Session A17: Focus Session: Multiferroic Skyrmions

Simulation on doping dependent phase transition in MnSi by Monte Carlo method

Recently, the skyrmion lattice has been found in the A phase of the itinerant helimagnet MnSi by small angle neutron scattering and the magnetic analogue of blue phases has been reported to explain a number of puzzling features of MnSi. Here we use a different approach based on Monte Carlo methods, showing the thermal behavior around transition temperatures in doped systems under the simplest Dzyaloshinsky-Moriya nearest-neighbor interactions. Interestingly, the transition temperature decreases with increasing doping concentrations, which is consistent with the experimental observations. We also show how the topological order parameter changes with temperature and its relation with the specific heat and thermal fluctuations.   

Observation of coherent helimagnons in the Skyrmionic helimagnets

In MnSi and Fe$_{1-x}$Co$_{x}$Si the interplay between the spin-orbit and exchange interactions leads to a variety of helical magnetically ordered states. Perhaps the most interesting of these is the Skyrmion lattice phase in which the spins form topologically-stabilized vortices which decouple from the host lattice to form their own lattice structure. We use pump-probe reflectivity and Kerr rotation to study the dynamics in these materials, observing coherent collective excitations unique to helimagnets known as helimagnons. Monitoring helimagnon decay in the time-domain directly yields the Gilbert damping parameter in these systems.   

The Chiral Hall Effect in the Presence of Impurities: a Study on Mn$_{1-x}$Fe$_x$Si

Recently much attention has been paid to the itinerant ferromagnet MnSi. This is due largely to the emergence of an exotic topological object--the so-called skyrmion, which forms a lattice near $T_c$ at ambient pressure. Past efforts to understand this configuration have observed its response to various perturbations, including temperature gradients, strong electric fields, and hydrostatic pressure. Here, we present Hall effect measurements on single crystals of Fe doped MnSi at ambient pressure, exploring how impurities interact with electronic charge and the long range magnetic order in this peculiar magnetic phase. In pure MnSi, the chiral Hall signal below $T_c$ is significantly enhanced as $T_c$ is suppressed by application of pressure. With chemical doping, though, the chiral Hall signal is substantially weakened, appearing in a narrower window of temperature and magnetic field relative to pure MnSi under pressure with comparable $T_c$. Interestingly, however, and in contrast to hall data taken under pressure, the chiral contribution in iron doped MnSi is found to have opposite sign as the anomalous Hall effect. We will discuss the implications of this Hall effect result and compare it to measurements on pure MnSi under pressure.   

Observation of Skyrmions in a Multiferroic Material

Magnetic skyrmion is a topologically stable particle-like object, which appears as nanometer-scale vortex-like spin texture in a chiral-lattice magnet [1]. In metallic materials (MnSi, FeGe, Fe$_{1-x}$Co$_x$Si etc), electrons moving through skyrmion spin texture gain a nontrivial quantum Berry phase, which provides topological force to the underlying spin texture and enables the current-induced manipulation of magnetic skyrmion [2]. Such electric controllability, in addition to the particle-like nature, is a promising advantage for potential spintronic device applications. Recently, we newly discovered that skyrmions appear also in an insulating chiral-lattice magnet Cu$_2$OSeO$_3$ [3,4]. We find that the skyrmions in insulator can magnetically induce electric polarization through the relativistic spin-orbit interaction, which implies possible manipulation of the skyrmion by external electric field without loss of joule heating [5]. The present finding of multiferroic skyrmion may pave a new route toward the engineering of novel magnetoelectric devices with high energy efficiency. In this talk, the latest experimental and theoretical results on the dynamical aspect of magnetoelectric skyrmions will also be discussed.\\[4pt] [1] S. M{\"u}hlbauer et al., Science {\bf 323}, 915 (2009).\\[0pt] [2] F. Jonietz et al., Science {\bf 330}, 1648 (2010).\\[0pt] [3] S. Seki et al., Science {\bf 336}, 198 (2012).\\[0pt] [4] S. Seki et al., Phys. Rev. B {\bf 85}, 220406(R) (2012).\\[0pt] [5] S. Seki et al., Phys. Rev. B {\bf 86}, 060403(R) (2012).   

