Session T8: Focus Session: Helical Phases and Skyrmions

Spin waves in a skyrmion crystal

We derive the spectrum of low-frequency spin waves in skyrmion crystals observed recently in noncentrosymmetric ferromagnets [1-4]. We treat the skyrmion crystal as a superposition of three helices whose wavevectors form an equilateral triangle [1]. The low-frequency spin waves are Goldstone modes associated with displacements of skyrmions. Their dispersion is determined by the elastic properties of the skyrmion crystal and by the kinetic terms of the effective Lagrangian, which include both kinetic energy and a Berry phase term reflecting a non-trivial topology of magnetization. The Berry phase term acts like an effective magnetic field, mixing longitudinal and transverse vibrations into a gapped cyclotron mode and a twist wave with a quadratic dispersion [5]. \\[4pt][1] Muehlbauer, Binz, Jonietz, Pfleiderer, Rosch, Neubauer, Georgii, Boeni, Science \textbf{323}, 915 (2009). \\[0pt][2] Muenzer, Neubauer, Adams, Muehlbauer, Franz, Jonietz, Georgii, et al., Phys. Rev. B \textbf{81}, 041203 (2010). \\[0pt][3] Yu, Onose, Kanazawa, Park, Han, Matsui, Nagaosa, Tokura, Nature \textbf{465}, 901 (2010). \\[0pt][4] Yu, Kanazawa, Onose, Kimoto, Zhang, Ishiwata, Matsui, Tokura, Nat. Mater. \textbf{10}, 106 (2011). \\[0pt][5] Petrova, Tchernyshyov, arXiv:1109.4990v2 [cond-mat.mes-hall]   

Skyrmion contribution to thermopower of MnSi

Skyrmions have recently been theoretically predicted [1] and experimentally observed [2] in MnSi. To identify whether skyrmions contribute to thermoelectric transport, we present a detailed map of the temperature, pressure and magnetic field behavior of thermopower $S$ in MnSi. $S/T(p,T)$ confirms the established phase diagram with Fermi liquid, non-Fermi liquid and partial order phases. In the high pressure non-Fermi liquid phase, $S(T)$ increases in the vicinity of the boundary with the Fermi liquid phase, at critical pressure $p_c\sim14.5$ kbar. This may be linked to the scattering of conduction electrons on fluctuating amorphous skyrmions [1]. On the contrary, the thermopower decreases when an ordered lattice of skyrmions is established in the magnetic field. A small suppression of $S(T)$ is observed in a narrow region, for 27 K $ [Preview Abstract]

Quantum order-by-disorder near criticality and the secret of the partially ordered phase of MnSi

The vicinity of quantum phase transitions has proven fertile ground in the search for new quantum phases. We propose a physically motivated and unifying description of the phase reconstruction near metallic quantum-critical points using the idea of quantum order-by-disorder. Certain deformations of the Fermi surface associated with the onset of competing order enhance the phase space available for low-energy, particle-hole fluctuations and self-consistently lower the free energy. Applying the notion of quantum order-by-disorder to the itinerant helimagnet MnSi, we show that near to the quantum critical point, fluctuations lead to an increase of the spiral ordering wave vector and a reorientation away from the lattice favoured directions. The magnetic ordering pattern in this fluctuation-driven phase is found to be in excellent agreement with the neutron scattering data in the partially ordered phase of MnSi.   

Density-functional electronic structure and the origin of the Dzyaloshinskii-Moriya spin interaction in MnSi

The metallic helimagnet MnSi has been found to exhibit skyrmionic spin textures when subjected to magnetic fields at low temperatures. The Dzyaloshinskii-Moriya (DM) interaction plays a key role in stabilizing the skyrmions, which arises from the anisotropic part of the super-exchange coupling and is of the form $\vec{D}\cdot(\vec{S_i}\times\vec{S_j})$. The constant $\vec{D}$ depends on the strength of spin-orbit interaction of Mn $d$ states and the orbital mixing induced by the distortion of MnSi$_6$ octahedra from the centrosymmetric rock salt phase. Using density functional theory based electronic structure calculations and symmetry analysis, we study the nature of the electronic ground state and the origin of the DM interaction in the B20 phase of MnSi. The ground state in the undistorted phase corresponds to $d^6$ configuration at Mn and $p^2$ at Si sites. The distortion reduces bandwidths and intermixes the ground state with the excited states, leading to a significant DM spin-orbit interaction.   

Criticality Induced First-Order Phase Transition in Dzyaloshinskii-Moriya Helimagnets

Almost two centuries of research on phase transitions have repeatedly highlighted the importance of critical phenomena. One fascinating implication of critical phenomena is that critical fluctuations may drive the associated phase transition first order if symmetry allows them to assume enough phase space. As discussed by Brazovski, this is in particular the case if critical fluctuations become soft on a sphere in momentum space. By means of combined specific heat, magnetic susceptibility and neutron scattering measurements of the model helimagnet MnSi we show that this scenario is realized for the helimagnetic phase transition in Dzyaloshinskii-Moriya(DM) helimagnets with weak magnetic anisotropy. The remarkable agreement observed between experiment and theory clarifies the longstanding issue of the nature of the helimagnetic transition in MnSi, but more importantly, our calculations are entirely based on symmetry arguments, making this result relevant to DM helimagnets in general. This is in particular noteworthy in the light of a series of new discoveries that show that DM helimagnetism is at the heart of problems such as topological magnetism, multiferroics, and spintronics.   

