Magnetic properties of erbium iron garnet in high magnetic fields up to 150kOe

The magnetic properties of single crystals of erbium iron garnet (ErIG) were studied in applied fields up to 150kOe between 1.4 and 300K. At low temperature, the macroscopic easy direction of the bulk magnetization is [100]; below the compensation temperature (80±2K), the magnetization presents non-linear field evolution. On the assumption of an isolated ground doublet, the anisotropy constantsK _i (i=1,2) of ErIG are given byK _i (Er)+K _i (YIG); theK _i are calculated as a function of theG andg tensor components. It is worthwhile noting that theK _i (Er) are strongly temperature dependent; so at low temperature the anisotropy of the garnet is determined by the rare earth ions, while in the 50 K regionK ₁(Er) becomes comparable toK ₁(YIG) with the opposite sign which results in a very weak anisotropy of the garnet. Above 50 K,K ₁(YIG) is predominant and the Fe³⁺ ions determine the garnet anisotropy.     

Some estimates for magnetic fluctuations in a turbulent medium

A new integral relationship between the fluctuations b(r, t) of a magnetic field and its mean B ₀(r, t) is derived for the steady-state magnetic field in a turbulent medium. This formula provides the estimate 〈b?curlb〉=?B ₀?curlB ₀. Simultaneously, the coefficient of amplification of the mean magnetic field α effect) is obtained: α=(η+β)B ₀? curlB ₀/B ₀ ² . The formula for α allows for a decrease in this coefficient owing to the back action of the magnetic field on the turbulent velocity field. It is shown that the Zel’dovich’s estimate 〈 b ²〉?β/η B ₀ ² for two-dimensional turbulence holds for magnetic fields at the instant the fluctuations 〈a ²〉 of the vector potential, rather than 〈b ²〉, reach a maximum. Here, η and β are the ohmic (molecular) and turbulent diffusion coefficients, respectively. This estimate is refined with allowance made for the fact that the condition for diffusion approximation itself relates the β, b, and B ₀ quantities to each other.     

Magnetic properties of HoFe3(BO3)4

The magnetic properties of an antiferromagnet with trigonal symmetry, namely, HoFe₃(BO₃)₄, have been investigated theoretically. The calculations have been performed in the molecular field approximation and in the framework of the crystal field model for the rare-earth subsystem. Extensive experimental data on the magnetic properties of HoFe₃(BO₃)₄ have been interpreted and good agreement between theory and experiment has been achieved using the obtained theoretical dependences. The spontaneous spin-reorientation transition and the spin-reorientation transition induced by a magnetic field B ‖ a from the easy-axis to easy-plane state, as well as the spin-flop transition in a magnetic field B ‖ c, have been described. It has been shown that the spontaneous spin-reorientation transition is a magnetic analog of the Jahn-Teller effect. The temperature dependences of the initial magnetic susceptibility at temperatures ranging from 2 to 300 K, the nonlinear curves of magnetization for B ‖ c and B ⊥ c in a magnetic field up to 1.2 T (which indicate the occurrence of first-order phase transitions), and their evolution with variations in the temperature have been described, as well as the temperature and field dependences of the magnetization in a magnetic field up to 9 T. The parameters of the trigonal crystal field for the rare-earth ion Ho³⁺ and the parameters of the Fe-Fe and Ho-Fe exchange interactions have been determined in the course of interpretation of the experimental data.     

Two-dimensional representation of position, velocity and acceleration by PFG-NMR

A novel view on the presentation of pulsed field-gradient nuclear magnetic resonance experiments to encode position and translational displacements is given. A conventional diffusion or flow experiment employing two magnetic field gradients of effective areak ₁, andk ₂ separated by a time interval Δ can formally be expressed as a means to probek space in a two-dimensional way. While for most applications, a full coverage of the [k ₁,k ₂] space is not necessary, an experiment withk ₁ = ?k ₂ can be regarded as a sampling of the secondary diagonal in [k ₁,k ₂] space. Likewise, the main diagonal is represented by the conditionk ₁ =k ₂ and encodes position. Thus, the [r ₁,r ₂] space conjugate to [k ₁,k ₂], which is obtained by Fourier transformation, can be transferred into a position/displacement correlation plot simply by rotation of the coordinate system by an angle of 45°. While displacementR =r ₂ ?r ₁ corresponds to an average velocity? =R/Δ, an extension towards higher-order derivations such as acceleration is straightforward by modification of the pulse sequence. We discuss this new concept in a general way, treating both the magnetic field and the particle position by Taylor expansions with respect to space and time, respectively, and present examples for fluid flowing through capillary systems in the light of the suggested interpretation.     

