Magnetization Mz Research Articles

A revisit to the Ising model in a transverse and random magnetic field

In this article we consider a Hamiltonian representing the Ising model in a random transverse magnetic field (RTIM). We use mean field theory via Bogoliubov’s inequality to calculate the Gibbs free energy and the longitudinal (mz) and transverse (mx) magnetizations. We show a quantum phase transition at zero temperature, i.e. the magnetization mz goes to zero only due to the transverse magnetic field. The temperature behavior as a function of the transverse magnetic field is also shown for different values of the anisotropy parameter p, where no tricritical behavior is observed. The behavior of mz and mx as a function of temperature and transverse magnetic field have been plotted, showing that there is no tricritical behavior.

Generation and stability of structurally imprinted target skyrmions in magnetic multilayers

Target Skyrmions (TSks) are extended topological spin textures with a constant chirality where the rotation of the z component of the magnetization is larger than π. TSks have topological charge 1 or 0, if the z component of the magnetization Mz goes through a rotation of nπ where n is an odd or even integer, respectively. TSks with a rotation of the z component of up to 4π have been imaged via high spatial resolution element-specific x-ray imaging. The TSks were generated by weakly coupling 30 nm thin Permalloy (Ni80Fe20, PY) disks with a 1 μm diameter to asymmetric (Ir 1 nm/Co 1.5 nm/Pt 1 nm) × 7 multilayers that exhibit Dzyaloshinskii-Moriya interaction. The PY disks stabilize the TSks in the multilayers due to reduced stray field energy and enforced circular symmetry from pinning of domain walls at the edges of the disks. Upon applying external magnetic fields, it is the skyrmion core at the center that ensures stability of the TSk, whereas the collapse of the extended structures in the TSk does not depend on the topological charge.

Spin-1 condensates at thermal equilibrium: A SU(3) coherent state approach

We propose a theoretical framework based on SU(3) coherent states as a convenient tool to describe the collective state of a Bose-Einstein condensate of spin-1 atoms at thermal equilibrium. We work within the single-mode approximation, which assumes that all atoms condense in the same spatial mode. In this system, the magnetization mz is conserved to a very good approximation. This conservation law is included by introducing a prior distribution for mz and constructing a generalized statistical ensemble that preserves its first moments. In the limit of large particle numbers, we construct the partition function at thermal equilibrium and use it to compute various quantities of experimental interest, such as the probability distribution function and moments of the population in each Zeeman state. When N is large but finite (as in typical experiments, where ), we find that fluctuations of the collective spin can be important.

Transverse thermoelectric conductivity and magnetization in high-Tc superconductors

We use the time-dependent Ginzburg-Landau (TDGL) equation with thermal noise to calculate the transverse thermoelectric conductivity αxy describing the Nernst effect and magnetization Mz in type-II superconductor in the vortex-liquid regime. The nonlinear interaction term in dynamics is treated within self-consistent Gaussian approximation. The expressions of the transverse thermoelectric conductivity and magnetization including all the Landau levels are presented in explicit form which are applicable essentially to the whole phase. Our results are compared to recent simulation data on high-Tc superconductor.

Phase transitions in the two-dimensional single-ion anisotropic Heisenberg model with long-range interactions

In the present work, we investigate the effects of long-range interactions on the phase transitions of a two-dimensional Heisenberg model with single-ion anisotropy at zero and finite temperatures. The Hamiltonian is given by H=∑i≠jJij(SixSjx+SiySjy+λSizSjz)+D∑i(Siz)2, where Jij=−J|rj−ri|−p(p≥3) is a long-range ferromagnetic interaction (J>0), 0≤λ≤1 is an anisotropic constant and D is the single-ion anisotropic constant. It is well-known that the single-ion anisotropy D creates a competition between an ordered state (favored by the exchange interaction) and a disordered state, even at zero temperature. For small values of D, the system has a spontaneous magnetization mz≠0, while in the large-D phase mz=0 because a state with 〈Sz〉≠0 is energetically unfavorable. Therefore a phase transition takes a place in some critical value Dc due to quantum fluctuations. For systems with short-range interaction Dc≈6J (depending of λ constant) but in our model we have found larger values of D due to the higher cost to flip a spin. Since low-dimensional magnetic systems with long range interaction can be ordered at finite temperature, we also have analyzed the thermal phase transitions (similar to the BKT transition). The model has been studied by using a Schwinger boson formalism as well as the self-consistent harmonic approximation (SCHA) and both methods provide according results.

