Transverse Susceptibility Research Articles

Transverse crack micromechanisms in high-strength steel weld metal with microstructure heterogeneity under hydrogen-containing environment

The transverse crack susceptibility for high-strength steel weld metal with microstructure heterogeneity was investigated under various environment. Transverse cracking probability (C%) increases with increasing microstructure heterogeneity and diffusible hydrogen content. The dominant transverse crack initiation are soft massive pre-eutectic ferrite (PF), the deformation-uncoordinated acicular ferrite (AF)-PF interface and inclusions aggregation. PF, AF-PF interface and inclusions acts as the principal crack extension channel during crack propagation. Transverse cracks pass AF mainly extend along {100} plane while only along {110} when passing PF. MAGBs and HAGBs impede crack propagation. The Ʃ3 boundaries promote the crack propagation, while Ʃ11, Ʃ13b and Ʃ17b hinder the crack propagation. The transverse crack of weld metal under hydrogen-containing environment is attributed to the combination of HEDE and HELP mechanisms in the presence of microstructure heterogeneity and inclusions.

The impacts of spin–orbit coupling and strain on transverse dynamical spin susceptibility in undoped phosphorene: Kane–Mele model study

We present the behaviors of dynamical transverse spin susceptibilities of undoped phosphorene monolayer using the Green’s function approach in the context of Kane–Mele model Hamiltonian. Such dynamical spin susceptibility is proportional to inelastic cross section of neutron beam from the layer. Specially, the effects of magnetic field and spin–orbit coupling strength on the spin excitation modes of phosphorene monolayer are investigated via calculating correlation function of spin density operators. Our results show the increase of magnetic field leads to move the magnetic excitation energy to higher values. Also, the intensity of peaks in inelastic cross section reduces with increase of magnetic field. We also show that applying both uniaxial and biaxial strains causes to decrease the intensity of peaks in dynamical spin susceptibility. Finally the effects of both compressive and tensile strains on frequency dependence of dynamical spin structure factor of phosphorene layer are studied. Moreover, the frequency positions of spin excitation mode of phosphorene layer have been investigated due to the effects of spin orbit coupling strength in details.

Nuclear magnetic resonance studies in a model transverse field Ising system

The suppression of ferroquadrupolar order in TmVO4 in a magnetic field is well-described by the transverse field Ising model, enabling detailed studies of critical dynamics near the quantum phase transition. We describe nuclear magnetic resonance measurements in pure and Y-doped single crystals. The non-Kramers nature of the ground state doublet leads to a unique form of the hyperfine coupling that exclusively probes the transverse field susceptibility. Our results show that this quantity diverges at the critical field, in contrast to the mean-field prediction. Furthermore, we find evidence for quantum critical fluctuations present near Tm-rich regions in Y-doped crystals at levels beyond which long-range order is suppressed, suggesting the presence of quantum Griffiths phases.

The local electronic interaction and strain effects on transverse dynamical spin susceptibility of [formula omitted]-graphyne

We present the behaviors of dynamical transverse spin susceptibilities of undoped β-graphyne monolayer using the Green’s function approach in the context of Hubbard model Hamiltonian. Such dynamical spin susceptibility is proportional to inelastic cross section of neutron beam from the layer. Specially, the effects of magnetic field, on-site coulomb repulsion strength and strain parameter on the spin excitation modes of β-graphyne monolayer are investigated via calculating correlation function of transverse components of spin density operators. Our results show the increase of absolute value of compressive strain parameter leads to move the magnetic excitation modes to higher energies. Also the intensity of peaks in inelastic cross section reduces with absolute value of compressive strain parameter. We also show that applying biaxial tensile strain causes to decrease the intensity of peaks in dynamical transverse spin susceptibility. Finally the effects of magnetic field and on-site coulomb repulsion interaction strength on frequency dependence of dynamical spin structure factor of β-graphyne layer are studied. Moreover the frequency positions of spin excitation mode of β-graphyne monolayer have been investigated due to the effects of biaxial strains, applied magnetic field and Hubbard parameter strength in details.

Temperature Evolution of Magnon Propagation Length in Tm3Fe5O12 Thin Films: Roles of Magnetic Anisotropy and Gilbert Damping.