Nuclear magnetic resonance in noncollinear antiferromagnet Mn3Al2Ge3O12

The ⁵⁵Mn nuclear magnetic resonance spectrum of noncollinear 12-sublattice antiferromagnet Mn₃Al₂Ge₃O₁₂ has been studied in the frequency range of 200–640 MHz in the external magnetic field H ‖ [001] at T = 1.2 K. Three absorption lines have been observed in fields less than the field of the reorientation transition H _c at the polarization h ‖ H of the rf field. Two lines have been observed at H > H _c and h ⊥ H. The spectral parameters indicate that the magnetic structure of manganese garnet differs slightly from the exchange triangular 120-degree structure. The anisotropy of the spin reduction and (or) weak antiferromagnetism that are allowed by the crystal symmetry lead to the difference of ≈3% in the magnetization of sublattices in the field H < H _c. When the spin plane rotates from the orientation perpendicular to the C ₃ axis to the orientation perpendicular to the C ₄ axis, all magnetic moments of the electronic subsystem decrease by ≈2% from the average value in the zero field.     

Nonmonotonic magnetic-field dependence of transport coefficients for n-Bi-Sb semiconducting alloys

The transport coefficients of tellurium-doped n-Bi_{1 ? x} Sb _x semiconducting alloys (0.07 ≤ x ≤ 0.15) are studied for single-crystal samples in the temperature range 1.5 ≤ T ≤ 40 K and in magnetic fields 0 ≤ H < 20 kOe. The theory developed in this study attributes the specific features in the behavior of the transport coefficients observed in a magnetic field to a strong anisotropy of the electron spectrum and anisotropy in the electron relaxation time. It is found that the dependences of the transport coefficients on the magnetic field for H ∥ C ₃ can be theoretically expressed through one anisotropy parameter δ, and those for H ∥ C ₂, by means of several anisotropy parameters, namely, γ, η, ζ, and m ₃/m ₁. It is established that the anisotropy parameter δ in the n-Bi-Sb semiconducting alloys can be estimated from measurements of the electrical resistivity ρ₂₂(∞)/ρ₂₂(0) ? δ and the Hall coefficient R _12.3(∞)/R _12.3(H → 0) ? δ in a magnetic field H ∥ C ₃. It is shown that the observed increase in the thermoelectric efficiency by a factor of 1.5–2.0 in the transverse magnetic fields H ∥ C ₃ and H ∥ C ₂ originates from the nonmonotonic dependence of the diffusion component of the thermopower Δα₂₂(H)(?T ∥ C ₁) on the magnetic field. The nonmonotonic dependence of the diffusion thermopower in n-Bi-Sb semiconducting alloys is associated with the strong anisotropy of the electron spectrum, the anisotropy in the electron relaxation time, and the many-valley pattern of the spectrum.     

Phase diagram of antiferromagnetic cobalt fluoride

The H-T phase diagram of antiferromagnetic cobalt fluoride in an external magnetic field H perpendicular to the easy magnetization axis A is completed and used to construct a phase diagram in the variables H _z and H _y . In this diagram, the lines corresponding to second-order phase transitions (between an angular phase and a phase with antiferromagnetic vector I ⊥ A) begin and end in fields of a spin-flip transition (i.e., in an exchange field). A peculiarity of these lines of phase transitions is that each of them has two tricritical points at which this line of second-order phase transitions transforms into a line of first-order phase transitions. A critical angle between the direction of the external magnetic field and the basal plane within which the first-order phase transition takes place is determined.     

Anisotropic resonant magnetoplasticity of NaCl crystals in the Earth’s magnetic field

