Session L34: Focus Session: Frustrated and Low-D Magnetism -- Strongly Frustrated Antiferromagnets in 2D

Successive Magnetic Transitions of the Kagome Plane and Field-Driven Chirality in BaMn$_{2.49}$Ru$_{3.51}$O$_{11}$

The magnetization of single-crystal BaMn$_{2.49}$Ru$_{3.51}$O$_{11}$ exhibits anomalies at temperatures T$_{1}$ = 183 K, T$_{2}$ = 171 K and T$_{3}$ = 128 K, which signal complex magnetic order induced by competing ferro- and antiferro-magnetic correlations, and magnetic frustration within the Kagome (hexagonal \textbf{ab-}) plane. The T$_{2}$- and T$_{3}$-anomalies and unconventional transverse magnetoresistance are observed only for magnetic field \textbf{H} applied in the Kagome plane. We conclude a topological Hall effect (THE) is generated by non-zero scalar chirality K$_{S}$ of spins canted out of the Kagome plane, but is suppressed in a collinear structure induced by only modest in-plane fields. BaMn$_{2.49}$Ru$_{3.51}$O$_{11}$ is a unique example of an unusually large and anisotropic THE in a magnetically ordered state. The THE is driven by nonzero scalar spin chirality and can be controlled by unusually modest applied fields $\mu _{o}H \quad <$ 1 T, implying low-field alteration of scalar spin chirality may provide a new way to control electronic properties in magnetic materials having requisite non-centrosymmetric structure.   

Dynamic Scaling in the susceptibility of the Spin-1/2 Kagom\'{e} Lattice Antiferromagnet Herbertsmithite

The spin-$\frac{1}{2}$ kagom\'{e} lattice antiferromagnet herbertsmithite, ZnCu$_{3}$(OH)$_{6}$Cl$_{2}$, appears to display a quantum disordered ground state with effectively gapless excitations. We show that the dynamic susceptibility of this material displays an unusual scaling relation in both the bulk ac susceptibility and the imaginary part of the dynamic susceptibility as measured by inelastic neutron scattering. This behavior is remarkably similar to that seen in certain heavy-fermion metals which are doped to be near a quantum critical point.   

Non-magnetic defects in the classical Kagome bilayer antiferromagnet

We consider non-magnetic substitutions in the quasi two-dimensional Kagome bilayer lattice (relevant to experiments on SCGO~\footnote{L.~Limot {\it et. al}, Phys. Rev. B 65, 14447(2002).}) which consists of both triangular and tetrahedral units. Correlated defects, where impurities substitute for all but one spin on a ``defective" triangle or tetrahedron, are particularly interesting in this context. The lone ``orphan spin"~\footnote{P.~Schiffer and R.~Daruka, Phys. Rev. B 56, 13712 (1997), R.~Moessner and A.~J.~Berlinsky, Phys. Rev. Lett. 83, 3293 (1999)} on the simplex acts like a paramagnetic spin as $T \rightarrow 0$ and induces a long-ranged spin texture around it~\footnote{C.~L.~Henley, Can. J. Phys. 79, 1307 (2001).} at zero temperature. We study such defects at low temperatures and magnetic fields by performing classical Monte-Carlo simulations. We also use a simple effective field theory to reasonably capture the features of the induced texture.   

A spin-1 kagome antiferromagnet

We study a spin-1 antiferromagnet on the kagom\'e lattice. We start by constructing a Klein-type SU(2) symmetric Hamiltonian which contains Heisenberg interactions between nearest and next-nearest neighbors as well as three-body terms. Our model Hamiltonian has an extensive degenerate ground state whose manifold is spanned by the AKLT-like valence bond states. We also perturb the parent Hamiltonian by introducing an enhancement to the nearest neighbor antiferromagnetic Heisenberg interactions. By projecting this perturbation onto the basis spanned by the unperturbed ground states, we derive an effective Hamiltonian which is dual to that of the transverse field antiferromagnetic Ising model on the triangular lattice. Based on the parameters of our model, we find it to be in the order-by-disorder phase. The ground state is a valence bond crystal stabilized by quantum fluctuations. We also discuss excitations, both magnetic and non-magnetic, and address their possible relevance to experiment.   

Dynamical structure factor of spin 1/2 Heisenberg antiferromagnet on Kagome lattice

The ground state of spin 1/2 anti-ferromagnet on kagome lattice can be viewed as a collection of small and heavy bound pairs of fermionic spinons [1]. Magnetic excitations of the model correspond to breaking such pairs into their constituents. In the current work, the dynamical structure factor is calcualted for low energy magnetic excitations just above the spin gap. It is observed that the structure factor is similar to the one of an isolated dimer due to the tightness of the bound state. The result is consistent with experiments done in Helton etal [2] and M.A. de Vries etal [3]. \\[4pt] [1] Zhihao Hao and Oleg Tchernyshyov, Phys. Rev. Lett. 103, 187203.\\[0pt] [2] J. S. Helton etal, Phys. Rev. Lett. 98, 107204.\\[0pt] [3] M. A. de Vries etal, arXiv:0902.3194.   

