Real Magnetic Materials Research Articles

Thermodynamic properties of the two-dimensional Heisenberg antiferromagnetic model on kagome lattice

Thermodynamic quantities as entropy and specific heat that are of evident interest, are obtained for the nearest-neighbor antiferromagnetic Heisenberg model on kagome lattice using the linear spin-wave approach. The results are obtained for different extensions of the model with single-ion anisotropy and out-of-plane Dzyaloshinskii–Moriya (DMI) interaction. We obtain the entropy as a function of the DMI interaction, single-ion anisotropy strength and anisotropy with aim to verify the effect of these corrections that occurs in real magnetic materials on entropy and specific heat. Furthermore, we obtain the specific heat as a function of temperature T and found a discontinuity in the range of large T indicating so, a phase transition in this range of temperature.

Multi-meron interactions and statistics in two-dimensional materials

As a fundamental type of topological spin textures in two-dimensional (2D) magnets, a magnetic meron carries half-integer topological charge and forms a pair with its antithesis to keep the stability in materials. However, it is challenging to quantitatively calculate merons and their dynamics by using the widely used continuum model because of the characteristic highly inhomogeneous spin textures. In this work, we develop a discrete method to address the concentrated spin structures around the core of merons. We reveal a logarithmic-scale interaction between merons when their distance is larger than twice their core size and obtain subsequent statistics of meron gas. The model also predicts how these properties of single and paired merons evolve with magnetic exchange interactions, and the results are in excellent agreement with the Monte Carlo simulations using the parameters of real 2D van der Waals magnetic materials. This discrete approach not only shows equilibrium static statistics of meron systems but also is useful to further explore the dynamic properties of merons through the quantified pairing interactions.

Model studies of topological phase transitions in materials with two types of magnetic atoms

We study the topological phase transitions induced by Coulomb engineering in three triangular-lattice Hubbard models $AB_2$, $AC_3$ and $B_2C_3$, each of which consists of two types of magnetic atoms with opposite magnetic moments. The energy bands are calculated using the Schwinger boson method. We find that a topological phase transition can be triggered by the second-order (three-site) virtual processes between the two types of magnetic atoms, the strengths of which are controlled by the on-site Coulomb interaction $U$. This new class of topological phase transitions have been rarely studied and may be realized in a variety of real magnetic materials.

Defect-induced ferromagnetism in a S\u2009=\u20091/2 quasi-one-dimensional Heisenberg antiferromagnetic chain compound

We present evidences that defects in the spin S = 1/2 Heisenberg antiferromagnetic chain (HAFC) compound can lead to ferromagnetism by studying the magnetic and thermal properties of the newly discovered quasi-one-dimensional (1D) metal–organic framework [CH3NH3][Cu(HCOO)3] (MACuF). Our findings suggest that the long-range ferromagnetic order at 3.7 K can be attributed to Cu2+ ions from the 2D networks constructed by the endpoints of the broken chains. In such a case, the intrinsic magnetism can emerge in this quasi-1D Heisenberg chain system at the background of the short-range antiferromagnetism. This unusual ferromagnetism found in HAFC not only enriches magnetic features in the low-dimensional systems, but helps to understand some of the exotic magnetic phenomena in other real quasi-1D magnetic materials.

Super-quantum discord in ferromagnetic and antiferromagnetic materials

Super-quantum discord is an extension of the quantum discord concept where weak measurements are made instead of projective measurements. We study the temperature behavior of the super-quantum discord for two real magnetic materials. We extract information about super-quantum discord from the magnetic susceptibility data for iron nitrosyl complexes $\mathrm{ Fe_2(SC_3 H_5N_2)_2(NO)_4}$ and binuclear Cu(II) acetate complex $\mathrm{[Cu_2 L(OAc)]\cdot 6 H_2O}$, where $\mathrm{ L}$ is a ligand that allows us to compare the super-quantum discord with the standard one. The dependence of the super-quantum discord on the parameter describing weak measurements is studied. Obtained difference between super-quantum and quantum discords confirms the detection of additional quantum correlations that are usually destroyed during projective measurements. The use of the approach allows to predict quantitatively in advance the advantages of use of weak measurements versus projective one for quantum technologies in real settings where quantum discord is used as resource. This can be relevant particularly in macroscopic quantum systems where weak measurements can be used to extract information about the system.

Nonlocal Gilbert damping tensor within the torque-torque correlation model

An essential property of magnetic devices is the relaxation rate in magnetic switching which depends strongly on the damping in the magnetisation dynamics. It was recently measured that damping depends on the magnetic texture and, consequently, is a non-local quantity. The damping enters the Landau-Lifshitz-Gilbert equation as the phenomenological Gilbert damping parameter $\alpha$, that does not, in a straight forward formulation, account for non-locality. Efforts were spent recently to obtain Gilbert damping from first principles for magnons of wave vector $\mathbf{q}$. However, to the best of our knowledge, there is no report about real space non-local Gilbert damping $\alpha_{ij}$. Here, a torque-torque correlation model based on a tight binding approach is applied to the bulk elemental itinerant magnets and it predicts significant off-site Gilbert damping contributions, that could be also negative. Supported by atomistic magnetisation dynamics simulations we reveal the importance of the non-local Gilbert damping in atomistic magnetisation dynamics. This study gives a deeper understanding of the dynamics of the magnetic moments and dissipation processes in real magnetic materials. Ways of manipulating non-local damping are explored, either by temperature, material's doping or strain.

