Tetragonal Crystal Field Research Articles

Magneto-transport properties of pseudo-single-crystal Mn4N thin films

The anisotropic magnetoresistance (AMR) effect and the anomalous Hall effect (AHE) were investigated in the temperature range of 5–300 K for a pseudo-single-crystal Mn4N thin film. The sign of the AMR ratio changed from positive to negative when the temperature was lowered. Below 100 K, the cos 2θ component of the AMR curves significantly increased in magnitude, and a cos 4θ component appeared. Based on the electron scattering theory, which takes into account the tetragonal crystal field effect, it is suggested that the dominant scattering process in the Mn4N film is up-spin conduction electrons into up-spin d orbitals. The magnitude of the anomalous Hall conductivity (σAH) slightly increased with decreasing temperature, from 300 K to 150 K, and then it drastically dropped when the temperature was below 100 K. A sign change for σAH, from negative to positive, was observed at 30 K. The starting temperature at 100 K for the drastic change in the AHE corresponds well with that of the AMR, suggesting that the splitting of the 3d orbitals due to the tetragonal crystal field effect causes these low-temperature anomalies.

Negative anisotropic magnetoresistance resulting from minority spin transport in NixFe4−xN (x = 1 and 3) epitaxial films

We grew 50 nm-thick NixFe4−xN (x = 1 and 3) epitaxial films on a SrTiO3(001) single-crystal substrate by molecular beam epitaxy and measured their anisotropic magnetoresistance (AMR) ratios rAMR in the temperature range of 5–300 K with current directions set along either NixFe4−xN [100] or [110]. A negative rAMR was obtained up to 200 K or higher. Their magnitude |rAMR| increased with decreasing temperature. From the negative AMR effect and the negative spin-polarization of density of states for NixFe4−xN at the Fermi level, it can be stated that the minority spin transport is dominant in NixFe4−xN, similar to Fe4N and Co3FeN. The rAMR depends on the current direction that arises from the current direction dependence of s-d scattering. In the case of Ni3FeN, the rAMR decreased to nearly zero at 260 K. This temperature agreed well with the Curie temperature determined from the temperature dependence of magnetization. The AMR curves were reproduced well by using both cos2ϕ and cos4ϕ components below 100 K, whereas a cos2ϕ component was enough to fit those obtained above 100 K. It is assumed that the tetragonal crystal field was enhanced at low temperatures (<100 K) similar to Fe4N (<50 K).

Vector chirality for effective total momentum Jeff in a nonfrustrated Mott insulator: Effects of strong spin-orbit coupling and broken inversion symmetry

I propose the emergence of the spin-orbital-coupled vector chirality in a non-frustrated Mott insulator with the strong spin-orbit coupling due to $ab$-plane's inversion-symmetry (IS) breaking. I derive the superexchange interactions for a $t_{2g}$-orbital Hubbard model on a square lattice with the strong spin-orbit coupling and the IS-breaking-induced hopping integrals, and explain the microscopic origins of the Dzyaloshinsky-Moriya (DM) -type and the Kitaev-type interactions. Then, by adopting the mean-field approximation to a minimal model including only the Heisenberg-type and the DM-type nearest-neighbor interactions, I show that the IS breaking causes the spin-orbital-coupled chirality as a result of stabilizing the screw state. I also highlight the limit of the hard-pseudospin approximation in discussing the stability of the screw states in the presence of both the DM-type and the Kitaev-type interactions, and discuss its meaning. I finally discuss the effects of tetragonal crystal field and $J_{\textrm{eff}}=\frac{3}{2}$ states, and the application to the iridates near the $[001]$ surface of Sr$_{2}$IrO$_{4}$ and the interface between Sr$_{2}$IrO$_{4}$ and Sr$_{3}$Ir$_{2}$O$_{7}$.

Nature of the Insulating Ground State of the 5d Postperovskite CaIrO3.

