Magnetic Field Splitting Research Articles

Spin-orbit-coupled fractional oscillators and trapped Bose-Einstein condensates.

We study the ensemble of pseudo-spin 1/2 ultracold bosons, performing Lévy flights, confined in a parabolic potential. The (pseudo-) spin-orbit coupling (SOC) is additionally imposed on these particles. We consider the structure and dynamics of macroscopic pseudospin qubits based on Bose-Einstein condensates, obtained from the above "fractional" bosons. Under "fractional" we understand the substitution of the ordinary second derivative (kinetic energy term) in the Gross-Pitaevskii equationby a so-called fractional Laplacian, characterized by the Lévy index μ. We show that the joint action of interparticle interaction, SOC, and Zeeman splitting in a synthetic magnetic field makes the dynamics of corresponding qubit highly nontrivial with evident chaotic features at both strong interactions and Lévy indices μ→1 when the Lévy trajectories of bosons with long jumps dominated over those derived from ordinary Gaussian distribution, corresponding to μ=2. Using analytical and numerical arguments, we discuss the possibilities to control the above qubit using the synergy of SOC, interaction strength, and "fractionality," characterized by the Lévy index μ.

Impurity Knight shift in quantum dot Josephson junctions

Spectroscopy of a Josephson junction device with an embedded quantum dot reveals the presence of a contribution to level splitting in external magnetic field that is proportional to \cos\phicosϕ, where \phiϕ is the gauge-invariant phase difference across the junction. To elucidate the origin of this unanticipated effect, we systematically study the Zeeman splitting of spinful subgap states in the superconducting Anderson impurity model. The magnitude of the splitting is renormalized by the exchange interaction between the local moment and the continuum of Bogoliubov quasiparticles in a variant of the Knight shift phenomenon. The leading term in the shift is linear in the hybridisation strength \GammaΓ (quadratic in electron hopping), while the subleading term is quadratic in \GammaΓ (quartic in electron hopping) and depends on \phiϕ due to spin-polarization-dependent corrections to the Josephson energy of the device. The amplitude of the \phiϕ-dependent part is largest for experimentally relevant parameters beyond the perturbative regime where it is investigated using numerical renormalization group calculations. Such magnetic-field-tunable coupling between the quantum dot spin and the Josephson current could find wide use in superconducting spintronics.

Ab-initio evaluation of Mn doped Cs2GeCl/Br6 halides for spintronics and energy harvesting applications

We utilized Ab-initio calculations to study electronic, structural, magnetic, and thermoelectric characteristics for Cs2GeCl/Br6 halides that were either undoped or doped with Manganese (Mn). We evaluated the total energy variation among ferromagnetic (FM) and antiferromagnetic (AFM) phases to determine the ferromagnetic structural stability of Mn-doped Cs2GeCl/Br6 halides. In addition, structural stability also justified through the calculations of elastic properties. To make precise predictions about the electronic properties of both undoped and Mn-doped Cs2GeCl/Br6 halides, we used modified Becke-Johnson local density approximation functional. Mn-doped Cs2GeCl/Br6 halides demonstrated FM semiconducting behavior, as indicated by their band structures and density of states plots, which are reported by magnetic moments and crystal field splitting energies. We systematically explored the thermoelectric characteristics by calculating parameters such as electrical and thermal conductivities, Seebeck coefficient, and Figure of merits. The Mn-doped Cs2GeCl/Br6 halides demonstrated a large value for Figure of merit and inconsequential lattice thermal conductivity, making them particularly suitable for thermoelectric applications.

C-Term Faraday Rotation in Low Symmetry tert-Butyl Substituted Polyferroceniums.

Molecular thin films are currently being investigated as candidate materials to replace conventional atomistic inorganic crystal-based Faraday rotators. High symmetry paramagnetic species have been reported to exhibit large Verdet constants via magnetic field splitting of degenerate ground states. However, lower symmetry open-shell species have not been extensively studied. Herein, we report the Faraday rotation of two poly di-tert-butylferroceniums with diphenylsilane and vinylene linkers. Thin films of oxidized poly[(1,1'-di-tert-butylferrocenyl)diphenylsilane] [poly(tBu2fc-SiPh2)] displayed a 30% increase in maximum Verdet constant relative to the previously reported decamethylferrocenium/PMMA composite, with Verdet constants of -4.52 × 104 deg T-1 m-1 at 730 nm and 4.46 × 104 deg T-1 m-1 at 580 nm. When a sp2-type linker was used, as with the oxidized poly(1,1'-di-tert-butyl-ferrocenylene)vinylene [poly(tBu2fc-C═C)], negligible Faraday rotation was observed. Hence, Faraday rotation can be maintained when molecular symmetry is broken, however orbital symmetry breaking in optical transitions of interest leads to a significant loss in magneto-optical activity.

