Polyoxometalates: Fascinating structures, unique magnetic properties

The electrical Hall effect is the production, upon the application of an electric field, of a transverse voltage under an out-of-plane magnetic field. Studies of the Hall effect have led to important breakthroughs, including the discoveries of Berry curvature and topological Chern invariants1,2. The internal magnetization of magnets means that the electrical Hall effect can occur in the absence of an external magnetic field2; this 'anomalous' Hall effect is important for the study of quantum magnets2-7. The electrical Hall effect has rarely been studied in non-magnetic materials without external magnetic fields, owing to the constraint of time-reversal symmetry. However, only in the linear response regime-when the Hall voltage is linearly proportional to the external electric field-does the Hall effect identically vanish as a result of time-reversal symmetry; the Hall effect in the nonlinear response regime is not subject to such symmetry constraints8-10. Here we report observations of the nonlinear Hall effect10 in electrical transport in bilayers of the non-magnetic quantum material WTe2 under time-reversal-symmetric conditions. We show that an electric current in bilayer WTe2 leads to a nonlinear Hall voltage in the absence of a magnetic field. The properties of this nonlinear Hall effect are distinct from those of the anomalous Hall effect in metals: the nonlinear Hall effect results in a quadratic, rather than linear, current-voltage characteristic and, in contrast to the anomalous Hall effect, the nonlinear Hall effect results in a much larger transverse than longitudinal voltage response, leading to a nonlinear Hall angle (the angle between the total voltage response and the applied electric field) of nearly 90 degrees. We further show that the nonlinear Hall effect provides a direct measure of the dipole moment10 of the Berry curvature, which arises from layer-polarized Dirac fermions in bilayer WTe2. Our results demonstrate a new type of Hall effect and provide a way of detecting Berry curvature in non-magnetic quantum materials.

Observation of the nonlinear Hall effect under time-reversal-symmetric conditions

In this contribution to the special issue on multiferroics we focus on multiferroicity driven by different forms of charge ordering. We will present the generic mechanisms by which charge ordering can induce ferroelectricity in magnetic systems. There is a number of specific classes of materials for which this is relevant. We will discuss in some detail (i) perovskite manganites of the type (PrCa)MnO3, (ii) the complex and interesting situation in magnetite Fe3O4, (iii) strongly ferroelectric frustrated LuFe2O4 and (iv) an example of a quasi-one-dimensional organic system. All these are 'type-I' multiferroics, in which ferroelectricity and magnetism have different origins and occur at different temperatures. In the second part of this article we discuss 'type-II' multiferroics, in which ferroelectricity is completely due to magnetism, but with charge ordering playing an important role, such as (v) the newly discovered multiferroic Ca3CoMnO6, (vi) possible ferroelectricity in rare earth perovskite nickelates of the type RNiO3, (vii) multiferroic properties of manganites of the type RMn2O5, (viii) perovskite manganites with magnetic E-type ordering and (ix) bilayer manganites.

/pdf/multiferroicity-due-to-charge-ordering-49atre8gbj.pdf

Multiferroicity due to charge ordering

In this contribution to the special issue on multiferroics we focus on multiferroicity driven by different forms of charge ordering. We will present the generic mechanisms by which charge ordering can induce ferroelectricity in magnetic systems. There is a number of specific classes of materials for which this is relevant. We will discuss in some detail (i) perovskite manganites of the type (PrCa)MnO3, (ii) the complex and interesting situation in magnetite Fe3O4, (iii) strongly ferroelectric frustrated LuFe2O4 and (iv) an example of a quasi-one-dimensional organic system. All these are ‘type-I’ multiferroics, in which ferroelectricity and magnetism have different origins and occur at different temperatures. In the second part of this article we discuss ‘type-II’ multiferroics, in which ferroelectricity is completely due to magnetism, but with charge ordering playing an important role, such as (v) the newly discovered multiferroic Ca3CoMnO6, (vi) possible ferroelectricity in rare earth perovskite nickelates of the type RNiO3, (vii) multiferroic properties of manganites of the type RMn2O5, (viii) perovskite manganites with magnetic E-type ordering and (ix) bilayer manganites. (Some figures in this article are in colour only in the electronic version)

http://absimage.aps.org/image/MAR12/MWS_MAR12-2011-020116.pdf

Multiferroicity due to Charge Ordering

The electrical Hall effect is the production of a transverse voltage under an out-of-plane magnetic field. Historically, studies of the Hall effect have led to major breakthroughs including the discoveries of Berry curvature and the topological Chern invariants. In magnets, the internal magnetization allows Hall conductivity in the absence of external magnetic field. This anomalous Hall effect (AHE) has become an important tool to study quantum magnets. In nonmagnetic materials without external magnetic fields, the electrical Hall effect is rarely explored because of the constraint by time-reversal symmetry. However, strictly speaking, only the Hall effect in the linear response regime, i.e., the Hall voltage linearly proportional to the external electric field, identically vanishes due to time-reversal symmetry. The Hall effect in the nonlinear response regime, on the other hand, may not be subject to such symmetry constraints. Here, we report the observation of the nonlinear Hall effect (NLHE) in the electrical transport of the nonmagnetic 2D quantum material, bilayer WTe2. Specifically, flowing an electrical current in bilayer WTe2 leads to a nonlinear Hall voltage in the absence of magnetic field. The NLHE exhibits unusual properties sharply distinct from the AHE in metals: The NLHE shows a quadratic I-V characteristic; It strongly dominates the nonlinear longitudinal response, leading to a Hall angle of about 90 degree. We further show that the NLHE directly measures the "dipole moment" of the Berry curvature, which arises from layer-polarized Dirac fermions in bilayer WTe2. Our results demonstrate a new Hall effect and provide a powerful methodology to detect Berry curvature in a wide range of nonmagnetic quantum materials in an energy-resolved way.