The magnon propagation length, ⟨ξ⟩, of a ferro-/ferrimagnet (FM) is one of the key factors that controls the generation and propagation of thermally driven magnonic spin current in FM/heavy metal (HM) bilayer based spincaloritronic devices. For the development of a complete physical picture of thermally driven magnon transport in FM/HM bilayers over a wide temperature range, it is of utmost importance to understand the respective roles of temperature-dependent Gilbert damping (α) and effective magnetic anisotropy (Keff) in controlling the temperature evolution of ⟨ξ⟩. Here, we report a comprehensive investigation of the temperature-dependent longitudinal spin Seebeck effect (LSSE), radio frequency transverse susceptibility, and broad-band ferromagnetic resonance measurements on Tm3Fe5O12 (TmIG)/Pt bilayers grown on different substrates. We observe a significant drop in the LSSE voltage below 200 K independent of TmIG film thickness and substrate choice. This is attributed to the noticeable increases in effective magnetic anisotropy field, HKeff (∝Keff) and α that occur within the same temperature range. From the TmIG thickness dependence of the LSSE voltage, we determined the temperature dependence of ⟨ξ⟩ and highlighted its correlation with the temperature-dependent HKeff and α in TmIG/Pt bilayers, which will be beneficial for the development of rare-earth iron garnet based efficient spincaloritronic nanodevices.

Finding the Dynamics of an Integrable Quantum Many‐Body System via Machine Learning

AbstractThe dynamics of the Gaudin magnet (“central‐spin model”) is studied using machine‐learning methods. This model is of practical importance, for example, for studying non‐Markovian decoherence dynamics of a central spin interacting with a large bath of environmental spins and for studies of nonequilibrium superconductivity. The Gaudin magnet is also integrable, admitting many conserved quantities. Machine‐learning methods may be well suited to exploiting the high degree of symmetry in integrable problems, even when an explicit analytic solution is not obvious. Motivated in part by this intuition, a neural‐network representation (restricted Boltzmann machine) is used for each variational eigenstate of the model Hamiltonian. Accurate representations of the ground state and of the low‐lying excited states of the Gaudin‐magnet Hamiltonian are then obtained through a variational Monte Carlo calculation. From the low‐lying eigenstates, the non‐perturbative dynamic transverse spin susceptibility is found, describing the linear response of a central spin to a time‐varying transverse magnetic field in the presence of a spin bath. Having an efficient description of this susceptibility opens the door to improved characterization and quantum control procedures for qubits interacting with an environment of quantum two‐level systems.

Thermodynamic properties of anisotropic antiferromagnets with four-spin exchange

Magnetic semiconductors are widely used in microelectronics, which is used to control spacecraft. The transport and electrical properties depend on the magnetic structure, which can be changed by the action of the magnetic field and controlled by the current. The magnetic structure of semiconductors with a strong spin-lattice interaction, which is reduced to a four-spin exchange interaction, is investigated. The magnetic characteristics are calculated in a classical Heisenberg model constructed from equivalent magnetic atoms forming a simple cubic and square lattice. The Hamiltonian of the system contains the exchange interaction between the nearest neighbors, the four-spin exchange, and the one-ion anisotropy of the light axis type. The Monte Carlo method calculates the thermodynamic characteristics: the sublattice magnetization, the quadrupole parameter, the pairwise spin-spin correlation functions, the spontaneous moment at the node directed along the light axis and in the basis plane, the internal energy, and the magnetic susceptibility. The magnetic order type was found to change from a collinear antiferromagnet (AFM) to a noncollinear (NAF) as the four-spin exchange constant increases. The dependence of the spin correlation functions on the distance has a weakly damped oscillatory character. In the AFM-NAP transition region, the near antiferromagnetic order is replaced by the ferromagnetic one, while the far antiferromagnetic order is preserved. A phase diagram of the antiferromagnetic (AFM) and non-collinear (NAF) on square and cubic lattices is constructed on the four-spin exchange-single-axis anisotropy plane. The longitudinal and transverse susceptibility of the NAF from temperature for different parameters of the four-spin exchange is calculated. The region of anisotropy and quadrupole exchange parameters in noncollinear NAF with a first-order phase transition, the sublattice magnetization jump, and the quadrupole parameter from temperature are determined. The anisotropy and four-spin exchange constants in a classical antiferromagnet with spontaneous momentum and far- and near-order parameters were found.

