We theoretically propose a mechanism for the anomalous Hall effect (AHE) in an antiferrromagnetic (AFM) state of $κ$-type organic conductors. We incorporate the spin-orbit coupling in the effective Hubbard model on the $κ$-type lattice structure taking into account the orientation of the molecules and their arrangement with dimerization. Treating this model by means of the Hartree-Fock approximation and the linear response theory, we find that an intrinsic contribution to the Hall conductivity becomes nonzero in the electron-doped AFM metallic phase with a small canted ferromagnetic moment. We show that, contrary to the conventional wisdom, the spin canting is irrelevant to the Hall response; the nonzero Hall conductivity originates from the collinear component of the AFM order in the presence of the spin-orbit coupling. These features are well explained analytically in the limit of strong dimerization on the anisotropic triangular lattice. Furthermore, we present an intuitive picture for the present AHE by considering the real-space configuration of emergent magnetic fluxes. We also find that the Hall response appears even in the undoped AFM insulating phase at nonzero frequency as the magneto-optical Kerr effect, which is enhanced around the charge transfer excitations. We discuss possible detections of the AHE in ET based compounds.
Using Raman scattering, the quasi-two dimensional organic superconductor k-(BEDT-TTF)2Cu[N(CN)2]Br (T_c=11.8 K) and the related antiferromagnet k-(BEDT-TTF)2Cu[N(CN)2]Cl are studied. Raman scattering provides unique spectroscopic information about magnetic degrees of freedom that has been otherwise unavailable on such organic conductors. Below T=200 K a broad band at about 500 cm-1 develops in both compounds. We identify this band with two-magnon excitation. The position and the temperature dependence of the spectral weight are similar in the antiferromagnet and in the metallic Fermi-liquid. W…
Although the isotope effect in superconducting materials is well-documented, changes in the magnetic properties of antiferromagnets due to isotopic substitution are seldom discussed and remain poorly understood. This is perhaps surprising given the possible link between the quasi-two-dimensional (Q2D) antiferromagnetic and superconducting phases of the layered cuprates. Here we report the experimental observation of shifts in the Néel temperature and critical magnetic fields ($ΔT_{\rm N}/T_{\rm N}\approx 4%$; $ΔB_{\rm c}/B_{\rm c}\approx 4%$) in a Q2D organic molecular antiferromagnets on subs…
We study the Hall effect in a system of weakly coupled Luttinger Liquid chains, using a Memory function approach to compute the Hall constant in the presence of umklapp scattering along the chains. In this approximation, the Hall constant decomposes into two terms: a high-frequency term and a Memory function term. For the case of zero umklapp scattering, where the Memory function vanishes, the Hall constant is simply the band value, in agreement with former results in a similar model with no dissipation along the chains. With umklapp scattering along the chains, we find a power-law temperature…
We report the observation of nonlinear anomalous Hall effect (NLAHE) in the multilayered organic conductor $α$-(BEDT-TTF)$_2$I$_3$ in the charge order (CO) insulating phase just under the critical pressure for transition into two-dimensional (2D) massless Dirac fermion (DF) phase. We successfully extracted the finite nonlinear Hall voltage proportional to square current at zero magnetic field. The observed NLAHE features, current direction dependence and correlation with CO, are consistent with the previous estimation assuming 2D massive DF with a pair of tilted Dirac cones. This is the first …
For temperatures T well above the ordering temperature T*=3.0+-0.2K the magnetic properties of the metal-organic material Mn[C10H6(OH)(COO)]2x2H20 built from Mn^2+ ions and 3-hydroxy-2-naphthoic anions can be described by a S=5/2 quantum antiferromagnet on a distorted honeycomb lattice with two different nearest neighbor exchange couplings J2 \approx 2J1 \approx 1.8K. Measurements of the magnetization M(H,T) as a function of a uniform external field H and of the uniform zero field susceptibility χ(T) are explained within the framework of a modified spin-wave approach which takes into account t…
The temperature dependences of the Hall coefficient and electrical resistivity recently measured by Moser et al. [Phys. Rev. Lett. 84, 2674 (2000)] in the quasi-one-dimensional organic conductor (TMTSF)2PF6 are quantitatively compared with our previous theoretical calculations [Synth. Met. 103, 2202 (1999); Eur. Phys. J. B 11, 385 (1999)]. We find a good agreement, albeit not with a fully consistent set of parameters for the two quantities, without appealing to the Luttinger liquid concept.
