arXiv subjects

A. N. Ignatenko

Publications and source records attributed to A. N. Ignatenko.

10 recordsLinked to original sources

arXiv2026

Monte Carlo study of the classical antiferromagnetic $J_1$-$J_2$-$J_3$ Heisenberg model on a simple cubic lattice

An extensive Monte Carlo study of the classical Heisenberg model on a simple cubic lattice with antiferromagnetic exchange interactions $J_n$ between the first, second, and third neighbors is performed in a broad region of $J_2 / J_1$, $J_3 / J_1$ ratios, and temperature. The character of the phase transitions is analyzed via the Binder cumulant method. The Neel temperature $T_{\mathrm{N}}$ and the frustration parameter (the ratio $f= |\theta|/T_{\mathrm{N}}$, $\theta$ being the Curie-Weiss temperature) are calculated. A comparison with the Tyablikov approximation is carried out. The strength of the frustration effects is explored. Possible applications to antiferromagnetic perovskites, such as CaMnO$_3$ and HgMnO$_3$, are discussed.

cond-mat.str-el↗

arXiv2018

Realization of anisotropic compass model on the diamond lattice of Cu$^{2+}$ in CuAl$_2$O$_4$

Spin-orbit (SO) Mott insulators are regarded as a new paradigm of magnetic materials, whose properties are largely influenced by SO coupling and featured by highly anisotropic bond-dependent exchange interactions between the spin-orbital entangled Kramers doublets, as typically manifested in $5d$ iridates. Here, we propose that a very similar situation can be realized in cuprates when the Cu$^{2+}$ ions reside in a tetrahedral environment, like in spinel compounds. Using first-principles electronic structure calculations, we construct a realistic model for the diamond lattice of the Cu$^{2+}$ ions in CuAl$_2$O$_4$ and show that the magnetic properties of this compound are largely controlled by anisotropic compass-type exchange interactions that dramatically modify the magnetic ground state by lifting the spiral spin-liquid degeneracy and stabilizing a commensurate single-$\boldsymbol{q}$ spiral.

cond-mat.str-el↗

arXiv2017

Universal Berezinskii-Kosterlitz-Thouless dynamic scaling in the intermediate timerange in frustrated Heisenberg antiferromagnets on triangular lattice

We investigate non-equilibrium properties of the frustrated Heisenberg antiferromagnets on the triangular lattice. Nonequilibrium critical relaxation of frustrated Heisenberg antiferromagnets shows a dynamic transition (or, at least, sharp crossover) at the same temperature $T_{\rm u}=0.282 J$ as for static properties due to unbinding of $\mathbb{Z}_2$-vortices. We show that starting from the high-temperature initial state, due to presence of $\mathbb{Z}_2$-vortices in the considering system, in a broad temperature range $T<T_{\rm u}$ the dynamic properties in the intermediate time range are similar to those of two-dimensional XY model below Berezinskii-Kosterlitz-Thouless transition. The interaction of $\mathbb{Z}_2$-vortices with spin-wave degrees of freedom does not emerge until rather long times.

cond-mat.str-el↗

arXiv2016

Frustrated Heisenberg Antiferromagnets on Cubic Lattices: Magnetic Structures, Exchange Gaps, and Non-Conventional Critical Behaviour

We have studied the Heisenberg antiferromagnets characterized by the magnetic structures with the periods being two times larger than the lattice period. We have considered all the types of the Bravais lattices (simple cubic, bcc and fcc) and divided all these antiferromagnets into 7 classes i.e. 3 plus 4 classes denoted with symbols A and B correspondingly. The order parameter characterizing the degeneracies of the magnetic structures is an ordinary Neel vector for A classes and so-called 4-complex for B classes. We have taken into account the fluctuation corrections for these states within the spin-wave and large-N expansions ($N$ is the number of spin components). Below the Neel temperature $T_{\rm{N}}$ quantum and thermal fluctuations lift the degeneracy making simple one-wave vector collinear structure preferable for all the classes. A satellite of this effect is opening of the exchange gaps at certain wave vectors in the spin wave spectrum (there is an analogous effect for the nonuniform static transverse susceptibility). However, as the temperature approaches $T_{\rm{N}}$, the exchange gaps are closing. We have calculated the critical indices $η$ and $ν$ to order of $1/N$ and found that they differ for A and B classes.

cond-mat.stat-mech↗

arXiv2015

Laser spectroscopy of finite size and covering effects in magnetite nanoparticles