Coherent dynamics of strongly interacting electronic spin defects in hexagonal boron nitride

Optically active spin defects in van der Waals materials are promising platforms for modern quantum technologies. Here we investigate the coherent dynamics of strongly interacting ensembles of negatively charged boron-vacancy ({{{{{{{{rm{V}}}}}}}}}_{{{{{{{{rm{B}}}}}}}}}^{-}) centers in hexagonal boron nitride (hBN) with varying defect density. By employing advanced dynamical decoupling sequences to selectively isolate different dephasing sources, we observe more than 5-fold improvement in the measured coherence times across all hBN samples. Crucially, we identify that the many-body interaction within the {{{{{{{{rm{V}}}}}}}}}_{{{{{{{{rm{B}}}}}}}}}^{-} ensemble plays a substantial role in the coherent dynamics, which is then used to directly estimate the concentration of {{{{{{{{rm{V}}}}}}}}}_{{{{{{{{rm{B}}}}}}}}}^{-}. We find that at high ion implantation dosage, only a small portion of the created boron vacancy defects are in the desired negatively charged state. Finally, we investigate the spin response of {{{{{{{{rm{V}}}}}}}}}_{{{{{{{{rm{B}}}}}}}}}^{-} to the local charged defects induced electric field signals, and estimate its ground state transverse electric field susceptibility. Our results provide new insights on the spin and charge properties of {{{{{{{{rm{V}}}}}}}}}_{{{{{{{{rm{B}}}}}}}}}^{-}, which are important for future use of defects in hBN as quantum sensors and simulators.

Surface Termination-Enhanced Magnetism at Nickel Ferrite/2D Nanomaterial Interfaces: Implications for Spintronics

Engineering of interfacial magnetic properties provides an extra edge in designing heterostructures with desired properties for spintronics and spincaloritronics, without drastically changing the structure of the neighboring nonmagnetic material. Here, we report on the surface termination-enhanced magnetic properties of the ferrimagnetic insulator (FMI) nickel ferrite (NFO) with the inclusion of graphene (Gr) and monolayer hexagonal boron nitride (hBN). Depth-dependent X-ray photoelectron spectroscopy (XPS) measurements reveal the presence of a layer of adsorbed oxygen at the NFO/Gr and NFO/hBN interfaces. Magnetometry and transverse susceptibility measurements indicate that the inclusion of monolayer Gr increases the saturation magnetization (Ms) by 40% and decreases the effective magnetic anisotropy by 50% across 5 K ≤ T ≤ 300 K. A similar but less pronounced effect is observed for the inclusion of hBN. Density functional theory calculations further indicate that the increase in MS due to the inclusion of Gr or hBN arises on oxygen-terminated NFO, as observed in XPS measurements. These results present ways for engineering strong interfacial magnetic effects in FMI/2D nanomaterial systems, controlling magnetism by surface termination, and developing advanced spinterfaces for applications in spincaloritronics and spin insulatronics.

Nonlinear Transverse Magnetic Susceptibility under Electric Toroidal Dipole Ordering

An electric toroidal dipole (ETD) moment is one of the fundamental dipole moments as well as electric and magnetic ones. Although it directly couples to neither an electric nor magnetic field due to its spatial inversion and time-reversal parities, its ordered state leads to unconventional transverse responses of the conjugate physical quantities. We here theoretically investigate nonlinear transverse magnetic susceptibility under the ETD ordering. By performing a self-consistent mean-field calculation for a five $d$-orbital model under a tetragonal crystalline electric field and using the nonlinear Kubo formula, we show that a third-order transverse magnetic susceptibility corresponding to a uniform magnetization perpendicular to the external magnetic field becomes nonzero once the ETD moment is ordered under tetragonal crystalline electric field. Moreover, we find that spin-orbital entanglement and a low-lying first excited crystal-field level are important for realizing large transverse responses.

흡착된 고분자가 자성 나노입자 분산액의 유변학적, 자기적 특성에 미치는 영향

자성입자 표면에 고분자를 흡착시켜 분산액을 제조하고 유변학적 특성과 분산 상태 사이의 관계를 조사하였다. 또한 자성입자의 분산도를 결정하기 위해 자기적 특성인 분산액의 가로축자화율(transverse susceptibility)을 측정하였다. Co-γ-FeSUB2/SUBOSUB3/SUB 나노입자 분산액은 자성체 표면에 흡착되는 극성 그룹을 가진 바인더 폴리머를 사용하여 제조되었고, 자성입자의 부피분율이 즐어들면 자성입자 표면의 흡착층에 많은 양의 용매 침투로 인해 흡착된 고분자의 반경이 증가하여 흡착층 두께가 증가한다. 한계상호작용 미만의 부피 분율을 갖는 자성 나노입자 분산액의 경우, 표면에 흡착된 고분자 간의 연결로 인해 전단 농화(shear thickening) 현상이 관찰되었다. 가로축자화율 측정에 의해 자성 나노 입자의 부피 분율이 적을수록 자성입자 분산도가 우수함을 알 수 있었다.

