Magnetic properties of Fe<Subscript>3</Subscript>O<Subscript>4</Subscript> surface

The magnetic properties of the magnetite Fe₃O₄(110) surface have been studied by spin resolved Auger electron spectroscopy (SRAES). Experimental spin resolved Auger spectra are presented. The results of calculation of Auger lines polarization carried out on the basis of electronic state density are presented. Problems related to magnetic moments of bivalent (Fe²⁺) and trivalent (Fe³⁺) ions on the Fe₃O₄(110) surface are discussed. It is established that the deposition of a thin bismuth film on the surface results in significant growth of polarization of iron Auger peaks, which is due to additional spin-orbit scattering of electrons by bismuth atoms.     

Electronic structure of paramagnetic In<Subscript>1-x</Subscript>Mn<Subscript>x</Subscript> As nanowires

The electronic structure, spin splitting energies, and g factors of paramagnetic In_1-xMn_xAs nanowires under magnetic and electric fields are investigated theoretically including the sp-d exchange interaction between the carriers and the magnetic ion. We find that the effective g factor changes dramatically with the magnetic field. The spin splitting due to the sp-d exchange interaction counteracts the Zeeman spin splitting. The effective g factor can be tuned to zero by the external magnetic field. There is also spin splitting under an electric field due to the Rashba spin-orbit coupling which is a relativistic effect. The spin-degenerated bands split at nonzero k_z (k_z is the wave vector in the wire direction), and the spin-splitting bands cross at k_z = 0, whose k_z-positive part and negative part are symmetrical. A proper magnetic field makes the k_z-positive part and negative part of the bands asymmetrical, and the bands cross at nonzero k_z. In the absence of magnetic field, the electron Rashba coefficient increases almost linearly with the electric field, while the hole Rashba coefficient increases at first and then decreases as the electric field increases. The hole Rashba coefficient can be tuned to zero by the electric field.     

Helimagnetism in gallium substituted LuMn<Subscript>6</Subscript>Ge<Subscript>6</Subscript> studied by nuclear magnetic resonance

Zero-field nuclear magnetic resonance (NMR) of all NMR isotopes (¹⁷⁵Lu, ⁵⁵Mn, ⁷³Ge, ^69,71Ga) in LuMn₆Ge_6-xGa_x, 0 ≤ x ≤ 1, is used to monitor the variation of the hyperfine interaction with the sequence of antiferromagnetic - helimagnetic - ferromagnetic arrangement of the manganese moments of subsequent Kagomé net planes achieved by variation of the gallium content x. According to the ⁵⁵Mn-NMR results, the local Mn moment varies by less than ±5% in this series. ¹⁷⁵Lu-NMR proves canting of the antiferromagnetic sublattices in LuMn₆Ge₆. The anisotropy of the Ge magnetic hyperfine interaction decreases with increasing separation from the hexagonal Lu plane, whereas the absolute value of its isotropic part is only qualitatively correlated with the average separation of the six nearest Mn neighbours. Due to the anisotropic magnetic and electric hyperfine interaction at Ge and Ga sites, the non-collinear magnetic structures are clearly reflected by the NMR spectra, which are described quantitatively in this contribution. The preferred Mn moment direction rotates away from the c direction with x. The conduction or bonding electron spin polarization at the Ga nuclei is increased by 35–80% compared to the Ge nuclei. We argue that this is related with the variation of the magnetic order with the Ga content.     

A phenomenological theory for polarization flop in spiral multiferroic TbMnO<Subscript>3</Subscript>

A phenomenological Landau theory has been used to explain magnetic field-driven polarization flop in TbMnO ₃. The Néel wall-like magnetic structure in spiral multiferroics induces a space-dependent internal magnetic field which exerts a torque on spins to rotate bc-spiral to ab-spiral. The external magnetic field is argued to be competing with easy axis anisotropy and the system stabilizes when anisotropy is minimum. With the help of Landau free energy with DM magnetoelectric coupling and a general ansatz for magnetization, the phenomenon of polarization flop has been explained. Relation between T_flop and critical magnetic field has been established and found to be in good agreement with the experiment. This could be an indication that anisotropy of the system is temperature- and magnetic field-dependent.     

