} \approx 59\,\rm K$, it transforms into a three-dimensional antiferromagnetic order., Comment: 14 pages, 10 figures, Phys. Rev. B, in press

We studied experimentally the high-temperature magnetoelectric $({\rm Ba}_{x}{\rm Sr}_{1-x})_3\rm Co_2Fe_{24}O_{41}$ prepared as ceramics (x = 0, 0.2) and a single crystal (x = 0.5) using inelastic neutron scattering, THz time-domain, Raman and far-infrared spectroscopies. The spectra, measured with varying temperature and magnetic field, reveal rich information about the collective spin and lattice excitations. In the ceramics, we observed an infrared-active magnon which is absent in $E^{\omega}\perp z$ polarized THz spectra of the crystal, and we assume that it is an electromagnon active in $E^{\omega} \| z$ polarized spectra. On heating from 7 to 250 K, the frequency of this electromagnon drops from 36 to 25 cm$^{-1}$ and its damping gradually increases, so it becomes overdamped at room temperature. Applying external magnetic field has a similar effect on the damping and frequency of the electromagnon, and the mode is no more observable in the THz spectra above 2 T, as the transverse-conical magnetic structure transforms into a collinear one. Raman spectra reveal another spin excitation with a slightly different frequency and much higher damping. Upon applying magnetic field higher than 3 T, in the low-frequency part of the THz spectra, a narrow excitation appears whose frequency linearly increases with magnetic field. We interpret this feature as the ferromagnetic resonance., Comment: Paper 8 pages + Suppl. Materials 3 pages

Spin and lattice dynamics of CaMn7O12 ceramics were investigated using infrared, THz and inelastic neutron scattering (INS) spectroscopies in the temperature range 2 to 590 K, and, at low temperatures, in applied magnetic fields of up to 12 T. On cooling, we observed phonon splitting accompanying the structural phase transition at Tc = 450K as well as the onset of the incommensurately modulated structure at 250 K. In the two antiferromagnetic phases below T_N1 = 90K and T_N2 = 48 K, several infrared-active excitations emerge in the meV range; their frequencies correspond to the maxima in the magnon density of states obtained by INS. At the magnetic phase transitions, these modes display strong anomalies and for some of them, a transfer of dielectric strength from the higher-frequency phonons is observed. We propose that these modes are electromagnons. Remarkably, at least two of these modes remain active also in the paramagnetic phase; for this reason, we call them paraelectromagnons. In accordance with this observation, quasielastic neutron scattering revealed short-range magnetic correlations persisting within temperatures up to 500K above T_N1.

Electromagnons are known from multiferroics as spin waves excited by the electric component of electromagnetic radiation. We report the discovery of an excitation in the far-infrared spectra of eps-Fe2O3 which we attribute to an electromagnon appearing below 110 K, where the ferrimagnetic structure becomes incommensurately modulated. Inelastic neutron scattering shows that the electromagnon energy corresponds to that of a magnon from the Brillouin zone boundary. Dielectric measurements did not reveal any sign of ferroelectricity in eps-Fe2O3 down to 10 K, despite its acentric crystal structure. This shows that the activation of an electromagnon requires, in addition to the polar ferrimagnetic structure, a modulation of the magnetic structure. We demonstrate that a combination of inelastic neutron scattering with infrared and / or terahertz spectroscopies allows detecting electromagnons in ceramics, where no crystal-orientation analysis of THz and infrared spectra is possible., Comment: accepted to Phys. Rev. B

Dielectric and magnetic properties of Eu0.5Ba0.25Sr0.25TiO3 are investigated between 10 K and 300 K in the frequency range from 10 Hz to 100 THz. A peak in permittivity revealed near 130 K and observed ferroelectric hysteresis loops prove the ferroelectric order below thistemperature. The peak in permittivity is given mainly by softening of the lowest frequency polar phonon (soft mode revealed in THz and IR spectra) that demonstrates displacive character of the phase transition. Room-temperature X-ray diffraction analysis reveals cubic structure, but the IR reflectivity spectra give evidence of a lower crystal structure, presumably tetragonal I4/mcm with tilted oxygen octahedra as it has been observed in EuTiO3. The magnetic measurements show that the antiferromagnetic order occurs below 1.8 K. Eu0.5Ba0.25Sr0.25TiO3 has three times lower coercive field than Eu0.5Ba0.5TiO3, therefore we propose this system for measurements of electric dipole moment of electron., Comment: Phase Transitions, in press

Sr_(9-x)PbxCe2Ti12O36 system is derived from the perovskite SrTiO3 and its chemical formula can be written as (Sr_(1-y)Pby)0.75Ce0.167TiO3. We investigated dielectric response of Sr_(9-x)PbxCe2Ti12O36 ceramics (x = 0-9) between 100 Hz and 100 THz at temperatures from 10 to 700 K using low- and high-frequency dielectric, microwave (MW), THz and infrared spectroscopy. We revealed that Sr9Ce2Ti12O36 is an incipient ferroelectric with the R-3c trigonal structure whose relative permittivity e' increases from 167 at 300 K and saturates near 240 below 30 K. The subsequent substitution of Sr by Pb enhances e' to several thousands and induces a ferroelectric phase transition to monoclinic Cc phase for x>=3. Its critical temperature Tc linearly depends on the Pb concentration and reaches 550 K for x=9. The phase transition is of displacive type. The soft mode frequency follows the Barrett formula in samples with x<=2 (typical for quantum paraelectrics) and the Cochran formula for x>=3. The MW dispersion is lacking and quality factor Q is high in samples with low Pb concentration, although the permittivity is very high in some cases. However, due to the lattice softening, the temperature coefficient of the permittivity is rather high. The best MW quality factor was observed for x=1: Q*f=5800 GHz and e'=250. Concluding, the dielectric properties of Sr_(9- x)PbxCe2Ti12O36 are similar to those of Ba_(1-x)SrxTiO3 so that this system can be presumably used as an alternative for MW devices or capacitors., Comment: subm. to Chem. Mater