Planar ferromagnets: Low-velocity kink dynamics near to the easy plane and static solitary spin structures bifurcating from the azimuthal kink

Ferromagnetic spin chains with planar single ion anisotropy, exchange anisotropy and with an external fieldb applied in the easy plane are considered in classical continuum approximation. It is pointed out that in the static case the sine-Gordon approximation is only accidentally exact: it breaks down in the neighborhood of the easy plane already for infinitesimal kink velocities, unlessb0. It is also shown that at certain valuesb _n ,n=0, 1, 2, 3, ... of the applied field there bifurcate from the static in-plane kink (azimuthal kink) other static out-of-plane kink solutions. The azimuthal kink is linearly stable below the critical strengthb ₀ of the applied field. For increasingb, there occurs at each of the bifurcation fieldsb ₁<b ₂<b ₃... an instability with respect to an additional mode. In the undamped system the instabilities atb _2k ,k=0, 1, 2, ... are associated with the recently discovered soft-velocity change mechanism of the critical slowing-down, whereas atb _2k+1 , soft localized dynamic modes occur. If phenomenological spin damping is included, soft relaxation modes occur in the neighborhood of all the bifurcation fields.Work supported by the Swiss National Science Foundation     

Out-of-plane exchange bias and magnetic anisotropy in MnPd/Co multilayers

Magnetic and structural properties in [MnPd/Co]₁₀ multilayers deposited onto Si(1 1 1) substrates have been investigated. The dependences of anisotropy and exchange bias on the thicknesses of both MnPd and Co layers have been studied. In most of the samples, the out-of-plane magnetic anisotropy and both large out-of-plane and in-plane exchange biases have been observed at cryogenic temperature below the blocking temperature T_B≈240 K. With appropriate MnPd and Co thicknesses, we have obtained samples with a large out-of-plane exchange bias along with a large out-of-plane magnetic anisotropy. The origin of the out-of-plane magnetic anisotropy in the samples has been suggested to be due to the formation of CoPd interfacial alloys which have tensile in-plane strains, while the spin structure of the antiferromagnetic layer at the interface which is believed to be responsible for exchange bias may be the same as that of the bulk material. Also, the present study shows that the interplay between the out-of-plane magnetic anisotropy and exchange bias is evident in our multilayers and plays an important role in the out-of-plane exchange-bias mechanism.     

Transport properties and the anisotropy of Ba1 − x K x Fe2As2 single crystals in normal and superconducting states

The transport and superconducting properties of Ba_{1 ? x} K _x Fe₂As₂ single crystals with T _c ≈ 31 K were studied. Both in-plane and out-of-plane resistivity was measured by a modified Montgomery method. The in-plane resistivity is almost the same for all studied samples, unlike the out-of-plane resistivity, which differs considerably. We have found that the resistivity anisotropy γ = ρ _c /ρ _ab is almost independent of temperature and lies in the range 10–30 for the studied samples. This indicates the extrinsic nature of high out-of-plane resistivity, which may be due to the presence of flat defects along Fe-As layers in the samples. This statement is supported by comparatively small effective mass anisotropy, obtained from the upper critical field measurements, and from the observation of the so-called “Friedel transition,” which indicates the existence of some disorder in the samples in the c-direction.     

Thickness dependence of magnetic anisotropic properties of FeCoNd films

The magnetic FeCoNd films with thickness (t) from 50 to 166 nm were fabricated by RF magnetron co-sputtering at ambient condition. The amorphous structures of all of the films were investigated by X-ray diffraction and transmission electron microscopy. A spin reorientation transition from in-plane single domain state to out-of-plane stripe domain state was observed as a function of t. When t is below a critical thickness, magnetic moments lie in the film plane corresponding to in-plane single domain state because of the strong demagnetization energy. However, when t is increased, out-of-plane stripe domain structure was developed due to a dominated perpendicular magnetic anisotropy. Scanning electron microscopy data indicate that the perpendicular anisotropy, which is responsible for the formation of stripe domains, may result from the shape effect of the columnar growth of the FeCo grains.     