A second species of spinons in the $S=1/2$ Heisenberg antiferromagnet on kagome

The $S=1/2$ Heisenberg model on kagome can be viewed as an ensemble of spinons, fermionic quasiparticles with $S=1/2$ bound into small, heavy pairs whose binding energy sets the spin gap [1]. The apparent lack of a spin gap in real kagome magnets (e.g. herbertsmithite) may be associated with the Dzyaloshinskii-Moriya (DM) term $\mathbf{D} \cdot (\mathbf{S}_i \times \mathbf{S}_j)$ in the Hamiltonian allowed by lattice symmetry. The DM term suppresses the spin gap and eventually induces long-range magnetic order [2]. A recent study [3] hints at the presence of an intermediate gapless phase without magnetic order. We propose that this phase arises as a result of condensation of a second spinon species (kinks). Here we study the motion of a single kink on the Husimi cactus, the analog of kagome in a hyperbolic plane. The kink is localized in the pure Heisenberg model and becomes mobile when $D \neq 0$. We calculate the one-particle density of states and the bandwidth. [1] Z. Hao and O. Tchernyshyov, Phys. Rev. Lett. \textbf{103,} 187203 (2009). [2] O. C{\'e}pas \textit{et al.}, Phys. Rev. B 78, 140405 (2008). [3] I. Rousochatzakis \textit{et al.}, Phys. Rev. B \textbf{79,} 214415 (2009).   

Valence Bond States on the kagome lattice: Linear Independence and RVB-Hamiltonian

A local SU(2)-invariant Hamiltonian on the kagome lattice is constructed for which the four Sutherland-Rokhsar-Kivelson-type spin-1/2 resonating valence bond (RVB) states on the torus are ground states. The uniqueness of these ground states within the subspace of nearest-neighbor valence bond states can be demonstrated, as opposed to the case of Klein-type models. The proof depends on the linear independence of the nearest-neighbor valence bond states on the (arbitrarily large) kagome lattice. This linear independence property can be demonstrated using tools that are of a piece with those leading to the construction of the RVB-Hamiltonian. The likely uniqueness of the RVB ground states within the full Hilbert space is also discussed. [Reference: A. Seidel, Phys. Rev. B 80, 165131 (2009).]   

Properties of a Single Hole in a Kagome Antiferromagnet

Various Spin Liquid states have been considered as candidate ground states for the frustrated Kagome Antiferromagnet. Ran \emph{et al} showed that the Dirac Spin Liquid(DSL) state has the lowest ground state energy amongst several proposals \footnote{Y. Ran et al, Phys. Rev. Lett. 98, 117205 (2007)} \footnote{M. Hermele et al, Phys. Rev. B 77, 224413 (2008)}. Assuming the DSL as the ground state, we consider the question of a single hole doped into the antiferromagnet. Our aim is to calculate the hole spectral function 1) at mean field level - where the DSL mean field decomposition of the Heisenberg exchange term forms a background field in presence of which the hole propagates, and 2) beyond mean field - where the question is whether the fluctuations of the DSL mean field renormalizes the hole in a nontrivial way or not.   

Chirality-driven heavy-fermion behavior in kagome Hubbard model

Recently, considerable attention has been focused on the heavy-fermion behavior of transition metal compounds, such as LiV$_2$O$_4$. As to the rare-earth materials, the origin of large quasiparticle mass is attributed to the entropy associated with the localized f-electron moments. In contrast, the mechanism of heavy-fermion behavior is still unclear for the transition metal compounds because they do not possess an obvious ``entropy reservoir". To explore an alternative scenario in the effect of geometrical frustration under electron correlation, we study the Hubbard model on the kagome lattice at half filling by adopting the cluster dynamical mean-field theory with the continuous-time quantum Monte Carlo method as an impurity solver. We find that the system exhibits a hierarchy of energy scale in charge, spin, and chirality degrees of freedom. The entropy associated with the chirality is released at a much lower temperature than other energy scales for spin and charge fluctuations, leading to a sharp peak in the specific heat and the single-particle spectrum. These results reveal a new chirality-driven heavy-fermion formation.   

Shastry-Sutherland tube in a magnetic field

We study a peculiar quasi-1D version of the 2D Shastry-Sutherland lattice, namely a spin tube made of two coupled orthogonal dimer chains with periodic boundary conditions in the transverse direction. The phase diagram is obtained at zero and at finite magnetic fields combining DMRG and PCUTs approaches. In the limit of small inter-dimer interactions $J'$ and below half the saturation value an infinite sequence of fractional plateaux is identified with the first few ones located at 1/6, 1/4, 1/3, and 3/8. Above, a pronounced plateau at 1/2 and a smaller one at 3/4 are found. In the limit of large $J'$ the system behaves as a Heisenberg spin-1 chain. At intermediate couplings ($0.65 \leq J' \leq 0.7$) a new plateau at 1/5 is realized whose structure cannot be understood in terms of individual triplet coverings of the dimers. We discuss possible implications for the 2D case and ongoing experiments on the plateau-material SrCu$_2$(BO$_3$)$_2$.   

