Uniform susceptibility of classical antiferromagnets in one and two dimensions in a magnetic field

We simulated the field-dependent magnetization m(H,T) and the uniform susceptibility of classical Heisenberg antiferromagnets in the chain and square-lattice geometry using Monte Carlo methods. The results confirm the singular behavior of at small T,H: and , where D=3 is the number of spin components, J ₀=zJ, and z is the number of nearest neighbors. A good agreement is achieved in a wide range of temperatures T and magnetic fields H with the first-order 1/D expansion results (D.A. Garanin, J. Stat. Phys. 83, 907 (1996)). Received 20 March 2000     

Nonmonotonic external field dependence of the magnetization in a finite Ising model: Theory and MC simulation

Using field theory and Monte Carlo (MC) simulation we investigate the finite-size effects of the magnetization M for the three-dimensional Ising model in a finite cubic geometry with periodic boundary conditions. The field theory with infinite cutoff gives a scaling form of the equation of state where is the reduced temperature, h is the external field and L is the size of system. Below and at the theory predicts a nonmonotonic dependence of f(x,y) with respect to at fixed and a crossover from nonmonotonic to monotonic behaviour when y is further increased. These results are confirmed by MC simulation. The scaling function f(x,y) obtained from the field theory is in good quantitative agreement with the finite-size MC data. Good agreement is also found for the bulk value at . Received 20 July 1999 and Received in final form 11 November 1999     

Magnetization dynamics below of EuO and EuS

Between 4.2 K and the Curie temperatures of the cubic Heisenberg ferromagnets EuS and EuO, their homogeneous dynamic susceptibilities have been investigated by means of a broad-band reflectometer operating from 0.1 GHz to 40 GHz. For internal magnetic fields larger than the anisotropy fields H A ( T ) of both materials, their static susceptibilities exhibit a -divergence, which reveals quantitatively the dominance of dipolar-anisotropic spin-wave fluctuations. displays a Lorentzian shape the damping frequency of which obeys scaling in terms of .The scaling function agrees quantitatively with work by Frey and Schwabl [#!FS88!#] for dipolar Heisenberg ferromagnets at temperatures above T_c. Building upon their approach, the resonance frequency of the Lorentzian can be related to a memory effect in the damping determined by the large value of the relaxation rate of the longitudinal magnetization fluctuations . For EuS, this relation is substantiated directly by inelastic neutron scattering. All these features reveal the hitherto uncovered importance of the dipolar anisotropic fluctuations below T_c of ferromagnets. Received: 4 March 1998 / Accepted: 12 May 1998     

Study of spin-wave dynamics in Fe65Ni35 ferromagnetic via small-angle polarized-neutron scattering

The results of studying the spin dynamics of a classical Fe₆₅Ni₃₅ invar alloy are presented and analyzed. The investigations are performed via small-angle polarized-neutron scattering in the oblique geometry of a magnetic field at various temperatures (T < T _C). This approach is based on the analysis of left-right asymmetry in the magnetic scattering of polarized neutrons. The asymmetry effect arises when the magnetization direction of a sample is inclined with respect to the wave vector of the incident beam. The spin-wave scattering is concentrated within a range bounded by the cutoff angle θ_c determined by the magnetic field: θ _c ² (H) = θ ₀ ² ?(gμ_B H)θ₀/E, where \(\theta _0 = \hbar ^2 \frac{1} {{2Dm_n }}\) , H is the external magnetic field, E is the initial neutron energy, D is the spin-wave stiffness constant, and m _n is the neutron mass. The scattering is blurred by spinwave damping in the vicinity of the cutoff angle. The spin-wave stiffness constant can be obtained from a comparison of the asymmetric contribution to scattering and a model function. The temperature dependence D = D(T) is well defined by the expression D = D ₀ |τ| ^x , where \(\tau = 1 - \frac{T} {{T_C }}\) , x = 0.47 ± 0.01, D ₀ = 137 ± 3 meVŲ, and τ > 0.1 in the entire temperature range. The given method enables us to construct the temperature dependence of the spin-wave stiffness constant with a high accuracy and a small step.     

Low-temperature results of the statistical theory of noninteracting spin waves

Low-temperature predictions of a free-spin-wave theory that includes the correct spin-wave kinematics for theS=1/2, quantum Heisenberg ferromagnet, as described in a previous paper, are obtained for three dimensions using analytic and Monte Carlo techniques. The low-temperature propagator is found to be of boson form, and the low-temperature magnetization goes asT ^3/2, which agrees with the interacting theory at lowest order inT.     

