We discuss the spin-wave interaction in two-dimensional (2D) Heisenberg ferromagnet (FM) with dipolar forces at $T_C\gg T\ge0$ using 1/S expansion. A comprehensive analysis is carried out of the first 1/S corrections to the spin-wave spectrum. In particular, similar to 3D FM discussed in our previous paper A.V. Syromyatnikov, PRB {\bf 74}, 014435 (2006), we obtain that the spin-wave interaction leads to the {\it gap} in the spectrum $ε_{\bf k}$ renormalizing greatly the bare gapless spectrum at small momenta $k$. Expressions for the spin-wave damping $Γ_{\bf k}$ are derived self-consistently and it is concluded that magnons are well-defined quasi-particles in both quantum and classical 2D FMs at small $T$. We observe thermal enhancement of both $Γ_{\bf k}$ and $Γ_{\bf k}/ε_{\bf k}$ at small momenta. In particular, a peak appears in $Γ_{\bf k}$ and $Γ_{\bf k}/ε_{\bf k}$ at small $k$ and at any given direction of $\bf k$. If $S\sim1$ the height of the peak in $Γ_{\bf k}/ε_{\bf k}$ is not larger than a value proportional to $T/D\ll1$, where $D$ is the spin-wave stiffness. In the case of large spins $S\gg1$ the peak in $Γ_{\bf k}/ε_{\bf k}$ cannot be greater than that of the classical 2D FM found at $k=0$ which height is small only {\it numerically}: $Γ_{\bf 0}/ε_{\bf 0}\approx0.16$ for the simple square lattice. Frustrating next-nearest-neighbor exchange coupling increases $Γ_{\bf 0}/ε_{\bf 0}$ in classical 2D FM only slightly. We find expressions for spin Green's functions and the magnetization. The latter differs from the well-known result by S.V. Maleev, Sov. Phys. JETP {\bf 43}, 1240 (1976). The effect of the exchange anisotropy is also discussed briefly.
Among the various methods for treating magnetic models, the Self-Consistent Harmonic Approximation (SCHA) has successfully described ferro and antiferromagnetism in many different scenarios. In particular, the SCHA is a valuable and easy formalism for determining transition temperatures as, for example, the Berezinskii-Kosterlitz-Thouless. The heart of the method includes thermal fluctuations through of a renormalization parameter depending on temperature. Nevertheless, most of the work has been done considering only short-range interactions, which results in an incomplete description of actua…
Two-component dipolar fermions in zigzag optical lattices allow for the engineering of spin-orbital models. We show that dipolar lattice fermions permit the exploration of a regime typically unavailable in solid-state compounds that is characterized by a novel spin-liquid phase with a finite magnetization and spontaneously broken SU(2) symmetry. This peculiar spin liquid may be understood as a Luttinger liquid of composite particles consisting of bound states of spin waves and orbital domain walls moving in an unsaturated ferromagnetic background. In addition, we show that the system exhibits …
Renormalization of the spin-wave spectrum is discussed in a cubic ferromagnet with dipolar forces at $T_C\gg T\ge0$. First 1/S-corrections are considered in detail to the bare spectrum $ε_{\bf k} = \sqrt{Dk^2 (Dk^2 + Sω_0\sin^2θ_{\bf k})}$, where $D$ is the spin-wave stiffness, $θ_{\bf k}$ is the angle between $\bf k$ and the magnetization and $ω_0$ is the characteristic dipolar energy. In accordance with previous results we obtain the thermal renormalization of constants $D$ and $ω_0$ in the expression for the bare spectrum. Besides, a number of previously unknown features are revealed. We ob…
We present a mean-field theory describing the influence of long-range dipolar forces on the temperature transition from the paramagnetic to ordered phases in frustrated Heisenberg spiral magnets. It is shown that the dipolar interaction produces a cascade of first- and second- order phase transitions between the paramagnetic and the spiral states upon temperature decreasing. Depending on system parameters, the following intermediate phases can arise: an incommensurate and a commensurate sinusoidally modulated states, spiral phases in which perpendicular spin components have different amplitude…
Magnetoelastic Waves in Ferromagnetic Thin Films Mediated by Dipolar Interactions
Institute of Science Tokyo（东京科学大学）；The University of Tokyo（东京大学）；NTT, Inc.（日本电报电话公司）；Japan Atomic Energy Agency（日本原子能研究开发机构）；RIKEN（理化学研究所）；Hiroshima University（广岛大学）
Using $1/S$ expansion, we discuss the magnon spectrum of Heisenberg antiferromagnet (AF) on a simple cubic lattice with small dipolar interaction at small temperature $T\ll T_N$, where $T_N$ is the Neel temperature. Similar to 3D and 2D ferromagnets, quantum and thermal fluctuations renormalize greatly the bare gapless spectrum leading to a gap $Δ\sim ω_0$, where $ω_0$ is the characteristic dipolar energy. This gap is accompanied by anisotropic corrections to the free energy which make the cube edges easy directions for the staggered magnetization (dipolar anisotropy). In accordance with previ…
Quantum annealing (QA) refers to an optimization process that uses quantum fluctuations to find the global minimum of a rugged energy landscape with many local minima. Conceptually, QA is often framed in the context of the disordered transverse field Ising model, in which a magnetic field applied perpendicular to the Ising axis tunes the quantum fluctuations and enables the system to tunnel through energy barriers, and hence reach the ground state more quickly. A solid state material closely related to this model, LiHo$_{0.45}$Y$_{0.55}$F$_4$, was shown to exhibit faster dynamics after a QA pr…
We study the Mott phases and superfluid-insulator transition of spin-three bosons in an optical lattice with an anisotropic two dimensional optical trap. We chart out the phase diagrams for Mott states with $n=1$ and $n=2$ atoms per lattice site. It is shown that the long-range dipolar interaction stabilizes a state where the chains of the ferromagnetically aligned spins run along the longer trap direction while the spin ordering is staggered between nearby chains, leading to an antiferromagnetic ordering along the shorter trap direction. We also obtain the mean-field phase boundary for the su…