Tricriticality and giant magneto-elasticity in CoMnSi

Tricritical magnets have previously facilitated the study of different critical phenomena and scaling laws by varying external parameters (pressure, field and temperature) instead of composition. We have studied tricritical magnets driven by interest in the enhanced magnetocaloric effects seen at the first order side of a tricritical point where hysteresis can be minimised. Here we describe the results of microcalorimetry, Hall probe imaging, dilatometry, magnetometry and neutron diffraction experiments and density functional calculations. We build a picture of the relation between structure and magnetism in CoMnSi and find a giant magneto-elasticity that underpins the evolution of first order behavior in this metamagnetic helical antiferromagnet [2]. We are then able to use density functional theory to predict new metamagnets based on this insight. These have been successfully synthesized [3]. \\[4pt] [1] K.G. Sandeman, Magnetics Technology International \textbf{1} 32 (2011).\\[0pt] [2] A. Barcza et al., Phys. Rev. Lett. \textbf{104} 247202 (2010).\\[0pt] [3] Z. Gercsi, K. Hono and K.G. Sandeman, Phys. Rev. B \textbf{83} 174403 (2011) and references therein.   

Hall effect of spin-chirality origin in a triangular-lattice helimagnet $\mbox{Fe}_{1.3} \mbox{Sb}$

We report on a topological Hall effect possibly induced by scalar spin chirality in a quasi-two-dimensional helimagnet$\mbox{Fe}_{1+x} \mbox{Sb}$. In the low-temperature region where the spins on interstitial-Fe (concentration $x\approx 0.3)$ intervening the $120^\circ $ spin-ordered triangular planes tend to freeze, a non-trivial component of Hall resistivity with opposite sign of the conventional anomalous Hall term is observed under magnetic field applied perpendicular to the triangular-lattice plane. The observed unconventional Hall effect is ascribed to the scalar spin chirality arising from the heptamer spin-clusters around the interstitial-Fe sites, which can be induced by the spin modulation by the Dzyaloshinsky-Moriya interaction.   

Vortex walls in helical magnets

The structure of domain walls determines to a large extent the properties of magnetic materials, in particular their hardness and switching behavior, it represents an essential ingredient of spintronics. In Bloch and Neel domain walls the magnetization rotates around a fixed axis in a one-dimensional magnetization profile. Surprisingly, domain walls in helical magnets, most relevant in multiferroics and metals, were never studied. We show that domain walls in helical magnets are fundamentally different from Bloch and Neel walls. They are generally two-dimensional patterns formed by a regular lattice of vortex singularities. Only at discrete exceptional orientations, domain walls are free of vortices, but still remain two-dimensional textures. In helical magnets with weak anisotropy the domain wall width and energy only weakly depend on the anisotropy, though domain wall does not exist without it. In conical phases vortices carry Berry phase flux resulting in the anomalous Hall effect. In multiferroics vortices are electrically charged allowing manipulating magnetic domain walls by the electric field. Our theory allows the interpretation of magnetic textures observed in helical magnetic structures.   

Spin scalar chiral ordering and hidden positive biquadratic interaction in frustrated Kondo lattice systems

Recently, noncoplanar spin configurations with spin scalar chirality have drawn considerable attention as an origin of the anomalous Hall effect. In this mechanism, itinerant electrons acquire an internal magnetic field according to the solid angle spanning three spins through the so-called Berry phase, which can result in the anomalous Hall effect. In order to explore such nontrivial magnetic states in spin-charge coupled systems, we investigate a ferromagnetic Kondo lattice model on a triangular lattice by variational and perturbative calculations. As a result, we find that a noncoplanar four-sublattice spin ordering emerges near 1/4 filling, in addition to the 3/4 filling reported in the previous study. This new phase is stabilized in a wider parameter region compared to the 3/4 filling phase [1]. We also find that a kinetic-driven positive biqaudratic interaction is critically enhanced and plays a crucial role on stabilizing a spin scalar chiral ordering near 1/4 filling. The origin of large positive biquadratic interaction is ascribed to the Fermi surface connection by the four sublattice ordering wave vectors, which we call the higher-order Kohn anomaly [2]. [1] Y. Akagi and Y. Motome, J. Phys. Soc. Jpn. 79 (2010) 083711. [2] Y. Akagi, M. Udagawa, and Y. Motome, submitted.   

First Principles Calculation of Helical Spin Order in Iron Perovskite SrFeO3 and BaFeO3

Motivated by recent discovery of ferromagnetism in cubic perovskite BaFeO3 under small magnetic field, we investigate spin order in BaFeO3 and isostructual SrFeO3 by a first principles calculation using local spin density approximation (LSDA). We find that on-site Coulomb interaction U is necessary for obtaining helical spin order consistent with experiments. SrFeO3 exhibits G-type helical order, while BaFeO3 exhibits the A-type with very small wave vector. The A-type order is stabilized by lattice expansion. Small energy difference between the A-type and ferromagnetic orders explains ferromagnetism under small field. The LSDA+U results are consistent with model calculation where negative charge-transfer energy in these compounds is explicitly taken into account.   