Ferroelectricity generated by spin-orbit and spin-lattice couplings in multiferroic DyMnO3

While the ferroelectricity in type-II multiferroic rare-earth manganites is believed to be generated by the inverse Dzyaloshinskii-Moriya (DM) interaction (spin-orbit coupling) associated with the Mn spiral spin order, recent results revealed the strong spin-lattice coupling arising from the Dy-Mn spin interaction in DyMnO₃, which may also be an ingredient contributing to the ferroelectricity. In this work, we summarize our recent experiments on this issue by performing a series of rare-earth site nonmagnetic Y and magnetic Ho substitutions at Dy site for DyMnO₃. It is demonstrated that the Dy-Mn spin interaction contributes to the ferroelectric polarization through the symmetric exchange striction mechanism (spin-lattice coupling). A coexistence of the spin-orbit coupling and spin-lattice coupling in one compound is confirmed. At the same time, the independent Dy antiferromagnetic spin order at low temperature can be effectively suppressed by the substitutions, beneficial to the polarization enhancement.     

Galvanomagnetic properties of polycrystalline manganese selenide Gd<Subscript>0.2</Subscript>Mn<Subscript>0.8</Subscript>Se

The electrical and galvanomagnetic properties of the Gd_0.2Mn_0.8Se solid solutions are investigated in zero magnetic field and in a field of 13 kOe in the temperature range of 80–400 K. The negative magnetoresistance below room temperature and hysteresis of the I–V characteristics are found. The change in the magnetoresistance sign and thermopower with increasing temperature is established. The carrier type is determined from the Hall constant; the difference between the thermopower and Hall coefficient signs at high temperatures is established. The experimental data are explained using the model of orbital ordering and spin-orbit interaction.     

Colossal magnetodielectric effect in SmFe<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript> multiferroic

The colossal (more than threefold) decrease in the dielectric constant ɛ in the easy-plane SmFe₃(BO₃)₄ ferroborate in a magnetic field of ∼5 kOe applied in the basal ab plane of the crystal has been found. A close relation of this effect to anomalies in the field dependence of the electric polarization has been established. It has been shown that this magnetodielectric effect is due to the contribution to ɛ from the electric susceptibility, which is related to the rotation of spins in the ab plane, arises in the region of the antiferromagnetic ordering T < T _N = 33 K, and is suppressed by the magnetic field. A theoretical model describing the main features of the behavior of ɛ and electric polarization in the magnetic field has been proposed, taking into account the additional anisotropy in the basal plane induced by the magnetoelastic stresses.     

Density-functional characterization of the multiferroicity in spin spiral chain cuprates

The ferroelectricity of the spiral magnets LiCu2O2 and LiCuVO4 was examined by calculating the electric polarizations of their spin spiral states on the basis of density-functional theory with spin-orbit coupling. Our work unambiguously reveals that spin-orbit coupling is responsible for the ferroelectricity with the primary contribution from the spin-orbit coupling on the Cu sites, but the asymmetric density distribution responsible for the electric polarization occurs mainly around the O atoms. The electric polarization is calculated to be much greater for the ab-plane than for the bc-plane spin spiral. The observed spin-spiral plane is found to be consistent with the observed direction of the electric polarization for LiCuVO4, but inconsistent for LiCu2O2.     

Effects of the Rashba spin-orbit coupling on Hofstadter's butterfly

We study the effect of Rashba spin-orbit coupling on the Hofstadter spectrum of a two-dimensional tight-binding electron system in a perpendicular magnetic field. We obtain the generalized coupled Harper spin-dependent equations which include the Rashba spin-orbit interaction and solve for the energy spectrum and spin polarization. We investigate the effect of spin-orbit coupling on the fractal energy spectrum and the spin polarization for some characteristic states as a function of the magnetic flux α and the spin-orbit coupling parameter. We characterize the complexity of the fractal geometry of the spin-dependent Hofstadter butterfly with the correlation dimension and show that it grows quadratically with the amplitude of the spin-orbit coupling. We study some ground state properties and the spin polarization shows a fractal-like behavior as a function of α, which is demonstrated with the exponent close to unity of the decaying power spectrum of the spin polarization. Some degree of spin localization or distribution around +1 or -1, for small spin-orbit coupling, is found with the determination of the entropy function as a function of the spin-orbit coupling. The excited states show a more extended (uniform) distribution of spin states.     

Perfect valley polarization in MoS<Subscript>2</Subscript>

We study perfect valley polarization in a molybdenum disulfide (MoS₂) nanoribbon monolayer using two bands Hamiltonian model and non-equilibrium Green’s function method. The device consists of a one-dimensional quantum wire of MoS₂ monolayer sandwiched between two zigzag MoS₂ nanoribbons such that the sites A and B of the honeycomb lattice are constructed by the molecular orbital of Mo atoms, only. Spin-valley coupling is seen in energy dispersion curve due to the inversion asymmetry and time-reversal symmetry. Although, the time reversal symmetry is broken by applying an external magnetic field, the valley polarization is very small. A valley polarization equal to 46% can be achieved using an exchange field of 0.13 eV. It is shown that a particular spin-valley combination with perfect valley polarization can be selected based on a given set of exchange field and gate voltage as input parameters. Therefore, the valley polarization can be detected by detecting the spin degree of freedom.     