The insulating ground state of the 5d transition metal oxide CaIrO3 has been classified as a Mott-type insulator. Based on a systematic density functional theory (DFT) study with local, semilocal, and hybrid exchange-correlation functionals, we reveal that the Ir t(2g) states exhibit large splittings and one-dimensional electronic states along the c axis due to a tetragonal crystal field. Our hybrid DFT calculation adequately describes the antiferromagnetic (AFM) order along the c direction via a superexchange interaction between Ir^{4+} spins. Furthermore, the spin-orbit coupling (SOC) hybridizes the t(2g) states to open an insulating gap. These results indicate that CaIrO_{3} can be represented as a spin-orbit Slater insulator, driven by the interplay between a long-range AFM order and the SOC. Such a Slater mechanism for the gap formation is also demonstrated by the DFT + dynamical mean field theory calculation, where the metal-insulator transition and the paramagnetic to AFM phase transition are concomitant with each other.

Theoretical studies of the optical and EPR spectra for VO^{2+} in Na_{3}C_{6}H_{5}O_{7}·2H_{2}O single crystal

On the basis of the perturbation formulas for a $d^{1}$ configuration ion in a tetragonal crystal field, the three optical absorption bands and electron paramagnetic resonance (EPR) parameters ($g$ factors $g_{i}$ and hyperfine structure constants $A_{i}$ for $i = \|$ and $\perp$, respectively) of VO$^{2+}$ in Na$_{3}$C$_{6}$H$_{5}$O$_{7}\cdot2$H$_{2}$O single crystals were studied using the perturbation theory method. By simulating the calculated optical and EPR spectra to the observed values, local structure parameters and negative signs of the hyperfine structure constants $A_{i}$ of the octahedral (VO$_{6}$)$^{8-}$ cluster in trisodium citrate dehydrate single crystal can be obtained.

Magnetic excitations in a spin-orbit-coupledd4Mott insulator on the square lattice

We study the magnetic order and excitations in strong spin-orbit coupled, Van Vleck-type, $d^4$ Mott insulators on a square lattice. Extending the previous work, we include the tetragonal crystal field splitting and explore its effects on magnetic phase diagram and magnon spectra. Two different ordered phases, with in-plane and out-of-plane orientation of the staggered moments, are found for the higher and lower values of the crystal field splitting, respectively. The magnetic excitation spectra for paramagnetic and magnetically ordered phases are calculated and discussed in the context of a candidate spin-orbit $d^4$ Mott insulator Ca$_2$RuO$_4$.

CaIrO3: a spin-orbit Mott insulator beyond the j(eff) ground state.

In CaIrO3, electronic correlation, spin-orbit coupling, and tetragonal crystal field splitting are predicted to be of comparable strength. However, the nature of its ground state is still an object of debate, with contradictory experimental and theoretical results. We probe the ground state of CaIrO3 and assess the effective tetragonal crystal field splitting and spin-orbit coupling at play in this system by means of resonant inelastic x-ray scattering. We conclude that insulating CaIrO3 is not a j(eff) = 1/2 iridate and discuss the consequences of our finding to the interpretation of previous experiments. In particular, we clarify how the Mott insulating state in iridates can be readily extended beyond the j(eff) = 1/2 ground state.

Resonant X-Ray Scattering and thejeff=1/2Electronic Ground State in Iridate Perovskites

The resonant x-ray scattering (magnetic elastic, RXMS, and inelastic, RIXS) of Ir4+ at the L2,3 edges relevant to spin-orbit Mott insulators A(n+1)Ir(n)O(3n+1) (A = Sr, Ba, etc.) are calculated using a single-ion model which treats the spin-orbit and tetragonal crystal-field terms on an equal footing. Both RXMS and RIXS in the spin-flip channel are found to display a nontrivial dependence on the direction of the magnetic moment, μ. Crucially, we show that for μ in the ab plane, RXMS in the cross-polarized channel at the L2 edge is zero irrespective of the tetragonal crystal field; spin-flip RIXS, relevant to measurements of magnons, behaves reciprocally, being zero at L2 when μ is perpendicular to the ab plane. Our results have important implications for the assignment of a j(eff) = 1/2 ground state on the basis of resonant x-ray experiments.