The low-temperature electronic state of the layered organic charge-transfer salt $κ$-(BETS)$_2$FeCl$_4$ was probed by interlayer electrical resistance measurements under magnetic field. Both above and below $T_{\mathrm{N}}=0.47\,$K, the temperature of antiferromagnetic ordering of $3d$-electron spins of Fe$^{3+}$ localized in the insulating anion layers, a non-saturating linear $R(T)$ dependence has been observed. A weak superconducting signal has been detected in the antiferromagnetic state, at temperatures $\leq 0.2\,$K. Despite the very high crystal quality, only a tiny fraction of the samp…
We have measured the Hall effect on recently synthesized single crystals of quasi-one-dimensional organic conductor TTF-TCNQ, a well known charge transfer complex that has two kinds of conductive stacks: the donor (TTF) and the acceptor (TCNQ) chains. The measurements were performed in the temperature interval 30 K < T < 300 K and for several different magnetic field and current directions through the crystal. By applying the equivalent isotropic sample (EIS) approach, we have demonstrated the importance of the choice of optimal geometry for accurate Hall effect measurements. Our results show,…
Long missing basic experiments in the normal phase of the anisotropic electron system of TMTSF2PF6 were performed. Both the Hall effect and the ab'-plane conduction anisotropy are directly addressing the unconventional electrical properties of this Bechgaard salt. We found that the dramatic reduction of the carrier density deduced from recent optical data is not reflected in an enhanced Hall-resistance. The pressure- and temperature dependence of the b'-direction resitivity reveal isotropic relaxation time and do not require explanations beyond the Fermi liquid theory. Our results allow a cohe…
We present the high-temperature (70 K < T < 300 K) resistivity anisotropy and Hall effect measurements of the quasi-one-dimensional (1D) organic conductor (TMTTF)2AsF6. The temperature variations of the resistivity are pronouncedly different for the three different directions, with metallic-like at high temperatures for the a-axis only. Above 220 K the Hall coefficient R_H is constant, positive and strongly enhanced over the expected value; and the corresponding carrier concentration is almost 100 times lower than calculated for one hole/unit cell. Our results give evidence for the existence o…
The interdependence of antiferromagnetism and superconductivity in the Bechgaard salts series of organic conductors is examined in the light of the anomalous temperature dependence of the nuclear spin-lattice relaxation rate. We apply the renormalization group approach to the electron gas model to show that the crossover from antiferromagnetism to superconductivity along with the anomalous nuclear relaxation rate of the Bechgaard salts can be well described within a unified microscopic framework. For sizable nesting deviations of the Fermi surface, scaling theory reveals how pairing correlatio…
I apply a two-step renormalization group method to the study of the competition between antiferromagnetism (AFM) and superconductivity in an anisotropic 2D Hubbard model. I show that this simple model captures the essentials of the ground-state phases of the quasi 1D organic conductors. As found experimentally, the ground-state phase diagram is mostly AFM. The AFM is localized in the strong-coupling limit where the electrons are confined in the chains. It is an SDW in the weak-coupling limit where interchain hopping is present. There is a tiny region in the weak-coupling regime where transvers…
Superconductivity in the Bechgaard salts series of quasi-one-dimensional organic conductors occurs on the verge of spin-density-wave ordering when hydrostatic pressure is applied. The sequence of instabilities is intimately connected to normal state anomalies in various quantities like the temperature dependence of electrical transport and nuclear spin-lattice relaxation rate. We discuss how such a connection takes its origin in the interference between the different pairing mechanisms responsible for antiferromagnetism and superconductivity, a duo that can be comprehended in terms of a weak c…
Spin current--a flow of electron spins without a charge current--is an ideal information carrier free from Joule heating for electronic devices. The celebrated spin Hall effect, which arises from the relativistic spin-orbit coupling, enables us to generate and detect spin currents in inorganic materials and semiconductors, taking advantage of their constituent heavy atoms. In contrast, organic materials consisting of molecules with light elements have been believed to be unsuited for spin current generation. Here we show that a class of organic antiferromagnets with checker-plate type molecula…
Skyrmions are topologically nontrivial, magnetic quasi-particles, that are characterized by a topological charge. A regular array of skyrmions - a skyrmion crystal (SkX) - features the topological Hall effect (THE) of electrons, that, in turn, gives rise to the Hall effect of the skyrmions themselves. It is commonly believed that antiferromagnetic skyrmion crystals (AFM-SkXs) lack both effects. In this Rapid Communication, we present a generally applicable method to create stable AFM-SkXs by growing a two sublattice SkX onto a collinear antiferromagnet. As an example we show that both types of…
We have experimentally confirmed the quantum Hall ferromagnetic state with Chern number ν=0, characterized by the helical edge state, in a layered organic Dirac fermion system α-(BEDT-TTF)_2I_3. The interlayer resistance saturates at low temperatures and high magnetic fields. It does not scale with the sample cross-sectional area in the saturating region, and resonantly depends on the magnetic field direction. These results strongly suggest that the helical edge state dominates transport. This is the first observation of the topological phase in organic molecular crystals.