Magnesium-rich intermetallic compounds RE 3Ag4Mg12 (RE = Y, La–Nd, Sm–Dy, Yb) and AE 3Ag4Mg12 (AE = Ca, Sr)

Abstract The magnesium-rich intermetallic compounds RE 3Ag4Mg12 (RE = Y, La–Nd, Sm–Dy, Yb) and AE 3Ag4Mg12 (AE = Ca, Sr) were synthesized from the elements in sealed tantalum ampoules through heat treatment in an induction furnace. X-ray powder diffraction studies confirm the hexagonal Gd3Ru4Al12 type structure, space group P63/mmc. Three structures were refined from single crystal X-ray diffractometer data: a = 973.47(5), c = 1037.19(5) pm, wR2 = 0.0296, 660 F 2 values, 30 variables for Gd3Ag3.82(1)Mg12.18(1), a = 985.27(9), c = 1047.34(9) pm, wR2 = 0.0367, 716 F 2 values, 29 variables for Yb3Ag3.73(1)Mg12.27(1) and a = 992.41(8), c = 1050.41(8) pm, wR2 = 0.0373, 347 F 2 values, 28 variables for Ca3Ag3.63(1)Mg12.37(1). Refinements of the occupancy parameters revealed substantial Ag/Mg mixing within the silver-magnesium substructure, a consequence of the Ag@Mg8 coordination. The alkaline earth and rare earth atoms build Kagome networks. Temperature dependent magnetic susceptibility measurements indicate diamagnetism/Pauli paramagnetism for the compounds with Ca, Sr, Y and YbII, while the others with the trivalent rare earth elements are Curie-Weiss paramagnets. Most compounds order antiferromagnetically at T N = 4.4(1) K (RE = Pr), 34.6(1) K (RE = Gd) and 23.5(1) K (RE = Tb) while Eu3Ag4Mg12 is a ferromagnet (T C = 19.1(1) K). 151Eu Mössbauer spectra confirm divalent europium (δ = −9.88(1) mm s−1). Full magnetic hyperfine field splitting (18.4(1) T) is observed at 6 K. Yb3Ag4Mg12 shows a single resonance in its 171Yb solid state NMR spectrum at 6991 ppm at 300 K indicating a strong, positive Knight shift.

APd2Zn3 (A=Ca, Sr, Eu) with a CaCu5 superstructure

AbstractThe intermetallic phases APd2Zn3 (A=Ca, Sr, Eu) were synthesized from the elements in sealed niobium ampules in an induction furnace. The phase purity of the samples was checked by powder X‐ray diffraction (Guinier technique). The structures were refined from single crystal X‐ray diffractometer data: YNi2Al3 type (CaCu5 superstructure), P6/mmm, a=936.97(4), c=420.75(2) pm, wR2=0.0206, 259 F2 values, 17 variables for CaPd2Zn3, a=953.63(6), c=425.38(3) pm, wR2=0.0185, 230 F2 values, 17 variables for SrPd2Zn3 and a=948.20(7), c=423.20(3) pm, wR2=0.0209, 228 F2 values, 18 variables for EuPd2.12(1)Zn2.88(1). The europium‐based crystal showed a small homogeneity range through Pd/Zn mixing. The striking structural motifs of the APd2Zn3 phases are Kagome networks formed by the palladium and zinc atoms. The superstructure formation (discussed on the basis of a Bärnighausen tree) results from a different Pd/Zn coloring and a shift of one A position by c/2. The divalent character of europium in EuPd2Zn3 was substantiated by magnetic susceptibility and 151Eu Mössbauer spectroscopic measurements. EuPd2Zn3 orders ferrimagnetically at TC=17.5(5) K. The magnetization behavior at 3 K (two‐step magnetization) confirms the existence of two crystallographically independent europium sites. The 151Eu Mössbauer spectrum at 5 K shows full magnetic hyperfine field splitting (δ=−8.99(4) mm s−1 and BHf=27.7(1) T).