Resonant relaxation of the dislocation structure under the action of crossed magnetic fields, i.e., constant magnetic field of the Earth (B _Earth) and alternating radio-frequency field ( $\tilde B$ ), has been experimentally studied in a series of dielectric (NaCl) crystals with various compositions of impurities under variations in the frequency, direction of the pumping field $\tilde B$ , and orientation of the samples in the Earth’s magnetic field. The frequency dependence of the dislocation path length l(ν) exhibits peaks with various heights (l _max) and resonant frequencies (ν_res). The maximum resonant effect has been observed for dislocations with the direction L orthogonal to the plane of crossed magnetic fields in a configuration of mutually perpendicular vectors {L, $\tilde B$ , B _Earth} belonging, together with sample edges {a, b, c}, to the 〈100〉 system. Variation of the concentration C of calcium impurity in crystals of the NaCl_Ca series only influenced the resonant peak height as $l_{\max } \propto 1/\sqrt C $ . Rotation of the magnetic field $\tilde B$ in the (b, c) plane from direction $\tilde B$ ⊥ B _Earth to $\tilde B$ ∥ B _Earth also did not influence the frequency of the resonance but changed its amplitude. Depending on the crystal type, this influence changed from rather insignificant (in crystals of the NaCl_LOMO series) to complete suppression of the effect for $\tilde B$ ∥ B _Earth (in the NaCl_Nik series). The resonant frequency ν_res is sensitive to orientation of the sample with respect to B _Earth. Upon rotation of the crystal by the angle θ = ∠(c, B _Earth) about the a ⊥ B _Earth edge, the initial peak for dislocations L ‖ a at the crystal orientation θ = 0 and the frequency ν _res ⁰ is replaced by a pair of peaks at frequencies ν_{1, 2} ≈ ν _res ⁰ cosθ_{1, 2}, where θ₁ = 90° ? θ and θ₂ = θ. Previously, these peaks were observed separately in NaCl_Nik crystals for $\tilde B$ ∥ c and $\tilde B$ ∥ b. In the present study, these peaks have been observed simultaneously for both orientations of $\tilde B$ in NaCl_LOMO and NaCl_Ca crystals, where the resonance is not completely suppressed for $\tilde B$ ∥ B _Earth.     

Effect of Temperature Anisotropy on Various Modes and Instabilities for a Magnetized Non-relativistic Bi-Maxwellian Plasma

Using kinetic theory for homogeneous collisionless magnetized plasmas, we present an extended review of the plasma waves and instabilities and discuss the anisotropic response of generalized relativistic dielectric tensor and Onsager symmetry properties for arbitrary distribution functions. In general, we observe that for such plasmas only those modes whose magnetic-field perturbations are perpendicular to the ambient magnetic field, i.e., B ₁ $\bot $ B ₀, are effected by the anisotropy. However, in oblique propagation all modes do show such anisotropic effects. Considering the non-relativistic bi-Maxwellian distribution and studying the relevant components of the general dielectric tensor under appropriate conditions, we derive the dispersion relations for various modes and instabilities. We show that only the electromagnetic R- and L- waves, those derived from them (i.e., the whistler mode, pure Alfvén mode, firehose instability, and whistler instability), and the O-mode are affected by thermal anisotropies, since they satisfy the required condition $\mathbf{B}_{1}\bot \mathbf{B}_{0}$ . By contrast, the perpendicularly propagating X-mode and the modes derived from it (the pure transverse X-mode and Bernstein mode) show no such effect. In general, we note that the thermal anisotropy modifies the parallel propagating modes via the parallel acoustic effect, while it modifies the perpendicular propagating modes via the Larmor-radius effect. In oblique propagation for kinetic Alfvén waves, the thermal anisotropy affects the kinetic regime more than it affects the inertial regime. The generalized fast mode exhibits two distinct acoustic effects, one in the direction parallel to the ambient magnetic field and the other in the direction perpendicular to it. In the fast-mode instability, the magneto-sonic wave causes suppression of the firehose instability. We discuss all these propagation characteristics and present graphic illustrations. The threshold conditions for different instabilities are also obtained.     

States of cobalt fluoride in a strong magnetic field

The behavior of the magnetic subsystem of cobalt fluoride is investigated in a strong magnetic field oriented in an arbitrary direction in space. In the case where the magnetic field is out of the planes passing through the easiest magnetization axis A and the axis [100] ‖ X or through the easiest magnetization axis A and the axis [010] ‖ Y, it follows from the derived system of equations that the antiferromagnetic vector l does not change direction to be align with the basal plane, provided the magnetic field has a nonzero component along the A axis. It is demonstrated that the antiferromagnetic vector l becomes parallel to the basal plane only when the magnetic field is perpendicular to the A axis. The case of the magnetic field directed parallel to the [110] axis is examined thoroughly. The critical value of the magnetic field is determined at which the antiferromagnetic vector l becomes parallel to the basal plane and perpendicular to the external magnetic field H for H _⊥ → ∞.     

Mössbauer absorption by soft ferromagnets in radio-frequency magnetic field

The simultaneous influence of periodical magnetic field reversals at the nucleus between the values ±h ₀ and of magnetostrictive vibrations on the shape of the Mössbauer absorption spectrum is analyzed. The effect of a constant external magnetic field is taken into account by assuming unequal durations of the states ?h ₀ and +h ₀. It is shown that such asymmetric reversals of the magnetic field lead to splitting of the absorption lines into Zeeman patterns corresponding to the time-averaged magnetic field h ₀ R, where R is the asymmetry parameter of the reversals. The calculations agree well with experiment.     