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 NiS$_2$ is also discussed.
Non-collinear triangular antiferromagnets with a coplanar spin arrangement and vanishing net magnetic moment can exhibit a large anomalous Hall effect owing to their non-vanishing momentum space Berry curvature. Here we show the existence of a large field induced topological Hall effect in the non-coplanar triangular antiferromagnetic geometry of Mn3Sn. A detailed magnetic and Hall effect measurements demonstrate the presence of three distinct Hall contributions; a high temperature anomalous Hall effect, a low temperature topological Hall effect and an intermediate temperature region with coex…
We study the anomalous Hall effect on the antiferromagnetic coloring-triangular lattice with a coplanar magnetic configuration in presence of a spin-orbit interaction. The effect of the spin-orbit coupling is included at effective level as a rotation of the electronic spin as the electrons hop from site to site. Our result reveals that a finite Hall conductivity in the planar 120$^{\circ}$ structure takes place if a finite spin-orbit coupling is present. A quantized Hall conductivity occurs at global band gaps resulting from the topologically non-trivial band structure.
We investigate the behavior of the Hall coefficient in the case of antiferromagnetism driven by Fermi surface nesting, and find that the Hall coefficient should abruptly increase with the onset of magnetism, as recently observed in vanadium doped chromium. This effect is due to the sudden removal of flat portions of the Fermi surface upon magnetic ordering. Within this picture, the Hall coefficient should scale as the square of the residual resistivity divided by the impurity concentration, which is consistent with available data.
It is well established that the anomalous Hall effect that a ferromagnet displays scales with its magnetization. Therefore, an antiferromagnet that has no net magnetization should exhibit no anomalous Hall effect. Here we show that the non-collinear triangular antiferromagnet Mn3Ge exhibits a large anomalous Hall effect comparable to that of ferromagnetic metals; the magnitude of the anomalous conductivity is 500 per ohm per cm at 2 K and 50 per ohm per cm at room temperature. The angular dependence of the anomalous Hall effect measurements confirm that the small residual in-plane magnetic mom…
We report the magnetic diffraction pattern and spin wave excitations in (CD$_3$)$_2$ND$_2$[Mn(DCO$_2$)$_3$] measured using elastic and inelastic neutron scattering. The magnetic structure is shown to be a G-type antiferromagnet with moments pointing along the $b$ axis. By comparison with simulations based on linear spin wave theory, we have developed a model for the magnetic interactions in this multiferroic metal-organic framework material. The interactions form a three-dimensional network with antiferromagnetic nearest-neighbour interactions along three directions of $J_1=-0.103(8)$~meV, $J_…
A clear thermal Hall signal ($κ_{xy}$) was observed in the spin liquid phase of the $S=1/2$ kagomé antiferromagnet Ca kapellasite (CaCu$_3$(OH)$_6$Cl$_2\cdot 0.6$H$_2$O). We found that $κ_{xy}$ is well reproduced, both qualitatively and quantitatively, using the Schwinger-boson mean-field theory with the Dzyaloshinskii--Moriya interaction of $D/J \sim 0.1$. In particular, $κ_{xy}$ values of Ca kapellasite and those of another kagomé antiferromagnet, volborthite, converge to one single curve in simulations modeled using Schwinger bosons, indicating a common temperature dependence of $κ_{xy}$ fo…
I point out that a magnetotransport theory on the basis of the fluctuation exchange (FLEX) approximation, which is proposed in order to explain anomalous transport properties in the normal state of high-$T_{\rm c}$ cuprate superconductors, is not compatible with the Fermi liquid theory and that the anomaly obtained there ascribes to the inconsistency of the approximation.