Observation of the nonlinear Hall effect under time reversal symmetric conditions.

Transitions between topologically distinct electronic states have been predicted in different classes of materials and observed in some. A major goal is the identification of measurable properties that directly expose the topological nature of such transitions. Here, we focus on the giant Rashba material bismuth tellurium iodine which exhibits a pressure-driven phase transition between topological and trivial insulators in three dimensions. We demonstrate that this transition, which proceeds through an intermediate Weyl semimetallic state, is accompanied by a giant enhancement of the Berry curvature dipole which can be probed in transport and optoelectronic experiments. From first-principles calculations, we show that the Berry dipole---a vector along the polar axis of this material---has opposite orientations in the trivial and topological insulating phases and peaks at the insulator-to-Weyl critical points, at which the nonlinear Hall conductivity can increase by over 2 orders of magnitude.

/pdf/strongly-enhanced-berry-dipole-at-topological-phase-4ci6ed99vk.pdf

Strongly Enhanced Berry Dipole at Topological Phase Transitions in BiTeI

Strongly enhanced Berry-dipole at topological phase transitions in BiTeI

We study single-ion and exchange anisotropy effects in equal-spin ${s}_{1}$ tetramer single-molecule magnets exhibiting ${T}_{d}$, ${D}_{4h}$, ${D}_{2d}$, ${C}_{4h}$, ${C}_{4v}$, or ${S}_{4}$ ionic site point group symmetry. We first write the group-invariant quadratic single-ion and symmetric anisotropic exchange Hamiltonians in the appropriate local coordinates. We then rewrite these local Hamiltonians in the molecular or laboratory representation, along with the group-invariant Dzyaloshinskii-Moriya (DM) and isotropic Heisenberg, biquadratic, and three-center quartic Hamiltonians. Using our exact, compact forms for the single-ion spin matrix elements, we analytically evaluate the eigenstate energies to first order in the microscopic anisotropy interactions, corresponding to the strong exchange limit, and provide tables of simple formulas for the anisotropy energies of the lowest four eigenstate manifolds of ferromagnetic (FM) and antiferromagnetic (AFM) tetramers with arbitrary ${s}_{1}$. For AFM tetramers, we illustrate the first-order level-crossing inductions for ${s}_{1}=1∕2$, 1, and $3∕2$, and obtain preliminary estimates of the microscopic parameters in a ${\mathrm{Ni}}_{4}$ from fits to magnetization data, indicating the presence of strong symmetric anisotropic exchange interactions. Accurate analytic expressions for the thermodynamics, electron paramagnetic resonance absorption, and inelastic neutron scattering cross section are given, allowing for a determination of three of the microscopic anisotropy interactions from the second excited state manifold of FM tetramers. We also predict that tetramers with symmetries ${S}_{4}$ and ${D}_{2d}$ should exhibit both DM interactions and multiferroic states, and we illustrate our predictions for ${s}_{1}=1∕2$ and 1.

Single-ion and exchange anisotropy effects and multiferroic behavior in high-symmetry tetramer single molecule magnets

We consider the orbital ordering in ${\mathrm{LaMnO}}_{3}$ and similar systems, proceeding from the band picture. We show that for a realistic magnetic structure of $A$ type there exists a complete nesting between two ${e}_{g}$ bands. As a result there occurs an instability toward an excitonic insulatorlike state---an electron-hole pairing with the wave vector $Q=(\ensuremath{\pi},\ensuremath{\pi})$, which opens a gap in the spectrum and makes the system insulating. In the resulting state there appears an orbital ordering, the orbital density wave, the type of which coincides with those existing in ${\mathrm{LaMnO}}_{3}$.

https://arxiv.org/pdf/cond-mat/0407656.pdf

Orbital ordering in manganites in the band approach

We present a model of equal spin $s_1$ dimer single molecule magnets. The spins within each dimer interact via the Heisenberg and the most general set of four quadratic anisotropic spin interactions with respective strengths $J$ and $\{J_j\}$, and with the magnetic induction ${\bf B}$. We solve the model exactly for $s_1=1/2, 1, 5/2$, and for antiferromagnetic Heisenberg couplings ($J<0$), present ${\bf M}({\bf B})$ curves at low $T$ for these cases. Low-$T$ $C_V({\bf B})$ curves for $s_1=1/2$ and electron paramagnetic susceptibility $\chi({\bf B},\omega)$ for $s_1=1$ are also provided. For weak anisotropy interactions, we employ a perturbative treatment, and show that the Hartree and extended Hartree approximations lead to reliable analytic results at low $T$ and large $B$ for these quantities and for the inelastic neutron scattering cross-section $S({\bf B}, {\bf q},\omega)$. Our results are discussed with regard to existing ${\bf M}({\bf B})$ experiments on $s_1=5/2$ Fe$_2$ dimer single molecule magnets, and suggest that one of them contains a substantial amount of single-ion anisotropy, without any sizeable global spin anisotropy. We urge further experiments of the above types on single crystals of Fe$_2$ and on some $s_=9/2$ [Mn$_4$]$_2$ dimers, in order to elucidate the precise values of the various microscopic interactions.

Dmitri V. Efremov

Papers

Strongly Enhanced Berry Dipole at Topological Phase Transitions in BiTeI

Strongly enhanced Berry-dipole at topological phase transitions in BiTeI

Single-ion and exchange anisotropy effects and multiferroic behavior in high-symmetry tetramer single molecule magnets

Orbital ordering in manganites in the band approach

Spin anisotropy effects in dimer single molecule magnets