Anomalies in the temperature dependence of the critical field in antiferromagnetic single crystal dysprosium

An intensive study of the temperature variation of the critical field, H_c, in antiferromagnetic dysprosium, reveals small, abrupt changes in the value of H_c at particular temperatures between the Néel temperature, T_N, and Curie temperature T_c. These measurements made on two single crystals of different quality, show that anomalies occur at ≈99, 114, 127, 131, 138, 146 and 153 K, and the jump in the critical field is ≈ 10^-2 T on each occasion. The anomalies are attributed to a distortion of the helical antiferromagnetic structure whenever the periodicity of the helix is commensurate with that of the hexagonal crystal lattice. Accompanying changes in the helical turn angle, Δω, are estimated and found to increase as the temperature approaches T_c.     

Green’s function approach to the low temperature properties of Cs<Subscript>2</Subscript>CuCl<Subscript>4</Subscript>: anisotropy effects

We have studied the effect of both axial and transverse anisotropy on the critical field and thermodynamic properties of the field induced three dimensional antiferromagnetic Heisenberg model on the frustrated hexagonal lattice for Cs₂CuCl₄ compound. The spin model is mapped to a bosonic one with the hard core repulsion constraint and the Green’s function approach has been implemented to get the low energy spectrum and the corresponding thermodynamic properties. To find the critical field (B _c ) we have looked for the Bose-Einstein condensation of quasi-particles (magnons) which takes place when the magnon spectrum vanishes at the ordering spiral wave vector. We have also obtained the dispersion of magnon spectrum in the critical magnetic field for each anisotropy parameter to find the spiral wave vector where the spectrum gets its minimum. The magnon energies show a linear dispersion relation close to the quantum critical point. The effect of hard core boson interaction on the single particle excitation energies leads to a temperature dependence of the magnon spectrum versus magnetic field. We have also studied the behavior of specific heat and static structure factor versus temperature and magnetic field.     

The magnetic phases of NdCu2

The magnetic phase diagram of a NdCu₂ single crystal is investigated by means of specific-heat measurements and neutron diffraction as a function of temperature and external magnetic field applied along the crystallographic b-direction. In the low temperature region we observe three commensurate phases AF1, F1, and F2. Their magnetic structures all consist of ferromagnetic (bc)-planes with different stacking sequences along the a-direction comprising 5, 3 and 8 chemical unit cells, respectively. Above 2.8 T the system is in a ferromagnetically aligned state (F3). Furthermore, there is an incommensurate phase AF3 between the low temperature commensurate phases and the paramagnetic state and, in a very narrow temperature region of only 0.2 K, an intermediate phase AF2 between AF1 and AF3. The Nd-moments are oriented along the b-direction in all phases.     

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.     

Anisotropy of Hc2 in Rb0.2WO3

The T_c and H_c2 of hexagonal single crystals Rb_0.2WO₃ were measured. Upper critical field rotation data in the plane perpendicular to the c-axis showed a large anisotropy with a 60° periodicity. Rotation in a plane containing the c-axis showed an even larger anisotropy having 180° symmetry.     

Deviations from the Curie-Weiss law in paramagnetic dysprosium and terbium-50% holmium

The magnetic susceptibilities of single crystal dysprosium and terbium-50% holmium have been measured in their paramagnetic phases. The effect of annealing has been investigated and heating the sample to ≈ 360 K for ≈ 18 h causes ≈ 4% reduction in χ₂₇₃. Abrupt departures from Curie-Weiss behaviour occur at ≈ 257, 227, 199 K in Dy, and at 250, 214 and 197 K in Tb-50% Ho, coinciding with previously observed anomalies in the thermal expansion. This behaviour is attributed to the presence of residual antiferromagnetic order in the paramagnetic phase which is perturbed when the periodicity of the helical spin structure, estimated from neutron diffraction data, is commensurate with the hexagonal crystal lattice.     

