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Multiferroic hexagonal rare-earth ferrites (h-RFeO3, R=Sc, Y, and rare earth), in which the improper ferroelectricity and canted antiferromagnetism coexist, have been advocated as promising candidates to pursue the room-temperature multiferroics, because of strong spin-spin interaction. The strong interactions between the ferroic orders and the structural distortions are appealing for high-density, energy-efficient electronic devices. Over the past decade, remarkable advances in atomic-scale synthesis, characterization, and material modeling enable the significant progresses in the understanding and manipulation of ferroic orders and their couplings in h-RFeO3 thin films. These results reveal a physical picture of rich ferroelectric and magnetic phenomena interconnected by a set of structural distortions and spin-lattice couplings, which provides guidance for the control of ferroic orders down to the nano scale and the discovery of novel physical phenomena. This review focus on state-of-the-art studies in complex phenomena related to the ferroelectricity and magnetism as well as the magnetoelectric couplings in multiferroic h-RFeO3, based on mostly the recent experimental efforts, aiming to stimulate fresh ideas in this field.

We demonstrate the formation of two types of symbiotic nondipolar droplet supersolid in a binary dipolar-nondipolar mixture with an interspecies atraction, where the dipolar (nondipolar) atoms are trapped (untrapped). In the absence of an interspecies attraction, in the first type, a dipolar droplet supersolid exists, whereas in the second type, there are no droplets in the dipolar component. To illustrate, we consider a $^{164}$Dy-$^{87}$Rb mixture, where the untrapped $^{87}$Rb supersolid sticks to the trapped $^{164}$Dy supersolid due to the interspecies attraction and forms a symbiotic supersolid with overlapping droplets. The first (second) type of symbiotic supersolid emerges for the scattering length $ a_1=85a_0$ ($a_1=95a_0$) of $^{164}$Dy atom, while under an appropriate trap a dipolar droplet supersolid exists (does not exist) for no interspecies interaction, where $a_0$ the Bohr radius. This study is based on the numerical solution of an improved binary mean-field model, where we introduce an intraspecies Lee-Huang-Yang interaction in the dipolar component, which stops a dipolar collapse and forms a dipolar supersolid.To observe this symbiotic droplet supersolid, one should prepare the corresponding fully trapped dipolar-nondipolar supersolid and then remove the trap on the nondipolar atoms.

Polycrystalline samples of RE2O2CO3 (RE = Pr, Nd, Gd, Tb, Dy, Ho, Er, and Yb) with a unique rare-earth bilayer of triangular lattice were synthesized and studied by DC and AC magnetic susceptibility. Data reveals various magnetic ground states including (i) a nonmagnetic ground state for the Pr sample; (ii) long range magnetic ordering for the Nd, Gd, Tb, Dy, Ho, and Er samples. Besides the Gd sample, they exhibit field-induced spin state transitions. More interestingly, the series spin state transitions in the Nd and Dy samples could be attributed to the field-induced up-up-down (UUD) spin structure. Neutron powder diffraction (NPD) measurements of the Er sample suggest a spiral spin structure below its TN; and (iii) a short-range ordering for the Yb sample. The disrupted inter-layer interaction due to the shift of Yb3+ ions within the bilayer prevents long range magnetic ordering down to 30 mK and makes it another Yb-related triangular lattice antiferromagnet that has the potential to realize a quantum spin liquid state.

DNA sequences encode vital genetic and biological information, yet these unfixed-length sequences cannot serve as the input of common data mining algorithms. Hence, various representation schemes have been developed to transform DNA sequences into fixed-length numerical representations. However, these schemes face difficulties in learning high-quality representations due to the complexity and sparsity of DNA data. Additionally, DNA sequences are inherently noisy because of mutations. While several schemes have been proposed for their effectiveness, they often lack semantic structure, making it difficult for biologists to validate and leverage the results. To address these challenges, we propose \textbf{Dy-mer}, an explainable and robust DNA representation scheme based on sparse recovery. Leveraging the underlying semantic structure of DNA, we modify the traditional sparse recovery to capture recurring patterns indicative of biological functions by representing frequent K-mers as basis vectors and reconstructing each DNA sequence through simple concatenation. Experimental results demonstrate that \textbf{Dy-mer} achieves state-of-the-art performance in DNA promoter classification, yielding a remarkable \textbf{13\%} increase in accuracy. Moreover, its inherent explainability facilitates DNA clustering and motif detection, enhancing its utility in biological research.

