Session Y27: Invited Session: Topological Phases in Magnets

Formation and dynamics of Skyrmions in B20-type chiral magnets

The topological stable spin texture called a Skyrmion, in which the directions of the spins wrap a sphere, has been attracting much attention as an arena for unconventional magneto-transport effects. Small angle neutron scattering (SANS) studies identify the formation of two-dimensional triangular Skyrmion lattice in B20-type transition-metal monosilicides, such as MnSi\footnote{S. M\"{u}hlbauer {\it et al}., Science {\bf 323}, 915 (2009).} and Fe$_{1-x}$Co$_x$Si.\footnote{W. M\"{u}nzer {\it et al}., Phys. Rev. B {\bf 81}, 041203 (2010).} In addition, novel transport properties due to its topological spin arrangement, namely the topological Hall effect\footnote{A. Neubauer {\it et al}., Phys. Rev. Lett. {\bf 102}, 186602 (2009).} and the current-induced rotation of the Skyrmion lattice\footnote{F. Joneitz {\it et al}., Science {\bf 330}, 1648 (2010).} are observed in MnSi. We have provided crucial evidence of the existence of Skyrmions in B20-type compounds by direct real-space observation using Lorentz transmission electron microscopy (TEM)\footnote{X. Z. Yu {\it et al}., Nautre {\bf 465}, 901 (2010).}$^,$\footnote{X. Z. Yu {\it et al}., Nautre Materials {\bf 10}, 106 (2011).} and also found a large topological Hall effect in much wider temperature region in MnGe than other B20-type magnets.\footnote{N. Kanazawa {\it et al}., Phys. Rev. Lett. {\bf 106}, 156603 (2011).} TEM observation reveals the detailed information on nucleation and fusion processes and topological defects besides the perfect hexagonal arrangement of Skyrmions. Furthermore, we have found that the Skyrmion lattice state is quite stabilized in a thin-plate formed sample with its thickness smaller than the skyrmion lattice constant. The orders of magnitude larger topological Hall effect in MnGe indicates the high-density Skyrmion crystal formation and distinguishable large responses in some novel electromagnetic phenomena. In addition, we have fabricated B20-type thin films where Skyrmions are more stabilized and applied electric current is more easily controlled than in bulk samples. This work was done in collaboration with X. Z. Yu, Y. Onose, J. H. Park, J. H. Han, N. Nagaosa, K. Kimoto, W. Z. Zhang, S. Ishiwata, Y. Matsui, T. Arima, D. Okuyama, K. Ohoyama, S. Wakimoto, K. Kakurai, A. Tsukazaki, M. Ichikawa, Y. Li, Y. Shiomi, K. Shibata, D. Inosov, J. H. Kim, J. White, N. Egetenmeyer, J. Gavilano, B. Keimer, and Y. Tokura.   

Magnetic Blue Phase in the Chiral Itinerant Magnet MnSi

In MnSi with the cubic crystal structure B20, the lack of inversion symmetry induces a chiral Dzyaloshinsky-Moriya interaction between magnetic moments. It locally favors helical magnetic order. In addition to a long-range helical order with the well-defined propagation vector, other locally helical phases such as skyrmions and partial order appear in its phase diagram. These enigmatic phases are suspected to be behind many unusual properties of MnSi. I will report results of model calculations, which show that such phases should arise naturally as a result of the basic Dyaloshinsky-Moriya Hamiltonian. Specifically, in the absence of an applied magnetic field, the free energy in MnSi should be minimized by the magnetic analogue of blue phases, which have previously been observed in chiral liquid crystals. This result is consistent with our recent neutron scattering measurements as well as those of others. The properties of this blue phase explain a number of previously reported puzzling features of MnSi such as partial magnetic order and a two-component specific-heat as well as, possibly, non-Fermi-liquid resistivity at high pressure.   