Using finite-temperature Lanczos method the frequency-dependent Hall response is calculated numerically for the t-J model on the square lattice and on ladders. At low doping, both the high-frequency RH* and the d.c. Hall coefficient RH0 follow qualitatively similar behavior at higher temperatures: being hole-like for T > Ts~1.5J and weakly electron-like for T < Ts. Consistent with experiments on cuprates, RH0 changes, in contrast to RH*, again to the hole-like sign below the pseudogap temperature T*, revealing a strong temperature variation for T->0.
Observations of $ν=1$ Quantum Hall Effect and Inter-Band Effects of Magnetic fields on Hall Conductivity in Organic Massless Dirac Fermion System $α$-(BETS)$_2$I$_3$ under Pressure
本文在压力下的 α-(BETS)₂I₃ 有机无质量 Dirac 费米子体系中观测到 ν=1 量子 Hall 态，并通过化学势跨越 Dirac 点揭示了磁场对 Hall 电导率的带间效应。
We report field-induced magnetic phase transitions and transport properties of antiferromagnetic DyPtBi. We show that DyPtBi hosts a delicate balance between two different magnetic ground states, which can be controlled by a moderate magnetic field. Furthermore, it exhibits giant anomalous Hall effect (σ_A=1540 (ohm cm)^{-1},θ_{AHE} = 24%) in a field-induced Type-I spin structure, presumably attributed to the enhanced Berry curvature associated with avoided band-crossings near the Fermi energy and / or non-zero spin chirality. The latter mechanism points DyPtBi towards a rare potential realiza…
We have studied the anomalous Hall effect (AHE) in strained thin films of the frustrated antiferromagnet Mn$_{3}$NiN. The AHE does not follow the conventional relationships with magnetization or longitudinal conductivity and is enhanced relative to that expected from the magnetization in the antiferromagnetic state below $T_{\mathrm{N}} = 260$\,K. This enhancement is consistent with origins from the non-collinear antiferromagnetic structure, as the latter is closely related to that found in Mn$_{3}$Ir and Mn$_{3}$Pt where a large AHE is induced by the Berry curvature. As the Berry phase induce…
A spin valve is a prototype of spin-based electronic devices found on ferromagnets, in which an antiferromagnet plays a supporting role. Recent findings in antiferromagnetic spintronics show that an antiferromagnetic order in single-phase materials solely governs dynamic transport, and antiferromagnets are considered promising candidates for spintronic technology. In this work, we demonstrated antiferromagnet-based spintronic functionality on an itinerant Ising antiferromagnet of Ca0.9Sr0.1Co2As2 by integrating nanoscale spin-valve-type structure and investigating anisotropic magnetic properti…
We study irradiated two-dimensional insulating bilayer honeycomb ferromagnets and antiferromagnets coupled antiferromagnetically with a zero net magnetization. The former is realized in the recently synthesized bilayer honeycomb chromium triiodide CrI$_{\bf 3}$. In both systems, we show that circularly-polarized electric field breaks time-reversal symmetry and induces a dynamical Dzyaloshinskii-Moriya interaction in each honeycomb layer. However, the resulting bilayer antiferromagnetic system still preserves a combination of time-reversal and space-inversion ($\mathcal{PT}$) symmetry. We show …
Shubnikov-De Haas effect (SdH) effect and angular dependent magnetoresistance oscillations (AMRO) were observed in the organic superconductor: $κ$-(BETS)$_2$FeBr$_4$. In contrast to its isostructural compound $κ-(BETS)$_2$FeCl$_4$, SdH oscillations, for fields perpendicular to the conducting planes, reveal three Fermi Surface (FS) closed orbits $α$, $β$, and $γ$ whose cross sectional areas are 19.8 %, 99.9 %, and 2.4 % of the first Brillouin zone, respectively. The conduction electron effective masses were found to be: $μ_α = (4.7 \pm 0.2)$ m$_e$, $μ_β = (8.0 \pm 1.0)$ m$_e$, and $μ_γ = (2.0 \…
We report the influence of the field effect on the dc resistance and Hall coefficient in the strain-induced Mott insulating state of an organic superconductor $κ$-(BEDT-TTF)$_{2}$Cu[N(CN)$_{2}$]Br. Conductivity obeys the formula for activated transport $σ_{\Box} = σ_{0}\exp(-W/k_{B}T)$, where $σ_{0}$ is a constant and $W$ depends on the gate voltage. The gate voltage dependence of the Hall coefficient shows that, unlike in conventional FETs, the effective mobility of dense hole carriers ($\sim1.6\times 10^{14}$ cm$^{-2}$) is enhanced by a positive gate voltage. This implies that carrier doping…