(INVITED)Zeeman interactions in lanthanide doped nanocrystals

We report a crystal-field analysis of Nd3+-doped KY3F10 nanocrystals. As well as electronic energy levels obtained from absorption and fluorescence, we fit to magnetic-field splittings for fields of up to 4T. The resulting parameters accurately account for the Zeeman interaction, including non-linear effects. The fitted parameters are similar to those for bulk crystals. The parameters are compared with ab-initio calculations and superposition-model analyses.

A europium kagome lattice in the solid solution Eu3−х Sr х Pt4Zn12 – first zinc representatives of the Gd3Ru4Al12 type

Abstract Eu3Pt4Zn12 and Sr3Pt4Zn12 form a complete solid solution Eu3−x Sr x Pt4Zn12. Samples with x = 0, 0.5, 1, 1.5, 2, 2.5 and 3 were synthesized from the elements in sealed tantalum ampoules in an induction furnace. All samples were characterized by powder X-ray diffraction and the structures of Sr3Pt3.93Zn12.07, Eu1.80Sr1.20Pt4Zn12 and Eu3Pt3.68Zn12.32 were refined from single crystal X-ray diffractometer data. The new compounds are isotypic with Gd3Ru4Al12, space group P63/mmc. The striking building units in these phases are the kagome networks occupied by the europium and strontium atoms and Pt1@Zn8 and Pt2@Zn8 distorted cubes. Besides the Eu/Sr mixing within the solid solution, the structure refinements indicated small homogeneity ranges induced by Pt/Zn mixing. The europium containing samples of the solid solution Eu3−x Sr x Pt4Zn12 are Curie–Weiss paramagnets and the experimental magnetic moments manifest stable divalent europium. The samples with x = 0, 0.5 and 2 order magnetically: T N = 15.4(1) K for x = 0, T C = 12.4(1) K for x = 0.5 and T N = 4.0(1) K for x = 2. The 3 K magnetization isotherms tend toward Brillouin type behavior with increasing europium dilution. The divalent ground state of Eu3Pt4Zn12 is further confirmed by 151Eu Mössbauer spectroscopy with an isomer shift of −9.66(2) mm s−1 at 78 K. In the magnetically ordered state Eu3Pt4Zn12 shows full magnetic hyperfine field splitting (23.0(1) T).

Tunable Valley Splitting and Bipolar Operation in Graphene Quantum Dots.

Quantum states in graphene are 2-fold degenerate in spins, and 2-fold in valleys. Both degrees of freedom can be utilized for qubit preparations. In our bilayer graphene quantum dots, we demonstrate that the valley g-factor gv, defined analogously to the spin g-factor gs for valley splitting in a perpendicular magnetic field, is tunable by over a factor of 4 from 20 to 90, by gate voltage adjustments only. Larger gv results from larger electronic dot sizes, determined from the charging energy. On our versatile device, bipolar operation, charging our quantum dot with charge carriers of the same or the opposite polarity as the leads, can be performed. Dots of both polarities are tunable to the first charge carrier, such that the transition from an electron to a hole dot by the action of the plunger gate can be observed. Addition of gates easily extends the system to host tunable double dots.

Nonlocal spin Seebeck effect in the bulk easy-plane antiferromagnet NiO

We report the observation of magnon spin currents generated by the Spin Seebeck effect (SSE) in a bulk single crystal of the easy-plane antiferromagnet NiO. A magnetic field induces a non-degeneracy and thereby an imbalance in the population of magnon modes with opposite spin. A temperature gradient then gives rise to a non-zero magnon spin current. This SSE is measured both in a local and a non-local geometry at 5$\,$K in bulk NiO. The magnetic field dependence of the obtained signal is modelled by magnetic field splitting of the low energy magnon modes, affecting the spin Seebeck coefficient. The relevant magnon modes at this temperature are linked to cubic anisotropy and magnetic dipole-dipole interactions. The non-local signal deviates from the expected quadratic Joule heating by saturating at a current from around 75$\,\mu A$ in the injector. The magnon chemical potential does not decay exponentially with distance and inhomogeneities may be the result of local magnon accumulations.