Magnetism and spin-dependent transport phenomena across Verwey and Morin transitions in iron oxide/Pt bilayers

Understanding the influence of phase coexistence and phase transitions on spin transport properties in a ferromagnet/heavy metal (FM/HM) system is of utmost importance for spintronics. Here, we report a comprehensive investigation of the magnetic and spin transport properties of biphase iron oxide (BPIO = α-Fe2O3 + Fe3O4)/Pt films over a wide temperature range, 10K≤T≤300K. In-plane (IP) and out-of-plane (OOP) magnetometry and radio frequency transverse susceptibility measurements confirm the characteristic features of the Verwey and Morin transitions at TV ∼ 120 K and TM ∼ 200 K, respectively. Anisotropic magnetoresistance (AMR) is observed in the BPIO film, which arises mainly from the spin polarized tunneling of conduction electrons between neighboring uniformly magnetized grains through the resistive grain boundary. Spin Hall magnetoresistance (SMR) and spin Hall anomalous Hall effect (SH-AHE) are detected in the BPIO/Pt films. Around the TV, the temperature evolution of SMR shows a sharp maximum, while SH-AHE exhibits a steep decrease. Both SMR and SH-AHE are strongly susceptible to the Verwey transition but the Morin transition, indicating that the interfacial magnetism of our BPIO/Pt film is dominated by the Fe3O4 phase rather than the α-Fe2O3 phase.

Local Ward identities for collective excitations in fermionic systems with spontaneously broken symmetries

We derive Ward identities for fermionic systems exhibiting a gauge symmetry that gets globally broken. In particular, we focus on the relation that connects the gauge field response functions to the transverse susceptibilities of the order parameter. We find that the long-wavelength and zero energy limit of the former are related to the coefficients of a low-energy expansion of the latter. We examine three physical cases: the superconductor, the N\'eel antiferromagnet and the spiral magnet. In the case of a metallic spiral magnet that completely breaks the SU(2) spin symmetry we explicitly show that the Ward identities are fulfilled within the random phase approximation. We subsequently derive microscopic expressions for the spin stiffnesses and spin wave velocities, which can be plugged into low energy models to study the effect of long-wavelength bosonic fluctuations on top of mean-field solutions.

Anisotropic pressure of magnetized quark matter with anomalous magnetic moment

We investigate magnetic field $(eB)$ dependence of constituent quark mass, the longitudinal and transverse pressure as well as the magnetization and magnetic susceptibility of strongly interacting quark matter. We employ the two-flavor Polyakov Nambu--Jona-Lasinio model with the inclusion of the anomalous magnetic moment (AMM) of the quarks at finite temperature ($T$) and finite quark chemical potential $({\ensuremath{\mu}}_{q})$ capturing different stages of chiral phase transition. We find that the transverse pressure, magnetization, and magnetic susceptibility become highly oscillatory for large values of $eB$ in the chiral symmetry broken phase. However, the oscillations cease to occur at higher values of $T$ and ${\ensuremath{\mu}}_{q}$ when chiral symmetry is (partially) restored and the anisotropic nature of the pressure becomes significant even at smaller values of $eB$. As the inclusion of AMM of the quarks leads to inverse magnetic catalysis of the transition temperature, we observe that the variations of transverse pressure, magnetization, and magnetic susceptibility are significantly modified in the vicinity of the chiral transition temperature. Furthermore, above the chiral transition temperature the magnetic susceptibility is found to remain positive for a wide range of $eB$, indicating a paramagnetic character of the strongly interacting quark matter. Finally, we have also examined the magnetism of strongly interacting matter in the quarkyonic phase. The obtained results could be useful for a magnetohydrodynamic evolution of hot and dense matter created in heavy-ion collisions.

