Vector Chirality Research Articles

CrRhAs: a member of a large family of metallic kagome antiferromagnets

Kagome lattice materials are an important platform for highly frustrated magnetism as well as for a plethora of phenomena resulting from flat bands, Dirac cones and van Hove singularities in their electronic structures. We study the little known metallic magnet CrRhAs, which belongs to a vast family of materials that includes 3d, 4f, and 5f magnetic elements, as well as numerous nonmagnetic metals and insulators. Using noncollinear spin density functional calculations (mostly spin spirals), we extract a model magnetic Hamiltonian for CrRhAs. While it is dominated by an antiferromagnetic second nearest neighbor coupling in the kagome plane, the metallic nature of the compound leads to numerous nonzero longer range couplings and to important ring exchange terms. We analyze this Hamiltonian and find unusual ground states which are dominated by nearly isolated antiferromagnetic triangles that adopt 120∘ order either with positive or with negative vector chirality. We discuss the connection to the few known experimental facts about CrRhAs. Finally, we give a brief survey of other interesting magnetic members of this family of kagome compounds.

Orbital antiferroelectricity and higher dimensional magnetoelectric order in the spin-1/2 XX chain extended with three-spin interactions

We study the spin-1/2 XX model extended with three-spin interactions of the XZX+YZY and XZY-YZX types. We solve the model exactly and obtain the ground state phase diagram as a function of the two three-spin coupling strengths. We show that even in absence of external electric and magnetic fields there is a phase which exhibits spontaneous magnetoelectric order when both XZX+YZY and XZY-YZX interactions are present. Specifically, in this regime, we show that there exists not only a non-zero magnetization and a scalar chirality but also a vector chiral order. Further, we show the existence of a plaquette vector chirality, or circulating chiral spin current loops, in the plaquettes n, n+1, n+2 with the sense of the current being opposite in adjacent plaquettes. Analogous to charge current loops giving rise to orbital magnetic dipole moments, the circulating spin current loops give rise to orbital electric dipole moments - a novel orbital antiferroelectricity. We characterize this phase by a higher-dimensional scalar and vector toroidal order. Such a novel phase with higher dimensional order arises because of the non-trivial topological connectivity resulting from the presence of both the three-spin interactions. We also study the combined effect of both types of three-spin interactions on the entanglement entropy.

Vortical effects in Dirac fluids with vector, chiral and helical charges

Helicity of free massless Dirac fermions is a conserved, Lorentz-invariant quantity at the level of the classical equations of motion. For a generic ensemble consisting of particles and antiparticles, the helical and chiral charges are different conserved quantities. The flow of helicity can be modelled by the helicity current, which is again conserved in the absence of interactions. Similar to the axial vortical effect which generates an axial (chiral) current, the helicity current is induced by vorticity in a finite temperature medium with vector (electrical) charge imbalance via the helical vortical effects, leading to new nondissipative transport phenomena. These phenomena lead to the appearance of a new hydrodynamic excitation, the helical vortical wave. Our results suggest the existence of a new type of triangle anomalies in QED which involve the helicity currents in addition to the standard vector and axial currents. Further exploiting the conservation of the helical current, we show that a finite helical chemical potential may be used to characterise thermodynamic ensembles of fermions similarly to, but independently of, the vector charge and chirality. We derive the pressure P for fermions at finite vector, axial and helical chemical potentials and show that the quantities arising in anomalous transport, including various vortical and circular conductivities and the shear-stress coefficients, can be obtained by differentiation of P with respect to the appropriate chemical potentials. Finally, we calculate the helicity relaxation time in the quark-gluon plasma above the crossover and show that it is similar to that for the axial charge.

Negative-chirality order in the S=12 kagome antiferromagnet CdCu3(OH)6(NO3)2·H2O

The neutron diffraction and nuclear magnetic resonance (NMR) measurements have been used to microscopically analyze the magnetic structure in the $S = 1/2$ kagome antiferromagnet CdCu$_{3}$(OH)$_{6}$(NO$_{3}$)$_{2}\cdot $H$_{2}$O. Below the magnetic ordering temperature $T_N\simeq 4$ K, magnetic Bragg reflections at (110) and (100) were found in the neutron diffraction pattern, which suggests a $q=0$ magnetic structure. Furthermore, the vector spin chirality for the $q=0$ structure was successfully identified from the internal field direction obtained by the $^{14}$N-NMR measurement. Our findings point to a chirality-ordered magnetic structure with negative vector chirality and $\langle 100 \rangle$ anisotropy.

