Non-collinear antiferromagnets and the anomalous Hall effect

Kübler, J.; Felser, Claudia

doi:10.1209/0295-5075/108/67001

EPL

2014

DOI: 10.1209/0295-5075/108/67001

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Non-collinear antiferromagnets and the anomalous Hall effect

J. Kübler¹,

Claudia Felser²

Abstract: The anomalous Hall effect is investigated theoretically for the non-collinear antiferromagnetic order of the hexagonal compounds Mn3Ge and Mn3Sn using various planar triangular magnetic configurations as well as unexpected non-planar configurations. The former give rise to anomalous Hall conductivities (AHC) that are found to be extremely anisotropic. For the planar cases the AHC is connected with Weyl-points in the energy-band structure, which are described in detail. If this case were observable in Mn3Ge, a … Show more

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Cited by 348 publications

(316 citation statements)

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“…This effect is closely related to the anomalous Hall effect predicted in the same class of materials [2,3], both of which are dictated by the absence of certain crystal symmetries. The appearance of magneto-optic effects in antiferromagnets is of intrinsic interest, since it would allow direct detection of the magnetic order and therefore could be useful for antiferromagnets-based memory devices [4].While non-collinear antiferromagnets have been the focus of recent interest [1][2][3], in this Letter we show that magneto-optic effects can also exist in the more commonly available collinear antiferromagnets. We start by analyzing the general symmetry requirements for magneto-optic effects, and demonstrate the symmetry principles by constructing a tight-binding model with a collinear Néel type order.…”

mentioning

confidence: 54%

“…While non-collinear antiferromagnets have been the focus of recent interest [1][2][3], in this Letter we show that magneto-optic effects can also exist in the more commonly available collinear antiferromagnets. We start by analyzing the general symmetry requirements for magneto-optic effects, and demonstrate the symmetry principles by constructing a tight-binding model with a collinear Néel type order.…”

mentioning

confidence: 72%

“…This assumption has been recently challenged by the theoretical demonstration of a rather large magneto-optic Kerr effect (MOKE) in certain non-collinear antiferromagnets with zero net magnetization [1]. This effect is closely related to the anomalous Hall effect predicted in the same class of materials [2,3], both of which are dictated by the absence of certain crystal symmetries. The appearance of magneto-optic effects in antiferromagnets is of intrinsic interest, since it would allow direct detection of the magnetic order and therefore could be useful for antiferromagnets-based memory devices [4].…”

mentioning

confidence: 99%

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Gate-Controllable Magneto-optic Kerr Effect in Layered Collinear Antiferromagnets

2016

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Using symmetry arguments and a tight-binding model, we show that for layered collinear antiferromagnets, magneto-optic effects can be generated and manipulated by controlling crystal symmetries through a gate voltage. This provides a promising route for electric field manipulation of the magneto-optic effects without modifying the underlying magnetic structure. We further demonstrate the gate control of magneto-optic Kerr effect (MOKE) in bilayer MnPSe3 using first-principles calculations. The field-induced inversion symmetry breaking effect leads to gate-controllable MOKE whose direction of rotation can be switched by the reversal of the gate voltage.PACS numbers: 75.50. Ee,75.70.Ak,78.20.Ls,85.70.Sq Magneto-optic effects are one of the defining features of time-reversal (T ) symmetry breaking in matter. Usually, the T symmetry is broken either by an external magnetic field, or by the spontaneous appearance of a macroscopic magnetization such as in ferromagnets. Similar to their ferromagnetic counterparts, the T symmetry is also broken in antiferromagnets. However, because of their vanishing net magnetization one would naively expect an absence of magneto-optic effects in antiferromagnets. This assumption has been recently challenged by the theoretical demonstration of a rather large magneto-optic Kerr effect (MOKE) in certain non-collinear antiferromagnets with zero net magnetization [1]. This effect is closely related to the anomalous Hall effect predicted in the same class of materials [2,3], both of which are dictated by the absence of certain crystal symmetries. The appearance of magneto-optic effects in antiferromagnets is of intrinsic interest, since it would allow direct detection of the magnetic order and therefore could be useful for antiferromagnets-based memory devices [4].While non-collinear antiferromagnets have been the focus of recent interest [1][2][3], in this Letter we show that magneto-optic effects can also exist in the more commonly available collinear antiferromagnets. We start by analyzing the general symmetry requirements for magneto-optic effects, and demonstrate the symmetry principles by constructing a tight-binding model with a collinear Néel type order. We show that, contrary to the general belief, lifting the spin degeneracy of the energy bands is not a sufficient condition to generate magnetooptic effects; it is the crystal symmetry that actually controls these effects.Based on this understanding, we predict that a perpendicular electric field can be used to generate and control the MOKE in layered antiferromagnets using firstprinciples calculations. Recent theoretical and experimental progress has identified several layered compounds as promising candidates to host magnetism in their thinfilm limit [5][6][7][8][9][10]. One of them is MnPSe 3 , a semiconductor with collinear antiferromagnetic order within each layer. We show that the field-induced inversion (I) symmetry breaking in bilayer MnPSe 3 gives rise to a MOKE whose direction of rotation can be switched by the reversal...

