Editor's Choice The spin kinetics of liquid 3He in contact with the microsized DyF3 powder at ferromagnetic ordering of Dy^{3+} For the first time the magnetic phase transition in DyF3 at low temperatures was observed by 3He NMR. The spin kinetics of liquid 3He in contact with a mixture of microsized powders LaF3 (99.67%) and DyF3 (0.33%) at temperatures 1.5-3 K was studied by pulse NMR technique. The DyF3 is a dipole dielectric ferromagnet with a phase transition temperature Tc = 2.55 K, while as the diamagnetic fluoride LaF3 used as a diluent for optimal conditions for observation of 3He NMR. The phase transition in DyF3 is accompanied by a significant changes in the magnetic fluctuation spectrum of the dysprosium ions. The spin kinetics of 3He in contact with the substrate is sensitive to this fluctuations. An significant change in the rates of the longitudinal and transverse nuclear magnetization of 3He in the region of magnetic ordering of solid matrix was observed. A technique is proposed for studying the static and fluctuating magnetic fields of a solid matrix at the low temperatures using liquid 3He as a probe. å.í. álakshin, å.I. Kondratyeva, V.V. Kuzmin, ë.R. Safiullin, á.á. Stanislavovas, á.V. Savinkov, á.V. Klochkov,  í.S. Tagirov JETP Letters 107 issue 2, 2018 Microparticles at the surface of liquid helium. Quantum version of Archimedes' principle Microspheres at the surface of liquid are widely used now for visualization of wave and vortex motion [1, 2]. The experiments of this kind had been performed recently to study of turbulence at the surface of liquid helium [3]. That’s why it is of interest to consider the corrections to a classic Archimedes' principle, because while the size of a particle floating at the surface decreases, the forces of surface tension and molecular interaction start to play a significant role.  We study the deviations from Archimedes' principle for spherical particles made of molecule hydrogen near the surface of liquid He4. Classic Archimedes' principle takes place if particle radius $R_0$ is greater than capillary length of helium $L_{k} \approx$ 500 µm and the height $h_+$  of the part of the particle above He is proportional to  $R_0$ . Over the range of $30 R_c...R_c$  can be expressed as  $R_c \approx (\frac {\hbar c}{\rho g}) \approx$ 1µm, $\hbar$ is Planck's constant, c is speed of light, $\rho$ is helium density. For the very small particles ( $R_01/2, we derive analytical expressions for the backscattering current at low and high voltages. We demonstrate that the differential conductance may exhibit a non-monotonous dependence on the voltage with several extrema. [1] X.-L. Qi, S.-C. Zhang, Topological insulators and superconductors, Rev. Mod. Phys. 83, 1057 (2011). [2] M. Z. Hasan, C. L. Kane, Colloquium: Topological insulators, Rev. Mod. Phys. 82, 3045 (2010). [3] M. Konig, S. Wiedmann, C. Brune, A. Roth, H. Buhmann, L. W. Molenkamp, X.-L. Qi, S.-C. Zhang, Quantum spin Hall insulator state in HgTe quantum wells, Science 318, 766 (2007) [4] K. C. Nowack, E. M. Spanton, M. Baenninger, M. Konig, J. R. Kirtley, B. Kalisky, C. Ames, P. Leubner, C. Brune, H. Buhmann, L. W. Molenkamp, D. Goldhaber-Gordon, K. A. Moler, Imaging currents in HgTe quantum wells in the quantum spin Hall regime, Nat. Mater. 12, 787 (2013). [5] G. Grabecki, J. Wrobel, M. Czapkiewicz, L. Cywinski, S. Gieratowska, E. Guziewicz, M. Zholudev, V. Gavrilenko, N. N. Mikhailov, S. A. Dvoretski, F. Teppe, W. Knap, T. Dietl, Nonlocal resistance and its fluctuations in microstructures of band-inverted HgTe/(Hg,Cd)Te quantum wells, Phys. Rev. B 88, 165309 (2013). [6] G. M. Gusev, Z. D. Kvon, E. B. Olshanetsky, A. D. Levin, Y. Krupko, J. C. Portal, N. N. Mikhailov, S. A. Dvoretsky, Temperature dependence of the resistance of a two-dimensional topological insulator in a HgTe quantum well, Phys. Rev. B 89, 125305 (2014). [7] E. M. Spanton, K. C. Nowack, L. Du, G. Sullivan, R.-R. Du, K. A. Moler, Images of edge current in InAs/GaSb quantum wells, Phys. Rev. Lett. 113, 026804 (2014). [8] L. Du, I. Knez, G. Sullivan, R.-R. Du, Observation of quantum spin Hall states in InAs/GaSb bilayers under broken time-reversal symmetry, Phys. Rev. Lett. 114, 096802 (2015). [9] J. Maciejko, Ch. Liu, Y. Oreg, X.-L. Qi, C. Wu, S.