Exact results for the dynamics of the classical one dimensional easy plane ferromagnet at low temperatures

The in-plane and out-of-plane dynamical correlation functions for the classical one dimensional easy plane ferromagnet are calculated asymptotically exactly at low temperatures. The results are restricted to temperatures much below the crossover temperature at which spins begin aligning in the plane. The long wavelength behavior of the in-plane fluctuations is consistent with dynamical scaling, in contrast to the isotropic case, and agrees with the results of Villain and of Nelson and Fisher. The linewidths for the in-plane fluctuations at short wavelengths are calculated exactly, and approach those of the isotropic model for small anisotropy. The theory of Villain, the theory of Cieplak and Sjolander, and the simulations of Loveluck, Jauslin, Schneider and Stoll all give incorrect results for these linewidths. The out of plane linewidths show an anomalous temperature dependence due to a singularity in the three spin wave density of states that is characteristic of one dimensional systems. The linewidth is proportional toT ² lnT except at the wavevector for which the second derivative of the spin wave frequency with respect to wavevector vanishes (/2 for CsNiF₃) where the linewidth is proportional toT ^5/3. The linewidth has a strong discontinuity as the wavevector increases as a result of a catastrophe occurring in the calculation of the three spin wave density of states. The position and strength of the discontinuity are temperature dependent. The diffusion coefficient is logarithmically dependent on the anisotropy, and diverges as (T ² lnD)^–1, which is consistent with the (lnT)^–1 behavior predicted for the isotropic ferromagnet in earlier work. The results are derived for the case of single ion anisotropy, using a spin wave theory for static correlations and the spin current damping function, and can be readily extended to the case of anisotropic exchange.     

Anisotropy and dynamic properties of Co2MnGe Heusler thin films

Co₂MnGe films of 30 and 50 nm in thickness were grown by RF-sputtering. Their magnetic anisotropies, dynamic properties and the different excited spin wave modes have been studied using conventional ferromagnetic resonance (FMR) and Microstrip line FMR (MS-FMR). From the in-plane and the out-of-plane resonance field values, the effective magnetization (4πM_eff) and the g-factor are deduced. These values are then used to fit the in-plane angular-dependence of the uniform precession mode and the field-dependence of the resonance frequency of the uniform mode and the first perpendicular standing spin wave to determine the in-plane uniaxial, the four-fold anisotropy fields, the exchange stiffness constant and the magnetization at saturation. The samples exhibit a clear predominant four-fold magnetic anisotropy besides a smaller uniaxial anisotropy. This uniaxial anisotropy is most probably induced by the growth conditions.     

Nuclear spin-electron coupling of copper at microkelvin temperatures

The nuclear spin-electron coupling of copper has been determined by establishing stationary temperature differences between nuclei and electrons at electronic temperatures of 15 K to 5 mK in magnetic fields of 2 mT to 440 mT using a well-defined heat flow from the electrons to the nuclear spin system. The measured Korringa constantk increases proportional toB/T _e ² with decreasing electronic temperatureT _e and with increasing magnetic fieldB. At the lowest temperaturesk is more than an order of magnitude larger than its high temperature value.     

Dynamics of the anisotropic two-dimensional XY model

In this paper we study the dynamics of the two-dimensional XY model with single-ion anisotropy, and spin S = 1, in the large D phase, and low temperatures, using the bond operator formalism. The in-plane structure factor is a delta function. The out of plane shows a three peak structure, which merges in a single peak at the Brillouin zone boundary. We analyze also spin currents generated by a magnetic field gradient. The spin conductivity is calculated, at finite temperature, using the Kubo formula. The model shows unconventional ballistic spin transport at finite temperature. The computed spin conductivity exhibits a nonzero Drude weight at finite temperature. For ω< 2m, where m is the energy gap, the spin conductivity is described solely by the Drude weight. There is a regular contribution to the spin conductivity for ω> 2m, which persist in the zero temperature limit. The conductivity at the critical point, and for small frequencies, is (gμ_B)²/ħ times a universal scaling function of ħω/k_B T.     

Spin fluctuations in the stacked-triangular antiferromagnet YMnO<Subscript>3</Subscript>

The spectrum of spin fluctuations in the stacked-triangular antiferromagnet YMnO₃ was studied above the Néel temperature using both unpolarized and polarized inelastic neutron scattering. We find an in-plane and an out-of-plane excitation. The in-plane mode has two components just above T _N : a resolution-limited central peak and a Debye-like contribution. The quasi-elastic fluctuations have a line width that increases with q as Dq ^z and the dynamical exponent z = 2.3. The out-of-plane fluctuations have a gap at the magnetic zone center and do not show any appreciable q dependence at small wave vectors.     

Magnetic flux distribution in the bulk of the pure type-II superconductor niobium measured with positive muons

The spin precession of positive muons in ultra-pure Nb single crystals of high perfection, cooled down in transverse magnetic fields 0.68B _c2≤B _appl≤0.84B _c2 (B _c2=upper critical field) from temperatures well above the superconducting transition temperatureT _c=9.25 K, has been investigated in the temperature range 2.6 K≤T≤8.0 K. The experiments confirm the periodic fieldB(r) of triangular flux-line lattices as calculated from numerical solutions of the microscopic BCS-Gor'kov theory. The observed broadening of the van Hove singularities in the field distribution is discussed in terms of the combined effects of muon diffusion and random perturbations of the flux-line lattice.     