We report the magnetic, magnetoelastic, and magnetotransport properties of single crystals of polar magnets $R$AuGe ($R=$ Dy, Ho, and Gd), grown by Au-Ge self-flux. Magnetization and magnetostriction measurements reveal multi-step metamagnetic transitions for the $c$-axis magnetic field ($H\parallel c$) for DyAuGe and HoAuGe, suggesting magnetic frustration in the triangular lattice of $R$ ions. The magnetic phase diagrams have clarified a close connection between the magnetoelastic property and the emergence of the intermediate metamagentic phase. The magnetic-field dependence of the resistivity and Hall resistivity reveal the semimetallic transport dominated by hole-type carriers, consistent with the behavior in a nonmagnetic analogue YAuGe. We also identify a signature of an anomalous Hall effect (AHE) proportional to the field-induced magnetization in $R=$ Dy, Ho, and Gd. GdAuGe shows magnetic and transport behavior as reported in a previous study using Bi-flux grown single crystals, while the self-flux grown crystal shows larger magnetoresistance ($\sim$ 345\%, at 1.8 K and 9 T) due to higher hole-type carrier mobility ($\sim$ 6400 cm$^2$/Vs). Using the two-band model analysis considering the mobility change during the magnetization process, we extract the anomalous Hall conductivity: $\sim 1200$ S/cm and $\sim 530$ S/cm for $R=$ Dy and Ho, respectively, at 1.8 K with 9 T for $H\parallel c$. The magnitude of conductivity suggests a contribution of intrinsic origin, possibly related to the Berry curvature in the electron bands induced by the time-reversal symmetry breaking and the polar lattice., Comment: 11 pages, 9 figures

We propose a theoretical method to calculate the bound-state $\beta$-decay half-lives of highly-ionized atoms, which is based on the combination of the Takahashi-Yokoi model and our recently-developed projected shell model that can take into account both allowed and first-forbidden transitions of nuclear $\beta$ decay. Three examples that are of much experimental interests, $^{163}$Dy$^{66+}$, $^{187}$Re$^{75+}$ and $^{205}$Tl$^{81+}$ are taken for calculations. The ground and low-lying states of related nuclei are described reasonably. The bound-state $\beta$-decay half-lives of $^{163}$Dy$^{66+}$ and $^{187}$Re$^{75+}$ are described within a factor of two and four by our calculations without and with the quenching factors in allowed and first-forbidden transitions. The bound-state $\beta$-decay half-life of the last $s$-process branching point $^{205}$Tl$^{81+}$ is predicted to be 58 and 305 days for cases without and with the quenching factors in calculations. The presented method provides a theoretical way to calculate systematically the bound-state $\beta$-decay half-lives of nuclei from light to heavy ones including odd-mass and even-mass cases for the first time., Comment: 8 pages, 6 figures, 2 tables, Comments and criticisms are welcome

We report experimental measurements of the dynamical polarizability of dysprosium, at a wavelength of 532 nm. We measure all three components (scalar, vector, tensor) of the anisotropic polarizability for the ground and the excited manifolds of the intercombination transition of Dy at 626 nm. The apparatus on which the measurements are performed is first presented. We obtain with this setup imaging of single Dy atoms with fidelity above 99 % and losses below 2.5 % induced by imaging. We then describe the methods used to extract the polarizability. In particular, we combine a measurement of trap frequency and trap depth on single atoms in optical tweezers, allowing us to obtain a measurement of the ground state polarizability free of errors in trap waist calibration. The obtained values give a magic condition between two Zeeman states in the ground and excited manifolds, which was used to image single atoms in optical tweezer arrays. The scalar polarizability of the ground state is in disagreement with theoretical expectations, calling for future investigations to resolve the discrepancy.

In orthoferrites the rare-earth (R) ion has a big impact on structural and magnetic properties in particular the ionic size influences the octahedral tilt and the R3+- Fe3+ interaction modifies properties like the spin reorientation. Growth induced strain in thin films is another means to modify materials properties since the sign of strain affects the bond length and therefore directly the orbital interaction. Our study focuses on epitaxially grown (010) oriented DyFeO3 and LuFeO3 thin films, thereby investigating the impact of compressive lattice strain on the magnetically active Dy3+ and magnetically inactive Lu3+ compared to uniaxially strained single crystal DyFeO3. The DyFeO3 films exhibits a shift of more than 20K in spin-reorientation temperatures, maintain the antiferromagnetic {\Gamma}4 phase of the Fe-lattice below the spin reorientation, and show double step hysteresis loops for both in-plane directions between 5 K and 390 K. This is the signature of an Fe-spin induced ferromagnetic Dy3+ lattice above the N\'eel temperature of the Dy. The observed shift in the film spin reorientation temperatures vs lattice strain is in good agreement with isostatic single crystal neutron diffraction experiments with a rate of 2 K/ kbar bar., Comment: 18 pages, 5 Figures