Magnons in antiferromagnetic bcc Cr andCr2O3from time-dependent density functional theory

We apply time-dependent density functional theory to calculate the transverse magnetic susceptibility of bcc Cr and ${\mathrm{Cr}}_{2}{\mathrm{O}}_{3}$, which constitute prototypical examples of antiferromagnets with itinerant and localized magnetic moments, respectively. The exchange-correlation kernel is rescaled in order to enforce the Goldstone condition and the magnon dispersion relations are extracted based on a symmetry analysis relying on the generalized Onsager relation. Doing so, our calculations yield the characteristic linear magnon dispersion of antiferromagnets in the long-wavelength limit. In the case of ${\mathrm{Cr}}_{2}{\mathrm{O}}_{3}$, we find that the adiabatic local density approximation yields a good qualitative agreement with the measured dispersion, but overestimates the magnon velocity and bandwidth by a factor of 2. Including a Hubbard correction improves the magnon velocity, but at the expense of the overall qualitative agreement with the experimental magnon dispersion. For bcc Cr we find a sharp acoustic magnon mode at low energies with a velocity in agreement with previously reported values. At higher energies, the acoustic magnon mode becomes subject to strong Landau damping and rapidly vanishes once it enters the Stoner continuum. In addition to the acoustic magnon mode, we also observe an additional collective mode along the $\mathrm{\ensuremath{\Gamma}}\ensuremath{\rightarrow}\mathrm{R}$ direction with an energy of $\ensuremath{\sim}1$ eV, which is located inside the Stoner continuum, but appears to elude the effect of Landau damping.

Measuring Demagnetization Factors in Magnetic Nanostructure Assemblies

Transverse susceptibility techniques shed significant new light on superparamagnetism.

Methods of investigating the demagnetization factors within assemblies of superparamagnetic nanoparticles

Three-dimensional distributions of demagnetization factors Nd within assemblies of magnetic nanoparticles have been investigated along the axes of cuboid containing vessels. From the results of a numerical polar-based model, a significant skew toward high values in the number distribution is observed and often overlooked by the assumed uniformity of the conventional analytical approach. To enable comparison with experiment, new transverse susceptibility techniques have been developed, which are also applicable to superparamagnetic assemblies that do not have the magnetization features normally required using conventional methods. Applying the two techniques to a system of ∼13 nm magnetite (Fe3O4) particles resulted in the difference between the in-plane and out-of-plane Nd factors of (0.21 ± 0.03) and (0.201 ± 0.009), respectively, which shows closest agreement with the simulation value for the mode of (0.19 ± 0.02). The median and mean results of the model move further away from the experimental result, yielding values of (0.17 ± 0.02) and (0.16 ± 0.02), respectively, which is consistent with the skewed distributions observed here. In all cases, the sum of the Nd factors from each orthogonal axis was equal to 1, giving further confidence in the model. The new methods allow measurements on the superparamagnetic systems often found at this scale, and the agreement with the model means that the spatial distribution of Nd factors may now be taken into account in studies on any nanoscale material that considers the whole structure as a distribution of magnetic elements.

Proximity enhanced magnetism at NiFe2O4/Graphene interface

Here, we explore the change in effective magnetic anisotropy of the ferrimagnetic (FM) insulator nickel ferrite (NFO) thin film due to the inclusion of monolayer graphene (MLG) grown on top of the NFO layer. This was done by performing radio frequency (RF) transverse susceptibility (TS) measurements on bare NFO and NFO/MLG bilayer samples for both in-plane (IP) and out-of-plane (OOP) configurations utilizing a tunnel diode oscillator technique. Our magnetometry measurements indicated an enhancement in the overall saturation magnetization of the NFO/MLG bilayer with respect to the bare NFO film. The TS measurements reveal that the inclusion of MLG reduces the effective magnetic anisotropy for both IP and OOP configurations drastically, by up to a factor of 2 over the temperature range 40 K ≤ T ≤ 280 K. Since NFO is a magnetic substrate, it is possible that NFO could induce magnetic ordering in MLG at the NFO/MLG interface via the magnetic proximity effect. Furthermore, since NFO is insulating and MLG is a semimetal, there likely exists a large conductivity difference at the interface, making charge transfer plausible. These two effects could modify the interfacial magnetism leading to a change in the effective magnetic anisotropy. These results highlight the importance of understanding the interfacial magnetism of FM/MLG heterostructures.