Critical thermodynamics of dysprosium ethyl sulphate, a pure dipolar Ising ferromagnet

Using a SQUID magnetometer the magnetization of the Ising ferromagnet dysprosium ethyl sulphate has been measured in the temperature range 0.015–3K and in external fields 0.004–30 Oe. The results atT0.4 K (precritical regime) confirm the pure dipolar nature of the magnetic interactions. Particular interest has been paid to the immediate neighbourhood of the critical pointT _c =118.17 mK andH=0 where the zero-field susceptibility(T) aboveT _c , the spontaneous magnetizationM _s (T), and the magnetization atT _c ,M _c (H), can be described by mean field laws modified by logarithmic singularities. The critical amplitudes, B, andD of, M _s andM _c , respectively, satisfy the relation (2/3B ²)^1/3=D. All these results agree with predictions of (i) the Larkin-Khmel'nitskii theory and (ii) exact solutions of the renormalization group equations for 3-dimensional dipolar Ising ferromagnets.     

An analytical study of the Curie temperature in the D-vector model

The successive analytical expressions up to fifth order for the Curie temperature, T_c(D,d), of the D-vector model on d-dimensional hypercubic lattices are evaluated by the Ginzburg-Landau theory based on cumulant expansion. The results by substituting d = 3 and D = 1, 2, 3 into the expressions approach order by order those of the Ising, XY, and Heisenberg models by Monte Carlo simulation (MC). The differences between ours and the other models are about 5.52, 6.86, and 7.94 percent, respectively.     

Size and anisotropy effects on magnetic properties of antiferromagnetic nanoparticles

Based on the Heisenberg model taking into account single-ion anisotropy and using a Green's function technique we have studied the influence of size and anisotropy effects on magnetization M, Neel temperature T_N, coercive field H_c and spin excitation energy of antiferromagnetic nanoparticles. The properties are compared with those of ferromagnetic nanoparticles. We have shown that the enhanced magnetization M and coercive field H_c of antiferromagnetic nanoparticles is a surface effect, which is due to uncompensated surface spins. Moreover, the shape of the coercive field curve can be significantly influenced by surface magnetic anisotropy.     

Quantization and confinement effects in superconducting nanostructures

The confinement of the flux lines by a lattice of submicron holes (‘antidots’) has been studied in nanostructured superconducting Pb/Ge multilayers. By introducing regular arrays of sufficiently large antidots, multi-quanta vortex lattices have been stabilized. Sharp cusp-like magnetization (M) anomalies, appearing at matching fieldsH_m=mφ₀/Sin superconducting films with the antidot lattices having a unit cell areaS, are successfully explained. These anomalies are, analogues of the well-knownM(H) cusp atH_c1, but for the onset of multi-quanta (m+1)φ₀-vortices penetration at each subsequent matching fieldH_m. It is shown that theM(H) curve between the matching fieldsH_m<H<H_m+1follows a simpleM∝ln(H−H_m) dependence. These experimental observations have revealed an unusual expansion of validity of the London limit in superconductors with lattices of relatively large antidots. The successful high quality fit of theM(H,T) curves convincingly demonstrates that a new type of the critical stateB=const (‘single-terrace critical state’) can be realized in superconductors with the antidot lattices.     

Monte Carlo simulation of spin-wave excitation for the magnetic films with structure and interaction fluctuations

Monte Carlo simulation studies are performed to examine influence of structure and interaction fluctuations on magnetic properties of a ferromagnetic system modelled with a Heisenberg Hamiltonian. It is found that the spontaneous magnetization at low temperature for the multilayered films decreases with temperature in a Bloch law of spin-wave excitations. Both Bloch coefficient B and exponent b vary evidently because of a strong surface and size effect in the finite magnetic films with free boundaries. For the disordered bulk FCC magnet with periodic boundary, the Bloch T^3/2 law is followed at low temperature and B is greatly influenced by the structure and interaction fluctuations. At the same time, Bloch coefficient B of the amorphous magnet with the coordination and interaction fluctuations has been derived. The simulated results are in good agreement with the theoretical predictions of spin-wave excitation, and explain the experimental facts well.     

