Concentration Of Nonmagnetic Impurities Research Articles

Effects of site dilution on Compensation in Ising Spin-1/2 trilayered triangular Ferrimagnets with non-equivalent planes

Using Monte Carlo simulations with the Metropolis algorithm, the magnetic and thermodynamic behaviours of a spin-1/2, trilayered ferrimagnetic system on triangular monolayers with quenched nonmagnetic impurities are studied. Two different theoretical atoms, A and B, make up the ABA and AAB types of distinct configurations. Like atoms (A-A and B-B) interact ferromagnetically, while unlike atoms (A-B) interact antiferromagnetically. Only the A-layers are randomly site-diluted with dilution percentages ranging from 5% to 45%. Such diluted magnetic thin systems exhibit magnetic compensation which depends sensitively on the concentration of impurities. The phase diagram in the Hamiltonian parameter space related to the occurrence of magnetic compensation phenomenon and the effect of site dilution is discussed in detail. Special attention is given to the mathematical dependencies of compensation temperature on the concentration of nonmagnetic impurities. Depending upon the concentration of nonmagnetic impurities, the compensation and critical points shift with the equilibrium magnetic behaviours changing between distinct ferrimagnetic behaviours. For each combination of the coupling strengths, with values of the impurity concentration above a threshold, compensation appears where previously was absent. Suggested mathematical formulae show how threshold impurity concentration relies on Hamiltonian parameters.

Disorder-induced trapping and antitrapping of vortices in type-II superconductors

We study the features of the superconductivity nucleation and vortex configurations in superconductors with modulated disorder. Using the Ginzburg-Landau-type theory with spatially varying diffusion coefficient, we uncover and explain the switching between the vortex-defect attraction to the repulsion upon the increase in the external magnetic field. It is shown that for rather weak applied magnetic fields, a superconducting nucleus localized near the region with the suppressed diffusion coefficient possesses a nonzero vorticity whereas the increase in the magnetic field can lead to a transition into the state with zero winding number. We demonstrate the manifestations of this switching phenomenon in superconductors with a large number of defects by performing numerical simulations of the vortex structures in superconductors with periodic spatial profiles of the diffusion coefficient. The obtained results clarify the physics of the vortex arrangement in several classes of the superconducting materials including one-dimensional superlattices and nanopatterned superconductors with regular arrays of the defects characterized by the increased concentration of nonmagnetic impurities.

Spin-wave theory in a randomly disordered lattice: A Heisenberg ferromagnet

Starting from the hamiltonian for the Heisenberg ferromagnet which comprise randomly distributed nonmagnetic ions as impurities in a Bravais lattice, we express the spin operators by means of the Dyson–Maleev transformation in terms of the Bose operators of the second quantization. Then by using methods of quantum statistical field theory, we derive the partition function and the free energy for the system. We adopt the Matsubara thermal perturbation method to a portion of the hamiltonian which describes the interaction between magnons and the stationary field of nonmagnetic ions. Upon averaging over all possible distributions of impurities, we express the free energy of the system as a function of the mean impurity concentration. Subsequently, we set up the double-time single particle Green function at temperature T in the momentum space in terms of magnon operators and derive the equation of motion for the Green function through the Heisenberg equation of motion and then solve the resulting equation. From this, we calculate the self-energy and then the spectral density function for the system. We apply the formalism to the case of the simple cubic lattice and compute the density of states, the spectral density function and the lifetime of the magnons as a function of energy for several values of the mean concentration of nonmagnetic ions in the ferromagnetic lattice. We calculate the magnon energy spectrum as a function of the average impurity concentration fraction c, which shows that for low lying states, the excitation energy increases continuously with c in the studied range 0.1≤c≤0.7. We also use the spectral density function to compute some thermodynamical quantities through the magnon occupation number. We have obtained closed form expressions for the configurationally averaged physical quantities of interest in a unified fashion as functions of the mean concentration of nonmagnetic impurities c to any order of c applicable below a critical percolation concentration cp. The quantities of interest comprise the thermodynamic potential (free energy), the spin-wave self-energy and the spectral density function from which other quantities can be derived.

Construction of an approximate solution for a dilute magnet based on the solution for a pure magnet on the same lattice

The paper proposes a method for approximate calculation of the magnetization of a dilute Ising magnet on a certain lattice, based on the use of an exact or approximate solution for a pure Ising magnet on the same lattice. Using the proposed method, it is possible to calculate the dependence of magnetization on temperature and concentration of non-magnetic impurities and the Curie temperature as a function of concentration for a diluted magnet. The proposed method is applied in the work to the solution in the mean field approximation, to the solution in the beta approximation, and to the exact solution on a square lattice. Keywords: phase transitions, Ising model, dilute magnet.

