Orbital Ferromagnetism and Anomalous Hall Effect in Antiferromagnets on the Distorted fcc Lattice

Abstract

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 = (

Noncommutative geometry and non-Abelian Berry phase in the wave-packet dynamics of Bloch electrons

“…It appears in the presence of magnetic Bloch bands and ferromagnetic backgrounds. [6,23,24,25]. On the other hand, the latter, Fk µxν and Fk µ t appear only in the presence of the time-dependent Bloch basis mentioned above.…”

“…As will soon become clearer, an interpretation in terms of reciprocal gauge field (strength) uncover the nature of various physical phenomena, such as anomalous Hall effect (AHE), [6,23,24,25], spin Hall effect, [10] and quantum charge/spin pumping. [14,15] 3.1 Assumption of slowly varying perturbation β(x, t) -concept of the local Hamiltonian and its local Bloch bands…”

“…B(k) encodes information on the topological nature of band structure, in particular, that of band crossings. [7] Indeed, a degeneracy point corresponds to a momopole of B(k), [5] which has played a crucial role in the understanding of anomalous Hall effect (AHE) [6,23,24,25]. In this paper we study the wave-packet dynamics of Bloch electrons subject to a perturbation β(x, t) varying slowly in space and time.…”

“…[22] Recently, the Berry phase in AHE has attracted a renewed attention, revealing its rich topological structures. [3,4,6,7,23,24,25,26] The Berry phase has also been generalized to a non-Abelian case. [27] The equations of motion (EOM) for a wave packet of Bloch functions 1 is instrumental in all the analyses done in the paper.…”

Controllable chirality-induced geometrical Hall effect in a frustrated highly correlated metal

“…Theoretically, the effect of the spin texture on the current can reach the equivalent of a local magnetic field of H~10 4-5 T, which is at least two orders of magnitude larger than the highest field currently generated in high magnetic-field laboratories. Furthermore, if this local effective field does not average to zero over the sample, then the predicted Hall response can be as large as the integer quantum Hall effect in every atomic plane [14][15][16][17] . As the local spin chirality leading to such a large effective magnetic field and associated Hall response can be tuned by applying a much smaller external field, a clean example of such an effect would open a new direction towards designing functional materials with exotic properties and states.…”