Investigation of temperature dependence of surface anisotropy field and constant in the system of BaFe12O19 nanocrystals

We show a possibility to determine the parameters characterizing surface magnetic anisotropy of platelet BaFe₁₂O₁₉ nanocrystals with thickness comparable to the magnetoperturbed surface layer of high-anisotropic hexagonal crystal. Taking into account the above-mentioned specific character of the particles, we introduce the constant K_S as the surface anisotropy energy per unit volume of near-surface layer. Temperature dependence of the surface anisotropy field as one of the components of effective anisotropy was corrected taking into account the thermal fluctuations. Discovered anomaly initiated calculation of the surface anisotropy constant with different approaches for two different temperature ranges. Analyzing the K_S sign changes with temperature, we conclude about the transformation of surface anisotropy from plane to axis type.     

On the field dependence of the interface energy in AF/FM bilayers

In the investigations of antiferromagnetic (AF)/ferromagnetic (FM) bilayer samples, often distinct experimental techniques yield different values for the measured exchange anisotropy field (H_E). We propose that the observed discrepancy may be accounted in part by the dependence of the unidirectional anisotropy with the value of the externally applied cooling field (h). Using a simple microscopic model for representing the AF/FM interface, which incorporates the effect of interface roughness, we show that the interface energy between the AF and FM layer indeed varies with h, as recently observed in anisotropic magnetoresistance measurements, lending support to our proposal.     

Determination of the in-plane anisotropy field in hexagonal systems via rotational magnetization: Theoretical model and Monte Carlo simulations

The magnetic anisotropy field in thin films with in-plane uniaxial anisotropy can be deduced from the VSM magnetization curves measured in magnetic fields of constant magnitudes. This offers a new possibility of applying rotational magnetization curves to determine the first- and second-order anisotropy constant in these films. In this paper we report a theoretical derivation of rotational magnetization curve in hexagonal crystal system with easy-plane anisotropy based on the principle of the minimum total energy. This model is applied to calculate and analyze the rotational magnetization process for magnetic spherical particles with hexagonal easy-plane anisotropy when rotating the external magnetic field in the basal plane. The theoretical calculations are consistent with Monte Carlo simulation results. It is found that to well reproduce experimental curves, the effect of coercive force on the magnetization reversal process should be fully considered when the intensity of the external field is much weaker than that of the anisotropy field. Our research proves that the rotational magnetization curve from VSM measurement provides an effective access to analyze the in-plane anisotropy constant K ₃ in hexagonal compounds, and the suitable experimental condition to measure K ₃ is met when the ratio of the magnitude of the external field to that of the anisotropy field is around 0.2. Supported by the National Natural Science Foundation of China (Grant Nos. 90505007 and 10774061) Recommended by LI FaShen     

Rapid anisotropic diffusion of lithium in electrochromic thin films based on the hexagonal tungsten bronze structure

The chemical diffusion coefficient of lithium in oxidized potassium hexatungstate and reduced hexagonal potassium tungsten bronze films was measured by the galvanostatic transient method. Two-dimensional anisotropic diffusion was found in the hexagonal hexatungstates, while no appreciable anisotropy was observed in samples with the potassium hexagonal tungsten bronze structure. The chemical diffusion coefficients along the c-axis in thin films of the tungstates K_0.33WO_3.165 and K_0.3WO_3.15 (about 6000 Å thick) are about 10^?10 cm²/s, while those along the a-axis are about 10^?7 cm²/s. This latter value is about the same to those measured in a potassium hexagonal tungsten bronze single crystal of composition K_0.28WO₃ which was grown electrochemically. It is most likely that the presence of the additional oxygen atoms in the tunnels within the hexatungstate structure is responsible for the large decrease in the rate of motion of lithium along the c-axis that leads to the anisotropy in the macroscopic diffusion coefficient in this crystal structure.     

