The <Superscript>55</Superscript>Mn Spin Echo Test of Magnon BEC State in MnCO<Subscript>3</Subscript>

The coherent quantum state of magnons—Bose–Einstein condensate (BEC) has been observed in several types of antiferromagnets. According to the Bose statistics of magnons, BEC appears when the magnon density exceeds the critical density N _BEC and the magnon gas condenses to a quantum liquid. The BEC state is characterized by a coherent precession of the magnetization. In this paper, the first experiments showing the suppression of the spin echo signal by the magnon BEC is presented. These experiments confirm the coherence of magnetic excitations in the BEC state.     

Spin transport of the quantum integer spin S one-dimensional Heisenberg antiferromagnet coupled to phonons

We study the effect of the spin-phonon coupling on spin transport in the S = 1 one-dimensional Heisenberg antiferromagnet. The spin conductivity is calculated using the modified spin wave theory and the Kubo formalism of transport. We calculate the regular part of the spin conductivity, σ ^reg (ω), as function of the frequency at finite temperature. We obtain a strong effect of the magnon-phonon interaction on magnon transport.     

Long-wavelength magnetic excitations in the Fe<Subscript>65</Subscript>Ni<Subscript>35</Subscript> alloy

A theoretical analysis of small-angle neutron scattering is performed for the Fe₆₅Ni₃₅ alloy at a temperature T=0.9T _C =450 K. The results obtained indicate the existence of long-wavelength magnetic excitations that do not correspond to spin waves of the Holstein-Primakoff type. The possible nature of these excitations is discussed.     

Semiclassical dynamics of vortices in 2D easy-plane ferromagnets

Semiclassical dynamics of magnetic vortices in 2D lattice models of easy-plane ferromagnets is investigated. It is shown that the low-energy part of the spectrum of vortices treated as quantum excitations of the system exhibits a nontrivial structure. The simplest spectrum is observed for standard magnetic vortices, in which magnetization at long distances from the center of a vortex is parallel to the basal plane. In this case, the spectrum has a band structure consisting of several nonintersecting bands, whose number is determined only by the value of atomic spin S and lattice symmetry. For purely 2D magnets with a single spin per unit cell, the number of bands is S or 2S for integral and half-integral values of spin S, respectively. For a lattice with the basis with an even number 2n of spins per unit cell, the number of bands is 2nS for any spins. The situation radically changes for vortices in the cone state as compared to standard vortices, for which the magnetization at a long distance from the center of a vortex rotates in the easy plane of the magnet. Vortices in the cone state are formed under the action of a constant external field perpendicular to the easy plane of the magnet. As a rule, the spectrum for such vortices is not a standard band spectrum and forms a set such that a forbidden energy value can be found in any small neighborhood of an allowed value, and vice versa. The possibility of an oscillatory motion of a vortex under the action of a constant external force is indicated (analog of Bloch oscillations of electrons in crystals). Possible realization of these effects in other ordered media with vortices is considered.     

Low-Temperature Transport Properties of Lanthanum Hexaboride La<Subscript>1–<Emphasis Type="Italic">x</Emphasis></Subscript>Ce<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>B<Subscript>6</Subscript> Single Crystals

Resistivity (ρ), thermal conductivity (k) and Seebeck coefficient (S) of La_1–xCe_xB₆ single crystals with various concentrations of cerium Ce ions was measured in a wide temperature range 3?300 K. The obtained data were analyzed in the framework of the Coqblin–Shrieffer model. The contributions of scattering of carriers on magnetic ions Ce for all transport parameters ρ(T), k(T), S(T) are revealed. Strong dependence of the magnetic scattering on concentration of the cerium ions are identified. The anomalous behavior of the transport parameters ρ(T), k(T), S(T) in the region near 30 K is attributed to the Δ ~ 30 K splitting of Г₈ level.     