-C. Zhang, Kondo effect in the helical edge liquid of the quantum spin Hall state, Phys. Rev. Lett. 102, 256803 (2009). [10] Y. Tanaka, A. Furusaki, K. A. Matveev, Conductance of a helical edge liquid coupled to a magnetic impurity, Phys. Rev. Lett. 106, 236402 (2011). [11] J. I. Vayrynen, M. Goldstein, L. I. Glazman, Helical edge resistance introduced by charge puddles, Phys. Rev. Lett. 110, 216402 (2013). [12] J. I. Vayrynen, M. Goldstein, Y. Gefen, L. I. Glazman, Resistance of helical edges formed in a semiconductor heterostructure, Phys. Rev. B 90, 115309 (2014). [13] V. Cheianov, L. I. Glazman, Mesoscopic fluctuations of conductance of a helical edge contaminated by magnetic impurities, Phys. Rev. Lett. 110, 206803 (2013). [14] L. Kimme, B. Rosenow, A. Brataas, Backscattering in helical edge states from a magnetic impurity and Rashba disorder, Phys. Rev. B 93, 081301 (2016). Kurilovich P.D. , Kurilovich V.D., Burmistrov I.S. , Goldstein M. JETP Letters 106 (9) (2017) Breather chimeras in the system of phase oscillators Chimera is, according to Greek mythology, a monstrous creature combining the parts of different animals (a lion with a head of a goat and a tail of a snake). Physicists recently adopted this name for complex states in nonlinear dynamical systems, where instead of an expected symmetric synchronous state one observes coexistence of synchronous and asynchronous elements [1]. Since the discovery of chimeras by Kuramoto and Battogtokh in 2002 [2], these states have been reported in numerous theoretical studies and experiments. In this paper, we study formation of chimeras in a one-dimensional medium of identical oscillators with nonlinear coupling. This coupling crucially depends on the local order parameter measuring the level of synchrony: the coupling promotes synchrony for asynchronous states and breaks synchrony if it is strong [3]. As a result, spatially homogenous state in this medium is that of partial synchrony. To study the evolution of this state we formulate the problem in terms of the local complex order parameter, which describes local level of synchrony, and formulate the system of partial differential equations for this quantity [4]. This allows us to formulate the problem of inhomogeneous states as the pattern formation one. First, we construct stationary chimeras and explore their linear stability properties. Next, based on numerical modeling, we show that within a certain range of parameters, such structures can evolve into periodically varying long-lived chimera states (breather-chimeras), or, for other values of the parameters, turn into more complex regimes with irregular behavior of the local order parameter (turbulent chimeras). [1] M. J. Panaggio, D. M. Abrams, Chimera states: coexistence of coherence and incoherence in networks of coupled oscillators, Nonlinearity 28 , R67 (2015). [2] Y. Kuramoto, D. Battogtokh, Coexistence of Coherence and Incoherence in Nonlocally Coupled Phase Oscillators, Nonlinear Phenom. Complex Syst. 5 , 380 (2002). [3] M. Rosenblum, A. Pikovsky, Self-Organized Quasiperiodicity in Oscillator Ensembles with Global Nonlinear Coupling, Phys. Rev. Lett. 98 , 064101 (2007). [4] L. A. Smirnov, G. V. Osipov, A. Pikovsky, Chimera patterns in the Kuramoto-Battogtokh model, J. Phys. A: Math. Theor. 50 , 08LT01 (2017). Bolotov M.I., Smirnov L.A., Osipov G.V., Pikovsky A. JETP Letters 106, issue 6 (2017) Faraday Waves and Vortices on the Surface of Superfluid He-II. Well-known Faraday waves can be parametrically generated on a free surface of ordinary (classical) fluids such as water or on superfluid helium He-II surface when a sample cell is vibrated vertically. Standing-wave patterns appear on the surface, and their frequencies are one-half the driving frequency. The acceleration threshold for the parametric excitation of Faraday waves on the surface of water is near an order of magnitude higher than on the surface of He-II at the same frequencies [1]. Generation of vorticity by interacting nonlinear surface waves has been predicted theoretically in a number of papers [2, 3] and generation of vortices by noncollinear gravity waves on a water surface has been observed experimentally [4].Our study has shown that classical 2-D vortices can be generated by Faraday waves on the surface of superfluid He-II also, more over one can observe formation of the vortex lattice in addition to the wave lattice on the surface of He-II in a rectangular cell. Combined with predictions [5] that the sharpest features (about nm sizes) in the cell walls can induce nucleation of quantum vortex filaments and coils on the interface and formation a dense turbulent layer of quantum vortices near the solid walls with a nonclassical average velocity profile which continually sheds small vortex rings into the bulk of vibrating He-II, this opens up new prospects for studying the properties of a quantum liquid and turbulent phenomena on the surface and in bulk of supefluid liquids. [1] Haruka Abe, Tetsuto Ueda, Michihiro Morikawa, Yu Saitoh, Ryuji Nomura, Yuichi Okuda, Faraday instability of superfluid surface, Phys. Rev. E 76, 046305 (2007). [2] S.V. Filatov, V.M. Parfenyev, S.S. Vergeles, M.Yu. Brazhnikov, A.A. Levchenko, V.V. Lebedev, Nonlinear Generation of Vorticity by Surface Waves, Phys. Rev. Lett. 116, 054501 (2016). [3] V. M. Parfenyev, S.S. Vergeles, V.V. Lebedev, Effects of thin film and Stokes drift on the generation of vorticity by surface waves, Phys. Rev. E 94, 052801 (2016). [4] S. V. Filatov, S. A. Aliev, A. A. Levchenko, D. A. Khramov, “Generation of vortices by gravity waves on a water surface”, JETP Letters, 104(10), 702–708 (2016). [5] G.W. Stagg, N. G. Parker, and C. F. Barenghi, Superfluid Boundary