Anomalous magnetism of the nanocrystalline oxide TiO<Subscript>2</Subscript> surface

The magnetic properties of an oxygen-deficient nanocrystalline undoped titanium dioxide synthesized by the gas-phase, electric-explosion, and chemical method have been studied. The defect state was controlled using reduction treatments in vacuum or in a hydrogen atmosphere. It is shown that the defect state of the surface of nanocrystalline oxides (for example, the existence of vacancies in the anion sublattice and other defects) has a dominant influence on the formation of the magnetic properties of the samples under study. The main contributions to the magnetism of TiO₂ nanoparticles after the reduction treatments are the paramagnetic contribution of the matrix, the paramagnetic Curie–Weiss contribution, and the contribution of the spontaneous magnetic moment provided by the existence of regions with different spin ordering. A heterogeneous magnetic state is found to exist in the TiO₂ nanopowders; for example, at low temperatures, shifted hysteresis loops are observed as a result of a possible set of magnetic states with different spin orders. It is shown that a soft compaction or grinding of nanopowders in an agate mortar lead to substantial increase in the magnetization, sometimes, by a factor of more than two, regardless of the nanopowder synthesis method and the initial phase state of TiO₂ (anatase or rutile structures). This experimental fact proves the key role of the surface defects and the magnetic moment carriers with different spin configurations localized mainly on the nanoparticle surface. The compaction changes the magnetization only in the case when the initial magnetic state has a nonlinear “quasi-superparamagnetic” character of the magnetization curve. As a result of predominant exchange interaction between the nanoparticles with a frustrated character of spin ordering on the nanoparticles surface, the ferromagnetic contribution increases as nanoparticles contact.     

Influence of the ground state of the Pr<Superscript>3+</Superscript> ion on magnetic and magnetoelectric properties of the PrFe<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript> multiferroic

The magnetic, magnetoelectric, and magnetoelastic properties of a PrFe₃(BO₃)₄ single crystal and the phase transitions induced in this crystal by the magnetic field are studied both experimentally and theoretically. Unlike the previously investigated ferroborates, this material is characterized by a singlet ground state of the rare-earth ion. It is found that, below T _N = 32 K, the magnetic structure of the crystal in the absence of the magnetic field is uniaxial (l ∥ c), while, in a strong magnetic field H ∥ c (H _cr ～ 43 kOe at T = 4.2 K), a Fe³⁺ spin reorientation to the basal plane takes place. The reorientation is accompanied by anomalies in magnetization, magnetostriction, and electric polarization. The threshold field values determined in the temperature interval 2–32 K are used to plot an H-T phase diagram. The contribution of the Pr³⁺ ion ground state to the parameters under study is revealed, and the influence of the praseodymium ion on the magnetic and magnetoelectric properties of praseodymium ferroborate is analyzed.     

Far-infrared optical excitations in multiferroic TbMnO<Subscript>3</Subscript>

We provide a detailed study of the reflectivity of multiferroic TbMnO₃ for wave numbers from 40 cm^-1 to 1000 cm^-1 and temperatures 5 K < T < 300 K. Excitations are studied for polarization directions E || a, the polarization where electromagnons are observed, and for E || c, the direction of the spontaneous polarization in this material. The temperature dependencies of eigenfrequencies, damping constants and polar strengths of all modes are studied and analyzed. For E || a and below the spiral ordering temperature of about 27 K we observe a transfer of optical weight from phonon excitations to electromagnons, which mainly involves low-frequency phonons. For E || c an unusual increase of the total polar strength and hence of the dielectric constant is observed indicating significant transfer of dynamic charge probably within manganese-oxygen bonds on decreasing temperatures.     

Interrelation between the soliton lattice and electric polarization in RMn<Subscript>2</Subscript>O<Subscript>5</Subscript> oxides

Magnetic transitions from the paramagnetic state to an incommensurate magnetic structure and then to an ordered phase with long-range antiferromagnetic order in RMn₂O₅ (R is a rare-earth ion) oxides are analyzed. It is shown that a transition from the paramagnetic to the incommensurate phase is associated with exchange as well as relativistic interactions and can be described, apart from the basic magnetic order parameter, by an associated order parameter (viz., electric polarization along the y axis of the crystal). As a result of such a transition, the emergence of electric polarization in the crystal is not accompanied by a change in crystal symmetry.     

