Dynamic Spin-fluctuation Theory Research Articles

Paramagnetic susceptibility and spin correlation function of ferromagnetic metals in the critical region

We study paramagnetic characteristics of ferromagnetic metals near the Curie temperature TC using the dynamic spin fluctuation theory. In contrast with most first-principles calculations, our results for the uniform paramagnetic susceptibility show a clear deviation from the Curie–Weiss law. We demonstrate that the susceptibility and correlation radius have the power-law behavior at temperatures up to 1.1–1.15TC, which gives an estimate for the region of critical temperatures in metals. Our theoretical critical exponents for Fe, Co, and Ni are in reasonable agreement with the low-field susceptibility measurements and neutron scattering experiments.

Kriticheskie yavleniya v dinamicheskoy teorii spinovykh fluktuatsiy

Paramagnetic susceptibility and spin-density correlation function near the Curie temperature TC are studied using the dynamic spin fluctuation theory. The calculated critical indices of the susceptibility and correlation radius for Fe, Co, and Ni are found in reasonable agreement with bulk susceptibility measurements and neutron scattering experiments. It is shown that the critical power-law behavior holds at temperatures up to 1.10–1.15TC, which gives an estimate of the critical temperature region in ferromagnetic metals.

Random iron-nickel alloys: From first principles to dynamic spin fluctuation theory

We provide a systematic analysis of finite-temperature magnetic properties of random alloys ${\mathrm{Fe}}_{x}{\mathrm{Ni}}_{1\ensuremath{-}x}$ with the face-centered-cubic structure over a broad concentration range $x$. By means of the spin-polarized relativistic Korringa-Kohn-Rostoker method we calculate the electronic structure of disordered iron-nickel alloys and discuss how a composition change affects magnetic moments of Fe and Ni and the density of states. We investigate how the Curie temperature depends on Fe concentration using conventional approaches, such as mean-field approximation or Monte Carlo simulations, and dynamic spin-fluctuation theory. Being devised to account for spin fluctuations explicitly, the latter method shows the best fit to experimental results.

Magnetic susceptibility in metals above the Curie temperature

We calculate the magnetic susceptibility in ferromagnetic metals above the Curie temperature TC using the dynamic spin fluctuation theory and make a detailed comparison with experiment. Calculation results for Fe, Co and Ni are found in good agreement with experiment over a wide temperature range. The paramagnetic Curie temperature is found 7–8% larger than the ferromagnetic one in agreement with experiment and various approximations of the Heisenberg model. We calculate the spin-density correlator to show that magnetic short-range order leads to deviation of the susceptibility from the Curie-Weiss law in the temperature interval up to1.1–1.2TC.

Numerical Continuation Method for Nonlinear System of Scalar and Functional Equations

We propose a numerical continuation method for a nonlinear system that consists of scalar and functional equations. At each parameter step, we solve the system by a modified Gauss–Seidel method. An advantage of this method is that the system is divided into two parts and each part is solved by a suitable numerical method with a desired precision. We solve the functional equations self-consistently at each step of the iteration process for the system of scalar equations. We apply the proposed method for calculating temperature dependence of magnetic characteristics of metals in the dynamic spin-fluctuation theory.

Effect of lattice vibrations on magnetic properties of metals at finite temperatures

We investigate the effect of electron-phonon interaction in the dynamic spin-fluctuation theory of metallic magnetism. Electron-phonon interaction is represented by fluctuations of the crystal lattice potential. We illustrate the theoretical results in the example of Fe and Ni. We show that the effect of phonons on temperature dependence of magnetic characteristics is appreciable in Fe, but not as large as in the static single-site spin-fluctuation theory and spin dynamics using classical Hamiltonians. On the contrary, in Ni the effect of phonons is small in agreement with the results of the spin dynamics.

Effect of Phonons on the Magnetic Characteristics of Metals at Finite Temperatures

We consider the electron-phonon interaction in the framework of dynamic spin-fluctuation theory and obtain an expression for the self-energy part that depends explicitly on the spin fluctuations and lattice vibrations. We illustrate the theoretical results with the example of iron. We show that the effect of phonons on temperature dependence of the magnetic characteristics of metals is appreciable but not as large as in the static single-site approximation of the spin-fluctuation theory and spin dynamics using classical Hamiltonians.

Magnetic short-range order in Fe and Ni above the Curie temperature

Abstract We study magnetic short-range order in Fe and Ni above the Curie temperature using the nonlocal dynamic spin-fluctuation theory with self-consistent calculation of the self-energy. We calculate the spatial correlation function of Fe and Ni at nearest neighbours, next-nearest neighbours, etc., in a wide range of temperatures. Our results are in agreement with neutron scattering experiments but give a larger short-range order compared to classical spin models. We show that the spatial spin correlator decreases ten times at distances of about 6 A in Fe and 8 A in Ni at T / T C = 1.1 and short-range order remains well above the Curie point.

Short-range order in metals above the Curie temperature

We use the dynamic spin-fluctuation theory to study spin-density correlations in ferromagnetic metals above the Curie temperature. We calculate the spatial spin-correlation function, dynamic susceptibility and local magnetic moment. The dynamic susceptibility is related to the energy-integrated scattering cross-section (effective moment). Calculated effective and local moments of Fe and Ni are found in good agreement with results of polarized neutron scattering experiment over a wide temperature range. We find that short-range order remains up to distances of about 6 Å in Fe and 8 Å in Ni at TTC = 1.1 and slowly decreases with temperature.