We give a quantitative analysis of the previously published nuclear magnetic resonance (NMR) experiments in the k-(ET)2X family of organic charge transfer salts by using the phenomenological spin fluctuation model of Moriya, and Millis, Monien and Pines (M-MMP). For temperatures above T_nmr ~ 50 K, the model gives a good quantitative description of the data in the metallic phases of several k-(ET)2X materials. These materials display antiferromagnetic correlation lengths which increase with decreasing temperature and grow to several lattice constants by T_nmr. It is shown that the fact that th…
We report a detailed characterization of quantum Hall effect (QHE) influence on the linear and non-linear resistivity tensor in FISDW phases of the organic conductor (TMTSF)2PF6. We show that the behavior at low electric fields, observed for nominally pure single crystals with different values of the resistivity ratio, is fully consistent with a theoretical model, which takes QHE nature of FISDW and residual quasi-particle density associated with different crystal imperfection levels into account. The non-linearity in longitudinal and diagonal resistivity tensor components observed at large el…
Recent advances in the physics of current-driven antiferromagnetic skyrmions have observed the absence of a Magnus force. We outline the symmetry reasons for this phenomenon, and show that this cancellation will fail in the case of spin polarized currents. Pairing micromagnetic simulations with semiclassical spin wave transport theory, we demonstrate that skyrmions produce a spin-polarized transverse magnon current, and that spin-polarized magnon currents can in turn produce transverse motion of antiferromagnetic skyrmions. We examine qualitative differences in the frequency dependence of the …
Helical Edge Transport in the ν= 0 Quantum Hall Ferromagnetic State of an Organic Dirac Fermion System
University of Tokyo（东京大学）；Institute for Solid State Physics, University of Tokyo（东京大学固体物理研究所）；National Institute for Materials Science（国立材料科学研究所）；Ewha Womans University（梨花女子大学）
We give a quantitative analysis of the published results of nuclear magnetic resonance (NMR) experiments for k-(ET)2X family of organic charge transfer salts by using the phenomenological spin fluctuation model of Moriya, and Millis, Monien and Pines (M-MMP). For temperatures above T_NMR ~ 50 K, the model gives a good quantitative description of the data for the paramagnetic metallic phase of several k-(ET)2X materials, with an antiferromagnetic correlation length which increases with decreasing temperature; growing to several lattice constants by T_NMR. It is shown that the fact that the dime…
In the organic superconducting κ-(BEDT-TTF) compounds, various transport phenomena exhibit striking non-Fermi liquid behaviors, which should be the important clues to understanding the electronic state of this system. Especially, the Hall coefficient ($R_H$) shows Curie-Weiss type temperature dependence, which is similar to that of high-Tc cuprates. In this paper, we study a Hubbard model on an anisotropic triangular lattice at half filling, which is an effective model of κ-(BEDT-TTF) compounds. Based on the fluctuation-exchange (FLEX) approximation, we calculate the resistivity ($ρ$) and $R_H…
Electrons, commonly moving along the applied electric field, acquire in certain magnets a dissipationless transverse velocity. This spontaneous Hall effect, discovered more than a century ago, has been understood in terms of the time-reversal symmetry breaking by the internal spin-structure of a ferromagnetic, noncolinear antiferromagnetic or skyrmionic form. Here we identify previously overlooked robust Hall effect mechanism arising from collinear antiferromagnetism combined with nonmagnetic atoms at non-centrosymmetric positions. We predict a large magnitude of this crystal Hall effect in a …