Incommensurate phases in ferromagnetic spin-chains with weak antiferromagnetic interchain interaction

We study planar ferromagnetic spin-chain systems with weak antiferromagnetic inter-chain interaction and dipole-dipole interaction. The ground state depends sensitively on the relative strengths of antiferromagnetic exchange and dipole energies κ = J′a ² c/(g _L μ _B )². For increasing values of κ, the ground state changes from a ferromagnetic via a collinear antiferromagnetic and an incommensurate phase to a 120° structure for very large antiferromagnetic energy. Investigation of the magnetic phase diagram of the collinear phase, as realized in CsNiF₃, shows that the structure of the spin order depends sensitivly on the direction of the magnetic field in the hexagonal plane. For certain angular domains of the field incommensurate phases appear which are seperated by commensurate phases. When rotating the field, the wave vector characterizing the structure changes continously in the incommensurate phase, whereas in the commensurate phase the wave vector is locked to a fixed value describing a two-sublattice structure. This is a result of the competition between the exchange and the dipole-dipole interaction.     

Anisotropy of the electrical conductivity in W-type hexagonal ferrites BaFe18O27 and BaCo2Fe16O27 from first principles

The electronic ground structure and the anisotropy of the electrical conductivity in W-type hexagonal ferrite BaFe₁₈O₂₇ and BaCo₂Fe₁₆O₂₇ have been investigated using the generalized gradient approximation (GGA) plus Hubbard U (GGA+U) calculation. In BaFe₁₈O₂₇, because of the presence of mixed valence states at Fe 6g sites, a half metallic peak appears in energy gap and it results in an “electrical conductive layer”. Using a model in which Fe at 6g sites is assumed to be partially replaced by Co, the electronic ground structure of BaCo₂Fe₁₆O₂₇ and the origin of the electrical conductive anisotropy have been studied. Replacement of Fe at 6g site of BaFe₁₈O₂₇ by Co causes the mixed valence states of Fe cations at 6g sites to vanish and the carrier density to lower. Also, it is shown that effective mass of carrier along c axis is much heavier than that perpendicular to c axis in both of materials from electronic energy band calculation. This is the reason why the electrical resistivities of both materials along c axis are much higher than that perpendicular to axis.     

Sinusoidal incommensurate structure in spiral antiferromagnets

It is shown, that in hexagonal antiferromagnets, the form of incommensurate structure depends on the ratio of dipole-dipole energy to the anisotropic interaction energy at fixed values of exchange constants. In CsCuCl₃-type compounds, in which the spiral magnetic structure realizes along the c-axis and 120° structure - in the c-plane, there appears a new sinusoidal phase in the external field H>H_c, where H_c is a critical field. Thus, in result, two modulated structures form at intermediate temperatures.     

Commensurability oscillations in NdBa2Cu3Oy single crystals

Commensurability between inter-vortex distance and crystal lattice constant is investigated by angular dependent magnetization in very pure twinned and twin-free NdBa₂ Cu₃ O_y single crystals. With increasing temperature the incommensurate states split up and become finally commensurate with half the vortex distance. These new commensurate states are related to a substructure of the intrinsic pinning potential within the unit cell and discussed with respect to temperature, field, anisotropy, and twin structure.     

Heat-Treatment Induced Magnetic Anisotropy of GaMnSb Films

Conditions and mechanisms of controlled variation of the magnetic anisotropy of GaMnSb films containing magnetic MnSb nanoinclusions by means of heat treatment have been determined. For this purpose, the temperature and magnetic-field dependences of the magnetic moments of samples before and after thermal annealing were measured using a SQUID magnetometer. It is established that the heat treatment of GaMnSb films leads to a significant increase in the values of characteristics determined by the magnetic anisotropy, including the growth of blocking temperature (from 95 to 390 K) and the magnetic anisotropy field (from 330 to 630 Oe). Results of transmission electron microscopy investigation indicate that a change in the magnetic anisotropy of GaMnSb films as a result of their thermal annealing can be related to a transition of the crystalline structure of magnetic MnSb nanoinclusions from hexagonal (space group P6₂/mmc) to cubic (space group F-43m).     