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mentioning

confidence: 54%

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confidence: 72%

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confidence: 99%

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Gate-Controllable Magneto-optic Kerr Effect in Layered Collinear Antiferromagnets

2016

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“…The inverse triangular spin structure for Mn 3 Sn reduces the lattice symmetry from six-fold to two-fold in the plane and thus based on the symmetry argument, the Hall effect may appear in the ab-plane 10,31 . Indeed, a recent calculation found that Mn 3 Sn may have a large anomalous Hall conductivity 20 , which can be estimated by integrating the Berry curvature of the occupied bands over the entire Brillouin zone 9 . More recently, the possibility of a Weyl metal has been proposed, where the bands crossing E F have several Weyl points, around which the Berry curvature diverges 11 .…”

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confidence: 99%

Large anomalous Nernst effect at room temperature in a chiral antiferromagnet

et al. 2017

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A temperature gradient in a ferromagnetic conductor can generate a transverse voltage drop perpendicular to both the magnetization and heat current. This anomalous Nernst e ect has been considered to be proportional to the magnetization 1-7 , and thus observed only in ferromagnets. Theoretically, however, the anomalous Nernst e ect provides a measure of the Berry curvature at the Fermi energy 8,9 , and so may be seen in magnets with no net magnetization. Here, we report the observation of a large anomalous Nernst e ect in the chiral antiferromagnet Mn 3 Sn (ref. 10). Despite a very small magnetization ∼0.002 µ B per Mn, the transverse Seebeck coe cient at zero magnetic field is ∼0.35 µV K −1 at room temperature and reaches ∼0.6 µV K −1 at 200 K, which is comparable to the maximum value known for a ferromagnetic metal. Our first-principles calculations reveal that this arises from a significantly enhanced Berry curvature associated with Weyl points near the Fermi energy 11 . As this e ect is geometrically convenient for thermoelectric power generation-it enables a lateral configuration of modules to cover a heat source 6 -these observations suggest that a new class of thermoelectric materials could be developed that exploit topological magnets to fabricate e cient, densely integrated thermopiles.Current intensive studies on thermally induced electron transport in ferromagnetic materials have opened various avenues for research on thermoelectricity and its application [12][13][14][15] . This trend has also triggered renewed interest in the anomalous Nernst effect (ANE) in ferromagnetic metals [3][4][5][6][7]15 , which is the spontaneous transverse voltage drop induced by heat current and is known to be proportional to magnetization (Fig. 1a). On the other hand, the recent Berry phase formulation of the transport properties has led to the discovery that a large anomalous Hall effect (AHE) may arise not only in ferromagnets, but in antiferromagnets and spin liquids, in which the magnetization is vanishingly small 10, [16][17][18][19][20][21][22] . As the first case in antiferromagnets, Mn 3 Sn has been experimentally found to exhibit a large AHE 10 . While the AHE is obtained by an integration of the Berry curvature for all of the occupied bands, the ANE is determined by the Berry curvature at E F (refs 8,9). Thus, the observation of a large AHE does not guarantee the observation of a large ANE. Furthermore, the ANE measurement should be highly useful to clarify the Berry curvature spectra near E F and to verify the possibility of the Weyl metal recently proposed for Mn 3 Sn (ref. 11).Mn 3 Sn has a hexagonal crystal structure with a space group of P6 3 /mmc (ref. 23). Mn atoms form a breathing type of kagome lattice in the ab-plane (Fig. 1b), and the Mn triangles constituting the kagome lattice are stacked on top along the c axis forming a tube of face-sharing octahedra. On cooling below the Néel temperature of 430 K, Mn magnetic moments of ∼3µ B lying in the ab-plane form a coplanar, chiral magnetic structure chara...