Spin current Kondo effect in frustrated Kondo systems

Magnetic frustrations can enhance quantum zero-point motion in spin systems and lead to exotic topological insulating states. When coupled to mobile electrons, they may lead to unusual non-Fermi liquid or metallic spin liquid states whose nature has not been well explored. Here, we propose a spin current Kondo mechanism underlying a series of non-Fermi liquid phases on the border of Kondo and magnetic phases in a frustrated three-impurity Kondo model. This mechanism is confirmed by renormalization group analysis and describes movable Kondo singlets called "holons" induced by an effective coupling between the spin current of conduction electrons and the vector chirality of localized spins. Similar mechanism may widely exist in all frustrated Kondo systems and be detected through spin-current noise measurements.

Control of a polar order via magnetic field in a vector-chiral magnet

Vector-chiral (VC) antiferromagnetism is a spiral-like ordering of spins which may allow ferroelectricity to occur due to loss of space inversion symmetry. In this paper we report direct experimental observation of ferroelectricity in the VC phase of $\beta$-TeVO$_4$, a frustrated spin chain system with pronounced magnetic anisotropy and a rich phase diagram. Saturation polarization is proportional to neutron scattering intensities that correspond to the VC magnetic reflection. This implies that inverse Dzyaloshinskii-Moriya mechanism is responsible for driving electric polarization. Linear magnetoelectric coupling is absent, however an unprecedented dependence of electric coercive field on applied magnetic field reveals a novel way of manipulating multiferroic information.

Multiferroic and phonon properties at the phase transition of S = 1/2 chain cuprates NaCu2O2. Comparison with LiCu2O2

ABSTRACT The multiferroic properties of NaCuO (NCO) around the phase transition temperature are studied theoretically. The total polarization P is zero without magnetic field h due to the antiferroelectric state induced by the alternate stacking of CuO layer with opposite spin vector chirality. Applying h P increases, goes through a maximum and vanishes at . The magnetic field dependence of is an evidence that NCO is multiferroic. For h = 0 there is no anomaly in the dielectric constant at which is an evidence for the antiferroelectric behavior of the compound. It is observed that and in NCO is quite different compared to that of LiCuO. Around the Neel temperature we observe in NCO an anomaly in the specific heat and the phonon energy due to strong anharmonic spin-phonon interaction. This kink disappears by applying an external magnetic field h.

The chiral Hall effect in canted ferromagnets and antiferromagnets

The anomalous Hall effect has been indispensable in our understanding of numerous magnetic phenomena. This concerns both ferromagnetic materials, as well as diverse classes of antiferromagnets, where in addition to the anomalous and recently discovered crystal Hall effect, the topological Hall effect in noncoplanar antiferromagnets has been a subject of intensive research in the past decades. Here, we uncover a distinct flavor of the Hall effect emerging in generic canted spin systems. We demonstrate that upon canting, the anomalous Hall effect acquires a contribution which is sensitive to the sense of imprinted vector chirality among spins. We explore the origins and basic properties of corresponding chiral Hall effect, and closely tie it to the symmetry properties of the system. Our findings suggest that the chiral Hall effect and corresponding chiral magneto-optical effects emerge as useful tools in characterizing an interplay of structure and chirality in complex magnets, as well as in tracking their chiral dynamics and fluctuations.