Crystal imperfections and structural phase transitions in perovskites

High‐resolution X-ray scattering measurements of the antiferrodistortive phase transitions in the perovskites SrTiO₃, RbCaF₃ and KMnF₃ have recently revealed the existence of two length scales in the critical scattering above T_e . Here we review these observations and discuss how they might be related to the well known existence of two time scales (the "central peak" problem) in the critical dynamic response function above T_e . We reach the tentative conclusion that within a few degrees of T_e both the time and length scales of the fluctuations are strongly influenced by defects and that the intrinsic critical behaviour is swamped by these effects in most crystals.     

Resistivity anisotropy and charge density wave in 2H - NbSe2 and 2H - TaSe2

The in-plane and out-of-plane resistivities of both 2H-TaSe₂ and 2H-NbSe₂ were determined down to 10 K. For both compounds, the resistivity anisotropy shows notably a slope change at temperatures where a CDW transition is expected to occur. On the other hand, for both compounds the resistivity anisotropy at the lowest temperature of measurement is much greater than expected by the Lawrence–Doniach model, which relates the critical magnetic field anisotropy to the normal state resistivity anisotropy for 3D-anisotropic superconductors.     

Strong Anisotropic Thermal Conductivity in Polycrystalline Layers of (AgxSn1-xS)1.2(TiS2)2 with Prospects Toward Improved Thermoelectric Performance

Anisotropic tuning is of crucial importance for designing and developing high-performance thermoelectric materials. Here, a prominent anisotropic thermoelectric characteristic of Ag-substituted misfit-layered (SnS)_1.2(TiS₂)₂ alloys is investigated in the perpendicular (in-plane) and parallel (out-of-plane) to the pressing direction. In the in-plane direction, the (Ag_xSn_1-xS)_1.2(TiS₂)₂ alloys possess a highest power factor of 0.86 mW K⁻² m⁻¹ at 520 K, while in the out-of-plane direction the lowest lattice thermal conductivity (0.37 W K⁻¹ m⁻¹) is achieved, which is driven by the natural intercalated structure where the out-of-plane phonon is strongly scattered without affecting the in-plane mobility. Moreover, along the in-plane orientation, the introduced point defects due to the substitution of Sn by Ag trigger a significant reduction of lattice thermal conductivity. In contrast, along the out-of-plane orientation, the decreased carrier concentration enables a large Seebeck coefficient and power factor, ultimately ensuring high thermoelectric performance. The present finding in the misfit-layered chalcogenide opens up a new route to manipulating thermoelectrics via anisotropy engineering.     

Theoretical study of enhanced ferromagnetism and tunable magnetic anisotropy of monolayer CrI3 by surface adsorption

Magnetic anisotropy energy (MAE) plays a key role for 2D magnetic materials, which have attracted significant attention for their promising applications in spintronic devices. Based on first-principles calculations, we have investigated the influence of surface adsorption on the ferromagnetism and MAE of monolayer CrI₃. We find that Li adsorption can dramatically enhance its ferromagnetism, and tune its easy magnetization axis to the in-plane direction from original out-of-plane at certain coverage of Li. The monotonic enhancement of in-plane magnetism in CrI₃ as the coverage of Li increases are attributed to electrostatic doping induced by charge transfer between Li atoms and I atoms, as supported by the charge doping simulation. The tunable robust magnetic anisotropy may open new promising applications of CrI₃–based materials in spintronic devices.     

Local magnetic properties of ultrathin ferromagnetic fcc-Fe-films on Cu(001)

Conversion electron Mössbayer spectroscopy (CEMS) on three monolayers (ML) thick metastable fcc-Fe(001) films grown epitaxially on a Cu(001) substrate under different conditions shows that these films are characterized by a distributionP(B _hf) of magnetic hyperfine fieldsB _hf. The vast majority of⁵⁷Fe nuclei experience relatively large hyperfine fields at low temperature. The temperature dependence of the most probable fieldB _peak was found to follow aT ^3/2 spin-wave law below 300 K. It is shown from the relative line intensities that preferential Fe spin orientation perpendicular to the film plane exists in films grown at 120 K, while preferential in-plane spin orientation is found for a growth temperature of 300 K. Coating a low-temperature grown Fe film by 2 ML of Cu(001) drastically reduces the hyperfine field, in contrast to the case of room-temperature grown Cu-coated films.Dedicated to Professor Ulrich Gonser on the occasion of his 70th birthday     

Strain-induced ferroelectric phase transitions in incipient ferroelectric rutile TiO2

