Off-diagonal Response Research Articles

Non-Hermitian off-diagonal magnetic response of Dirac fermions

We perform a comparative study for the magnetization dynamics within linear response theory of one and two dimensional massive Dirac electrons, after switching on either a real (hermitian) or an imaginary (non-hermitian) magnetic field. While hermitian dc magnetic fields polarize the spins in the direction of the external magnetic field, non-hermitian magnetic fields induce only off diagonal response. An imaginary dc magnetic field perpendicular to the mass term induces finite magnetization in the third direction only according to the right hand rule. This can be understood by analyzing the non-hermitian equation of motion of the spin, which becomes analogous to a classical particle in crossed electric and magnetic fields. Therein, the spin expectation value, the mass term and imaginary magnetic field play the role of the classical momentum, magnetic and electric field, respectively. The latter two create a drift velocity perpendicular to them, which gives rise to the off-diagonal component of the dc spin susceptibility, similarly to how the Hall effect develops in the classical description.

Temperature effect on GMI sensor: Comparison between diagonal and off-diagonal response

In this paper, the effect of temperature on Giant Magneto-Impedance (GMI) sensors is studied in amorphous wire Co-Fe-Si-B from Unitika. Both diagonal, Z11, and the off-diagonal, Z21, components of the impedance tensor are considered, with a primary focus on the changes of intrinsic sensitivity and offset, which are the most crucial relevant quantities for practical sensor implementation. Experiments are conducted in the almost industrial temperature range of [−20 °C, 120 °C]. For the component Z11, the results show a maximum change of the offset of −0.13 (A/m)/°C (170 nT/°C), at a 33 A/m bias field. The sensitivity at this field increases for temperatures between −20 °C and + 40 °C, and then it decreases (a maximum change of −0.5%/°C). For the off-diagonal component, Z21, the change of the offset near the zero-field is smaller (−0.015 (A/m)/°C or −19 nT/°C), whereas the sensitivity increases with temperature by about +0.4%/°C.

Analysis of the off-diagonal component of giant magnetoimpedance effect in Co-based (as-cast and stress-annealed) amorphous ribbons

We investigated the effect of the application of dc bias current IB on the off-diagonal magnetoimpedance (MI) components at 50 MHz in nearly-zero magnetostrictive Co66.5Fe3.5Si12.0B18.0 amorphous ribbons in as-cast and stress-annealed state. The off-diagonal MI component is anti-symmetrical with near-linear behavior within a certain field interval. For the off-diagonal response, the dc bias current is necessary to eliminate transverse domains present in the ribbon. A highly asymmetry of the off-diagonal dependence with the axial magnetic field was obtained when the bias current is applied along the ribbon. A rather high slope at the zero-field point was obtained, being more pronounced in the stress-annealed samples. This is probably related with the domain structure reorganization under the effect of the bias current. This behavior is ideal for a practical sensor circuit design.

Theory for oblique-incidence magneto-optical Faraday and Kerr effects in interfaced monolayer graphene and their characteristic features

The rigorous magneto-optical response coefficients of the oblique-incidence Faraday and Kerr effects in anisotropic monolayer graphene interfaced with bulk media in general are presented for the first time, to the author’s knowledge. The dependencies of magneto-optical rotation angle and ellipticity on the incident angle, incident polarization, and refractive indices of interfaced media are numerically analyzed and characteristic features are discussed in detail. It is shown that the Kerr effect has the substantially same off-diagonal response coefficient as the Faraday effect, in contrast with the case of conventional media. It is found that supergiant Kerr rotation angles of ∼±90° are produced in the graphene with a transparent substrate when illuminated with p-polarized light in the vicinity of the substrate’s Brewster angle.

New quiolinium polymorph with optimal packing for maximal off-diagonal nonlinear optical response

The influence of polymorphism on the nonlinear optical properties of HMQ-MBS (2-(4-hydroxy-3-methoxystyryl)-1-methylquinolinium 4-methoxybenzenesulfonate) crystals is investigated. By changing the solvent for crystal growth, a new polymorph has been found. While the previously reported α-phase of HMQ-MBS, having monoclinic Pc space group symmetry exhibits an optimal molecular packing for maximizing the diagonal component of the second-order nonlinear optical response, the β-phase of HMQ-MBS has monoclinic Pn space group symmetry and exhibits an optimal molecular packing for maximizing the off-diagonal response. HMQ-MBS is therefore a very interesting compound for a wide range of second-order nonlinear optical applications. HMQ-MBS exhibits two interesting acentric polymorphs for second-order nonlinear optical applications. In one phase the chromophores pack in an optimal way to maximize the off-diagonal nonlinear susceptibility response, while in the other phase optimally to maximize the diagonal response.