Helical spin liquid in a triangular XXZ magnet from Chern-Simons theory

We propose a finite-temperature phase diagram for the 2D spin-$1/2$ $J_1-J_2$ $XXZ$ antiferromagnet on the triangular lattice. Our analysis, based on a composite fermion representation, yields several phases. This includes a zero-temperature helical spin liquid with $N=6$ {\it anisotropic} Dirac cones, and with nonzero vector chirality implying a broken $\mathbb{Z}_2$ symmetry. It is terminated at $T=0$ by a continuous quantum phase transition to $120^\circ$ ordered state around $J_2/J_1\approx0.089$ in the XX limit; these phases share a double degeneracy, which persists to finite $T$ above the helical spin liquid. By contrast, at $J_2/J_1 \simeq 0.116$, the transition into a stripe phase appears as first order. We further discuss experimental and numerical consequences of the helical order and the anisotropic nature of the Dirac dispersion.

Magnetic-field-induced reorientation in the spin-density-wave and the spin-stripe phases of the frustrated spin- 12 chain compound β−TeVO4

$\beta$-TeVO$_4$ is a frustrated spin 1/2 zig-zag chain system,where spin-density-wave (SDW), vector chiral (VC)and an exotic dynamic spin-stripe phase compete at low temperatures. Here we use torque magnetometry to study the anisotropy of these phases in magnetic fields of up to 5 T. Our results show that the magnetic-field-induced spin reorientation occurs in the SDW and in the spin stripe phases for $\mu_0 H \geq 2$~T. The observed spin reorientation is a new element of the anisotropic phase diagram for the field directions in the $ac$ and $a^*b$ crystallographic planes. The presented results should help establishing the model of anisotropic magnetic interactions, which are responsible for the formation of complex magnetic phases in $\beta$-TeVO$_4$ and similar quantum systems.

Anomalous electrical magnetochiral effect by chiral spin-cluster scattering

The non-collinear spin configurations give rise to many nontrivial phenomena related to the Berry phase. They are often related to the vector and scalar spin chiralities. The scalar spin chirality leads to the topological Hall effect in metals, while the vector spin chirality to the ferroelectricity of spin origin, i.e., multiferroics in insulators. However, the role of the vector spin chirality in conducting systems has not yet been elucidated. Here we show theoretically that the spin correlation with vector spin chirality in chiral magnets scatters electrons asymmetrically, resulting in nonreciprocal transport phenomena, i.e., electrical magnetochiral effect (eMCE). This asymmetric scattering appears in the leading-order scattering term, implying a large nonreciprocity in the charge and spin currents. We find that the temperature and magnetic field dependence of the eMCE reproduces that observed in MnSi. Our results reveal the microscopic mechanism of eMCE and its potential in producing a large nonreciprocal response.

Multiparticle Interactions for Ultracold Atoms in Optical Tweezers: Cyclic Ring-Exchange Terms.

Dominant multiparticle interactions can give rise to exotic physical phases with anyonic excitations and phase transitions without local order parameters. In spin systems with a global SU(N) symmetry, cyclic ring-exchange couplings constitute the first higher-order interaction in this class. In this Letter, we propose a protocol showing how SU(N)-invariant multibody interactions can be implemented in optical tweezer arrays. We utilize the flexibility to rearrange the tweezer configuration on short timescales compared to the typical lifetimes, in combination with strong nonlocal Rydberg interactions. As a specific example, we demonstrate how a chiral cyclic ring-exchange Hamiltonian can be implemented in a two-leg ladder geometry. We study its phase diagram using density-matrix renormalization group simulations and identify phases with dominant vector chirality, a ferromagnet, and an emergent spin-1 Haldane phase. We also discuss how the proposed protocol can be utilized to implement the strongly frustrated J-Q model, acandidate for hosting a deconfined quantum critical point.

Multiple phase transitions and high-field quadrupolar order in a model for β−TeVO4

Motivated by the complex behavior of the frustrated magnet $\beta$-TeVO$_4$, we study an anisotropic Heisenberg model for coupled spin-$1/2$ zigzag chains. Using cluster mean field approach to capture quantum correlations we find, upon reducing temperature in the absence of applied field, (i) a partially ordered state, (ii) a collinear antiferromagnetic phase, and (iii) an elliptical spiral state characterized by finite vector chirality. For finite fields, we find metamagnetic response close to saturation magnetization. We show via explicit calculations that the quadrupolar order parameter is finite in the metamagnetic regime. The exchange parameters reported in the ab-initio study of $\beta$-TeVO$_4$ are used in our study. We compare our results with those reported in recent experiments on $\beta$-TeVO$_4$ and highlight similarities as well as differences between experimental results and our cluster mean field calculations.