Dynamic phenomena connected with magnetic and antiferroelectric interactions in trirutiles

Dynamic effects caused by the magnetoelectric and antiferroelectric interactions in tetragonal antiferromagnets are studied. The analysis is based on the example of trirutiles that are a series of antiferromagnets with different exchange structures and orientation states. We are mainly dealing with the excitation by an alternating electric field E(t) of spin waves typical of these magnets (antiferroelectric resonance) and the nuclear magnetoelectric resonance connected with these interactions. In the first case, special emphasis is placed on specific magnons (antimagnons), where only the antiferromagnetism vectors L take part in oscillations, whereas the total ferromagnetism vector M remains unchanged. The nuclear magnetoelectric resonance can be generated by oscillations of both L and M caused by field E(t). In this way, the field contributes to the hyperfine field, which acts on the nuclear spins. It is shown that the magnetic and antiferroelectric interactions in the dynamics can manifest themselves both at high (usually, exchange) frequencies ωw_E (antiferroelectric resonance) and at rather low nuclear frequencies of ω_n?ω_E. Particular cases of magnetic structures (phases) are considered where field E(t) can excite not only antimagnons, but also quasiantiferromagnons that have lower eigenfrequencies than those of quasimagnons (relativistic and semirelativistic).     

High-frequency susceptibility and ferromagnetic resonance in multidomain thin films of the yttrium-iron garnet type

The field dependence of the high-frequency susceptibility and the ferromagnetic resonance were experimentally studied in a thin (d≈0.1 µm) (111)-oriented single-crystal film of substituted yttrium-iron garnet with the factor q?1. It was shown that the anomaly in the high-frequency susceptibility observed in a magnetic field H parallel to the normal to the film surface in the magnetization saturation region (H≈H_s) has a dual nature; more specifically, this anomaly is associated with an abrupt collapse of the stripe domain structure and a ferromagnetic resonance in the experimental configuration H ∥ [111] and h ⊥ H. In this case, the film transition from the inhomogeneous multidomain state to the homogeneous (single-domain) state at the point H≈H_s has no indications of a second-order phase transition. The experimental frequency-field dependence of ferromagnetic resonance (FMR) in the sample under study, having a characteristic minimum at the point ω₀=5 MHz and H_FMR=H_s, agrees qualitatively and quantitatively with calculations. The influence of the cubic magnetic anisotropy and the film thickness on the FMR spectrum and the orientation of the spontaneous magnetization in domains with respect to the film plane in the zero field H was theoretically studied.     

Electrodynamic features of anisotropic hard superconductors

The low-frequency electromagnetic response of superconducting plates characterized by strong anisotropy of current-carrying capacity in the plane of the sample is studied experimentally and theoretically. Measurements are made on polycrystalline textured plates of the Y-123 system with the c axis lying in the plane of the sample and on a single crystal with a single preferred direction of twinning boundaries. It is shown that the shape of the curves describing the dependence of the relative losses q on the ac field amplitude h ₀ is quite sensitive to the orientation of vector h ₀ in the sample plane. As in the case of isotropic samples, the q(h ₀) dependence is characterized by a single size peak if vector h ₀ is oriented along one of the principal symmetry directions of the anisotropic critical current density. If h ₀ deviates considerably from principal directions, two size peaks are observed on the q(h ₀) curve. A detailed analysis of the evolution of the q(h ₀) curves upon a rotation of vector h ₀ in the sample plane is carried out.     

Commensurate and incommensurate states of a spin density wave in a quasi-two-dimensional system with an anisotropic energy spectrum in an external magnetic field of arbitrary direction relative to magnetization

A theory of thermodynamic properties of a spin density wave (SDW) in a quasi-two-dimensional system (with a preset impurity concentration x) is constructed. We choose an anisotropic dispersion relation for the electron energy and assume that external magnetic field H has an arbitrary direction relative to magnetic moment M _Q . The system of equations defining order parameters M _Q ^z , M _Q ^σ , M _z , and M ^σ is constructed and transformed with allowance for the Umklapp processes. Special cases when H ‖ M _Q and H ⊥ M _Q (H _Z H ^σ = 0) are considered in detail as well as cases of weak fields H of arbitrary direction. The condition for the transition of the system to the commensurate and incommensurate states of the SDW is analyzed. The concentration dependence of magnetic transition temperature T _M is calculated, and the components of the order parameter for the incommensurate phase are determined. The phase diagram (T,~x) is constructed. The effect of the magnetic field on magnetic transition temperature T _M is analyzed for H _Z H ^σ = 0, and longitudinal magnetic susceptibility χ‖ is calculated; this quantity demonstrates the temperature dependence corresponding to a system with a gap for x < x _c and to a gapless state for x > x _c . In the immediate vicinity of the critical impurity concentration (x ～ x _c ), the temperature dependence of the magnetic susceptibility acquires a local maximum. The effect of anisotropy of the electron energy spectrum on the investigated physical quantities is also analyzed.     