Excitonic representation: Collective excitation spectra in the quantized Hall regime and spin biexciton

The excitonic representation method for describing collective excitations in the quantized Hall regime makes it possible to simplify analysis of the spectra and to obtain new results in the strong magnetic field limit, when E _C ??ω_c (ω_c is the cyclotron frequency and E_C is the characteristic Coulomb energy). For an integer odd filling factor ν greater than unity (i.e., for ν = 3, 5, 7,...), the spectra of one-cyclotron magneto-plasma excitations are calculated. For unit filling factor, the existence of a spin biexciton (bound state of two spin waves) corresponding to excitation with a spin change (δ_S = δ_Sz = ?2) is proved. The exact equation determining the ground state of the biexciton is derived in the thermodynamic limit N_Φ → ∞ (_N? is the system degeneracy). The exchange energy of this state is lower than for a single spin wave (with δ_S = δ_Sz = ?1) for the same value of the 2D wavevector q. In the limit q → ∞ corresponding to the decay of a biexciton into a pair of quasiparticles one of which is a trion with a spin of ?3/2, the energy is found to be lower than the energy (e²/εl _B )√π/2 required for exciting an electron-hole pair in the strictly 2D case (l_B is the magnetic length and ε is the dielectric constant), although this energy is higher than another “classical” result (e²/εl _B )√π/2, corresponding to the excitation of a skyrmion-antiskyrmion pair (|δS|=|δS _z |?1). The solution of the exact equation gives the trion binding energy and the activation gap for quasiparticles whose excitation corresponds to a change in the total spin by δS = δ S_z =?3. The energy of a spin biexciton is calculated for values of the wavevector such that ql _B ?1.     

Calculation of the Cross Sections for Neutron Scattering at Spin Waves in Helimagnets

An analytical dependence of the cross section for the small-angle scattering of polarized neutrons at spin waves in helimagnets formed because of Dzyaloshinskii—Moriya interaction in cubic crystals without an inversion center (the space group is P2₁3) is obtained. It is assumed that the dispersion of spin waves in helimagnets with the wave vector k _s polarized by a magnetic field is larger than the critical field H_C2 of the transition to the ferromagnetic phase and has the form E _q = A(q ? k _s ) + gμ_B(H ? H_С2). It is shown that the cross section for neutron scattering at the two-dimensional map of angles (θ _x , θ _y ) is two circles of the radii θ_C with the centers ±θ _S , corresponding to the Bragg angle of diffraction by a helix oriented along the applied magnetic field H. The radii of these two circles θ_C are directly related to the stiffness of spin waves A of the magnetic system and depends on the applied magnetic field: \(\theta _C^2 = \theta _0^2 - \frac{{g{\mu _B}H}}{{{E_n}}}{\theta _0}\), where \({\theta _0} = \frac{{{h^2}}}{{2A{m_n}}}\) and E _n and m _n are the neutron energy and mass. It is shown that the scattering cross section depends on the neutron polarization, which is evidence of the chiral character of spin waves in the Dzyaloshinskii—Moriya helimagnets even in the completely polarized phase. The cases of neutron scattering at magnons where θ₀ ≤ θ _S and θ _S ≥ θ₀ are considered. The case of neutron scattering at spin waves in helimagnets is compared with analogous scattering at ferromagnets where θ _S → 0.     

Wärmewiderstand durch Spinwellen —Spinwellenstreuung in einem Ferromagnetikum

The heat conduction by spin waves is obtained using the Boltzmann equation and considering only magnon-magnon scattering. In contrast to the case of phonons with a linear energy-momentum relationship, Umklapp processes need not be considered to obtain a non-vanishing collision-term in the Boltzmann equation for magnons. In a spin system with a Hamiltonian consisting of exchange and anisotropy energies the temperature dependence of the thermal resistivity isa+bT ^3/2 within the spin wave approximation.     