Inertia and chiral edge modes of a skyrmion magnetic bubble

Dynamics of topological defects is a topic of longstanding interest in magnetism. The attention to it stems from rich basic physics as well as from its connection to technological applications. The dynamics of a vortex in a thin-film ferromagnet resembles the motion of a charged massless particle in a uniform magnetic field. Similar dynamics is expected for other magnetic textures with a nonzero skyrmion number. However, recent numerical simulations revealed that skyrmion magnetic bubbles show significant deviations from this model. In this talk we present the derivation of the correct dynamical model of a skyrmion magnetic bubble. We first introduce our model phenomenologically and then derive it from the standard theory of a thin-film ferromagnet. This allows us to characterize not only the center-of-mass motion of the bubble but also the dynamics of its shape within the same framework.We show that a skyrmion bubble possesses inertia and derive its mass from the standard theory of a thin-film ferromagnet. Besides center-of-mass motion, other low energy modes are waves on the edge of the bubble traveling with different speeds in opposite directions.   

Universal current-velocity relation of skyrmion motion in chiral magnets

Current-driven motion of the magnetic domain wall requires large critical current density $j_c \sim 10^9-10^{12}$ A/m$^2$, at which the joule heating is a serious problem. The skyrmions recently discovered in chiral magnets, on the other hand, have much smaller critical current of $j_c \sim 10^5-10^6$ A/m$^2$. We present a numerical simulation of the Landau-Lifshitz-Gilbert equation, which reveals a remarkably robust and universal current-velocity relation of the slyrmion motion driven by the spin transfer torque unaffected by either impurities or nonadiabatic effect in sharp contrast to the case of domain wall or spin helix (HL). Simulation results are analyzed using a theory based on Thiele's equation, and it is concluded that this surprising behavior is due to the Magnus force and flexible shape-deformation of individual skyrmions and skyrmion crystal (SkX), which enable them to avoid pinning centers and then weaken the net pinning force. Dynamical deformation of SkX leads to the fluctuation of Bragg peak with large amplitude, which can be detected by the recent neutron-scattering experiment.   

Cooperative organization of local and itinerant moments in antiferromagnetic GdSi

With strong correlations and reduced dimensionality, spin and charge instabilities emerge in a broad range of materials. Direct magnetic exchange, interactions mediated by the conduction electrons, and coupling to the lattice are all familiar drivers of density waves. In materials which have significant localized and itinerant spins, it is not obvious which will induce order. We combine transport, magnetic diffraction, and photoemission studies with band structure calculations to elucidate the nature of successive antiferromagnetic transitions in GdSi. GdSi has both sizable local moments and a partially-nested Fermi surface of itinerant spins, without confounding contributions from orbital effects. We propose a new route to incommensurate order, based on a cooperative feedback mechanism between localized Gd 4f and itinerant Gd 5d electronic spins. The nested Fermi surface of the itinerant electrons induces a strong interaction between local moments at the nesting vector, while the presence of ordered local moments in turn provides the necessary coupling strength for a spin density wave to form among the itinerant electrons. This mechanism echoes the cooperative interactions between itinerant electrons and localized ionic cores in charge density wave materials, and should be germane across a spectrum of transition metal and rare earth intermetallic compounds.   

Magnetic Phase Diagram of the Binary Intermetallic GdSi

The magnetic phase diagram of the binary intermetallic GdSi is investigated via magnetotransport and magnetization measurements along all three principal crystal axes. At zero applied field, two distinct phase transitions are observed at 53 and 54.7 K, corresponding to a spin flip and Neel transition, respectively. An additional ordered antiferromagnetic state appears for magnetic fields applied in the a-c plane, transitioning to a ferromagnetic ground state at $H\sim20$ T. Although Gd ions are well characterized by local spin-only moments, and the magnetic anisotropy is small in this system, the additional antiferromagnetic ordering transition is observed to be considerably softer along c than along a. The interplay between this complex magnetic phase diagram, the band structure, and quantum effects will be discussed.   