Magnetic structure of the quasi-one-dimensional frustrated antiferromagnet LiCu<Subscript>2</Subscript>O<Subscript>2</Subscript> with Spin <Emphasis Type="Italic">S</Emphasis> = 1/2

The magnetic properties of LiCu₂O₂ single-crystal samples without twinning are investigated using electron spin resonance and nuclear magnetic resonance spectroscopy. The experimental results obtained are described in terms of the model of a planar spiral antiferromagnet for the orientation of the magnetic field H ‖ b or H ‖ c and the model of a collinear spin-modulated antiferromagnet for the orientation of the static magnetic field H ‖ a.     

Magnetic Properties of Sm0.7Ho0.3Fe3(BO3)4

The magnetic properties of a ferroborate single crystal of substituted composition Sm_0.7H_0.3Fe₃(BO₃)₄ with competing Sm-Fe and Ho-Fe exchange interactions are studied. The measured properties and effects are interpreted in terms of a general theoretical approach based on the molecular field approximation and calculations using the crystal field model for a rare-earth ion. The experimental temperature dependences of the initial magnetic susceptibility in the temperature range 2?C300 K, the anomalies in the magnetization curves for B ?? c and B ?? c in fields lower than 1.2 T, and the field and temperature dependences of magnetization in fields lower than 9 T are described. The crystal field parameters and the parameters of the R-Fe and Fe-Fe exchange interactions are determined during the interpretation of the experimental data.     

Phosphorus(V)corrole- Porphyrin Based Hetero Trimers: Synthesis,Spectroscopy and Photochemistry

‘Axial-bonding’-type hetero trimers have been constructed by employing a simple ‘inorganic’ reaction such as axial bond formation of main group element containing phosphorus corrole. The approach is simple and modular in nature. The architecture of these hetero trimers such that, while a phosphorus(V)corrole forms the basal scaffolding unit, either two free-base porphyrins [(H ₂ ) ₂ –PCor] or Zn^II porphyrins [(Zn) ₂ –PCor] occupy the two axial sites via an aryloxy bridge. Both hetero trimeric species have been completely characterized by mass (FAB), UV/Vis, proton nuclear magnetic resonance spectroscopies and also by the differential pulse voltammetric method. Comparison of their spectroscopic and electrochemical data of these trimers with those of the corresponding reference compounds reveal that there is no apparent ring-to-ring interactions in these ‘vertically’ linked hetero trimers. Reduced fluorescence quantum yields were observed for [(H ₂ ) ₂ –PCor] and [(Zn) ₂ –PCor] when compared to corresponding monomeric chromophores. Finally, a comparison is made between the presently reported phosphorus(V)corrole based hetero arrays and the previously reported analogous arrays based on Ge(IV)corrole with regard to their spectroscopic properties and photochemical activities.     

Resonant dislocation motion in NaCl crystals in the EPR scheme in the Earth’s magnetic field with pulsed pumping

Resonant dislocation motions in NaCl(Ca) crystals under the simultaneous action of the Earth’s magnetic field B _Earth (～66 μT) and a pulsed pump field $\tilde B$ of sufficient amplitude $\tilde B_m $ and certain duration τ have been detected and studied. The measured dislocation path peaks l(τ) have a maximum at τ = τ _r ≈ 0.53 μs. The resonance criterion has been found to be the ordinary EPR condition in which the g-factor is close to 2 and the optimum inverse pulse duration τ _r ^?1 is used instead of the harmonic pump field frequency ν _r . The largest peak l(τ) height is reached at mutually orthogonal dislocation (L) and magnetic field (B _Earth and $\tilde B$ ) orientations. Pulsed field rotation to the position $\tilde B$ ‖ B _Earth significantly decreases but does not “kill” the effect. For dislocations parallel to the Earth’s field (L ‖ B _Earth), the resonance almost disappears even at $\tilde B$ ⊥ B _Earth. In the optimum geometry of experiments, as the pump field amplitude $\tilde B_m $ decreases from 17.6 to 10 μT, the path peak height l _r = l(τ _r ) decreases only by 7.5%, remaining at the level of l _r ～ 10² μm, and at a $\tilde B_m $ further fall-off to 4 μT, it rapidly decreases to background values. In this case, the relative density of mobile dislocations similarly decreases from ～90 to 40%. Possible physical mechanisms of the observed effect have been discussed.