Investigation of the role of spin-texture on the Na0.46CoO2

We will present magnetotransport properties and their relationship to a possible chiral spin texture in ultra-thin Na$_{0.46}$CoO$_{2}$ devices in high magnetic fields. This composition exhibits a weakly insulating state, with a frustrated local spin texture, unique, among the hexagonal Na$_{x}$CoO$_{2}$ family. Previous a large large Hall effect was found for composition $x$=0.5 (M. Foo \textit{et al.}, Phys. Rev. Lett. 92, 247001 (2004)) and prior high-field studies (L. Balicas \textit{et al.}, Phys. Rev. Lett. 94, 236402 (2005).) have found the existence of a small Fermi surface in the system and a two-fold angular magnetoresistance. To date however, the Hall-conductivity has not been investigated in magnetic fields strong enough to suppress the charge-order, above 41~T. Herein, we investigate the role of local spin-texture (in the charge-ordered state) on the Hall conductance by measuring both bulk and devices with only several monolayers thick in strong magnetic fields. Our investigations under magnetic fields ($B<$60 T) show that the high resistivity charge-order region is suppressed with out-of-plane field at $B\sim $41 T with highly non-monotonic -\textit{$\rho $}$_{xy}$ with a maximum at $B\sim $27 T and rapidly decreases to zero. However, magnetization measurements show no significant features within measurement accuracy indicating that magnetization changes are small at the field-induced phase transition. Recent theoretical advances suggest that this compound exhibits a quantum Hall state coupled with spin chirality (I. Martin, C. D. Batista, Phys. Rev. Lett. 101, 156402 (2008)).   

Spin spiral state in hexagonal NiS

Previous nesting function calculations on NiS have found instabilities for the magnetic ordering vectors q=(2/3,2/3,0) and q=(1/2,2/9,1) suggesting that the magnetic structure of NiS is non- collinear which does not agree with the experimentally determined antiferromagnetic state. We investigated the electronic and magnetic structure of NiS by means of a full-potential linearized augmented plane wave method within the local spin density approximation plus the Hubbard parameter U. Our method is specially suitable to study noncollinear magnetism where the magne- tization density is allowed to vary in magnitude and direction continuously everywhere in space. Our results show that the ground state is metallic and that the antiferromagnetic state is almost degenerate with spin spirals along certain directions of the Brillouin zone.   

Incommensurate antiferromagnetism in GdSi

Rare earth magnets are interesting model systems to study correlated spin, orbital and lattice degrees of freedom. Here we present a study of the antiferromagnetism in single crystal GdSi, using high-resolution, x-ray magnetic diffraction techniques. Our results clearly show an incommensurate magnetic structure at 6.5 K, with a lattice distortion from orthorhombic to monoclinic accompanying the magnetic phase transition in a second order fashion. We discuss implication to the anisotropic susceptibility in lights of the detailed magnetic structure.   

Spin-Orbital Locking, Emergent Pseudo-Spin, and Magnetic order in Na$_2$IrO$_3$

The nature of magnetic order in the honeycomb lattice Iridate Na$_2$IrO$_3$ is explored by considering trigonal crystal field effect and spin-orbit coupling. An effective Hamiltonian is derived in terms of an emergent pseudo-spin-1/2, resulting from a spin-orbital locking, which is different from $j_{\rm eff}=1/2$ that is obtained when the spin-orbit coupling dominates. The resulting Hamiltonian is anisotropic and frustrated. Mean field theory suggests a ground state with 4-sublattice {\em zig-zag} magnetic order in the relevant parameter regime, in conformity with experiments. Various properties of the phase, the spin-wave spectrum and experimental consequences are discussed. Our approach contrasts with the recent proposal of a Heisenberg-Kitaev system for this material, and we point out the intrinsic difficulties with the latter approach for describing the magnetic properties of Na$_2$IrO$_3$.   

Magnetic order on a frustrated lattice due to orbital degrees of freedom in $R$O$_2$ hyperoxides

The alkali $R$O$_2$ hyperoxides ($R$=Rb,Cs,K) crystallize in a frustrated bct lattice. Nevertheless, all of the members of the family of alkali $R$O$_2$ hyperoxides have long range layered $C$-type antiferromagnetic ($C$-AF) order at low temperature. We show that including the almost degenerate $p$-orbital degrees of freedom in a realistic spin-orbital model can resolve this contradiction [1]. Although {\it a priori} the orbital degrees of freedom do not remove frustration in spin system, we show that the anomalously large interorbital hopping together with the orbital order induced by the lattice stabilize the $C$-AF order in this class of compounds, in agreement with generalized Goodenough-Kanamori rules formulated here. \\[4pt] [1] K. Wohlfeld, M. Daghofer, and A.M. Ole\'{s}, EPL \textbf{96}, 27001 (2011).