The experiments on the impact of the size of magnetite clusters on various magnetic properties (magnetic moment, Curie temperature, blocking temperature etc.) have been carried out. The methods of magnetic separation, centrifuging of water suspensions of biocompatible iron oxide nanoparticles (NPs) allow producing fractions with diameter of nanoparticles in the range of 4÷22 nm. The size of NPs are controlled by the methods of dynamic light scattering (DLS), transmission electron microscopy (TEM) and atomic force microscopy (AFM). For the first time the DLS method is applied in real time to control the size during the process of the separation of the NPs in aqueous suspensions. The changes of the size of NPs cause a shift in the Curie temperature and in the changes in the specific magnetic properties of the iron NPs. The experimental data is interpreted on the basis of Monte Carlo simulations for the classical Heisenberg model with different bulk and surface magnetic moments. It is demonstrated experimentally and by theoretical modeling that magnetic properties of magnetite NPs are determined not only by their sizes, but also by the their surface spin states, while both growing and falling dependences of the magnetic moment (per Fe3O4 formula unit) being possible, depending on the number of magnetic atoms in the nanoparticle. Both NPs clean and covered with a bioresorbable layer clusters have been investigated.

cond-mat.mtrl-sci↗

arXiv2014

Anomalous temperature and field behaviors of magnetization in cubic lattice frustrated ferromagnets

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 $E_{\mathbf{k}}\sim D k^{2}$ 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 too strong frustration this leads to an unusual "concave" shape of the temperature dependence of magnetization, which is in agreement with experimental data on the europium chalcogenides. Anomalous temperature behavior of magnetization is confirmed by Monte Carlo simulation. Strong field dependence of magnetization (paraprocess) at finite temperature is found near the frustration point.

cond-mat.str-el↗

arXiv2013

Strong fluctuations near the frustration point in cubic lattice ferromagnets with localized moments

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 $E_{\mathbf{k}}\sim D k^{2}$ 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 too strong frustration this leads to an unusual "concave" shape of the temperature dependence of magnetization, which is in agreement with experimental data on the europium chalcogenides. The phase diagram is constructed by means of Monte Carlo simulation, and suppression of magnetization and Curie temperature is found in comparison with the results of the spin-wave theory. This effect is explained by the the presence of non-analytical corrections to the spin-wave spectrum which are represented in the lowest order by the term $\sim (T/S)^{2} k^{2}\log{k}$.

cond-mat.str-el↗

arXiv2011

The Neel temperature and sublattice magnetization for the stacked triangular-lattice antiferromagnet with a weak interlayer coupling

The quantum Heisenberg antiferromagnet on the stacked triangular lattice with the intralayer nearest-neighbor exchange interaction J and interlayer exchange J' is considered within the non-linear $σ$-model with the use of the renormalization group (RG) approach. For J' << J the asymptotic formula for the Neel temperature $T_{Neel}$ and sublattice magnetization are obtained. RG turns out to be insufficient to describe experimental data since it does not take into account the $\mathcal{Z}_2$-vortices. Therefore $T_{Neel}$ is estimated using the Monte-Carlo result for the 2D correlation length [10] which has a Kosterlitz-type behavior near the temperature $T_{KT}$ where the vortices are activated.

cond-mat.stat-mech↗

arXiv2008

Universal properties of frustrated spin systems: 1/N-expansion and renormalization group approaches

We consider a quantum two-dimensional O(N)xO(2)/O(N-2)xO(2) nonlinear sigma model for frustrated spin systems and formulate its 1/N-expansion which involves fluctuating scalar and vector fields describing kinematic and dynamic interactions, respectively. The ground state phase diagram of this model is obtained within the 1/N-expansion and 2+εrenormalization group approaches. The temperature dependence of correlation length in the renormalized classical and quantum critical regimes is discussed. In the region of the symmetry broken ground state ρ_in<ρ_out, χ_in<χ_out (rho_in,out and chi_in,out are the in- and out-of-plane spin stiffnesses and susceptibilities), where the mass M_μof the vector field can be arbitrarily small, physical properties at finite temperatures are universal functions of rho_in,out, chi_in,out, and temperature T. For small M_μthese properties show a crossover from low- to high temperature regime at T \sim M_μ. For ρ_in>ρ_out or χ_in>χ_out finite-temperature properties are universal functions only at sufficiently large M_μ. The high-energy behaviour in the latter regime is similar to the Landau-pole dependence of the physical charge e in quantum electrodynamics, with mass M_μplaying a role of e^{-1}. The application of the results obtained to the triangular-lattice Heisenberg antiferromagnet is considered.

cond-mat.str-el↗

arXiv2008

Strong short-range magnetic order in a frustrated FCC lattice and its possible role in the iron structural transformation

We investigate magnetic properties of a frustrated Heisenberg antiferromagnet with a face-centered cubic (FCC) lattice and exchange interactions between the nearest- and next-nearest neighbours, J1 and J2. In a collinear phase with the wave vector Q = (pi,pi,pi) the equations of the self-consistent spin-wave theory for the sublattice magnetization and the average short range order parameter are obtained and numerically solved. The dependence of the Neel temperature T_N on the ratio J2/J1 is obtained. It is shown, that at strong enough frustration there is a wide temperature region above T_N with strong short range magnetic order. Application of this result to description of structural phase transition between alpha and gamma-phase of Fe is considered.

cond-mat.str-el↗