Построение приближенного решения для разбавленного магнетика на основе решения для чистого магнетика на той же решетке

The paper proposes a method for approximate calculation of the magnetization of a dilute Ising magnet on a certain lattice, based on the use of an exact or approximate solution for a pure Ising magnet on the same lattice. Using the proposed method, it is possible to calculate the dependence of magnetization on temperature and concentration of non-magnetic impurities and the Curie temperature as a function of concentration for a diluted magnet. The proposed method is applied in the work to the solution in the mean field approximation, to the solution in the beta approximation, and to the exact solution on a square lattice.

Magnetocaloric Effect in Two-Dimensional Diluted Ising Model: Appearance of Frustrations in the Ground State

The magnetocaloric effect in a two-dimensional Ising model is considered for different ratios between parameters of inter-site repulsion of nonmagnetic impurities and exchange coupling. Classical Monte Carlo simulations on a square lattice show that in case of weak coupling and at sufficiently high concentrations of nonmagnetic impurities the long-range ferromagnetic ordering breaks down to give isolated spin clusters in the ground state of the system. This leads to appearance of a paramagnetic response in the system at the zero temperature and nonzero entropy of the ground state. The feasibility to detect frustration of ground state using data on the magnetic entropy variation is discussed

Nonlinear dynamics and dissipation of a curvilinear vortex driven by a strong time-dependent Meissner current

We report numerical simulations of large-amplitude oscillations of a trapped vortex line under a strong ac magnetic field $H(t)=H\sin\omega t$ parallel to the surface. The power dissipated by an oscillating vortex segment driven by the surface ac Meissner currents was calculated by taking into account the nonlinear vortex line tension, vortex mass and a nonlinear Larkin-Ovchinnikov (LO) viscous drag coefficient $\eta(v)$. We show that the LO decrease of $\eta(v)$ with the vortex velocity $v$ can radically change the field dependence of the surface resistance $R_i(H)$ caused by trapped vortices. At low frequencies $R_i(H) $ exhibits a conventional increases with $H$, but as $\omega$ increases, the surface resistance becomes a nonmonotonic function of $H$ which decreases with $H$ at higher fields. The effects of frequency, pin spacing and the mean free path $l_i $ on the field dependence of $R_{i}(H) $ were calculated. It is shown that, as the surface gets dirtier and $l_i$ decreases, the anomalous drop of $ R_{i}(H) $ with $H$ shifts to lower fields which can be much smaller than the lower critical magnetic field. Our numerical simulations also show that the LO decrease of $\eta(v)$ with $v$ can cause a vortex bending instability at high field amplitudes and frequencies, giving rise to the formation of dynamic kinks along the vortex. Measurements of $R_i(H)$ caused by sparse vortices trapped perpendicular to the surface can offer opportunities to investigate an extreme nonlinear dynamics of vortices driven by strong current densities up to the depairing limit at low temperatures. The behavior of $R_i(H)$ which can be tuned by varying the rf frequency or concentration of nonmagnetic impurities is not masked by strong heating effects characteristic of dc or pulse transport measurements.

Проявление фрустраций основного состояния двумерной разбавленной модели Изинга в магнитокалорическом эффекте

The magnetocaloric effect is considered in the 2D dilute Ising model for various ratios of the parameters of inter-site repulsion of nonmagnetic impurities and exchange interaction. Numerical simulations using the classical Monte Carlo method on a square lattice shows that in the case of weak exchange at sufficiently high concentrations of nonmagnetic impurities, long-range ferromagnetic ordering is destroyed with the formation of isolated spin clusters in the ground state of the system. This leads to the appearance of a paramagnetic response of the system at zero temperature and a nonzero entropy of the ground state. In the paper, we discuss the possibility of detecting the frustration of the ground state using data on changes in magnetic entropy.

Extinction of the long-range order on site diluted quantum two-dimensional antiferromagnet in Bose–Einstein condensation

We study the two-dimensional Heisenberg antiferromagnet with ion single anisotropy in the square lattice in the presence of nonmagnetic impurities at T=0 using the SU(3) Schwinger boson theory. In particular we discuss the influence of site disorder on the quantum phase transition of this model at Dc that separates the Néel phase, D<Dc, which is gapless, from the disordered phase, gapped phase, D>Dc. We find that the long-range order in D<Dc for the model without impurities is destroyed for a concentration of nonmagnetic impurities xc≈0.15.

Current states in symmetrical SNINS junction for arbitrary concentrations of nonmagnetic impurities

Equilibrium current states in superconducting junctions of SNINS-type (S – superconductor, N – normal metal, I – insulator) for arbitrary concentrations of nonmagnetic impurities in superconducting regions were investigated using the Ginzburg–Landau theory near the critical temperature. We found the current-phase relation valid in a wide range of electron transmission coefficient values and an arbitrary thickness of the normal layer. The influence of depairing effects was taken into account. A new analytical formula for the dependence of the current on the phase difference was obtained and a number of particular cases were considered.