Soft mode behavior and evidence for pressure-induced magnetostructural effects in Pr2O3

The authors use Raman spectroscopy to study anomalous phonon-softening with decreasing temperature and the pressure- and magnetic field-dependent crystal electric field splittings in hexagonal Pr${}_{2}$O${}_{3}$.

Solid solutions EuAu4Cd2−x Mg x with a remarkably stable ferromagnetic ground state

Abstract Samples of the solid solutions EuAu4Cd2−x Mg x were synthesized from the elements in sealed tantalum ampoules. The elements were reacted at a maximum temperature of 1273 K followed by slow cooling. For crystal growth, the polycrystalline samples were ground to powders, pressed to pellets and annealed again. All samples crystallize with the tetragonal YbAl4Mo2-type structure, space group I4/mmm. The solid solution extends up to x = 1 and the Cd/Mg substitution has only a minor influence on the lattice parameters. The samples have been characterized by powder X-ray diffraction and the structure of EuAu4Cd1.58(2)Mg0.42(2) was refined from single crystal X-ray diffractometer data: a = 715.46(14), c = 549.96(11) pm, wR2 = 0.0334, 180 F 2 values and 11 variables. The striking crystal chemical motifs of the EuAu4Cd2−x Mg x structures are Eu@Au12 and (Cd/Mg)@Au8(Cd/Mg)2 polyhedra and linear Cd/Mg chains in form of a tetragonal rod packing with distances of 275 pm for Cd/Mg–Cd/Mg. Temperature dependent magnetic susceptibility measurements of all samples from the solid solutions EuAu4Cd2−x Mg x revealed Curie–Weiss behavior and stable divalent europium. All samples are ordered ferromagnetically around T = 16 K, and magnetization isotherms at 3 K classify these materials as soft ferromagnets. It is remarkable that the structural Cd/Mg disorder within the chains does not influence the ferromagnetic ground state. The divalent nature of europium in these intermetallics was exemplarily studied for the EuAu4Cd1.4Mg0.6 sample by 151Eu Mössbauer spectroscopy. At 6 K the isomer shift is −9.95(4) mm s−1 and one observes full magnetic hyperfine field splitting with B hf = 27.1(1) T.

Ternary plumbides ATPb2 (A = Ca, Sr, Ba, Eu; T = Rh, Pd, Pt) with distorted, lonsdaleite-related substructures of tetrahedrally connected lead atoms

Abstract The plumbides CaTPb2 (T = Rh, Pd), EuTPb2 (T = Rh, Pd, Pt), SrTPb2 (T = Rh, Pd, Pt) and BaTPb2 (T = Pd, Pt) were obtained by direct reactions of the elements in sealed tantalum tubes in an induction furnace. The moisture sensitive polycrystalline samples were characterized by X-ray powder diffraction. They crystallize with the orthorhombic MgCuAl2-type structure, space group Cmcm. The structures of CaRhPb2 (a = 433.78(3), b = 1102.06(8), c = 798.43(6) pm, wR = 0.0285, 432 F2 values and 16 variables) and EuPdPb2 (a = 457.24(5), b = 1158.27(13), c = 775.73(8), wR = 0.0464, 464 F2 values and 16 variables) were refined from single crystal X-ray diffractometer data. The characteristic structural motif is the distorted tetrahedral substructure built up by the lead atoms with Pb–Pb distances of 326–327 pm in CaRhPb2 and of 315–345 pm in EuPdPb2. With increasing size of the alkaline earth (Eu) cation, the lead substructure becomes more anisotropic with a shift of the [TPb2] polyanions from three- to two-dimensional, leading to significantly increased moisture sensitivity. Temperature dependent magnetic susceptibility studies reveal Pauli paramagnetism for SrRhPb2, SrPtPb2, BaPdPb2 and BaPtPb2. EuRhPb2 and EuPdPb2 are Curie–Weiss paramagnets with stable divalent europium as is also evident from 151Eu Mössbauer spectra. EuRhPb2 is a ferromagnet with T C = 17.7(2) K, while EuPdPb2 orders antiferromagnetically at T N = 15.9 K. This is in agreement with the full magnetic hyperfine field splitting of the 151Eu Mössbauer spectra at T = 6 K.

