Магнитный резонанс в низкотемпературных парамагнетиках

Phases analogous to supersolids can be realized in spin systems. Here we have obtained, using a bond-operator representation, a mean-field theory and a generalized spin-wave theory, the phase diagram of a frustrated dimer-spin-$\frac{1}{2}$ system on a square lattice and study the collective excitation spectra, focusing on the supersolid (SS) state. In the phase diagram on a parameter space of the exchange interaction and magnetic field, we have identified not only the SS phase, but a phase that has no counterpart in the Bose-Hubbard model and this state becomes dominant at the region where the enhancement of SS occurs in the Bose-Hubbard model. We then investigate the excitation spectrum and spin-spin correlation, detectable by neutron-scattering experiments. We obtain an analytic expression for the spin-wave velocity, which agrees with hydrodynamic relations. The intensity of excitation modes in the spin-spin correlation function is calculated and their change in the supersolid and superfluid states is discussed.

Dimensionality is a critical factor in determining the properties of solids and is an apparent built-in character of the crystal structure. However, it can be an emergent and tunable property in geometrically frustrated spin systems. Here, we study the spin dynamics of the tetrahedral cluster antiferromagnet, pharmacosiderite, via muon spin resonance and neutron scattering. We find that the spin correlation exhibits a two-dimensional characteristic despite the isotropic connectivity of tetrahedral clusters made of spin 5/2 Fe3+ ions in the three-dimensional cubic crystal, which we ascribe to two-dimensionalisation by geometrical frustration based on spin wave calculations. Moreover, we suggest that even one-dimensionalisation occurs in the decoupled layers, generating low-energy and one-dimensional excitation modes, causing large spin fluctuation in the classical spin system. Pharmacosiderite facilitates studying the emergence of low-dimensionality and manipulating anisotropic responses arising from the dimensionality using an external magnetic field.

We utilize the graphon—a continuous mathematical object which represents the limit of convergent sequences of dense graphs—to formulate a general, continuous description of quantum spin systems in thermal equilibrium when the average coordination number grows extensively in the system size. Specifically, we derive a closed set of coupled nonlinear Fredholm integral equations which governs the properties of the system. The graphon forms the kernel of these equations, and their solution yields exact expressions for the macroscopic observables in the system in the thermodynamic limit. We analyze these equations for both quantum and classical spin systems, recovering known results and providing analytical solutions for a range of more complex cases. We supplement this with controlled, finite-size numerical calculations using Monte Carlo and tensor network methods, showing their convergence towards our analytical results with increasing system size. Published by the American Physical Society 2024

Spin waves (SWs) are emerging as a potential alternative to electrical signals for computing and signal processing. Because SWs have relatively short wavelengths at microwave frequencies, they have the potential for applications in high-speed chip-scale electronics [1]. This work seeks to design and fabricate a spin-wave-based real-time spectrum analyzer that exploits SW interference in analogy to an optical spectrometer [2]. Here, microwave electrical signals are converted into SWs. All processing is then done by the diffraction and interference of SWs as they propagate in a magnetic thin film. After the interference pattern forms, SWs are then converted back into electrical signals.This type of device requires SWs having an isotropic dispersion relation, which, in turn, requires an out-of-plane DC bias field. These spin waves are forward-volume spin waves (FVSW). The focus of the work presented here is to explore the design space of a microwave-to-spin-wave transducer for FVSWs, where the microwave signal is introduced by a coplanar waveguide (CPW).The SW excitation spectrum of an external RF magnetic field acting on a magnetic thin film is the result of the interference between SWs launched from all points of the film that are excited by the magnetic field. For a magnetic field from a CPW, this interference results in a comb-like spatial-frequency response, which is equivalent to the Fourier transform (FT) of the spatial distribution of the magnetic field that acts on the magnetic film [3]. However, because the device described above requires a relatively constant transfer function over the full bandwidth, i.e., without nulls, the comb-like excitation spectrum from a CPW would not be suitable for our applications.Launching spin waves from the edge of the film can be used to improve the spin-wave excitation spectrum for a couple of reasons. First, it has been shown that the edge of a film can be an efficient broadband source of spin-waves [4]. And second, because only part of the CPW’s field acts on the magnetic film, the FT of only that part describes the excitation spectrum; the FT of the spatial distribution is more delta-function-like and therefore is more broadband than the previous case.To design the edge-launched SW transducer, micromagnetic simulations were done in Mumax3 [5] using the magnetic field from CPWs simulated in Ansys HFSS. Our simulations (Fig. 1) show the frequency response of this simulated structure with the edge 2 μm away from the CPW. These simulations verify that the transducer’s excitation spectrum is improved, i.e., made more uniform, by placing the CPW beside the edge of the film rather than on top of the film. This improved bandwidth comes at the cost of transducer efficiency, since only the field to the side of the CPW acts on the magnetic film.Because the magnetic field decreases rapidly with distance from the CPW, the edge of the film should be as close to the CPW as possible to increase coupling between the CPW and the film. Representative waveforms given in Fig. 2 show that because the small out-of-plane component of the RF magnetic field is parallel to the large DC-bias magnetic field, it contributes very little to the excitation of a SW compared to the in-plane components of the field. The results of the simulations show that for the same magnetic field, raising the bottom of the CPW increases the in-plane component of the field and increases the amplitude of the SW.Yet another configuration would be to place the CPW on the magnetic film and create an edge-launcher by etching a gap in the film to the side of the CPW. Excessively large fields can produce unstable spin-waves with additional unwanted undesirable frequency components [6]. With a gap in the magnetic material, the internal magnetic field crosses the gap at a reduced field strength, removing the unwanted structure and resulting in SWs at the desired wavelength, as well as a smoother frequency response (Fig. 1.).The structure of the previous paragraph was simulated with the properties of an YIG thin film having different thicknesses (30 nm and 243 nm). It is found that increasing the distance between the gap and the CPW increases the amplitude of the resulting SW with diminishing returns, as shown in Fig. 2.With a gap that is 2 μm wide and 6 μm away from the CPW, we find that for the thinner film this structure produces a SW with a smaller amplitude than when the material underneath the CPW is nonmagnetic and the edge is flush with CPW. However, with the thicker film (Fig. 2), the structure with the magnetic film under the CPW produces a larger SW than the structure without the magnetic material under the CPW. **