Spin-Density Correlations and Short-Range Order in Metals above the Curie Temperature

In the dynamic spin-fluctuation theory, we calculate the effective and local magnetic moments and spatial spin-density correlator. Our theoretical results are demonstrated by the example of bcc Fe. The effective and local moments are found in good agrement with results of polarized neutron scattering experiment over a wide temperature range. The calculated short-range order is small (up to 5 Å) and slowly decreases with temperature

Spin–density correlations and magnetic neutron scattering in ferromagnetic metals

We obtain expressions for the spatial spin-density correlator and for effective and local magnetic moments in the dynamic spin-fluctuation theory. We derive formulas for the magnetic scattering cross section in the theory of itinerant electron magnets. We calculate magnetic characteristics of bcc Fe in the paramagnetic state and compare our numerical results with the polarized neutron scattering experiment. We show that the short-range order in bcc Fe persists up to a temperature much higher than the Curie temperature but at rather small distances (up to 5A).

Magnetism of metals in the dynamic spin-fluctuation theory

We overview new developments in spin-fluctuation theory, which describes magnetic properties of ferromagnetic metals at finite temperatures. We present a detailed analysis of the underlying techniques and compare numerical results with experiment.

Spin-density correlations in the dynamic spin-fluctuation theory: Comparison with polarized neutron scattering experiments

To study the spin-density correlations in the ferromagnetic metals above the Curie temperature, we relate the spin correlator and neutron scattering cross-section. In the dynamic spin-fluctuation theory, we obtain explicit expressions for the effective and local magnetic moments and spatial spin-density correlator. Our theoretical results are demonstrated by the example of bcc Fe. The effective and local moments are found in good agreement with results of polarized neutron scattering experiment over a wide temperature range. The calculated short-range order is small (up to 4Å) and slowly decreases with temperature.

Short-range order above the Curie temperature in the dynamic spin-fluctuation theory

Based on the dynamic spin-fluctuation theory, we study the spin-density correlations in the ferromagnetic metals. We obtain computational formulae for the correlation function and correlation radius in different approximations of the theory. Using these formulae, we calculate the magnetic short-range order above the Curie temperature in bcc Fe. Results of the calculation confirm our theoretical prediction that the inverse correlation radius increases linearly with temperature for T sufficiently large. The calculated short-range order is small but sufficient to correctly describe neutron scattering experiments. A considerable amount of the short-range order is shown to persist up to temperatures much higher than the Curie temperature.

Low-Temperature Spin Fluctuations beyond Spin Waves

A simple low-temperature dynamic spin-fluctuation theory of ferromagnetic metals is developed. The theory is based on the functional integral formalism for the multiband Hubbard Hamiltonian and takes into account both single-site and nonlocal spin fluctuations. We show that our approach correctly reproduces the T3/2 law at low temperatures. The calculated results of magnetic properties for Fe and Fe0.65Ni0.35 Invar demonstrate that the approach works on a much wider temperature interval than the spin-wave approximation.

Short-range Order Above TC in Ferromagnetic Metals

We study the spin-density correlations in ferromagnetic metals using the dynamic spin-fluctuation theory. We derive computational formulae for the spatial correlation function and use them to calculate the short-range order above TC in bcc Fe. Results of the calculation confirm our theoretical prediction that the inverse correlation radius increases linearly with temperature for T sufficiently large. The calculated short-range order is small but sufficient to correctly describe neutron scattering experiments. We show that considerable amount of the short-range order persists up to temperatures much higher than TC.

Transverse susceptibility and the T3/2 law in the dynamic spin-fluctuation theory

We obtain explicit expressions for elements of the magnetic susceptibility tensor in the dynamic spin-fluctuation theory. Using an analytic continuation of the Green’s functions, we show that the transverse susceptibility has spin-wave poles at low temperatures, yielding the asymptotic T3/2 law for magnetization. We derive an explicit expression for the coefficient in the T3/2 law based on the multiband Hubbard Hamiltonian and real band structure. We demonstrate the correct low-temperature behavior of magnetization in the example of iron.

Low-Temperature Magnetism of Metals in the Dynamic Spin-Fluctuation Theory

The low-temperature behavior of magnetization in ferromagnetic metals is studied by means of the dynamic spin-fluctuation theory. An expression is derived for the dynamic magnetic susceptibility, which extends the one in the random phase approximation. The transverse susceptibility is shown to have the spin-wave poles, which yield the asymptotic T 3/2 law for magnetization. An explicit expression for the coefficient in the T 3/2 law is derived on the basis of the multiband Hubbard Hamiltonian and real band structure. The temperature dependence of magnetization is demonstrated by the example of Fe and disordered Fe-Ni Invar.

Extended Dynamic Spin-Fluctuation Theory with Application to Iron

The problem of discontinuous phase transition in the dynamic spin-fluctuation theory is resolved by taking into account large anharmonic spin fluctuations and nonlocality of the mean Green function. The extended theory is applied to the calculation of magnetic properties of iron.

Local Moments in the Dynamic Spin-Fluctuation Theory of Metallic Magnetism

In the dynamic spin-fluctuation theory extended by taking into account higher-order terms of the free energy and uniform fluctuations along with the local ones, simple computational formulae for local magnetic moment are obtained. The temperature dependence of local magnetic moment in the Fe0.65Ni0.35 Invar is calculated. Good agreement with the experimentally estimated value of the magnetic volume change is achieved.