Uniaxial strain induced ferroelectric phase transitions in rutile TiO₂ are investigated by first-principles calculations. The calculated results show that the in-plane tensile strain induces rutile TiO₂, paraelectric phase with P_4-2/mnm (D_4h) space group, to a ferroelectric phase with P_m (C_s) space group,driven by the softening behaviour of the E_u1 mode. In addition, the out-of-plane tensile strain, vertical to the ab plane, leads to a ferroelectric phase with P_42nm (C_4v) space group, driven by the softening behaviour of the A_2u mode. The critical tensile strains are 3.7% in-plane and 4.0% out-of-plane, respectively. In addition, the in-plane compression strain, which has the same structure variation as out-of-plane tensile strain due to Poisson effect, leads the paraelectric rutile TiO₂ to a paraelectric phase with P_nnm (D_2h) space group driven by the softening behaviour of the B_1g mode. These results indicate that the sequence ferroelectric (or paraelectric) phase depends on the strain applied. The origin of ferroelectric stabilization in rutile TiO₂ is also discussed briefly in terms of strain induced Born effective charge transfer.     

Polarized neutron scattering studies of the kagomé lattice antiferromagnet

We report polarized neutron scattering studies of spin-wave excitations and spin fluctuations in the lattice antiferromagnet KFe₃(OH)₆(SO₄)₂ (jarosite). Inelastic polarized neutron scattering measurements at 10 K on a single crystal sample reveal two spin gaps, associated with in-plane and out-of-plane excitations. The polarization analysis of quasi-elastic scattering at 67 K shows in-plane spin fluctuations with XY symmetry, consistent with the disappearance of the in-plane gap above the Néel temperature . Our results suggest that jarosite is a promising candidate for studying the 2D XY universality class in magnetic systems.     

Possible Fulde-Ferrell-Larkin-Ovchinnikov inhomogeneous superconducting state in CeCoIn5

We present specific heat and thermal conductivity of the heavy fermion superconductor CeCoIn5 in the vicinity of the superconducting critical fieldH _c2, measured with magnetic field in the plane of this quasi-2D compound and at temperatures down to 50 mK. The superconducting phase diagram and the first order nature of the superconducting phase transition at high fields close to a critical fieldH _c2 indicate the importance of the Pauli limiting effect in CeCoIn₅. In the same range of magnetic field we observe a second specific heat anomaly within the superconducting state, and interpret it as a signature of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) inhomogeneous superconducting state. In addition, the thermal conductivity data as a function of field display a kink at a fieldH _k below the superconducting critical field, which closely coincides with the low temperature anomaly in specific heat tentatively identified with the appearance of the FFLO superconducting state. The enhancement of thermal conductivity within the FFLO state calls for further theoretical investigations of the real space structure of the order parameter (and in particular, the structure of vortices) and of the thermal transport within the inhomogeneous FFLO state.     

Photon mass and the fieldB (3)

The connection between finite photon mass and the fieldB ⁽³⁾ is developed with reference to special relativity in the vacuum. The existence of the physical and longitudinal fieldB ⁽³⁾ implies that there are three degrees of polarization associated with the photon, which cannot therefore be a massless boson. The fieldB ⁽³⁾ can be observed experimentally through the magnetization of a plasma with microwave pulses, and this experiment serves to demonstrate unequivocally the existence of photon mass.     

Magnetization and configurational anisotropy in magnetic clusters: Monte Carlo simulation

Based on the Monte Carlo simulation, the magnetic properties of the clusters, e.g. magnetization, Curie temperature, hysteresis, coercivity, natural angle and energy distribution etc., have been calculated. It has been found that, for the pure ferromagnetic cluster, the T^3/2 Bloch law is well satisfied at low temperature (T < 0.5 T_C) and B_sur is equal to 3 B_bulk. Meanwhile, there are clear indications that B increases drastically with the reducing atomic number Nwhich is consistent with the experimental facts. The results have been evalucted using the Bloch exponent law in the approximate crystalline approximation. It has also been demonstrated that the size dependence of the Curie temperature can be described by finite-size scaling theory. The investigation of the hysteresis and the spin configurations in different magnetization processes reveals the existence of an easy magnetization direction and anisotropy. The thermal coercivity for the clusters with zero and finite uniaxial anisotropy matches the experimental results well. The simulated results for the natural angle and energy distribution in the clusters prove further the existence of the configurational anisotropy in the clusters. It has been discussed that the natural angle and energy distribution influence the hysteresis of a cluster.Received: 10 September 2003, Published online: 15 March 2004PACS: 75.75. + a Magnetic properties of nanostructures - 75.40.Mg Numerical simulation studies - 75.60.Ej Magnetization curves, hysteresis, Barkhausen and related effects - 75.40.Cx Static properties (order parameter, static susceptibility, heat capacities, critical exponents, etc.)