Density functional theory simulation of liquid helium-4 in aerogel

Thermodynamic properties of cubic Heisenberg ferromagnets with competing exchange interactions are considered near the frustration point where the coefficient D in the spin-wave spectrum E _k ～ Dk ² vanishes. Within the Dyson-Maleev formalism, it is found that, at low temperatures, thermal fluctuations stabilize ferromagnetism by increasing the value of D. For not overly strong frustration, this leads to an unusual “concave” shape of the temperature dependence of magnetization, which is in agreement with experimental data on europium chalcogenides. The phase diagram is constructed by means of Monte Carlo simulation, and suppression of the magnetization and Curie temperature is found in comparison with the results of the spin-wave theory. This effect is explained by the presence of nonanalytical corrections to the spin-wave spectrum which are represented in the lowest order by the term ～(T/S)² k ²lnk.     

Critical thermodynamics of dysprosium ethyl sulphate,a pure dipolar Ising ferromagnet

Using a SQUID magnetometer the magnetization of the Ising ferromagnet dysprosium ethyl sulphate has been measured in the temperature range 0.015–3K and in external fields 0.004–30 Oe. The results atT0.4 K (precritical regime) confirm the pure dipolar nature of the magnetic interactions. Particular interest has been paid to the immediate neighbourhood of the critical pointT _c =118.17 mK andH=0 where the zero-field susceptibility(T) aboveT _c , the spontaneous magnetizationM _s (T), and the magnetization atT _c ,M _c (H), can be described by mean field laws modified by logarithmic singularities. The critical amplitudes, B, andD of, M _s andM _c , respectively, satisfy the relation (2/3B ²)^1/3=D. All these results agree with predictions of (i) the Larkin-Khmel'nitskii theory and (ii) exact solutions of the renormalization group equations for 3-dimensional dipolar Ising ferromagnets.A project of the Sonderforschungsbereich 65 Festkörperspektroskopie Darmstadt-Frankfurt, financed by special funds of the Deutsche Forschungsgemeinschaft     

Thermomagnetic history effects in niobium and its implication for H c1 in highT c superconductors

The existence of a remanent magnetization (M _rem) on switching off the field of a field cooled (FC) sample of a highT _c superconductor is often reported. It has recently been argued thatM _rem should equal the difference in FC and zero field cooled (ZFC) magnetizations (M _FC —M _ZFC) in hard superconductors and this has been demonstrated to hold in single crystals of YBCO at 4.2K over a limited range ofH values. We report the detailed magnetization measurements under various thermomagnetic histories (of whichM _rem is one special case) on two specimens of Nb, which show different extents of flux trapping. We find that there are in general three regions inH, T space, corresponding toM _rem+M _ZFC−M _FC=0,M _rem<(M _FC−M _ZFC) andM _rem>(M _FC−M _ZFC). At anyT, the equality holds forH<H _c1(T), and forH→H _c2 (M _FC−M _ZFC) asymptotically vanishes and thereM _rem>(M _FC−M _ZFC). We show that there exists an intermediate region in all hard superconductors, whereM _rem<(M _FC−M _ZFC). The range over which this situation persists, however, depends on the degree of irreversibility in a sample. We can explain qualitatively all the history dependent magnetization data in terms of the critical state model. We point out an inconsistency in an earlier analysis to determineH _c1(T) from such data in YBCO. We also propose a new criterion for putting limits onH _c1(T) in hard superconductors.     

Landau level quantization and possible superconducting instabilities in highly oriented pyrolitic graphite

Measurements of the basal-plane resistivity ρ _a(T,H) performed on highly oriented pyrolitic graphite, with magnetic field H∥c-axis in the temperature interval 2–300K and fields up to 8 T, provide evidence for the occurrence of both field-induced and zero-field superconducting instabilities. Additionally, magnetization M(T,H) measurements suggest the occurrence of Fermi surface instabilities which compete with the superconducting correlations. Fiz. Tverd. Tela (St. Petersburg) 41, 2135–2138 (December 1999)     

A frustrated heisenberg antiferromagnet on a triangular lattice with next-nearest neighbor interactions

Using the Monte Carlo method, we study the critical properties of the three-dimensional frustrated Heisenberg model on a triangular lattice with allowance for next-nearest neighbor interactions. Using the theory of finite-size scaling, we calculate the static magnetic and chiral critical exponents of heat capacity α, susceptibility γ, γ _k , magnetization β, β _k , and correlation length ν.     