Destruction of long-range order in noncollinear two-dimensional antiferromagnets by random-bond disorder

We consider frustrated Heisenberg antiferromagnets, whose clean-limit ground state is characterized by non-collinear long-range order with non-zero vector chirality, and study the effects of quenched bond disorder, i.e., random exchange couplings. A single bond defect is known to induce a dipolar texture in the spin background independent of microscopic details. Using general analytical arguments as well as large-scale simulations for the classical triangular-lattice Heisenberg model, we show that any finite concentration of such defects destroys long-range order for spatial dimension $d\leq 2$, in favor of a glassy state whose correlation length in $d=2$ is exponentially large for small randomness. Our results are relevant for a wide range of layered frustrated magnets.

Multiferroic properties of melanothallite Cu2OCl2

Here we report on $P\text{\ensuremath{-}}E$ hysteresis loop measurements that unravel the ferroelectric nature of melanothallite ${\mathrm{Cu}}_{2}{\mathrm{OCl}}_{2}$, a new multiferroic material with high critical temperature. Its spin structure was investigated by polarized and unpolarized neutron scattering experiments which reveal a cycloidal magnetic structure with vector chirality (magnetic polarity) that can be inverted by opposite poling of the sample with an inverted electric field. This shows that ${\mathrm{Cu}}_{2}{\mathrm{OCl}}_{2}$ is a spin-induced ferroelectric material. Finally, we show that the ferroelectric properties of ${\mathrm{Cu}}_{2}{\mathrm{OCl}}_{2}$ are driven by the inverse Dzyaloshinskii-Moriya interaction mechanism which is also able to predict the observed direction of the ferroelectric polarization properly. The origin of the noncollinear spin structure in melanothallite are competing AFM-FM exchange couplings which we estimate from a combined ab initio $+$ cluster configuration interaction calculation.

Magnetic ground state of the frustrated spin- 12 chain compound β–TeVO4 at high magnetic fields

Frustrated spin-1/2 chains, despite the apparent simplicity, exhibit remarkably rich phase diagram comprising vector-chiral (VC), spin-density-wave (SDW) and multipolar/spin-nematic phases as a function of the magnetic field. Here we report a study of $\beta$-TeVO$_4$, an archetype of such compounds, based on magnetization and neutron diffraction measurements up to 25 T. We find the transition from the helical VC ground state to the SDW state at $\sim$3 T for the magnetic field along the $a$ and $c$ crystal axes, and at $\sim$9 T for the field along the $b$ axis. The high-field (HF) state, existing above $\sim$18 T, i.e., above $\sim$1/2 of the saturated magnetization, is an incommensurate magnetically ordered state and not the spin-nematic state, as theoretically predicted for the isotropic frustrated spin-1/2 chain. The HF state is likely driven by sizable interchain interactions and symmetric intrachain anisotropies uncovered in previous studies. Consequently, the potential existence of the spin nematic phase in $\beta$-TeVO$_4$ is limited to a narrow field range, i.e., a few tenths of a tesla bellow the saturation of the magnetization, as also found in other frustrated spin-1/2 chain compounds.

Photo-induced Floquet Weyl magnons in noncollinear antiferromagnets

We study periodically driven insulating noncollinear stacked kagome antiferromagnets with a conventional symmetry-protected three-dimensional (3D) in-plane 120° spin structure, with either positive or negative vector chirality. We show that the symmetry protection of the in-plane 120° spin structure can be broken in the presence of an off-resonant circularly or linearly polarized electric field propagating parallel to the in-plane 120° spin structure (say along the x direction). Consequently, topological Floquet Weyl magnon nodes with opposite chirality are photoinduced along the kx momentum direction. They manifest as the monopoles of the photoinduced Berry curvature. We also show that the system exhibits a photoinduced magnon thermal Hall effect for circularly polarized electric field. Furthermore, we show that the photoinduced chiral spin structure is a canted 3D in-plane 120° spin structure, which was recently observed in the equilibrium noncollinear antiferromagnetic Weyl semimetals Mn3Sn/Ge. Our result not only paves the way towards the experimental realization of Weyl magnons and photoinduced thermal Hall effects, but also provides a powerful mechanism for manipulating the intrinsic properties of 3D topological antiferromagnets.