String order and degenerate entanglement spectrum of S = 1 / 2 and S = 1 Heisenberg bond-alternating chains

Generalized string orders and entanglement spectrum of S = 1/2 and S = 1 Heisenberg bond-alternating chains have been investigated by the infinite time-evolving block decimation (iTEBD) method. Generalized string order parameters with appropriate θ are capable of distinguishing all the topological phases. Central charges c ? 1 and critical exponents β ?1/12 indicate all the topological QPTs belong to the Gaussian universality class. Interestingly, odd- and even-fold degeneracies of the entanglement spectrum are observed. Even-fold (doubly) degenerate entanglement spectra and the typical two-fold degenerate lowest-lying level are found to exist in both the spin-1/2 dimer and the S = 1 Haldane phases. However, odd-fold degenerate entanglement spectra with three-fold degenerate lowest-lying level are observed in both the S = 1 dimer and the S = 2 Haldane phase. The degeneracy of the lowest-lying entanglement spectrum level, which can be understood by entanglement spectra in the dimer limit (J ₁ = 0), is adopted to estimate the lowest boundary of the bipartite entanglement. The entanglement spectrum and the generalized string orders are valuable for uncovering the underlying features of these symmetry-protect topological (SPT) states. Similar entanglement spectrum shows that the S = 1 (S = 2) Haldane phase is essentially the same as the S = 1/2 (S = 1) dimer phase.     

Intersubband magnetoplasmon as a detector of the spin polarization in two-dimensional electron systems

The magnetic field dynamics of intersubband collective excitations in two-dimensional electron systems based on Mg _x Zn_1-x O/ZnO heterostructures is studied by the Raman scattering method. It is found that, upon the change in the spin polarization under conditions of the transition from the filling factor ν = 2 to ν = 1, the energy of the intersubband magnetoplasmon changes considerably. The performed theoretical analysis shows that this effect is attributed to the concomitant change in the exchange interaction in the excitation energy.     

2 + 1 Flavors QCD Equation of State in NJL Model with Proper Time Regularization

Totally symmetric A_1g phonons are studied for the equilibrium and coherent states of a Bi₂Te₃ lattice. Equilibrium phonons were investigated in the frequency domain by the method of spontaneous Raman scattering, whereas coherent phonons were studied by the method of active femtosecond spectroscopy in the time domain. In the latter case, femtosecond laser pulses were used both for generating and detecting coherent A_1g phonons having a well-defined phase allowing the selective optical control of the lattice dynamics. A comparison of the results obtained in the frequency and time domains suggests that diagonal and nondiagonal elements of the density matrix of lattice excitations relax with the same characteristic time to the equilibrium and zero values, respectively.     

Magnetization of beryllium oxide in the presence of nonmagnetic impurities: Boron,carbon, and nitrogen

The electronic and magnetic states of a nonmagnetic insulator, namely, beryllium oxide, doped with nonmagnetic 2p elements (boron, carbon, and nitrogen) are studied using the density functional theory. The spin polarization of the 2p impurity states, as well as the transition of the doped BeO:(B,C,N) systems to the states of semiconducting or half-metallic magnets, is observed. The prospects for creating new magnetic materials by doping nonmagnetic insulators with nonmagnetic p impurities are discussed.     

Study of the atom-phonon coupling model for (SC) partition function: first order phase transition for an infinite linear chain

In spin-conversion (SC) compounds containing molecules organized around an iron (II) ion the fundamental level of the ion is low spin (LS), S = 0, and its first excited one is high spin (HS), S = 2. This energy diagram is due to the ligands field interaction on 3d electrons and to the spin pairing energy. Heating the compound increases the magnetic susceptibility which corresponds to a change of populations of both levels and consequently a change of spin value of the molecules. This mechanism, called spin conversion (SC), can be accompagnied by thermal hysteresis observed by studying magnetic susceptibility or high spin fraction. In that case one considers that the (SC) takes place through a first-order phase transition due to intermolecular interactions. In the atom-phonon coupling model the molecules are considered as two-level systems, or two-level atoms, and it is assumed that the elastic force constant value of the spring which links two atoms first neighbours is depending on the electronic states of both atoms. In this study we calculate the partition function of a linear chain of N atoms (N ≤ 16) and we describe the role of phonons and that of the parameter Δ which corresponds to the distance in energy between both levels. The chain free-energy function is F _atph . We introduce for the chain a free-energy function defined by the set (F _HS , F _LS , F _barr ) and we show that F _atph tends towards the previous set when N → ∞. The previous set allows to describe a first order phase transition between a (LS) phase and a (HS) one. At the crossing point between the function F _LS and F _HS , and around this point, there is an intermediate free-energy barrier which prevents the chain to change phase which can lead to thermal hysteresis. The energy gap between the free-energy function F _atph and that defined by the set (F _HS , F _LS , F _barr ) is small. So we can expect that a nanoparticule takes for free-energy function that defined by the set and then displays a thermal hysteresis.     