Near room temperature helical magnetism in Fe(1-x)Cr(x)Ge

Helical magnetic structures in chiral metallic magnets have attracted much interest recently because of the observation of complex spin textures, for example the skyrmion lattice.~ FeGe is a known B20 spiral ferromagnet that orders at the relatively high temperature of 280K with a helical modulation period of 700 angstroms, which propagates along either the [100] or [111] directions depending on temperature. ~Here we report a study on the evolution of helimagnetism as a function of Cr doping on a series of Fe(1-x)Cr(x)Ge samples with x $=$ 0.03 to 1. Magnetic susceptibility measurements have shown that the ferromagnetic-like transition associated with helimagnetism in FeGe is suppressed around x $=$ 0.4.~   

Ferromagnetic ordering and halfmetallic state in a shandite: Co$_3$Sn$_2$S$_2$

The rapid advance in spintronics challenges an improved understanding of the underlying microscopic properties. Here, we present a joint experimental and theoretical study of Co$_3$Sn$_2$S$_2$ (shandite) and related compounds. From magnetic susceptibility, specific heat and magneto-transport measurements on a shandite single crystal sample we find a phase transition to a ferromagnetic metallic state at 177\,K with a saturation moment of 0.92 $\mu_B$/f.u. Full potential electronic structure calculations within the local spin density approximation result in a halfmetallic ferromagnetic groundstate with a moment of 1 $\mu_B$/f.u.\ and a tiny gap in the minority spin channel. The calculated structure optimization and structure variations show that the size of the gap is rather sensitive to the lattice geometry. Possiblities to stabilize the halfmetallic ferromagnetic behavior by various substitutions have been studied theoretically and will be discussed.   

Thermodynamic and anisotropic properties of single crystalline RCo$_{2}$Ge$_{2}$ (R = Y, La-Nd, Sm-Tm)

Single crystals of RCo$_{2}$Ge$_{2}$ (R = Y, La-Nd, Sm-Tm) were grown using a self-flux method and were characterized from 1.8-300 K by heat capacity, magnetization and in-plane resistivity measurements. Anisotropic metamagnetism was studied at 1.8 K up to 9 T. Due to a strong crystal electric field (CEF) effect, the magnetic ordering temperatures of the heavy rare earth members do not follow the de Gennes scaling, but rather a CEF modified trend. The RCo$_{2}$Ge$_{2}$ series offers an opportunity to study different types of magnetic anisotropy ranging from Heisenberg-like GdCo$_{2}$Ge$_{2}$ to Ising-like TbCo$_{2}$Ge$_{2}$. Correlation between the local moments and conduction electrons as well as the influence of interplay between CEF effect and long-range indirect exchange interaction (RKKY type) will also be discussed.   

Resistivity and anisotropic magnetization of single crystalline $R$Ni$_{\mathrm{1-x}}$Bi$_{\mathrm{2\pm y}}$ (R $=$ La--Nd, Sm, Gd--Dy)

We present a detailed study of $R$Ni$_{\mathrm{1-x}}$Bi$_{\mathrm{2\pm y}}$ (R $=$ La--Nd, Sm, Gd--Dy) single crystals by measurements of temperature dependent magnetic susceptibility, magnetization, and electrical resistivity. The isostructural compounds \textit{RT}Bi$_{2}$ and \textit{RT}Sb$_{\mathrm{2}}$ are known to have widths of formation, except for $T =$ Ag. The $R$Ni$_{\mathrm{1-x}}$Bi$_{\mathrm{2\pm y}}$ series forms with partial Ni occupancy as well as a variable Bi occupancy. For R $=$ Ce--Nd, Gd--Dy, the $R$Ni$_{\mathrm{1-x}}$Bi$_{\mathrm{2\pm y}}$ compounds show local-moment-like behavior and order antiferromagnetically at low temperatures. Determination of anisotropies as well as antiferromagnetic ordering temperatures for $R$Ni$_{\mathrm{1-x}}$Bi$_{\mathrm{2\pm y}}$ (R $=$ Ce--Nd, Sm, Gd--Dy) have been made. Although crystalline samples from this family exhibit minority, second phase, superconductivity at low temperatures associated with Ni-Bi and Bi contamination, no evidence of bulk superconductivity has been observed.