Angle-dependent AC susceptibility, low-field magnetoresistance and switching behaviour of La0.66Sr0.34MnO3/YSZ(001) films

The La0.66Sr0.34MnO3 (LSMO) films with thickness 200–330 nm have been grown at 750 °C on lattice-mismatched (001)-plane oriented yttria-stabilized zirconia (YSZ) using radio frequency magnetron sputtering technique. The films demonstrated columnar growth structure characterized by coexistance of grains with the averaged diameter of about 50 nm and well defined crystallographic orientations of a pseudocubic LSMO lattice, namely, (001)LSMO[110]//(001)YSZ[100] and (110)LSMO[110;100]//(100)YSZ[100]. Alternating current (AC) magnetic susceptibility, χ(H) ∼ dM/dH, and magnetoresistance, MR(H), of the films were measured at 78 and 295 K with DC magnetic field (H) applied either in-plane or out-of-plane. Unusually sharp peaks at H = ±HSW and clearly defined switching behaviour have been indicated at 78 K in both the χ(H) and MR(H) plots. The HSW values were found to increase with the out-of-plane angle, α, according to the relationship HSW = HSW0/cosα (HSW0 = 4.0 and 1.4 kA/m at 78 and 295 K, respectively) while negligible variation of HSW has been indicated by varying direction of H in a film plane. The investigations revealed close correlation between χ(H) and low-field magnetoresistance. The observed angle-dependent peak-like χ(H) anomalies have been explained assuming magnetization reversal of the multigrain films governed by interparticle interaction and pinning of magnetic domains at grain boundaries. Unusual pit-like anomaly of the transverse biased susceptibility (TS) indicated at H = ±HSW has been explained in a framework of the TS theory developed for isolated uniaxal ferromagnetic particles assuming coexistance of grains with several fixed easy axis orientations in a film plane.

Constraints for the semileptonic B→D(*) form factors from lattice QCD simulations of two-point correlation functions

In this work we present the first nonperturbative determination of the hadronic susceptibilities that constrain the form factors entering the semileptonic $B\ensuremath{\rightarrow}{D}^{(*)}\ensuremath{\ell}{\ensuremath{\nu}}_{\ensuremath{\ell}}$ transitions due to unitarity and analyticity. The susceptibilities are obtained by evaluating moments of suitable two-point correlation functions obtained on the lattice. Making use of the gauge ensembles produced by the Extended Twisted Mass Collaboration (ETMC) with ${N}_{f}=2+1+1$ dynamical quarks at three values of the lattice spacing ($a\ensuremath{\simeq}0.062$, 0.082, 0.089 fm) and with pion masses in the range $\ensuremath{\simeq}210--450\text{ }\text{ }\mathrm{MeV}$, we evaluate the longitudinal and transverse susceptibilities of the vector and axial-vector polarization functions at the physical pion point and in the continuum and infinite volume limits. The ETMC ratio method is adopted to reach the physical $b$-quark mass ${m}_{b}^{\mathrm{phys}}$. At zero momentum transfer for the $b\ensuremath{\rightarrow}c$ transition we get ${\ensuremath{\chi}}_{{0}^{+}}({m}_{b}^{\mathrm{phys}})=7.58(59)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, ${\ensuremath{\chi}}_{{1}^{\ensuremath{-}}}({m}_{b}^{\mathrm{phys}})=6.72(41)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}\text{ }\text{ }{\mathrm{GeV}}^{\ensuremath{-}2}$, ${\ensuremath{\chi}}_{{0}^{\ensuremath{-}}}({m}_{b}^{\mathrm{phys}})=2.58(17)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$ and ${\ensuremath{\chi}}_{{1}^{+}}({m}_{b}^{\mathrm{phys}})=4.69(30)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}\text{ }\text{ }{\mathrm{GeV}}^{\ensuremath{-}2}$ for the scalar, vector, pseudoscalar and axial susceptibilities, respectively. In the case of the vector and pseudoscalar channels the one-particle contributions due to ${B}_{c}^{*}$ and ${B}_{c}$ mesons are evaluated and subtracted to improve the bounds, obtaining ${\ensuremath{\chi}}_{{1}^{\ensuremath{-}}}^{\mathrm{sub}}({m}_{b}^{\mathrm{phys}})=5.84(44)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}\text{ }\text{ }{\mathrm{GeV}}^{\ensuremath{-}2}$ and ${\ensuremath{\chi}}_{{0}^{\ensuremath{-}}}^{\mathrm{sub}}({m}_{b}^{\mathrm{phys}})=2.19(19)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$, respectively.