Topological phases have been explored in various fields in physics such as spintronics, photonics, liquid helium, correlated electron system and cold-atomic system. This leads to the recent foundation of emerging materials such as topological band insulators, topological photonic crystals and topological superconductors/superfluid. In this paper, we propose a topological magnonic crystal which provides protected chiral edge modes for magnetostatic spin waves. Based on a linearized Landau-Lifshitz equation, we show that a magnonic crystal with the dipolar interaction acquires spin-wave volume-mode band with non-zero Chern integer. We argue that such magnonic systems are accompanied by the same integer numbers of chiral spin-wave edge modes within a band gap for the volume-mode bands. In these edge modes, the spin wave propagates in a unidirectional manner without being scattered backward, which implements novel fault-tolerant spintronic devices.Comment: 12 pages, 7 figure

The Berry phase due to the spin wavefunction gives rise to the orbital ferromagnetism and anomalous Hall effect in the non-coplanar antiferromagnetic ordered state on face-centered-cubic (fcc) lattice once the crystal is distorted perpendicular to (1,1,1) or (1,1,0)-plane. The relevance to the real systems γ-FeMn and NiS2 is also discussed.PACS numbers: 11.30. Er, 11.30.Rd, 71.27.+a It has been recognized for a long term that the chirality plays important roles in the physics of frustrated spin systems [1][2][3][4][5][6]. These degrees of freedom are distinct from the (staggered) magnetization, and could show phase transition without magnetic ordering [1][2][3]. Especially since the discovery of the high-Tc cuprates, the scalar spin chiralityhas been a key theoretical concept in the physics of strongly correlated electronic systems [4][5][6]. This spin chirality acts as the gauge flux for the charge carriers moving in the background of the fluctuating spins. In order for the spin chirality χ ijk to be ordered, both the time-reversal (T) and parity (P) symmetries must be broken. Broken T and P symmetries in 2D bring about many intriguing physics such as parity anomaly [7,8] , anyon superconductivity [9], and quantized Hall effect without external magnetic field [10]. A physical realization of the last one has been discussed [11] in the context of anomalous Hall effect (AHE) in ferromagnets via the spin chirality mechanism [12][13][14][15]. In this paper we explore the chiral spin state in the ordered antiferromagnet (AF) on the three-dimensional face-centered-cubic (fcc) lattice. The AF on the fcc lattice is a typical frustrated system, and nontrivial spin structure with the finite spin chirality in eq. (1) is expected. For example, in the charge transfer (CT) insulator NiS 2 [16] and in the metallic alloy γ-FeMn [17] the non-coplanar spin structure (so-called triple-Q structure shown in Fig. 1a) has been observed. A theoretical explanation for this structure is the following. Let us consider the case where the lattice points are divided into 4-sublattices as shown in Fig. 1a. Denoting the (classical) spin moment at each sublattice as S a (a = 1, 2, 3, 4), the 2-spin exchange interaction energy is written as H 2 ∝ ( a=1,4 S a )2 . Therefore the condition of the lowest energy a=1,4 S a = 0 does not determine the spin structure and leaves many degenerate lowest energy configurations. Then the interactions which lift this degeneracy such as the 4-spin exchange interaction become important [18,19]. In paticular the phenomenological Ginzburg-Landau theory for the 4-spin exchange interaction is given as H 4 = J 4 a =b ( S a · S b ) 2[19]. With positive J 4 , the ground state configuration is given by S 1 = (

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We studied effects of disorder in a three dimensional layered Chern insulator. By calculating the localization length and density of states numerically, we found two distict types of metallic phases between Anderson insulator and Chern insulator; one is diffusive metallic (DM) phase and the other is renormalized Weyl semimetal (WSM) phase. We show that longitudinal conductivity at the zero energy state remains finite in the renormalizd WSM phase as well as in the DM phase, while goes to zero at a semimetal-metal quantum phase transition point between these two. Based on the Einstein relation combined with the self-consistent Born analysis, we give a conductivity scaling near the quantum transition point.

Based on a linearized Landau-Lifshitz equation, we show that two-dimensional periodic allay of ferromagnetic particles coupled with magnetic dipole-dipole interactions supports chiral spin-wave edge modes, when subjected under the magnetic field applied perpendicular to the plane. The mode propagates along a one-dimensional boundary of the system in a unidirectional way and it always has a chiral dispersion within a band gap for spin-wave volume modes. Contrary to the well-known Damon-Eshbach surface mode, the sense of the rotation depends not only on the direction of the field but also on the strength of the field; its chiral direction is generally determined by the sum of the so-called Chern integers defined for spin-wave volume modes below the band gap. Using simple tight-binding descriptions, we explain how the magnetic dipolar interaction endows spin-wave volume modes with non-zero Chern integers and how their values will be changed by the field.Comment: 18 pages, 16 figures, some trivial typo in equations are fixe