The paper is devoted to stochastic equations describing the evolution of classical and quantum unbounded spin systems on discrete lattices and on Euclidean spaces. Existence and asymptotic properties of the corresponding transition semigroups are studied in a unified way using the theory of dissipative operators on weighted Hilbert and Banach spaces. This paper is an enlarged and rewritten version of the paper [7].

The ground-state properties of a generalized quantum $s=\frac{1}{2}$ $\mathrm{XY}$ model (including the ferromagnetic and antiferromagnetic cases) in a $Z$ field on a triangular lattice are examined. The exact values of critical fields above which the gap opens are obtained. A real-space renormalization-group method is used to estimate the ground-state energy and to analyze the critical behavior. There is some evidence that certain features of frustration in classical spin systems still persist in quantum systems.

A one-dimensional system of electrons and classical isotropic $n$-component spins both interacting with a single phonon mode of the harmonic lattice is investigated. The spin system is treated exactly. Self-consistent equations for spin- and electron-phonon coupling induced lattice distortion (Peierls transition) and its critical temperatures are obtained and discussed for various values of the coupling constants. In the absence of the electron-phonon interaction it is concluded that at $T=0$ a distorted and spin dimerized ground state is obtained for $|{J}_{0}|l\frac{{J}_{1}^{2}}{4{\ensuremath{\omega}}_{0}}$, where ${J}_{0}$, ${J}_{1}$, and ${\ensuremath{\omega}}_{0}$ are the spin-spin, spin-lattice, and characteristic lattice frequency constants, respectively. For $|{J}_{0}|g\frac{{J}_{1}^{2}}{4{\ensuremath{\omega}}_{0}}$, the ground state is undistorted. In the presence of electron-phonon interaction large ${J}_{0}$ suppresses the dimerized state but does not affect the lattice distortion due to electron-phonon interaction. The relation to the Peierls instability on the $S=\frac{1}{2}$ Heisenberg chain is discussed.

We study spin relaxation and dynamics of collective spin excitations in correlated double-exchange ferromagnets. For this, we introduce an expansion of the Green's functions equations of motion that treats nonperturbatively all correlations between a given number of spin and charge excitations and becomes exact within a subspace of states. Our method treats relaxation beyond Fermi's golden rule while recovering previous variational results for the spin-wave dispersion. We find that the momentum dependence of the spin-wave dephasing rate changes qualitatively due to the on-site Coulomb interaction, in a way that resembles experiment, and depends on its interplay with the magnetic exchange interaction and itinerant spin lifetime. We show that the collective spin relaxation and its dependence on the carrier concentration depend sensitively on three-body correlations between a spin excitation and a Fermi sea electron and hole. The above spin dynamics can be controlled via the itinerant carrier population.