Circular dichroism in non-chiral metal halide perovskites.

We demonstrate theoretically that non-chiral perovskite layers can exhibit circular dichroism (CD) in the absence of a magnetic field and without chiral activation by chiral molecules. The effect is shown to be due to splitting of helical excitonic states which can form in structures of orthorhombic or lower symmetry that exhibit Rashba spin effects. The selective coupling of these helical exciton states to helical light is shown to give rise to circular dichroism. Polarization dependent absorption is shown to occur due to the combined effect of Rashba splitting, in-plane symmetry breaking, and the effect of the exciton momentum on its fine structure, which takes the form of Zeeman splitting in an effective magnetic field. This phenomenon, which can be considered as a manifestation of extrinsic chirality, results in significant CD with an anisotropy factor of up to 30% in orthorhombic perovskite layers under off-normal, top illumination conditions, raising the possibility of its observation in non-chiral perovskite structures.

Magnetic field mixing and splitting of bright and dark excitons in monolayer MoSe2

Monolayers of semiconducting transition metal dichalcogenides (TMDCs) with unique spin-valley contrasting properties and remarkably strong excitonic effects continue to be a subject of intense research interests. These model 2D semiconductors feature two fundamental intravalley excitons species–optically accessible ‘bright’ excitons with anti-parallel spins and optically inactive ‘dark’ excitons with parallel spins. For applications exploiting radiative recombination of bright excitons or long lifetime dark excitons, it is essential to understand the radiative character of the exciton ground state and establish the energy separation between the lowest energy bright and dark excitons. Here, we report a direct spectroscopic measure of dark excitons in monolayer MoSe2 encapsulated in hexagonal boron nitride. By applying strong in-plane magnetic field, we induce mixing and splitting of bright and dark exciton branches, which enables an accurate spectroscopic determination of their energies. We confirm the bright character of the exciton ground state separated by a 1.5 meV gap from the higher energy dark exciton state, much smaller compared to the previous theoretical expectations. These findings provide critical information for further improvement of the accurate theoretical description of TMDCs electronic structure.

Giant Fine Structure Splitting of the Bright Exciton in a Bulk MAPbBr3 Single Crystal.

Exciton fine structure splitting in semiconductors reflects the underlying symmetry of the crystal and quantum confinement. Because the latter factor strongly enhances the exchange interaction, most work has focused on nanostructures. Here, we report on the first observation of the bright exciton fine structure splitting in a bulk semiconductor crystal, where the impact of quantum confinement can be specifically excluded, giving access to the intrinsic properties of the material. Detailed investigation of the exciton photoluminescence and reflection spectra of a bulk methylammonium lead tribromide single crystal reveals a zero magnetic field splitting as large as ∼200 μeV. This result provides an important starting point for the discussion of the origin of the large bright exciton fine structure splitting observed in perovskite nanocrystals.

Magnetism and optical properties of Yb3Al5O12 hosted Er3+ – experiment and theory

Using the recently developed method based on a combination of DFT plane wave code applied to extract the crystal field parameters and a local atomic like Hamiltonian involving electron-electron, spin-orbit and Zeeman terms we calculated the energy levels of ground and excited multiplets of Yb3+ and Er3+ ions hosted in ytterbium and yttrium aluminum garnet (YbAG and YAG) including their crystal and magnetic field splitting. The obtained energy levels and derived magnetic properties are compared with the experimental data from magnetometry, photoluminiscence and near-infrared spectroscopy.

From 3D to 2D: Structural, Spectroscopic and Theoretical Investigations of the Dimensionality Reduction in the [PtAl2 ]δ- Polyanions of the Isotypic MPtAl2 Series (M=Ca-Ba, Eu).