The time evolution of magnons subject to a time-dependent microwave field is usually described within the so-called "S-theory", where kinetic equations for the distribution function are obtained within the time-dependent Hartree-Fock approximation. To explain the recent observation of "Bose-Einstein condensation of magnons" in an external microwave field [Demokritov et al., Nature 443, 430 (2006)], we extend the "S-theory" to include the Gross-Pitaevskii equation for the time-dependent expectation values of the magnon creation and annihilation operators. We explicitly solve the resulting coupl…
Many-body systems subject to a high-frequency drive can show intriguing thermalization behavior. Prior to heating to a featureless infinite-temperature state, these systems can spend an exponentially long time in prethermal phases characterized by various kinds of order. Here, we uncover the rich non-equilibrium phase diagram of a driven frustrated two-dimensional Ising magnet with competing short-range ferromagnetic and long-range dipolar interactions. We show that the ordered stripe and nematic phases, which appear in equilibrium as a function of temperature, underpin subsequent prethermal p…
Iron is one of the archetypical ferromagnets to study the critical fluctuations at a continuous phase transition thus serving as a model system for the application of scaling theory. We report a comprehensive study of the critical dynamics at the transition from the ferro- to the paramagnetic phase in Fe, employing the high-resolution neutron spin echo technique MIEZE. The results show that the dipolar interactions lead to an additional damping of the critical spin fluctuations at small momentum transfers $\bf q$. The results agree essentially with scaling theory if the dipolar interactions ar…
We present a comprehensive experimental and theoretical study of the pyrochlore Tb$_2$Ge$_2$O$_7$, an exemplary realization of a material whose properties are dominated by competition between magnetic dipolar and electric quadrupolar correlations. The dipolar and quadrupolar correlations evolve over three distinct regimes that we characterize via heat capacity, elastic and inelastic neutron scattering. In the first regime, above $T^*=1.1$ K, significant quadrupolar correlations lead to an intense inelastic mode that cannot be accounted for within a scenario with solely magnetic dipole-dipole c…
We study phase transitions in the two-dimensional Heisenberg model with the Dzyaloshinskii-Moriya interaction, the Ising anisotropy ($η$), and the dipolar interaction under zero and finite magnetic fields ($H$). For three typical strengths (zero, weak, and strong) of the dipolar interaction, we present the $H$-$η$ phase diagrams by estimating order parameters for skyrmion-lattice and helical phases and in-plane magnetization by using a Monte Carlo method with an $O(N)$ algorithm. We find in the phase diagrams three types of skyrmion-lattice phases, i.e., two square lattices and a triangular la…
We study the emergence of several magnetic phases in dipolar bosonic gases subject to three-body loss mechanism employing numerical simulations based on the density matrix renormalization group(DMRG) algorithm. After mapping the original Hamiltonian in spin language, we find a strong parallelism between the bosonic theory and the spin-1 Heisenberg model with single ion anisotropy and long-range interactions. A rich phase diagram, including ferromagnetic, antiferromagnetic and non-local ordered phases, emerges in the half-filled one-dimensional case, and is preserved even in presence of a trapp…
Spin ice, a peculiar thermal state of a frustrated ferromagnet on the pyrochlore lattice, has a finite entropy density and excitations carrying magnetic charge. By combining analytical arguments and Monte Carlo simulations, we show that spin ice on the two-dimensional kagome lattice orders in two stages. The intermediate phase has ordered magnetic charges and is separated from the paramagnetic phase by an Ising transition. The transition to the low-temperature phase is of the three-state Potts or Kosterlitz-Thouless type, depending on the presence of defects in charge order.
This is a comment on publication in Phys. Rev. Lett. 90, 087205 (2003): ``Exchange interaction parameters and adiabatic spin-wave spectra of ferromagnets: A `renormalized magnetic force theorem'''
The emergence of complex modulated structures in the magnetization pattern of thin films is a well-established experimental phenomenology caused by the frustrating effects of competing interactions. Using a coarse-grained version of the Ising ferromagnet with dipolar interactions, we develop a method that uses the information from the microscopic Hamiltonian to predict the specific topological phases present in the temperature-external magnetic field phase diagram. This is done by the combination of mean-field variational calculations and the renormalization group equations from the classical …
We investigate spin correlations in the dipolar Heisenberg antiferromagnet Gd2Sn2O7 using polarised neutron-scattering measurements in the correlated paramagnetic regime. Using Monte Carlo methods, we show that our data are sensitive to weak further-neighbour exchange interactions of magnitude ~0.5% of the nearest-neighbour interaction, and are compatible with either antiferromagnetic next-nearest neighbour interactions, or ferromagnetic third-neighbour interactions that connect spins across hexagonal loops. Calculations of the magnetic scattering intensity reveal rods of diffuse scattering al…