Nonlinear strain dependence of magnetic anisotropy in CoFe2O4 films on MgO(001) substrates

CoFe2O4 films were deposited on MgO(001) substrates using pulsed laser deposition with various laser energy densities. We found that the CoFe2O4 films were grown in the (001) orientation and that the lattice constant of the CoFe2O4 films was dependent on the laser energy densities. Perpendicular magnetic anisotropy (PMA) was observed, but the lattice strain dependence was not consistent with the phenomenological model in which the PMA is in proportion to the lattice strain. The lattice strain dependence of PMA was compared with an electron theory in which the spin-orbit interaction and the tetragonal crystal field in the electronic state of a single Co ion are considered. The experimental result does not contradict with the calculation, which shows that the magnetic anisotropy is not proportional to the lattice strain and asymmetric in respect to negative and positive lattice strain.

Synthesis, XRD, TEM, EPR, and Optical Absorption Spectral Studies of CuZnO2Nanocompound

Synthesis of nano CuZnO2compound is carried out by thermal decomposition method. The crystalline phase of the material is characterized by XRD. The calculated unit cell constants area=3.1 Åandc=3.4786 Åand are of tetragonal structure. The unit cell constants are different from wurtzite (hexagonal) which indicate that a nanocompound is formed. Further TEM images reveal that the metal ion is in tetragonal structure with oxygen ligands. The prepared CuZnO2is then characterized for crystallite size analysis by employing transmission electron microscopy (TEM). The size is found to be 100 nm. Uniform bright rings are noticed in the TEM picture suggesting that the nanocrystals have preferential instead of random orientations. The selected-area electron diffraction (SAED) pattern clearly indicates the formation of CuO-ZnO nanocompound. The nature of bonding is studied by electron paramagnetic resonance (EPR). The covalency character is about 0.74 and thus the compound is electrically less conductive. Optical absorption spectral studies suggest that Cu(II) is placed in tetragonal elongation crystal field. The spin-orbit coupling constant,λ, is calculated using the EPR and optical absorption spectral results suggest some covalent bond between metal and ligand. Near infrared (NIR) spectra are due to hydroxyl and water fundamentals.

Theoretical investigation of the local structure of Cu2+ doped Bi2O3-ZnO-B2O3-Li2O glasses by their EPR and optical spectra

In this paper, the crystal-field theory and third-order perturbation formula of g factor and the hyperfine structure constants A for the 3d9 electronic configuration in the tetragonal crystal field are applied into the calculate of the electron paramagnetic resonance (EPR) parameters (g-factors g//, g⊥ and hyperfine structure constants A//, A⊥) and optical spectra. The quantitative relationship between the local lattice structure and EPR, optical spectra for the Cu2+ in Bi2O3-ZnO-B2O3-Li2O are established in the calculation. The obtained results are in good consistency with experimental findings. From the study, the core polarization constant κ≈0.37 was obtained. The variety of the bond length of tetragonal octahedron is ΔR≈R//−R//h≈0.05 Å. Thus, when Cu2+ doped in Bi2O3-ZnO-B2O3-Li2O glasses, due to the static Jahn–Teller effect, the lattice relaxation will lead to the small elongation distortion in the tetragonal octahedron.

Electronic Structure of CoO Nanocrystals and a Single Crystal Probed by Resonant X-ray Emission Spectroscopy

We have performed 2p X-ray absorption (XAS) and 2p3d resonant X-ray emission (RXES) experiments on a CoO bulk single crystal as well as on 4.2 nm CoO nanocrystals. The single crystal data were measured with linearly polarized incident X-rays in the scattering and perpendicular to the scattering plane. An unprecedented total experimental resolution of 100 meV allowed the first X-ray observation of the CoO 4T1g(4F) manifold that occurs 120 meV above ground state. Detailed theoretical modeling was performed to assess the tetragonal crystal field splitting, spin–orbit, and superexchange parameters for both the single crystal and the nanocrystals. We show that 2p XAS is mainly sensitive to the octahedral field and 3d spin–orbit coupling, while the 4T1g(4F) manifold in 2p3d RXES probes the tetragonal distortion and the superexchange interactions with high sensitivity. We observe that the nanocrystals have a reduced cubic crystal field splitting and a broadened 4T1g(4F) RXES manifold that we ascribe to a larger ...