Effect of the applied magnetic field and the layer thickness on the magnon properties in bilayers Co/Pt and symmetrical trilayer Pt/Co/Pt

We have studied the elementary magnetic excitations and their dynamics in multilayer Co(t Co)/Pt(t Pt) and Pt(t Pt)/Co(t Co)/Pt(t Pt) under an applied magnetic field. The Heisenberg hamiltonian used takes into account the magneto-crystalline and surface anisotropies, the exchange and dipolar interactions. The calculated excitation spectrum εN(k) presents a structure with two sub-bands corresponding to the magnons of surface and volume respectively. The existence of a gap of creating these magnons is also highlighted. The lifetimes deduced from these gaps are in good agreement with the results of previous studies. The thermal evolution of the magnetization mz indicates that the system undergoes a dimensional crossover 3D–2D when the temperature increases. The calculated and measured magnetizations are compared and they are in good agreement. The exchange integral and critical temperature values deduced from these adjustments are in very good agreement with the results of previous works.

Dynamic magnetization processes in magnetostrictive amorphous wires

We have performed the theoretical studies on the longitudinal dynamic magnetization process of magnetostrictive amorphous wires characterized by a large single Barkhausen jump (magnetic bistability) based on our previous experimental measurements on these wires. The domain structures of these wire samples consist of a single domain inner core with axial magnetization surrounded by the outer domain shell with the magnetization oriented perpendicular (λs>0) or circular (λs<0) to the wire axis. In the present work we use the resultant magnetization vector M⃗ tilting θ angle to z axis to describe the sample’s domain structures. In terms of solving the Landau-Lifshitz-Gilbert equation followed by M⃗ the analytical solution of the dimensionless axial component of the magnetization mz=MZ∕Ms has been obtained, and mz[t(H0,fe),τ,γ] is a function of the field amplitude H0, field frequency fe, and the samples’ material parameters such as the damping constant τ and the gyromagnetic ratio γ. The function mz[t(H0,fe),τ,γ] allows us to study the dynamic properties of the magnetization process of a wire sample. It has been found that the switching time ts, the switching field Hsw, and the dynamic coercive field Hdc depend on a magnetic field and material parameters. We found that the parameter α=γτ∕(1+τ2) related to the rate of M⃗, rotating the direction of the effective field, plays an important role in the magnetization process. By fitting the experimental data to the theoretical magnetization curve the value of the damping constant τ of the magnetostrictive amorphous wires can be estimated.

Photoinduced magnetic uniaxial anisotropy and molecular orientation of polymer containing azobenzene side groups with free radical end

A polymer containing azobenzene side groups each with an organic free radical end was synthesized. Before irradiation by an Ar+ laser beam, the polymer was magnetically isotropic. However, with the irradiation of a polarized Ar+ laser beam, the photoisomerization and reorientation of the azobenzenes took place bringing about a magnetic anisotropy in the radical containing polymer film. The magnetic anisotropy was studied by using a superconducting quantum interference device. It was found that when the applied magnetic field H≈1 Oe, the magnetization Mz(H) in the direction perpendicular to the polymer film was 3.63×10−4 emu/g, while those parallel to the polymer film were Mx(H)=My(H)=−1.1×10−5 emu/g.

A k-Space Analysis of MR Tagging

We present a k-space approximation that directly relates a pulse sequence to its residual pattern of z-directed magnetization Mz, in a manner akin to the k-space approximation for small tip-angle excitation. Our approximation is particularly useful for the analysis and design of tagging sequences, in which Mz is the important quantity—as opposed to the transverse magnetization components Mx and My considered in selective excitation. We demonstrate that our approximation provides new insights into tagging, can be used to design novel tag patterns, and, more generally, may be applied to selective presaturation sequences for purposes other than tagging.