The collective spin excitations in the unbounded 2D paramagnetic system with dipole interactions are studied. The model Hamiltonian includes Zeeman energy and dipole interaction energy, while the exchange vanishes. The system is placed into a constant uniform magnetic field which is orthogonal to the lattice plane. It provides the equilibrium state with spin ordering along the field direction, and the saturation is reached at zero temperature. We consider the deviations of spin magnetic moments from its equilibrium position along the external field. The Holstein-Primakoff representation is applied to spin operators in low-temperature approximation. When the interaction between the spin waves is negligible and only two-magnon terms are taken into account, the Hamiltonian diagonalisation is possible. We obtain the dispersion relation for spin waves in the square and hexagonal honeycomb lattice. Bose-Einstein statistics determine the average number of spin deviations, and total system magnetization. The lattice structure does not influence on magnetization at the long-wavelength limit. The dependencies of the relative magnetization and longitudinal susceptibility on temperature and external field intensity are found. The internal energy and specific heat of the Bose gas of spin waves are calculated. The collective spin excitations play a significant role in the properties of the paramagnetic system at low temperature and strong external magnetic field.

We demonstrate that a quantum field theory (QFT) in general two-dimensional curved spacetimes can be realized by a system of quantum spins or qubits. We consider a spin-1/2 model on a one-dimensional ring with spatially and temporally varying exchange couplings and magnetic fields. This model reduces to a QFT of Majorana fermions in the continuum limit. From this correspondence, we establish a dictionary for translating between the spacetime-dependent parameters of the spin model and the general metric on which the QFT is defined. After addressing the general case, we consider the Friedmann-Lemaître-Robertson-Walker (FLRW) metric as a simple example. According to the dictionary, the QFT of Majorana fermions on the FLRW metric corresponds to the Ising model with a time-dependent transverse magnetic field. We demonstrate that the production of Majorana particles in the expanding universe can be simulated with the transverse-field Ising model by increasing the strength of the magnetic field. Furthermore, we examine the Unruh effect through the spin system by using our prescription and show the direct relation between the entanglement (or modular) Hamiltonian in the spin system and the Rindler Hamiltonian. This approach provides an experimentally viable system for probing various phenomena in QFT within curved spacetime, while also opening the door to uncovering nontrivial phenomena in spin systems inspired by curved spacetime physics. It offers fresh perspectives on both QFT in curved spacetimes and quantum many-body spin systems, revealing profound connections between these fields. Published by the American Physical Society 2025

Dimensional reduction and catalysis of dynamical symmetry breaking by a magnetic field

Using the Milburn equation, we have studied the properties of the entanglement and fidelity dynamics in a spin system with different Dzyaloshinskii-Moriya interaction and magnetic field in detail. Effects of different Dzyaloshinskii-Moriya interaction, different magnetic fields, and the initial states on the entanglement and fidelity are discussed. Results show that entanglement decoherence can be suppressed by inhomogeneous magnetic fields. Initial state affects greatly the entanglement, and a proper entanglement can be obtained by adjusting the directions of Dzyaloshinskii-Moriya interaction. For a particular initial state, an optimal fidelity is obtained by changing the direction of the Dzyaloshinskii-Moriya interaction. Moreover, no matter how homogeneous or inhomogeneous the magnetic fields are, they cannot enhance the fidelity. The dependence of entanglement and fidelity on the angle of initial state shows periodicity. Hence we can select an optimal initial state for a specific condition according to requirement.

Computer simulation results for the dynamic structure factors of a ferromagnetically coupled classical one-dimensional easy-plane spin system are compared with calculations based on a linear spin wave theory for the case where a magnetic field is applied in the easy plane. It is found that the spin wave theory gives an adequate representation of the simulation results at sufficiently low temperature. At higher temperatures the authors demonstrate the failure of linear spin wave theory evinced by the appearance of a central-peak structure and a crossover to the isotropic Heisenberg behaviour. This central-peak feature is analogous to the behaviour of Ising-Heisenberg chains recently interpreted in terms of thermally induced bound-state transitions, corresponding in the classical limit to envelope solitons. The case of zero applied field is also considered.

It was found recently that the liquid dynamics of several metals (Li, Zn, Ni, Fe, Tl, Pb) under pressure is characterized by transverse spectral functions containing an additional high-frequency peak. To rationalize the pressure dependence of the contributions from different propagating processes to transverse spectral functions in liquid metals, ab initio molecular dynamics simulations were performed for two typical liquid metals (Na and Al) in a wide range of pressures. The influence of density/pressure is investigated for Na by considering four pressures ranging from 15 to 147 GPa, while the temperature influence is considered for Al between 600 K in the deep supercooled liquid up to 1700 K well above the melting point at ambient pressure. Both temperature and density dependence of the spectra of collective excitations are analyzed with a focus on the appearance of a second high-frequency mode in the transverse spectra. A correspondence between spectra of transverse collective excitations and the peak positions of the Fourier-spectra of velocity autocorrelation functions (vibrational density of states) is found.

A transcription of Rugh's geometrical approach to temperature is given for classical Heisenberg spin systems. For the simple case of a paramagnet with small and large numbers of spins we verify the approach. A numerical check for long spin chains using spin dynamics shows its practicality.