Topological Hall Effect in Itinerant Helimagnets
In this chapter, we focus on the topological Hall effect in itinerant helimagnets. As described in Chap. 1 , there have been few helimagnets which show topological Hall effect except for Skyrmion lattice phases of chiral helimagnets (e.g. MnSi and MnGe).
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Topological Hall Effect in Itinerant Helimagnets
Abstract In this chapter, we focus on the topological Hall effect in itinerant helimagnets. As described in Chap. 1, there have been few helimagnets which show topological Hall effect except for Skyrmion lattice phases of chiral helimagnets (e.g. MnSi and MnGe). This is because the total scalar spin chirality summed over the whole lattice sites often becomes zero due to structural symmetry, although the noncoplanar spin configuration is generally realized in helical magnets under applied H . In the first and second sections of this chapter, we report two new examples of helimagnets in which the scalar spin chirality does not cancel out owing to the modulation of spin structure by DM interaction and thus topological Hall effect occurs. In the third section, we investigate the topological Hall effects by heat current, i.e. topological thermal Hall effect and topological Nernst effect, for MnGe. In contrast to the cases of MnSi and (Fe,Co)Si, the Skyrmion lattice phase of MnGe has been considered to prevail in wide temperature and magnetic-field window. This enables us to examine thoroughly the topological Hall effects by heat current in the Skyrmion lattice phase. Keywords Topological Hall effect · Itinerant helimagnet · Scalar spin chirality Dzyaloshinsky-Moriya interaction · Berry phase of electrons
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5.1 Topological Hall Effect in Fe1.3 Sb In the case of the triangular lattice with three-sublattice spin order (e.g. 120◦ -spin structure), the whole scalar spin chirality cancels out and the contribution to Hall effect is not expected [1, 2]. Recently, however, in a triangular-lattice antiferromagnet PdCrO2 where Cr3+ spins order with a 120◦ -structure below TN = 37 K, an unconventional Hall effect was observed under H applied parallel to the c axis below T ∗ ∼ 20 K that is noticeably lower than TN [3]. It was speculated in [3] that the spin structure would change so as to have a finite scalar spin chirality below T ∗ under
Y. Shiomi, Anomalous and Topological Hall Effects in Itinerant Magnets, Springer Theses, DOI: 10.1007/978-4-431-54361-9_5, © Springer Japan 2013
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5 Topological Hall Effect in Itinerant Helimagnets
(a) 10
(c) ρ
ρ xx (mΩ cm)
5
Fe Sb
1
c
ρ//
0.5
excess
a
Fe a
0.1
(b)
(d) H // c
M (emu/mol)
30
S2 H c ( 50)
20 H
c
10
S1
S1 S3
S2
c
μ 0 H =0.1T S2
0 0
100 T (K)
S1
200
Fig. 5.1 a Temperature dependence of the in-plane and out-of-plane resistivities, ρ|| and ρ⊥ , for Fe1.3 Sb [4]. b T dependence of the magnetization (M) in external magnetic field (H ) parallel or perpendicular to the c axis [4]. Two triangles indicate the ordering temperatures of the in-plane Fe(l) spins (TN ) and the interstitial-Fe(i) spins, respectively. c Schematic view of the crystal structure of Fe1+δ Sb [4]. Fe(i) atoms, whose concentration is δ, randomly occupy the sites shown by dotted circles. d Top view of the Fe(l) and Fe(i) sites where the (red) arrows indicate the directions of the Fe(l) spins in the 120◦ -spin structure below TN [4]
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