Valence fluctuations in CeIn3 under the effect of pressure

The impacts of pressure on the structural and electronic properties of CeIn₃ have been calculated. The calculations are performed in the presence and the absence of spin-orbit interaction as well as GGA+U using density functional theory within the PBE-GGA approximation. It is shown that energy and density of states analyses are considerably influenced by the spin-orbit interaction. The spin and orbital magnetic moments of Ce are calculated under pressure up to 22 GPa. An almost linear relation is observed between the magnetic moment and the density of states of Ce-4f at Fermi level. At ambient pressure, a good agreement between the values of the electric field gradients, EFG, and bulk modulus with experimental results is observed. The strongest anisotropy in charge distribution originates from In-5p orbital, which has the main contribution to EFG.     

The magnetoelectric effects in weak ferromagnetic YMn<Subscript>2</Subscript>O<Subscript>5</Subscript> modulated structure: a Landau theory approach

According to the group theory approach, linear magnetoelectric effect (ME) can not be obtained for the spatial group of YMn₂O₅, which was known to be mmm. Regard to the magnetic structure of these type of materials, we propose a magnetic group structure for the YMn₂O₅ by considering spin orientation of the Mn³⁺ and Mn⁴⁺ ions. According to the landau theory of phase transition it can be shown, how symmetrical rules result in relationship between quantities such as magnetic order, polarization, and etc. This relation shows a weak ferromagnetic state, associated with spontaneous polarization, arisen by Dzyaloshinskii-Moriya type interaction and a field induced change in magnetoelectrical susceptibility.     

Magnetic phase transitions,soliton lattices,and electric polarization in <Emphasis Type="Italic">R</Emphasis>Mn<Subscript>2</Subscript>O<Subscript>5</Subscript> multiferroics

The magnetic phase transitions in RMn₂O₅ oxides were analyzed. It was shown that the transition from the paramagnetic phase to the incommensurate phase is described by not only the basic magnetic parameter but also an associated order parameter: electric polarization along the y axis of the crystal. It was established that the antiferromagnetic-incommensurate phase transformation is a second-order phase transition, accompanied by a decrease in electric polarization.     

Dynamical magnetoelectric coupling in helical magnets

We develop a theory of collective mode dynamics in the helical magnets coupled to electric polarization via spin-orbit interaction. The low-lying modes associated with the ferroelectricity are not the transverse optical phonons, but are the spin waves hybridized with the electric polarization. This hybridization leads to the Drude-like dielectric function epsilon(omega) in the limit of zero magnetic anisotropy. There are two additional low-lying modes: phason of the spiral and rotation of helical plane along the polarization axis. Role of these low-lying modes in the neutron scattering and antiferromagnetic resonance is revealed, and a novel experiment to detect the dynamical magnetoelectric coupling is discussed.     

Ferroelectricity in the magnetic E-phase of orthorhombic perovskites

We show that the symmetry of the spin zigzag chain E phase of the orthorhombic perovskite manganites and nickelates allows for the existence of a finite ferroelectric polarization. The proposed microscopic mechanism is independent of spin-orbit coupling. We predict that the polarization induced by the E-type magnetic order can potentially be enhanced by up to 2 orders of magnitude with respect to that in the spiral magnetic phases of TbMnO3 and similar multiferroic compounds.     

Electronic structures of ternary iron arsenides <Emphasis Type="Italic">A</Emphasis>Fe<Subscript>2</Subscript>As<Subscript>2</Subscript> (<Emphasis Type="Italic">A</Emphasis> = Ba,Ca, or Sr)

We have studied the electronic and magnetic structures of the ternary iron arsenides AFe₂As₂ (A = Ba, Ca, or Sr) using the first-principles density functional theory. The ground states of these compounds are in a collinear antiferromagnetic order, resulting from the interplay between the nearest and the next-nearest neighbor superexchange antiferromagnetic interactions bridged by As 4p orbitals. The correction from the spin-orbit interaction to the electronic band structure is given. The pressure can reduce dramatically the magnetic moment and diminish the collinear antiferromagnetic order. Based on the calculations, we propose that the low energy dynamics of these materials can be described effectively by a t-J _H -J ₁-J ₂-type model [2008, arXiv: 0806.3526v2].