The in-plane spin helicity of coplanar helical spin configurations of frustrated single trimer V3 and Cu3 nanomagnets, inversion (switching) of spin helicity

The in-plane spin helicities of coplanar non-collinear spin configurations of frustrated spin states of the single trimer V3 and Cu3 molecular nanomagnets with the Dzialoshinsky-Moriya (DM) coupling in transverse magnetic fields are considered. Spin operators of the in-plane helicity were proposed. These operators provide the quantum numbers of the in-plane spin helicity, which characterize helicities of all classical coplanar 120° helical spin configurations and distinguish helical configurations of the same vector chirality. The in-plane spin helicity depends on direction and strength of transverse magnetic field. The increase of the field strength leads to the non-linear reduction of magnitude of the spin helicity of spin configurations correlated with their energy, magnetizations and vector chirality. The in-plane spin helicity is inverse proportional to the energy; the decrease of helicity correlates with an increase of magnetization. Spin helicity of distorted DM trimers was considered, distortions result in reduction of magnitude of the spin helicity of deformed coplanar helical spin configurations. The in-plane spin helicity of coplanar helical spin configurations in the ground state demonstrates the field- and deformation- induced inversion (switching) that can be used in applications of the spin helicity in molecular devices.

Chiral liquid phase of simple quantum magnets

We study a $T=0$ quantum phase transition between a quantum paramagnetic state and a magnetically ordered state for a spin $S=1$ XXZ Heisenberg antiferromagnet on a two-dimensional triangular lattice. The transition is induced by an easy plane single-ion anisotropy $D$. At the mean-field level, the system undergoes a direct transition at a critical $D = D_c$ between a paramagnetic state at $D > D_c$ and an ordered state with broken U(1) symmetry at $D < D_c$. We show that beyond mean field the phase diagram is very different and includes an intermediate, partially ordered chiral liquid phase. Specifically, we find that inside the paramagnetic phase the Ising ($J_z$) component of the Heisenberg exchange binds magnons into a two-particle bound state with zero total momentum and spin. This bound state condenses at $D > D_c$, before single-particle excitations become unstable, and gives rise to a chiral liquid phase, which spontaneously breaks spatial inversion symmetry, but leaves the spin-rotational U(1) and time-reversal symmetries intact. This chiral liquid phase is characterized by a finite vector chirality without long range dipolar magnetic order. In our analytical treatment, the chiral phase appears for arbitrarily small $J_z$ because the magnon-magnon attraction becomes singular near the single-magnon condensation transition. This phase exists in a finite range of $D$ and transforms into the magnetically ordered state at some $D<D_c$. We corroborate our analytic treatment with numerical density matrix renormalization group calculations.

Spin-reorientation transitions in the Cairo pentagonal magnet Bi4Fe5O13F

We show that interlayer spins play a dual role in the Cairo pentagonal magnet Bi$_4$Fe$_5$O$_{13}$F, on one hand mediating the three-dimensional (3D) magnetic order and on the other driving spin-reorientation transitions both within and between the planes. The corresponding sequence of magnetic orders unraveled by neutron diffraction and M\"ossbauer spectroscopy features two orthogonal magnetic structures described by opposite local vector chiralities, and an intermediate, partly disordered phase with nearly collinear spins. A similar collinear phase has been predicted theoretically to be stabilized by quantum fluctuations, but Bi$_4$Fe$_5$O$_{13}$F is very far from the relevant parameter regime. While the observed in-plane reorientation cannot be explained by any standard frustration mechanism, our ab initio band-structure calculations reveal strong single-ion anisotropy of the interlayer Fe$^{3+}$ spins that turns out to be instrumental in controlling the local vector chirality and the associated interlayer order.