Pressure Tuning of the Spin-Orbit Coupled Ground State inSr2IrO4

X-ray absorption spectroscopy studies of the magnetic-insulating ground state of Sr2IrO4 at ambient pressure show a clear deviation from a strong spin-orbit (SO) limit J(eff)=1/2 state, a result of local exchange interactions and a nonzero tetragonal crystal field mixing SO split J(eff)=1/2, 3/2 states. X-ray magnetic circular dichroism measurements in a diamond anvil cell show a magnetic transition at a pressure of ∼17 GPa, where the "weak" ferromagnetic moment is quenched despite transport measurements showing insulating behavior to at least 40 GPa. The magnetic transition has implications for the origin of the insulating gap and the nature of exchange interactions in this SO coupled system. The expectation value of the angular part of the SO interaction, <L·S>, extrapolates to zero at ∼80-90 GPa where an increased bandwidth strongly mixes J(eff)=1/2, 3/2 states and SO interactions no longer dominate the electronic ground state of Sr2IrO4.

An investigation of the spin-Hamiltonian parameters for Gd3+-doped YBa2Cu3O6+y (y = 0.06) superconductor

The spin-Hamiltonian parameters (g factors g∥ and g⊥ and zero-field splittings , , , and ) for Gd3+ ions at the tetragonal Y3+ site of YBa2Cu3O6+y (y = 0.06) superconductor are calculated together from a diagonalization (of the energy matrix) method based on the one-electron crystal field mechanism. In the method, a 56 × 56 energy matrix concerning the ground multiplet 8S7/2 and the excited multiplets 8L7/2 (where L = P, D, F, G, H, I) for 4f7 ions at a tetragonal crystal field and under an external magnetic field is constructed and used. The crystal field parameters in the energy matrix are obtained from the superposition model. The calculated results are in reasonable agreement with the experimental values. The defect structure (characterized by the angular distortion Δθ) of the Gd3+ impurity centers in YBa2Cu3O6+y is also acquired from the calculation. The results are discussed.

Investigations of the spin-Hamiltonian parameters and defect structures for Gd3+ ions in YMO4 (M=V, P, As) crystals

A 56×56 energy matrix containing the ground multiplet 8S7/2 and the excited multiplets 6L7/2 (where L=P, D, F, G, H, I) for 4f7 ion Gd3+ at a tetragonal crystal field and under an external magnetic field is constructed. By diagonalizing the energy matrix, the spin-Hamiltonian parameters (g factors g‖, g⊥ and zero-field splittings b20, b40, b44, b60, b64) for Gd3+ ion at the tetragonal Y3+ site of YMO4 (M=V, P, As) crystals are calculated. The calculated results are in reasonable agreement with the experimental values. The defect structures of Gd3+ centers in YMO4 crystals are estimated from the calculation. The results are discussed.

Alternating spin-orbital order in tetragonal Sr2VO4

Considering spin-orbit coupling, the tetragonal crystal field, and all relevant superexchange processes including quantum interference, we derive expressions for the energy levels of the vanadium ions in tetragonal Sr${}_{2}$VO${}_{4}$. The used parameters of the model Hamiltonian allow us to describe well the excitation spectra observed in neutron scattering and optical experiments at low temperatures. The free energy exhibits a minimum which corresponds to a novel alternating spin-orbital order with strong thermal fluctuation of the orbital mixing parameter.

Zero-field splitting of the ground state and local lattice distortions for Fe3+ ions at the tetragonal FeF5O cluster center in Fe3+:KMgF3 crystals