Four new MPtAl2 (M=Ca, Sr, Ba, Eu) compounds, adopting the orthorhombic MgCuAl2 -type structure, have been synthesized from the elements using tantalum ampoules. All compounds are obtained as platelet-shaped crystallites and exhibit an increasing moisture sensitivity with increasing size of the formal M cation. Structural investigations indicate a pronounced elongation of the crystallographic b-axis, which results in a significant distortion of the [PtAl2 ]δ- polyanion. Within the polyanion, layer-like arrangements can be found with bonding Pt-Al interactions within the slab; the increase of the b-axis can be attributed to increasing Al-Al distances and therefore decreasing interactions between the slabs, caused by the differently-sized formal M cations. While the alkaline earth (M=Ca, Sr) representatives exhibit Pauli paramagnetism, BaPtAl2 shows diamagnetic behavior, finally EuPtAl2 is ferromagnetic with TC =54.0(5) K. The effective magnetic moment indicates that the Eu atoms are in a divalent oxidation state, which is confirmed by 151 Eu Mössbauer spectroscopic investigations. Measurements below the Curie-temperature show a full magnetic hyperfine field splitting with Bhf =21.7(1) T. 27 Al and 195 Pt magic-angle spinning NMR spectroscopy corroborates the presence of single crystallographic sites for the Pt and Al atoms. The large 27 Al nuclear electric quadrupolar coupling constants confirm unusually strong electric field gradients, in agreement with the structural distortions and the respective theoretical calculations. X-ray photoelectron spectroscopy has been utilized to investigate the charge transfer within the polyanion. The Pt 4f binding energy decreases with decreasing electronegativity / ionization energy of the alkaline earth elements, suggesting an increasing electron density at the Pt atoms. Theoretical investigations underline the platinide character of the investigated compounds by Bader charge calculations. The analysis of the integrated crystal orbital Hamilton population (ICOHP) values, electron localization function (ELF) and isosurface analyses lead to a consistent structural picture, indicating stable layer-like arrangements of the [PtAl2 ]δ- polyanion.

Interface states in polariton topological insulators

We address linear and nonlinear topological interface states in polariton condensates excited at the interface of the honeycomb and Lieb arrays of microcavity pillars in the presence of spin-orbit coupling and Zeeman splitting in the external magnetic field. Such interface states appear only in total energy gaps of the composite structure when parameters of the honeycomb and Lieb arrays are selected such that some topological gaps in the spectrum of one of the arrays overlap with topological or nontopological gaps in the spectrum of the other array. This is in contrast to conventional edge states at the interface of periodic topological and uniform trivial insulators, whose behavior is determined exclusively by the spectrum of the topological medium. The number of emerging interface states is determined by the difference of the Chern numbers of the overlapping gaps. Illustrative examples with one or two coexisting unidirectional interface states are provided. The representative feature of the system is the possibility of wide tuning of the concentration of power of the interface states between two limiting cases when practically all power is concentrated either in the Lieb or the honeycomb array. Localization of the interface states and their penetration depth into arrays drastically vary with Bloch momentum or upon modification of the amplitude of the interface state in the nonlinear regime. We illustrate topological protection of the interface states manifested in the absence of backscattering on interface defects, and study their modulation instability in the nonlinear regime. The latter leads to formation of quasisolitons whose penetration into different arrays also depends on Bloch momentum. In addition, we discuss the impact of losses and coherent pump leading to bistability of the interface states.

Transverse magneto-optical Kerr effect at narrow optical resonances

Abstract Magneto-optical spectroscopy based on the transverse magneto-optical Kerr effect (TMOKE) is a sensitive method for investigating magnetically-ordered media. Previous studies were limited to the weak coupling regime where the spectral width of optical transitions considerably exceeded the Zeeman splitting in magnetic field. Here, we investigate experimentally and theoretically the transverse Kerr effect in the vicinity of comparatively narrow optical resonances in confined quantum systems. For experimental demonstration we studied the ground-state exciton resonance in a (Cd,Mn)Te diluted magnetic semiconductor quantum well, for which the strong exchange interaction with magnetic ions leads to giant Zeeman splitting of exciton spin states. For low magnetic fields in the weak coupling regime, the Kerr effect magnitude grows linearly with increasing Zeeman splitting showing a dispersive S-shaped spectrum, which remains almost unchanged in this range. For large magnetic fields in the strong coupling regime, the magnitude saturates, whereas the spectrum becomes strongly modified by the appearance of two separate peaks. TMOKE is sensitive not only to the sample surface but can also be used to probe in detail the confined electronic states in buried nanostructures if their capping layer is sufficiently transparent.