In this paper, we report on the magnetic and magnetocaloric features of Dy-substituted YMn$_2$O$_5$ (Y$_{1-x}$Dy$_x$Mn$_2$O$_5$) with $x=$ 0.6, 0.8, and 1 series elaborated by sol-gel method. X-ray diffraction and Raman measurements attest well the high quality of our polycrystalline samples that crystallize in an orthorhombic structure with the Pbam space group. The Raman phonon frequencies were carried out and compared with the lattice dynamics calculations to identify the vibrational properties of all detected modes at room temperature. As expected, our magnetic study reveals that the magnetization was enhanced by the substitution of Y$^{3+}$ by Dy$^{3+}$. The Dy-substituted YMn$_2$O$_5$ sets the N\'eel transition [TN (Mn)] in the temperature range going from 40 to 45 K favoring the emergence of a transition at a very low temperature due to the long-range ordering of the Dy3+ magnetic moments below 13K [TN (Dy)]. Dual peaks in the magnetic entropy change curve are also observed being in good agreement with magnetization data, which enlarges the range of application of these materials. On the other hand, a large magnetocaloric effect is observed close to 13 K which is mainly due the ordering of Dy$^{3+}$ magnetic moments. Also, the incommensurate antiferromagnetic transition of Mn magnetic moment taking place around 40 K affects slightly the entropy change. Our refrigerant capacity (RC) findings are higher compared to the average of RC for a, b, c axis of single crystal samples as HoMn$_2$O$_5$ and TbMn$_2$O$_5$, which confirms that our polycrystalline materials stand for promising magnetic refrigerant candidates that can be invested in space technology, hydrogen and helium liquefaction at cryogenic temperature.

The tunneling dynamics of a magnetic $^{164}$Dy quantum gas in an elongated or pancake skewed double-well trap is investigated with a time-dependent extended Gross-Pitaevskii approach. Upon lifting the energy offset, different tunneling regimes can be identified. In the elongated trap and for sufficiently large offset, the different configurations exhibit collective macroscopic tunneling. For smaller offset, partial reflection from and transmission through the barrier lead to density accumulation in both wells, and eventually to tunneling-locking. One can also reach the macroscopic self-trapping regime for increasing relative dipolar interaction strength, while tunneling vanishes for large barrier heights. A richer dynamical behavior is observed for the pancake-like trap. For instance, the supersolid maintains its shape, while the superfluid density gets distorted signifying the emergence of peculiar excitation patterns in the macroscopic tunneling regime. The findings reported here may offer new ways to probe distinctive dynamical features in the supersolid and droplet regimes., Comment: 14 pages, 10 figures

The paper presents the investigation of ordinary and ternary vanadates with zircon and monazite structures. Vanadates LnVO4 and CaLnZr(VO4)3 , where (Ln = La, Nd, Sm, Eu, Gd, Dy, Yb) and solid solution La0.3Nd0.5Sm0.1Eu0.1VO4, were prepared by precipitation reaction. Bulk ceramic samples were obtained from powders by Spark Plasma Sintering (SPS). The powders and ceramics were examined with several physicochemical methods. The coefficients of thermal expansion at 900{\deg}C were determined. The hydrolytic stability of ceramic materials was studied. The peculiarities of high-rate SPS of powders of ordinary and ternary vanadates were analyzed., Comment: 56 pages, 22 figures, 4 tables, 65 refernces, 1 appendix

Single crystals of DyRh$_2$Si$_2$ and HoRh$_2$Si$_2$ were investigated by thermal expansion and magnetostriction. The different types of magnetic order can clearly be seen in these measurements, particularly the canting of the moments away from the crystallographic $c$ direction below about 12~K and the spin-flip for magnetic field applied along the $c$ direction. For HoRh$_2$Si$_2$, an additional transition just below $T_{\rm N}$ is analyzed by means of the Gr\"{u}neisen ratio and is likely caused by a change of the magnetic structure. Our results nicely corroborate findings from other magnetic and thermodynamic measurements on these materials and provide further evidence suggesting the formation of magnetic domains., Comment: 9 pages, 8 figures