The relations between the zero-field splitting (ZFS) parameters and the structural parameters of the tetragonal FeF5O cluster center in Fe3+:KMgF3 crystals have been established by means of the microscopic spin Hamiltonian theory and the superposition model (SPM). On the basis of this, the local structure distortions, the second-order ZFS parameter D, the fourth-order one (a+2F/3), and the energy level separations Δ1 and Δ2 of the ground spin state for Fe3+ ion doped in Fe3+:KMgF3 crystals are theoretically investigated. We use complete diagonalization method (CDM) and take into account the electronic magnetic interactions, i.e. the spin–spin (SS), the spin-other-orbit (SOO), and the orbit–orbit (OO) interactions, besides the well-known spin–orbit (SO) interaction. This investigation reveals that the replacement of O2− for F− and the induced lattice relaxation ΔR2(O), combined with an inward relaxation of the nearest five fluorine ions ΔR1(F) give rise to a strong tetragonal crystal field, which yields the large ZFS of the ground state. The theoretically calculated parameters D, (a+2F/3), Δ1, and Δ2 for Fe3+:KMgF3 crystals are in good agreement with experimental ones when the five F− ions move toward Fe3+ by |ΔR1(F)|=6.40×10−4nm and the O2− ion toward Fe3+ by |ΔR2(O)|=10.55×10−3nm.

Crystal electric field parameters for Yb3+ ion in YbRh2Si2

The tetragonal crystal electric field parameters for Yb3+ ion in YbRh2Si2 are determined from the analysis of the literature data on angle-resolved photoemission, inelastic neutron scattering and electron paramagnetic resonance.

Local structure distortion and spin Hamiltonian parameters for Cr3+−VZn tetragonal defect centre in Cr3+ doped KZnF3 crystal

The quantitative relationship between the spin Hamiltonian parameters (D, g‖, Δg) and the crystal structure parameters for the Cr3+−VZn tetragonal defect centre in a Cr3+:KZnF3 crystal is established by using the superposition model. On the above basis, the local structure distortion and the spin Hamiltonian parameter for the Cr3+−VZn tetragonal defect centre in the KZnF3 crystal are systematically investigated using the complete diagonalization method. It is found that the VZn vacancy and the differences in mass, radius and charge between the Cr3+ and the Zn2+ ions induce the local lattice distortion of the Cr3+ centre ions in the KZnF3 crystal. The local lattice distortion is shown to give rise to the tetragonal crystal field, which in turn results in the tetragonal zero-field splitting parameter D and the anisotropic g factor Δg. We find that the ligand F− ion along [001] and the other five F− ions move towards the central Cr3+ by distances of Δ1 = 0.0121 nm and Δ2 = 0.0026 nm, respectively. Our approach takes into account the spin—orbit interaction as well as the spin—spin, spin—other-orbit, and orbit—orbit interactions omitted in the previous studies. It is found that for the Cr3+ ions in the Cr3+:KZnF3 crystal, although the spin—orbit mechanism is the most important one, the contribution to the spin Hamiltonian parameters from the other three mechanisms, including spin—spin, spin—other-orbit, and orbit—orbit magnetic interactions, is appreciable and should not be omitted, especially for the zero-field splitting (ZFS) parameter D.

Theoretical investigations of the local structure distortion and the spin Hamiltonian parameters of Cr 3+ ions at tetragonal charge-compensation defect CrF 5O site in Cr 3+: KMgF 3 crystals

The local structure distortion and the spin Hamiltonian (SH) parameters, including the zero-field splitting (ZFS) parameter D and the Zeeman g-factors g ‖ and g ⊥, are theoretically investigated by means of complete diagonalization method (CDM) and the microscopic spin Hamiltonian theory for tetragonal charge compensation CrF 5O defect center in Cr 3+:KMgF 3 crystals. The superposition model (SPM) calculations are carried out to provide the crystal field (CF) parameters. This investigation reveals that the replacement of O 2− for F − and its induced lattice relaxation Δ 1(O 2−) combined with an inward relaxation of the nearest five fluorine Δ 2(F −) give rise to a strong tetragonal crystal field, which in turn results in the large ZFS and large anisotropic g-factor Δg. The experimental SH parameters D and Δg can be reproduced well by assuming that O 2− moves towards the central ion Cr 3+ by Δ 1(O 2−)=0.172R 0 and the five F − ions towards the central ion Cr 3+ by Δ 2(F −)=0.022 R 0. Our approach takes into account the spin–orbit (SO) interaction as well as the spin–spin (SS), spin–other-orbit (SOO), and orbit–orbit (OO) interactions omitted in previous studies. This shows that although the SO interaction is the most important one, the contributions to the SH parameters from other three magnetic interactions are appreciable and should not be omitted, especially for the ZFS parameter D.