Dynamic Polarizability of Rotating Particles in Electrorheological Fluids

A rotating particle in electrorheological (ER) fluid leads to a displacement of its polarization charges on the surface which relax toward the external applied field E0, resulting in a steady-state polarization at an angle with respect to E0. This dynamic effect has shown to affect the ER fluid properties dramatically. In this paper, we develop a dynamic effective medium theory (EMT) for a system containing rotating particles of finite volume fraction. This is a generalization of established EMT to account for the interactions between many rotating particles. While the theory is valid for three dimensions, the results in a special two-dimensional configuration show that the system exhibits an off-diagonal polarization response in addition to a diagonal polarization response, which resembles the classic Hall effect. The diagonal response monotonically decreases with increasing rotational speed, whereas the off-diagonal response exhibits a maximum at a reduced rotational angular velocity omega0, compared to the case of isolated rotating particles. This implies a way of measurement on the interacting relaxation time. The dependencies of the diagonal and off-diagonal responses on various factors, such as omega0, the volume fraction, and the dielectric contrast, are discussed.

Quantum Projection in an Ising Spin Liquid

A transverse magnetic field is used to scan the diagonal and off-diagonal susceptibility of the uniaxial quantum magnet, LiHo(0.045) Y(0.955)F(4). Clusters of strongly coupled spins act as the primary source for the response functions, which result from a field-induced quantum projection of the system into a classically forbidden (meaning non-Ising) regime. Calculations based on spin pairs reproduce only some features of the data and fail to predict the measured off-diagonal response, providing evidence of a multispin collective state.

Off-Diagonal Impedance in Amorphous Wires and Its Application to Linear Magnetic Sensors

We investigated the magnetic-field behavior of the off-diagonal impedance in Co-based amorphous wires under sinusoidal (50 MHz) and pulsed (5 ns rise time) current excitations. For comparison, we measured the field characteristics of the diagonal impedance as well. In general, when an alternating current is applied to a magnetic wire, the voltage signal is generated not only across the wire but also in a pickup coil wound on it. These voltages are related to the diagonal and off-diagonal impedances, respectively. We demonstrate that these impedances have a different behavior as functions of axial magnetic field: the diagonal impedance is symmetrical, whereas the off-diagonal one is antisymmetrical with a near-linear portion within a certain field interval. For the off-diagonal response, the dc bias current is necessary to eliminate circular domains. In the case of the sinusoidal excitation without a dc bias current, the off-diagonal response is very small and irregular. In contrast, the pulsed excitation, combining both high- and low-frequency harmonics, produces the off-diagonal voltage response without additional biasing. This behavior is ideal for a practical sensor circuit design. We discuss the principles of operation of a linear magnetic sensor based on a complementary metal-oxide-semiconductor transistor circuit.

Shape of plasmon bands at the Brillouin-zone boundary.

Recently an off-diagonal element of the density response function was measured by inelastic scattering of x rays from standing wave fields (coherent inelastic x-ray scattering). The observed peak-valley structure demonstrated the existence of plasmon bands separated by a plasmon band gap for scattering vectors k close to the L point of the Brillouin zone in Si. In standard inelastic x-ray scattering spectroscopy which yields the diagonal density response the plasmon band gap is obscured by strong line broadening of the two plasmons resulting in a single broad peak. Here we explain that by measuring both the diagonal and the off-diagonal response for k=${\mathbf{G}}_{111}$/2 the line shapes of the two plasmons at the Brillouin-zone boundary can be reconstructed. Theoretical results obtained from a 2\ifmmode\times\else\texttimes\fi{}2 effective dielectric matrix evaluated to second order in the local pseudopotential are in very good qualitative agreement with experiment.

Off-diagonal response by means of inelastic x-ray scattering

Off-diagonal elements ϵ -1 (q, q + g h , ω) of the inverse dielectric matrix are shown to be measurable by means of inelastic scattering of X-ray photons from two different modes of the wave field, which is generated within the analyzer of a Laue-case X-ray interferometer at the interference position.