We report systematic measurements of anomalous Hall effect(AHE) and spin orbit torques(SOT) in MnGa/IrMn films,, in which a single MnGa epitaxial layer reveals obvious orbital two-channel Kondo (2CK) effect. As increasing the thickness of the antiferromagnet IrMn, the strong spin Hall effect(SHE)has gradually suppressed the orbital 2CK effect and modified the AHE of MnGa.A scaling involving multiple competing scattering mechanisms has been used to distinguish different contributions to the modified AHE. Finally, the sizeable SOT in the MnGa/IrMn films induced by the strong SHE of IrMn have bee…
The external field control of antiferromagnetism is a significant subject both for basic science and technological applications. As a useful macroscopic response to detect magnetic states, the anomalous Hall effect (AHE) is known for ferromagnets, but it has never been observed in antiferromagnets until the recent discovery in Mn3Sn. Here we report another example of the AHE in a related antiferromagnet, namely, in the hexagonal chiral antiferromagnet Mn3Ge. Our single-crystal study reveals that Mn3Ge exhibits a giant anomalous Hall conductivity $|σ_{xz}|$ ~ 60 per ohm per cm at room temperatu…
We report the observation of anomalous Hall resistivity in single crystals of EuAl$_4$, a centrosymmetric tetragonal compound, which exhibits coexisting antiferromagnetic (AFM) and charge-density-wave (CDW) orders with onset at $T_\mathrm{N} \sim 15.6$ K and $T_\mathrm{CDW} \sim 140$ K, respectively. In the AFM state, when the magnetic field is applied along the $c$-axis direction, EuAl$_4$ undergoes a series of metamagnetic transitions. Within this field range, we observe a clear hump-like anomaly in the Hall resistivity, representing part of the anomalous Hall resistivity. By considering dif…
This is a reply to the comment by O. Narikiyo (cond-mat/0012505) on our paper J. Phys. Soc. Jpn. {\bf 68}, (1999) 1614. We point out mistakes about his arguments, and we show that our analysis is compatible with the established Fermi liquid theory, so the obtained result is justified.
We demonstrate theoretically that the thermal Hall effect of magnons in collinear antiferromagnetic insulators is an indicator of magnetic and topological phase transitions in the magnon spectrum. The transversal heat current of magnons caused by a thermal gradient is calculated for an antiferromagnet on a honeycomb lattice. An applied magnetic field drives the system from the antiferromagnetic phase via a spin-flop phase into the field-polarized phase. Besides these magnetic phase transitions we find topological phase transitions within the spin-flop phase. Both types of transitions manifest …
Ab initio prediction of anomalous Hall effect in antiferromagnetic CaCrO$_3$
Institute of Scientific and Industrial Research, Osaka University（大阪大学科学工业研究所）；Department of Precision Engineering, Graduate School of Engineering, Osaka University（大阪大学大学院工学研究科精密工程专攻）
We have investigated magnetotransport properties and the topological electronic structure of the half-Heusler compound TbPtBi. Our experiments reveal an exceptionally large anomalous Hall effect (AHE) in the canted antiferromagnetic state of TbPtBi with the anomalous Hall angle (AHA) reaching ~0.68-0.76, which is a few times larger than the previously reported record in GdPtBi. First-principles electronic structure and the associated anomalous Hall conductivity were computed in order to interpret the experimental results. Our analysis shows that the AHE in TbPtBi does not originate from the We…
The kagome lattice antiferromagnets Mn$_3$X(= Sn, Ge) have a noncollinear 120$^\circ$ ordered ground state, which engenders a strong anomalous Hall response. It has been shown that this response is linked to the magnetic order and can be manipulated through it. Here we use a combination of strain and spin-transfer torques to control the magnetic order and hence switch deterministically between states of different chirality. Each of these chiral ground states has an anomalous Hall conductivity tensor in a different direction. Furthermore, we show that a similar manipulation of the strained samp…