Quasi-two-dimensional Skyrmion lattices and other exotic structures in confined chiral nematic liquid crystals

Skyrmions are localized particle-like topological entities in a number of continuous fields that play important roles in various condensed matter systems, including two-dimensional electron gases exhibiting the quantum Hall effect, Bose--Einstein condensates, and chiral ferromagnets [1, 2]. Here we are using Landau - de Gennnes theoretical approach and numerical techniques to show that in a highly chiral nematic liquid crystal confined to a thin film between two parallel surfaces imposing normal alignment nematic director can exhibit thermodynamically stable states characterized by quasi-two-dimensional Skyrmion lattices of disclinations [3]. By confining a chiral nematic, that in bulk forms blue phases characterized by cubic lattices of nematic defect lines, to a layer with thickness comparable to the lattice constant of the blue phase [3-5], various quasi 2D defect lattices can be stable. Depending on the anchoring direction of the nematic director on confining surfaces, temperature, and layer thickness, beside skyrmion structures, lattices of double helical half-integer dislinations running along the layer [4], and lattices of ring defects [5] are the most interesting. A chiral nematic liquid crystal film can thus serve as a model system, allowing direct investigation of numerous defect lattices by a variety of optical techniques at conditions that are less demanding than used for other condensed matter Skyrmion systems. \\[4pt] [1] U.K. R\"{o}{\ss}ler, A. N. Bogdanov, {\&} C. Pfleiderer, Spontaneous skyrmion ground states in magnetic metals. Nature 442, 797 (2006). \\[0pt] [2] A. Hamann, D. Lamago, Th. Wolf, H. v. L\"{o}hneysen, and D. Reznik, Magnetic Blue Phase in the Chiral Itinerant Magnet MnSi, Phys. Rev. Lett. 107, 037207 (2011). \\[0pt] [3] J. Fukuda and S. Zumer, Quasi-two-dimensional Skyrmion lattices in a chiral nematic liquid crystal, Nature Communications 2, 246 (2011). \\[0pt] [4] J. Fukuda and S. Zumer, Novel defect structures in a strongly confined liquid-crystalline blue phase. Phys. Rev. Lett. 104, 017801 (2010). \\[0pt] [5] J. Fukuda and S. Zumer, Ring Defects in a Strongly Confined Chiral Liquid Crystal, Phys. Rev. Lett. 106, 097801 (2011).   

Unusual Hall effect Anomaly in MnSi under pressure

Recent works in B20 type transition metal compounds have revealed a new topological object in spin systems -- the skyrmion, a particle-like object in which spins point all directions to wrap around the sphere. While neutron scattering and scanning probe experiments\footnote{S. M\"{u}hlbauer {\it et al.,} Science {\bf 323,} 915 (2009).}$^,$\footnote{X. Z. Yu, {\it et al.}, Nature, {\bf 465,} 901 (2010).} confirmed the existence of individual skyrmions and skyrmion lattices in a particular part of the phase diagram, the interaction between skyrmions and electronic degrees of freedom remains to be unveiled. In this talk, we report the observation of a highly unusual Hall current in the helical magnet MnSi under pressure.\footnote{M.Lee {\it et al.,} Phys. Rev. Lett {\bf 102,} 186601 (2009).} In addition to the normal Hall effect and the anomalous part that arises from spontaneous magnetization, the Hall conductivity displays a distinctive stepwise field profile quite unlike any other Hall response observed in solids. This additional contribution was observed in a much larger range of temperature and applied field than the so-called $A$-phase,where the skyrmion lattice was observed in ambient pressure. It suggests that fluctuating, {\it i.e.} non-static, skyrmions might be present over a broad range of the phase diagram under pressure when the magnetic ordering becomes weakened.   

Cosmic Strings Meet Multerroics: Understanding topological defects in spontaneous symmetry breaking phase transitions

Jumping from the expanse of galactic scales to land in the laboratory might seem a gargantuan task. Common to both, however, is the the concept of symmetry breaking and in particular the formation of topological defects. Here I discuss the formation of topological defects in multiferroic YMnO3 whose ferroelectric behavior enables the direct imaging of these defects. I also show how this material can be used to study the Kibble-Zurek model of topological defect formation in the early universe and give quantitative insights on the number of domains formed during the spontaneous symmetry breaking phase transition.