Magnetostriction and the magnetic phases of single crystal terbium-50% holmium

The c-axis magnetostriction, λ_c, has been measured in terbium-50% holmium in fields up to 2 T between the Néel and Curie temperatures. The magnitude and temperature dependence of λ_c are similar to those previously reported for dysprosium. Detailed strain measurements between the critical field, H_c, which destroys the antiferromagnetic spiral spin structure and the field induced ferromagnetic phase show that the extent of an intermediate fan phase is more limited than previous theoretical analyses have predicted. The difference between the experimental data and strains calculated from theory can be explained only in part by the influence of magnetostry calline anisotropy.     

Studies of selenium and selenium dioxide isochromats

The allotropic forms of selenium, hexagonal and amorphous, and selenium dioxide have been studied by the isochromat method. A high vacuum spectrometer provided with bent crystal and water cooled targets was used. It is shown that a shift of the short wave-length limit of the continuous X-ray spectrum occurs for a semiconductor in comparison with a metal. The shift of hexagonal Se is found to be 1.7 ± 0.2 V, amorphous Se 1.5±0.3 V and SeO₂ 1.3 ± 0.2 V. The temperature was held at about 320 °K for the amorphous sample and at 400 °K for the others. The shifts of hexagonal and amorphous Se are in good agreement with the energy band gaps found by other methods. The fine structure near the short wave-length limit is discussed considering the Nijboer theory. Attempts have been made to explain the isochromat structure by comparison withL _I -absorption and characteristic energy loss spectra. The characteristic energy loss values found by the present method, which impliesreappearing intervals in the isochromats, have been compared with the theoretical values of? ω _p , given by the plasma oscillation theory.     

Temperature dependence of coercivity and metamagnetism in Tb0.5Y0.5Ni

The temperature dependences of magnetic properties of the FeB structure compound Tb_0.5Y_0.5Ni are examined with the aim to elucidate the origin of intrinsic magnetic hardness in this compound. The easy a axis coercivity of an aligned powder sample is found to be strongly temperature dependent. A domain wall activation model is employed to obtain the parameters H₀(0)=30kOe, V_V(0)=0.24K^?1, and β=0.016K^?1, where H₀(0) is the coercive force at absolute zero, V_T(0) the domain wall activation parameter, and β the coefficient for the linear temperature dependence of the reduced anisotropy. From polycrystalline data, we find a strong temperature dependence of the c axis metamagnetic transition only for the ferromagnetic (F) to antiferromagnetic (AF) direction. From the relative constancy of the AF to F c axis metamagnetic transition compound to the a axis coercivity we conclude that the coercive force is not directly related to the local molecular fields as had been previously suggested.     

Crystalline anisotropy energy of uniaxial antiferromagnets evaluated from low field torque data

The influence of the magnetocrystalline anisotropy energy on the static torque of uniaxial antiferromagnets is investigated. It is shown that this influence provides a method for accurate determination of the first anisotropy constant K₁ of most uniaxial antiferromagnets. Experimental results are shown from measurements on the hexagonal polymorph of FeGe.     

Time relaxation of dielectric constant in the commensurate phase of TlGaSe2

The results of measurements of the time dependences of the dielectric constant of TlGaSe₂ in the commensurate ferroelectric phase are presented. From the result of the observation of the decay of ε at different stabilized temperatures below the commensurate phase transition temperature after cooling from the incommensurate phase, the presence of two different characteristic relaxation time constants with the same temperature behaviour has been revealed. This peculiarity is considered as a result of a coexistence of two polar sublattices in the temperature range below 110 K. According to these results, the previously reported dielectric anomaly at about 103 K is considered as a final lock-in phase transition accompanied by the forming of the antiferroelectric state in TlGaSe₂.