Entanglement in site diluted quantum two-dimensional antiferromagnet

The von Neumann entanglement entropy is studied for the two-dimensional Heisenberg antiferromagnet with ion single anisotropy in the square lattice and in the presence of nonmagnetic impurities, at T=0 using the SU(3) Schwinger boson theory. In particular, we discuss the influence of site disorder on the quantum entanglement of this model that is characterized by a quantum phase transition at Dc, that separates a Néel phase, D<Dc, which is gapless, from a disordered phase, gapped phase, D>Dc. We find that the quantum entanglement in D<Dc for the model is destroyed for a concentration of nonmagnetic impurities xc≈0.5.

Influence of the site dilution on quantum phase transition of the biquadratic Heisenberg model at low dimension

We use the SU(3) Schwinger’s boson formalism to study the quantum phase transition of the S=1 biquadratic Heisenberg model in one and two dimensions, (1D) and (2D), with non-magnetic impurities on the lattice. In the 2D case, we consider the square lattice. We have verified the influence of the site dilution in the dependence of the gap with the force of coupling of the biquadratic term, β, on the Bose–Einstein condensation. Our results show that the inclination of the curve of decreasing of the gap with the −β parameter changes. However, the value of −β where the gap cancel does not change. We also obtain that the exciton energy cancels in a concentration of non-magnetic impurities x→0.5 indicating therefore, an absence of quasi-particles (excitons) to form a spin current in this concentration of impurities.

Effect of nonlinearity, magnetic and nonmagnetic impurities, and spin-orbit scattering on the nonlocal microwave response of ad-wave superconductor

By using linear response theory the low-temperature microwave response of a nonlocal and nonlinear d-wave superconductor with magnetic and nonmagnetic impurities is calculated. We will show that for the local, linear, and pure sample, penetration depth, Δλ(T), and conductivity, Δσ1(T), vary linearly with temperature, consequently the resistance, ΔR(T), would change linearly with temperature in agreement with experimental results and for the nonlocal, nonlinear sample the linear temperature dependences ΔR(T) change to quadratic function. For impure samples the nonlocality and nonlinearity effects are completely hidden by impurities and the temperature dependences Δλ(T) and Δσ1(T) are determined by temperature interval namely the ranges of T < T* and T* ≪ T ≪ Tc which T* is determined by nonmagnetic impurity concentration and the strength of impurity scattering. For T < T*, ΔR(T) varies as T2, on the other hand for, T* ≪ T ≪ Tc, ΔR(T) varies linearly with temperature. We will also show that the temperature dependence of surface resistance is unaffected by spin-orbit interaction and magnetic impurities.

Influence of dilution in the spin transport in the quantum anisotropic two-dimensional Heisenberg antiferromagnet

We study the influence of the site disorder in the long range order and in the spin transport in the two-dimensional Heisenberg antiferromagnet with ion-single anisotropy, in the square lattice in T=0 using the SU(3) Schwinger boson theory. We analyze these properties in the regime of Bose–Einstein condensation, where the bosons tz are condensed: 〈tz〉=〈tz†〉=t. In particular, we discuss the influence of the site disorder in the spin transport of this model and in the critical properties, where Dc separates Néel's phase, D<Dc, gapless phase, of the disordered phase, gapped phase, D>Dc, in the spin conductivity. We find that the behavior of the long-range order for D<Dc in the model without impurities with the concentration of nonmagnetic impurities does not affect the spin conductivity.

Controlling spin Hall effect by using a band anticrossing and nonmagnetic impurity scattering

The spin Hall effect (SHE) is one of the promising phenomena to utilize a spin current as spintronics devices, and the theoretical understanding of its microscopic mechanism is essential to know how to control its response. Although the SHE in multiorbital systems without inversion symmetry (IS) is expected to show several characteristic properties due to the cooperative roles of orbital degrees of freedom and a lack of IS, a theoretical understanding of the cooperative roles has been lacking. To clarify the cooperative roles, we study the spin Hall conductivity (SHC) derived by the linear-response theory for a $t_{2g}$-orbital tight-binding model of the $[001]$ surface or interface of Sr$_2$RuO$_4$ in the presence of dilute nonmagnetic impurities. We find that the band anticrossing, arising from a combination of orbital degrees of freedom and a lack of IS, causes an increase of magnitude and a sign change of the SHC at some nonmagnetic impurity concentrations. Since a similar mechanism for controlling the magnitude and sign of the response of Hall effects works in other multiorbital systems without IS, our mechanism provides an ubiquitous method to control the magnitude and sign of the response of Hall effects in some multiorbital systems by introducing IS breaking and tuning of the nonmagnetic impurity concentration.