Long-range Interaction Effect on Fractional Magnetization Plateaus in the Shastry-Sutherland Lattice Model

We investigate magnetic properties of the S=1/2 Ising-like XXZ model on the hastry-Sutherland lattices (SSLs) with long-range interactions, using the quantum Monte Carlo method. This model shows magnetization plateau phases at one-half and one-third of the saturation magnetization when additional couplings are considered. We study the finite temperature transition to one-half and one-third plateau phases. The obtained results suggest that the former case is of the first order and the latter case is of the second order. We also find that the system undergoes two successive transitions with the 2D Ising model universality, although there is a single phase transition in the Ising limit case[1]. In recent experiments, a large magnetization plateau has been observed in a rare-earth SSL compound TmB4[2]. We estimate the coupling ratio to explain the magnetization process. [1] T. Suzuki, Y. Tomita, and N. Kawashima, Phys. Rev. B 80, 180405(R) (2009). [2] K. Siemensmeyer, et al, Phys. Rev. Lett. 101, 037202 (2008).   

Local physics of magnetization plateaux in the Shastry-Sutherland model

We address the physical mechanism responsible for the emergence of magnetization plateaux in the Shastry-Sutherland model. By using a hierarchical mean-field approach we demonstrate that a plateau is stabilized in a certain {\it spin pattern}, satisfying {\it local} commensurability conditions derived from our formalism. Our results provide evidence in favor of a robust local physics nature of the plateaux states, and are in agreement with recent NMR experiments on ${\rm SrCu_2(BO_3)_2}$.   

Two-dimensional atomic-scale magnetic skyrmion lattice of Fe/Ir(111)

Skyrmions are topologically protected field configurations with particle-like properties which were believed to crystallize only under non-equilibrium conditions. Recently, it has been predicted that they can also become ground states in magnetic systems with broken inversion symmetry [1]. We give theoretical evidence of a two-dimensional lattice of atomic-scale skyrmions as the magnetic ground state of a monolayer Fe on Ir(111), a system which has been studied by spin-polarized scanning tunneling microscopy [2]. We apply an extended Heisenberg model based on parameters determined from first-principles to identify the four-spin interaction as its microscopic origin. This interaction couples degenerate spin spirals and enforces a square-symmetry on the skyrmionic spin texture decoupled from the underlying hexagonal atomic lattice. [1] U. K. R\"o{\ss}ler et al., Nature 442, 797 (2006). [2] K. von Bergmann et al., PRL 96, 167203 (2006).   

Classification of quantum phases for the star-lattice antiferromagnet via a projective symmetry group analysis

We study possible quantum ground states of the Heisenberg antiferromagnet on the star lattice, which may be realized in the recently discovered polymeric Iron Acetate, Fe$_3$($\mu_3$-O)($\mu$-OAc)$_6$(H$_2$O)$_3$[Fe$_3$($\mu_3$-O)($\mu$-OAc)$_{7.5}$]$_2\cdot$ 7H$_2$O. Even though the Fe$^{\rm III}$ moment in this material carries spin-5/2 and the system eventually orders magnetically at low temperatures, the magnetic ordering temperature is much lower than the estimated Curie-Weiss temperature, revealing the frustrated nature of the spin interactions. Anticipating that a lower spin analog of this material may be synthesized in future, we investigate the effect of quantum fluctuations on the star-lattice antiferromagnet using a large-$N$ Sp($N$) mean field theory and a projective symmetry group analysis for possible bosonic quantum spin liquid phases. It is found that there exist only two distinct gapped $Z_2$ spin liquid phases with bosonic spinons for non-vanishing nearest-neighbor valence-bond-amplitudes. In particular, the spin liquid phase which has a lower energy in the nearest-neighbor exchange model can be stabilized for relatively higher spin magnitudes.   

First-principles study of electronic and magnetic structures of the triangular-lattice magnet PdCrO$_2$

Quite recently {\em unconventional\/} anomalous Hall effect has been observed in some geometrically frustrated magnets, where the Hall resistivity does not follow the empirical relation and the noncollinear spin configuration seems to play the key role. PdCrO$_2$[1] is a perfect example of such magnets. It crystallizes in delafossite structure, which is made of alternating stack of triangular layers of Pd and Cr. Its metallic conductivity is attributed to Pd 4d electrons and shows strong two-dimensional anisotropy. Cr$^{3+}$ localized moments show antiferromagnetic ordering at 37.5 K, forming 120 degree noncollinear spin structure. At temperatures lower than 20 K, unconventional Hall effect was measured. So far, its microscopic mechanism has not been clarified yet. In this study, we carry out noncollinear LSDA FLAPW calculations for PdCrO$_2$. We will investigate several magnetic structures with and without spin-orbit coupling. We will focus on the conducting states at the Fermi level and examine how they are affected by the Cr spin structure. [1] H.~Takatsu H.~Yoshizawa, S.~Yonezawa, and Y.~Maeno, PRB {\bf 79}, 104424 (2009).