Heat conduction in low-dimensional quantum magnets

Transport properties provide important information about the mobility, elastic and inelastic of scattering of excitations in solids. Heat transport is well understood for phonons and electrons, but little is known about heat transport by magnetic excitations. Very recently, large and unusual magnetic heat conductivities were discovered in low-dimensional quantum magnets. This article summarizes experimental results for the magnetic thermal conductivity κ_mag of several compounds which are good representations of different low-dimensional quantum spin models, i.e. arrangements of S=1/2 spins in the form of two-dimensional (2D) square lattices and one-dimensional (1D) structures such as chains and two-leg ladders. Remarkable properties of κ_mag have been discovered: It often dwarfs the usual phonon thermal conductivity and allows the identification and analysis of different scattering mechanisms of the relevant magnetic excitations.     

Temperature behavior of resistivity of a two-dimensional doped antiferromagnet depending on its spin susceptibility

The temperature dependence of resistivity ρ(T) of a two-dimensional doped antiferromagnet is studied for different forms of spin susceptibility χ(q, ω): with allowance for the damping and renormalization of the magnetic excitation spectrum and for the so-called strongly damped magnons. The kinetic equation is constructed on the basis of the spin-fermion model for the carrier scattering from spin fluctuations. The temperature-dependent scattering anisotropy is taken into account using the seven-moment approximation for the nonequilibrium distribution function. It is demonstrated that the resistivity calculation on the basis of the self-consistent expression for χ(q, ω) with allowance for damping qualitatively reproduces the experimental anomalous behavior of ρ(T) in high-temperature superconductors. At the same time, the strongly damped magnon approximation, which is widely used for χ(q, ω) representation, proves to be incorrect in the high-temperature region.     

Low-energy Ce spin excitations in CeFeAsO and CeFeAsO<Subscript>0.84</Subscript>F<Subscript>0.16</Subscript>

We use inelastic neutron scattering to study the low-energy spin excitations of polycrystalline samples of nonsuperconducting CeFeAsO and superconducting CeFeAsO_0.84F_0.16. Two sharp dispersionless modes are found at 0.85 and 1.16 meV in CeFeAsO below the Ce antiferromagnetic (AF) ordering temperature of T _N ^Ce ? 4 K. On warming to above T _N ^Ce ? 4 K, these two modes become one broad dispersionless mode that disappears just above the Fe ordering temperature T _N ^Fe ? 140 K. For superconducting CeFeAsO_0.84F_0.16, where Fe static AF order is suppressed, we find a weakly dispersive mode center at 0.4 meV that may arise from short-range Ce-Ce exchange interactions. Using a Heisenberg model, we simulate powder-averaged Ce spin wave excitations. Our results show that we need both Ce spin wave and crystal electric field excitations to account for the whole spectra of low-energy spin excitations.     