The Effect of Nonmagnetic Impurities on Phase-Transition Kinetics and Correlation Effects in a Quasi-1D Ising Nanomagnetic

Using a Monte Carlo simulation, the effect of external field, temperature, system’s dimensions and interaction of non-nearest neighbors on the relaxation time and critical indices of an antiferromagnetic-to-ferromagnetic phase transition is investigated taking into account nonmagnetic impurities within a modified, onedimensional, nanosized Ising model. It is shown that the non-equilibrium processes taking place in the magnetic material could be classified as fast and slow, whose velocities differ by more than a thousand times. In the case of fast processes, metastable (including ferromagnetic) states (observed experimentally) are the first to form, while in the case of slow processes the system transits into a stable state. The behavior of the dynamic critical exponent (z) and static correlation-length critical exponent (ν) is revealed for the model of a 1D ferromagnetic for the case of arbitrary concentrations of nonmagnetic impurities.

Effect of impurities on the superheating field of type-II superconductors

We consider the effect of nonmagnetic and magnetic impurities on the superheating field $H_s$ in a type-II superconductor. We solved the Eilenberger equations, which take into account the nonlinear pairbreaking of Meissner screening currents, and calculated $H_s(T)$ for arbitrary temperatures and impurity concentrations in a single-band s-wave superconductor with a large Ginzburg-Landau parameter. At low temperatures nonmagnetic impurities suppress a weak maximum in $H_s(T)$ which has been predicted for the clean limit, resulting instead in a maximum of $H_s$ as a function of impurity concentration in a moderately clean limit. It is shown that nonmagnetic impurities weakly affect $H_s$ even in the dirty limit, while magnetic impurities suppress both $H_s$ and the critical temperature $T_c$. The density of quasiparticles states $N(\epsilon)$ is strongly affected by an interplay of impurity scattering and current pairbreaking. We show that a clean superconductor at $H=H_s$ is in a gapless state, but a quasiparticle gap $\epsilon_g$ in $N(\epsilon)$ at $H=H_s$ appears as the concentration of nonmagnetic impurities increases. As the nonmagnetic scattering rate $\alpha$ increases above $\alpha_c=0.36$, the quasiparticle gap $\epsilon_g(\alpha)$ at $H=H_s$ increases, approaching $\epsilon_g\approx 0.32\Delta_0$ in the dirty limit $\alpha\gg 1$, where $\Delta_0$ is the superconducting gap parameter at zero field. The effects of impurities on $H_s$ can be essential for the nonlinear surface resistance and superconductivity breakdown by strong RF fields.

Magnification of the spin Hall effect in a bilayer electron gas

Spin transport properties of a coupled bilayer electron gas with Rashba spin-orbit coupling are studied. The definition of the spin currents in each layer as well as the corresponding continuitylike equations in the bilayer system are given. The curves of the spin Hall conductivities obtained in each layer exhibit sharp cusps around a particular value of the tunneling strength and the conductivities undergo sign changes across this point. Our investigation on the impurity effect manifests that an arbitrarily small concentration of nonmagnetic impurities does not suppress the spin Hall conductivity to zero in the bilayer system. Based on these features, an experimental scheme is suggested to detect a magnification of the spin Hall effect.

Ab initiostudies of possible magnetism in aBNsheet by nonmagnetic impurities and vacancies

We performed first-principles calculations to investigate the possible magnetism induced by different concentrations of nonmagnetic impurities and vacancies in a $\mathrm{BN}$ sheet. Atoms of Be, B, C, N, O, Al, and Si are used to replace either B or N in the system as impurities. We discuss the changes in the density of states as well as the extent of the spatial distribution of the defect states, the possible formation of magnetic moments, the magnitude of the magnetization energies, and finally the exchange energies due to the presence of these defects. It is shown that the magnetization energy tends to increase as the concentration of the defects decreases in most of the defect systems, which implies a definite preference for finite magnetic moments. The calculated exchange energies are in general tiny but not completely insignificant for two of the studied defect systems, i.e., one with O impurities substituting for N and the other with B vacancies.

Minigap, parity effect, and persistent currents in SNS nanorings

We have evaluated a proximity-induced minigap in the density of states (DOS) of SNS junctions and SNS nanorings at an arbitrary concentration of non-magnetic impurities. We have demonstrated that an isotropic energy minigap in the electron spectrum opens up already at arbitrarily weak disorder, while angle resolved DOS at higher energies can remain strongly anisotropic. The minigap value $\epsilon_g$ can be tuned by passing a supercurrent through an SNS junction or by applying a magnetic flux $\Phi$ to an SNS ring. A non-monotonous dependence of $\epsilon_g$ on $\Phi$ has been found at weak disorder. We have also studied persistent currents in isolated SNS nanorings. For odd number of electrons in the ring we have found a non-trivial current-phase (current-flux) relation which -- at relatively high disorder -- may lead to a $\pi$-junction state and spontaneous currents in the ground state of the system.