Temperature dependence of local states due toS=12impurities and their correlation in aS=1Heisenberg chain

We study the temperature dependence of the low temperature spin configurations, investigating the magnetization profile of the local states due to the impurities and the two point correlation function centered in one of the impurities. This correlation is found to be weak against temperature effects although the magnetization profile in the triplet state is visible up to higher temperatures. Here we introduce a loop cluster quantum Monte-Carlo method with a fixed magnetization Mz in order to study the correlations in the ground state of a given value of Mz. From the population distribution of magnetization, the very small energy gap between the quasi degenerate states due to the impurities is obtained.

Torsional mode magnetoelastic resonance in ferromagnetic amorphous wire

A torsional pendulum has been built using a stress relieved FeSiB amorphous wire. Torsional motion is magnetoelastically induced by means of the simultaneous application of longitudinal Hz and circular Hφ magnetic fields. The experimental setup allows one to determine both the torsional deformation and the changes in the longitudinal magnetization Mz of the wire. Free and forced oscillations are observed depending on the parameters of the applied fields. In both forced and free oscillation modes two resonant peaks are observed. Their frequency and amplitude dependences on the axial Hz and circular fields Hφ have been studied. Changes in shear modulus ΔG valued 60% in excess have been measured. To interpret the experimental results a theoretical model is developed taking into account the existence of two different magnetic regions in the wire, core, and shell having a different distribution of axial, radial, and shear stresses. The calculations explain the more remarkable aspects of the observed behavior.

On the nature of the order parameter in quantum antiferromagnets

The first moments of the magnetization mz of the d = 2, S = j quantum Heisenberg antiferromagnet with nearest neighbor interactions on the square lattice are computed for T = 0 vta path integral Monte Carlo Simulations. The results for the ratio R = (mf / (ml )~ show a cross-over at a system size of N m 100 to the classical behavtor, hmN-m R = 9/5. This supports the arguments that the long range order in the ground state is reached by a spontaneous symmetry breaking, just as in the classical case.

The initial Matteucci effect

The magnetoelastic anisotropy introduced by torsional twist in ferromagnetic wires allows the measurements of the circular magnetization Mphi as a function of the longitudinal magnetic field Hz and the longitudinal magnetization Mz as a function of the circular magnetic field Hphi . For two types of samples, twisted to saturation the Mphi -Hz and Mz-Hphi curves were obtained. These curves show two different types of behaviour.

Nuclear magnetic relaxation due to slow molecular reorientation and fast internal rotation interference

The relaxation of the two-proton system longitudinal magnetization Mz(t) is considered theoretically, using the Bloch equations with a diffusion term. The condition τc ≥ 1, τ ≪ 1 is fulfilled here, where is the energy of the proton dipole-dipole interaction, τ is the correlation time of molecular diffusion rotation and τ is the correlation time for the proton rotation relative to the molecule. Unlike the ordinary Bloch equations a two-exponential law for the evolution of Mz(t) is obtained for definite values , τc and τ. The results of the present work may be useful for the consideration of the system having mobile proton groups in viscous media.

Spin-Lattice Relaxation Time in Yttrium Iron Garnet

The spin-lattice relaxation time in yttrium iron garnet (YIG) has been measured by a pulsed ferromagnetic resonance method similar to that of Bloembergen and Wang and Damon, in which the z component of magnetization is directly observed. A microwave pulse with 2×10−8 sec rise and decay time, 5×10−7 sec long, and 2 w peak power is applied to a TE102 rectangular cavity operating at 9300 mc sec. The z component of magnetization Mz changes at the beginning and at the end of the rf pulse. The time of decay of the changing Mz signal at the trailing edge of the pulse (at which time the applied rf field is zero) is a measure of the spin-lattice relaxation time. A spherical sample of YIG, 0.03 in. diam, is placed in a quartz tube, 0.05 in. o.d., about which a five turn coil of No. 38 wire is wound. The coil with sample is inserted in the center of the cavity with the axis of the coil in the z direction. At this position, the rf magnetic field is maximum and the electric field is a minimum. The presence of the coil does not measurably change the properties of the cavity. The voltage induced in the coil is proportional to the change in Mz and is observed on a high speed oscilloscope. The time constant of the equipment is approximately that of the exciting pulse. Thus the spin-lattice relaxation time can be accurately determined directly if it is appreciably larger than this value. The ferromagnetic resonance line width is 2.3 oersteds and the measured spin-lattice relaxation time is 7×10−8 sec. Discussion is given relating these measurements to those reported in the accompanying papers.