Terahertz Cyclotron Photoconductivity in a Highly Unbalanced Two-Dimensional Electron–Hole System

The magnetic properties of the α-Fe₂O₃ hematite at a high hydrostatic pressure have been studied by synchrotron Mössbauer spectroscopy (nuclear forward scattering (NFS)) on iron nuclei. Time-domain NFS spectra of hematite have been measured in a diamond anvil cell in the pressure range of 0–72 GPa and the temperature range of 36–300 K in order to study the magnetic properties at a phase transition near a critical pressure of ~50 GPa. In addition, Raman spectra at room temperature have been studied in the pressure range of 0–77 GPa. Neon has been used as a pressure-transmitting medium. The appearance of an intermediate electronic state has been revealed at a pressure of ~48 GPa. This state is probably related to the spin crossover in Fe³⁺ ions at their transition from the high-spin state (HS, S = 5/2) to a low-spin one (LS, S = 1/2). It has been found that the transient pressure range of the HS–LS crossover is extended from 48 to 55 GPa and is almost independent of the temperature. This surprising result differs fundamentally from other cases of the spin crossover in Fe³⁺ ions observed in other crystals based on iron oxides. The transition region of spin crossover appears because of thermal fluctuations between HS and LS states in the critical pressure range and is significantly narrowed at cooling because of the suppression of thermal excitations. The magnetic P–T phase diagram of α-Fe₂O₃ at high pressures and low temperatures in the spin crossover region has been constructed according to the results of measurements.     

On the spin wave spectrum in a layered antiferromagnetic structure of the LaMnO<Subscript>3</Subscript> compound

Theoretical expressions are obtained for the energy of spin waves in a layered antiferromagnetic structure (A type) of the perovskite-like compound LaMnO₃. The Heisenberg exchange interactions of the central spin moment of the trivalent manganese ion (spin S = 2) with its eighteen neighbors from five coordination shells and the single-ion magnetic anisotropy energy are taken into account. The analysis is performed using six parameters: five exchange integrals and one anisotropy constant. Three of these five integrals determine the interactions in the two-dimensional ferromagnetic planes and two integrals characterize the interplanar interaction. The expressions derived for the magnon energy are valid for any direction and any magnitude of the quasi-momentum in the first Brillouin zone. For the three principal crystallographic directions, the theoretical results are compared with the experimental data for the dispersion curves obtained from inelastic neutron scattering studies of the LaMnO₃ compound. It is shown that the in-plane ferromagnetic interaction can be more than sixteen times as great as the interplanar antiferromagnetic interaction. The conclusions drawn in this study are compared with the results obtained by other authors.     

Proximity effect of a superconductor on an antiferromagnetic metal

There should be two contributions to the pair breaking energy in an antiferromagnetic metal. The first, already discussed byde Gennes andSarma, is due to disorder on the magnetic sites. The second is a temperature dependent contribution from electron magnon scattering. This term is calculated for the temperature rangeT _N(J/μ)²?T?T _N and found to be of orderT ²/T _N. (T _N = Néel temperature,μ = Fermi energy,J = exchange coupling between conduction electrons and magnetic ions.)     

Doping-induced temperature evolution of a helicoidal spin structure in the MnGe compound

The helicoidal magnetic structure of a MnGe compound doped with 25% Fe is studied by means of small-angle neutron scattering in a wide temperature range of 10–300 K. Analysis of the scattering-function profile demonstrates that magnetic structures inherent to both pure MnGe and its doped compounds are unstable. The doping of manganese monogermanide is revealed to lead to higher destabilization of the magnetic system. In passing from MnGe to Mn_0.75Fe_0.25Ge, the magnetic-ordering temperature T _N decreases from 130 to 95 K, respectively. It is demonstrated that, at temperatures close to 0 K, the intensity of the contribution to scattering from stable spin helices decreases and the intensity of scattering by spin helix fluctuations increases with increasing impurity-metal concentration. An increased intensity of anomalous scattering caused by spin excitations existing in the system is observed. Helicoidal fluctuations and spin excitations corresponding to low temperatures indicate the quantum nature of the instability in the doped compound. However, MnGe doping with Fe atoms has no influence on the compound’s magnetic properties at temperatures of higher than T _N. The temperature range of short-range ferromagnetic correlations is independent of concentrations and is restricted by temperatures T ranging from 175 to 300 K.