The studies of electronic effects in reduced dimensionality have become a frontier in nanoscience due to exotic and highly tunable character of quantum phenomena. Recently, a new class of 2D ultrathin Ln$X_2$ metalloxenes composed of a triangular lattice of lanthanide ions (Ln) coupled with 2D-Xenes of silicene or germanene ($X_2$) was introduced and studied with a particular focus on magnetic and transport properties. However, the electronic properties of metalloxenes and their effective functionalization remain mainly unexplored. Here, using a number of experimental and theoretical techniques, we trace the evolution of electronic properties and magnetic ground state of metalloxenes triggered by external perturbations. We demonstrate that the band structure of Ln$X_2$ films can be uniquely modified by controlling the Xenes stacking, thickness, varying the rare-earth and host elements, and applying an external electric field. Our findings suggest new pathways to manipulate the electronic properties of 2D rare-earth magnets that can be adjusted for spintronics applications., Comment: 7 pages, 3 figures

Experimental and theoretical studies of the dynamic magnetization in swept magnetic fields of the orthorhombic SrY$_2$O$_4$ single-crystals doped with the Dy$^{3+}$ Kramers ions (0.01 and 0.5 at.%) with natural abundances of even and odd Dy isotopes are presented. Impurity ions substitute for Y$^{3+}$ ions at two nonequivalent crystallographic sites with the same local $C_s$ symmetry but strongly different crystal fields. Well pronounced double-loop hysteresis is observed at temperatures 2, 4, 5 and 6 K for sweeping rates of 5 and 1 mT/s. The microscopic model of spectral, magnetic and kinetic properties of Dy$^{3+}$ ions is developed based on the results of EPR, site selective optical spectra and magnetic relaxation measurements. The derived approach to the dynamic magnetization in the sweeping field based on the numerical solution of generalized master equations with time-dependent transition probabilities induced by the electron-phonon interaction, quantum tunneling and cross-relaxation allowed us to reproduce successfully the evolution of the hysteresis loop shape with temperature, sweeping rate and concentration of paramagnetic ions., Comment: 11 pages, 6 figures, 2 tables, 52 references

The nuclear level density is a fundamental quantity in nuclear physics, governing various nuclear reactions and astrophysical processes. In this study, we report on the collective enhancement of nuclear level density and its fade-out with excitation energy in the deformed $^{161}$Dy, obtained through an exclusive measurement of neutron evaporation spectra. The $^{162}$Dy nucleus was populated via the transfer of a triton in a $^{7}$Li-induced reaction on $^{159}$Tb. Statistical model analysis of the neutron spectra revealed a large collective enhancement factor of 42$\pm$2, consistent with microscopic calculations. This enhancement factor is similar to the one obtained for mass A$\sim$170 in our previous measurement. The energy-dependent collective enhancement over a wide range of excitation energies was inferred by combining the present results with the available Oslo level density below the neutron binding energy., Comment: 6 pages, 5 figures, Accepted in Physical Review C

Recent experimental realization of the heteronuclear dipolar mixture of Dy and Er atoms opens fascinating prospects for creating intriguing novel phases in dipolar quantum gases. The experimentally measured value of intra-species $s$-wave scattering length of $^{166}$Er condensate in a $^{164}$Dy-$^{166}$Er mixture is larger than its intra-species dipolar length, implies that the $^{166}$Er condensate itself will not be in a regime of dominated dipole-dipole interaction (DDI). However, we find that the presence of $^{164}$Dy atoms with high magnetic moment induces droplet nucleation and supersolidity in $^{166}$Er condensate via the long-range and anisotropic inter-species DDI. Remarkably, we find that the imbalance in the magnetic dipole moment combined with its strong anisotropic coupling led to the emergence of unique ground state phases. The emerging phases include doubly superfluid states, a mixture of insulating droplets and supersolid states, binary supersolids with uniform and alternating domains and a combination of supersolid-superfluid mixed states. We delineate the properties of all these ground state phases and construct a phase diagram. We also explore the dynamical evolution across these phase boundaries via a linear quench of inter-species scattering length. Although we have demonstrated the result for the $^{164}$Dy-$^{166}$Er mixture, our results are generally valid for other dipolar bosonic mixtures of different Dy-Er isotope combinations and may become an important benchmark for future experimental scenarios., Comment: 11 pages, 8 figures