Probing the field-induced variation of the chemical potential in Bi2Sr2CaCu2Oy via magneto-thermopower measurements

Approximating the shape of the magneto-thermoelectric power (TEP) ΔS(T,H) measured in Bi₂Sr₂CaCu₂O_y by an asymmetric linear triangle of the form ΔS(T,H)≃S _p (H)±B ^±(H)(T _c −T) with positive B ⁻(H) and B ⁺(H) defined below and above T _c , we observe that B ⁺(H) ≃2B ⁻(H). To account for this asymmetry, we explicitly introduce the field-dependent chemical potential μ(H) of holes into the Ginzburg-Landau theory and calculate both an average ΔS _av(T,H) and fluctuation contribution ΔS _fl(T,H) to the total magneto-TEP ΔS(T,H). As a result, we find a rather simple relationship between the field-induced variation of the chemical potential in this material and the above-mentioned magneto-TEP data around T _c , viz. Δ μ(H)∝S _p (H). Zh. éksp. Teor. Fiz. 116, 257–262 (July 1999) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

Improvement of the remanence properties and the weakening of interparticle interactions in BaFe12O19 particles by B2O3 addition

In the present study, the effects of B₂O₃ addition on the remanence properties of barium ferrite magnets are examined. The relationship between isothermal magnetization remanence M_R(H) and demagnetization remanence M_D(H) for non-interacting single domain particles, M_D(H)=M_R(H_max)−2M_R(H), was used in order to investigate the interactions between particles. We have found that remanence magnetization M_R increased by 40% in magnitude with B₂O₃ addition in addition to the weakened couplings between particles. The B₂O₃ addition seems to supply the required conditions for usage of these materials in the magnetic recording media.     

The 2<Superscript>1/3</Superscript> rule for magnetic susceptibility of gadolinium

The dependences of the magnetization M and the magnetic susceptibility χ = ∂M/∂H of pure gadolinium (the concentration of foreign impurities is lower than 0.1 wt %) on the temperature T and the magnetic field H have been measured using a Quantum Design MPMS-5XL SQUID magnetometer. In this material, inhomogeneities of the atomic structure should not lead to a nonuniform distribution of the magnetic characteristics (including the Curie temperature T _C) over the volume of the sample. The obtained dependences of M and χ have been used to investigate the possibility of suppressing magnetic inhomogeneities of other types by magnetic fields with a strength of up to 50 kOe. It has been assumed that these inhomogeneities are suppressed when the specific relationship, namely, the 2^1/3 rule is fulfilled. The rule relates the portions of the dependence χ(T, H) which at the temperature T = T _C and at the maximum in the curve χ(T) (T = T _m ) depend on H in accordance with the H ^2/3 law. It has been shown that the portions separated from the experimental curves χ(T _C, H) and χ(T _m , H) obey the 2^1/3 rule.     

Magnetic properties of Fe<Subscript>3</Subscript>C ferromagnetic nanoparticles encapsulated in carbon nanotubes

The low-temperature dependences of magnetic characteristics (namely, the coercive force H _c , the remanent magnetization M _r , local magnetic anisotropy fields H _a, and the saturation magnetization M _s ) determined from the irreversible and reversible parts of the magnetization curves for Fe₃C ferromagnetic nanoparticles encapsulated in carbon nanotubes are investigated experimentally. The behavior of the temperature dependences of the coercive force H _c (T) and the remanent magnetization M _r (T) indicates a single-domain structure of the particles under study and makes it possible to estimate their blocking temperature T _B = 420–450 K. It is found that the saturation magnetization M _s and the local magnetic anisotropy field H _a vary with temperature as ～T ^5/2.     

Temperature-dependent Heisenberg exchange coupling constants from linking electronic-structure calculations and Monte Carlo simulations

We propose a method to calculate the temperature dependence of Heisenberg exchange coupling constants J_ij. Within the formalism of disordered local moments (DLM), the magnetization and the J_ij are computed from first principles for any concentration c of the magnetic constituents. The exchange coupling constants are then used in Monte Carlo (MC) simulations to compute the temperature dependence of the magnetization for the given c. By comparing the magnetization from DLM calculations and from MC simulations we obtain a mapping of temperature versus concentration and eventually temperature-dependent J_ij. The approach which is applied to bulk Fe and Co can for example improve critical exponents.