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“…Here we attack these issues in the family of noncollinear antiferromagnets including Mn 3 Sn and Mn 3 Ge, for which a strong AHE was predicted and then experimentally verified to exist [19][20][21]. First principles calculations further indicate that in Mn 3 Sn and Mn 3 Ge there are Weyl nodes around the Fermi level [22,23]. We argue that these materials possess a hierarchy of energies scales which permits a description of the microstructure and spin dynamics as an XY model with Z 6 anisotropy.…”

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confidence: 99%

Anomalous Hall Effect and Topological Defects in Antiferromagnetic Weyl Semimetals: Mn3Sn/Ge

2017

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We theoretically study the interplay between bulk Weyl electrons and magnetic topological defects, including magnetic domains, domain walls, and Z6 vortex lines, in the antiferromagnetic Weyl semimetals Mn3Sn and Mn3Ge with negative vector chirality. We argue that these materials possess a hierarchy of energies scales which allows a description of the spin structure and spin dynamics using a XY model with Z6 anisotropy. We propose a dynamical equation of motion for the XY order parameter, which implies the presence of Z6 vortex lines, the double-domain pattern in the presence of magnetic fields, and the ability to control domains with current. We also introduce a minimal electronic model which allows efficient calculation of the electronic structure in the antiferromagnetic configuration, unveiling Fermi arcs at domain walls, and sharp quasi-bound states at Z6 vortices. Moreover, we have shown how these materials may allow electronic-based imaging of antiferromagnetic microstructure, and propose a possible device based on domain-dependent anomalous Hall effect. PACS numbers:The Hall effect has long been a nucleation center for geometry and topology in the physics of solids. In the 1950s, prescient work of Karplus and Luttinger identified Berry curvature of electron wavefunctions as the heart of the anomalous Hall effect (AHE) in ferromagnets [1,2]. In the 1980s, topology entered with the discovery of the quantum Hall effect. These ideas came together in the mid-2000s to unveil broad applications to electronic systems in the form of topological insulators, superconductors [3,4] and semimetals with topological Weyl (and other) fermion excitations [5][6][7][8][9][10][11][12][13][14][15][16][17][18]. The AHE re-appears as one of the key emergent properties of topological semimetals, and coming full circle, most ferromagnets are now believed to host Weyl fermions to which their AHE is at least in part attributed.The dissipationless nature of the Hall effect also makes it interesting for applications. Uses based on ferromagnets may, however, be limited by the difficulty of miniaturization posed by large fields generated by the magnetization. For this reason, antiferromagnetic realizations of AHE may be of practical interest, but the microstructure, dynamics, and AHE of antiferromagnets are relatively uninvestigated. Here we attack these issues in the family of noncollinear antiferromagnets including Mn 3 Sn and Mn 3 Ge, for which a strong AHE was predicted and then experimentally verified to exist [19][20][21]. First principles calculations further indicate that in Mn 3 Sn and Mn 3 Ge there are Weyl nodes around the Fermi level [22,23]. We argue that these materials possess a hierarchy of energies scales which permits a description of the microstructure and spin dynamics as an XY model with Z 6 anisotropy. We propose a dynamical equation of motion for the XY order parameter, which implies a rich domain structure, the presence of Z 6 vortex lines, and the ability to control domains with current. We further introduce a ...

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Non-collinear antiferromagnets and the anomalous Hall effect

Cited by 348 publications

References 30 publications

Gate-Controllable Magneto-optic Kerr Effect in Layered Collinear Antiferromagnets

Gate-Controllable Magneto-optic Kerr Effect in Layered Collinear Antiferromagnets

Large anomalous Nernst effect at room temperature in a chiral antiferromagnet

Anomalous Hall Effect and Topological Defects in Antiferromagnetic Weyl Semimetals: Mn3Sn/Ge

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