Layer. PRL 118, 135301 (2017). DOI: 10.1103/PhysRevLett.118.135301 Levchenko A.A., Mezhov-Deglin L. P., Pel’menev A.A. JETP Letters 106, issue 4 (2017) Superradiance Properties of a Suspension of Composite Nanoscale integration of organic and metallic particles is expected to open up new opportunities for the design high-performance nanoscale devices. Optimization of heterostructures requires experimental and theoretical analysis of their specific physical properties. Nanosystem consisting in gold nanospheres covered by silica shell impregnated with the organic dye molecules comes into focus as a possible plasmonic based nanolaser, i.e. "spaser" [1]. Depending on the distance between the emitters and metal there are possible various phenomena [2,3]. In this paper we experimentally studied the characteristics of a suspension of spasers at the temperatures$T_N=77.4K,T_R=293K$. It was found that the system possesses characteristics of a laser medium. The S-shaped dependence of the radiation intensity and the compression of the lasing line with increase of the pumping power were observed. Ten-fold increase of the intensity of the radiation generated by the medium and line narrowing with temperature change$T_R\to T_N$was found. The experimental results were compared with a numerical simulation of a spaser model consisting of 20 two-level media and a metallic nanosphere. The temperature effects were modeled by the introduction of the Markov process. It was found that observed effects can be explained by means of the feedback caused by the nonlinear interaction of polarizations with their total reflection in the metallic core. At low temperatures Bloch vectors related with two-level systems form an analog of a ferromagnetic state. With increasing fluctuations, antiferromagnetic states are formed along with the desynchronization of ferromagnetic one. These properties allows us to explain the observed changes in the intensity of the and line form of laser generation with temperature. Experimental and numerical results of the work demonstrate that the synchronization of the polarization of dye molecules caused by inverse nonlinear coupling yields an analog of plasmon-polariton superradiance. 1. D.J. Bergman and M.I. Stockman, Phys.Rev.Lett. 90, 027401 (2003). 2. M. Haridas et al, J. Appl. Phys.114, 064305 (2013). 3. M. Praveena et al, Phys. Rev. B 92, 235403 (2015). A. S. Kuchyanov, A.A. Zabolotskii, Plekhanov A.I. JETP Letters 106 (2) (2017) Energy Spectrum of the Spin States in$Sr_2FeSi_2O_7\$ and Origin of the Magneto- Electric Coupling Recently Sr2FeSi2O7 comes into focus as a possible compound with unusual magneto-electric coupling or, in other words, as a novel potential multiferroic [1,2]. Results of terahertz spectroscopy in the paramagnetic state show that the multiplet Fe+2(S=2) of the ground state splits due to the spin-orbit coupling. However the energy intervals between the low-lying singlet state and excited states are quite small so that all spin states are populated at the temperature of about 100 K. The Fe+2 ion occupies the center of a tetragonally distorted tetrahedron. In the present communication the origin of the magneto-electric coupling is described as follows. The odd crystal field from the tetrahedral environment induces the coupling of the orbital momentum of the Fe+2( 5D) state with the external electric field. On the other hand, the orbital momentum is coupled with spin via the spin –orbit interaction. Both angular momenta are coupled with the external magnetic field, which is enhanced due to the presence of the superexchange interaction between neighboring Fe+2 ions. Combining all these couplings, the author derived the affective spin Hamiltonian for the magneto-electric coupling, which made it possible to calculate relative intensities of the electric dipole transitions between spin states and estimate the magnetization caused by the external electric field as well as the electric polarization induced by the magnetic field.     Thuc T. Mai, C. Svoboda, M. T. Warren, T.-H. Jang, J. Brangham, Y. H. Jeong, S.-W. Cheong, and R. Valdes Aguilar. Phys. Rev. B,  94, 224416 (2016) Yongping Pu, Zijing Dong, Panpan Zhang, Yurong Wu, Jiaojiao Zhao, Yanjie Luo. Journal of Alloys and Compounds, 672 , 64-71 (2016)                                                                                   M.V. Eremin                                                                               JETP Letters 105 (11) (2017) Electron-topological transition in copper-oxide high-TC superconductors before superconducting transition It is well known the conductivity of high-temperature superconductors (HTSCs) with TC ~100 K (YBaCuO, BiSrCaCuO, etc.) is provided at T~300 K by hole (h) fermions [1]. It is also known the superconducting transition in such cuprates is accomplished by means of the Cooper pairing, while the fluctuating Cooper pairs with charge -2e exist even at T=TC+(~30 K) [2]. Hence it inevitably follows in the interval TC