Magnetic Characterization and Low-Temperature Heat Transport Properties of the Orthoferrites <italic>R</italic>FeO<sub>3</sub> (<inline-formula> <tex-math notation="LaTeX">$R =$ </tex-math></inline-formula> Rare Earth) Single Crystals

Orthoferrites RFeO 3 (except R=Y, La and Lu) possess two sets of magnetic sublattice, that is, Fe3+ sub-system and R3+ sub-system. Magnetic properties and interactions between the two sub-systems including Fe-Fe, R-Fe, and R-R interactions depend on external parameters, such as temperature, magnetic field, etc.[1-3] So real magnetic materials can exhibt rich low temperature characteristics. We have successfully grown the orthoferrites RFeO 3 (R = Dy, Ho and Y) and Ho 1−x Y x FeO 3 (x = 0.1 and 0.3) by the floating zone technique using a four-mirror image furnace. The halogen lamp power and crystal growth atmosphere were identified to be the most important parameters. High-quality single crystals have been demonstrated by the X-ray diffraction data and X-ray Laue photograph. The magnetic transitions with decreasing temperature and the field-induced magnetic phase transitions in RFeO 3 for the rare earth ions and Fe3+ can be characterized by low-temperature magnetization and specific heat measurements. In addition, we report the low-temperature heat transport measurements of these orthoferrites single crystals to probe the magnetic properties and find that they show strong magnetic field dependence. The characteristic fields have a good correspondence with some transformations of the magnetic structure. These special behaviors demonstrate the magnetic field-induced transitions of the Fe3+ and R3+ spin structure.

Protection against a spin gap in two-dimensional insulating antiferromagnets with a Chern-Simons term

We propose a mechanism for the protection against spin gapped states in doped antiferromagnets. It requires the presence of a Chern-Simons term that can be generated by a coupling between spin and an insulator. We first demonstrate that in the presence of this term the vortex loop excitations of the spin sector behave as anyons with fractional statistics. To generate such a term, the fermions should have a massive Dirac spectrum coupled to the emergent spin field of the spin sector. The Dirac spectrum can be realized by a planar spin configuration arising as the lowest-energy configuration of a square lattice antiferromagnet Hamiltonian involving a Dzyaloshinskii-Moriya interaction. The mass is provided by a combination of dimerization and staggered chemical potential. We finally show that for realistic parameters, anyonic vortex loop condensation will likely never occur and thus the spin gapped state is prevented. We also propose real magnetic materials for an experimental verification of our theory.

Spin waves damping in nanometre-scale magnetic materials (Review Article)

Spin dynamics in magnetic nanostructured materials is a topic of great current interest. To describe spin motions in such magnetic systems, the phenomenological Landau–Lifshitz (LL), or the LL–Gilbert (LLG), equation is widely used. Damping term is one of the dominant features of magnetization dynamics and plays an essential role in these equations of motion. The form of this term is simple; however, an important question arises whether it provides a proper description of the magnetization coupling to the thermal bath and the related magnetic fluctuations in the real nanometre-scale magnetic materials. It is now generally accepted that for nanostructured systems the damping term in the LL (LLG) equation fails to account for the systematics of the magnetization relaxation, even at the linear response level. In ultrathin films and nanostructured magnets particular relaxation mechanisms arise, extrinsic and intrinsic, which are relevant at nanometre-length scales, yet are not so efficient in bulk materials. These mechanisms of relaxation are crucial for understanding the magnetization dynamics that results in a linewidth dependence on the nanomagnet's size. We give an overview of recent efforts regarding the description of spin waves damping in nanostructured magnetic materials. Three types of systems are reviewed: ultrathin and exchange-based films, magnetic nanometre-scale samples and patterned magnetic structures. The former is an example of a rare case where consideration can be done analytically on microscopic footing. The latter two are typical samples when analytical approaches hardly have to be developed and numerical calculations are more fruitful. Progress in simulations of magnetization dynamics in nanometre-scale magnets gives hopes that a phenomenological approach can provide us with a realistic description of spin motions in expanding diverse of magnetic nanostructures.

Preisach Images of a Simple Mechanical System

This work is an an early stage of a larger project aiming at answering the question whether or not the Preisach map is really ngerprinting magnetic materials. More precisely, we are interested whether the Preisach model of magnetic hysteresis indeed contains any physics or is just a convenient modeling tool. To this extent we study a very simple mechanical system, thus fully tractable, subjected to the external force. Despite of its simplicity, our model captures all the fundamental features of real magnetic materials, namely their hysteretic behavior, coercivity, remanent magnetization, and saturation at high elds. Both the overall shape of major hysteresis loop as well as rst order reversal curves are reproduced quite correctly; they are very similar to those observed in magnetic materials. The model essentially consists of a single, spring loaded, rigid and rotative bar with non-zero friction torque. The length of a projection of this bar onto the direction of an external force is identi ed with magnetization. The friction torque and the spring constant are the only freely adjustable parameters of our model. Here we investigate, and present, their in uence on the inferred Preisach maps.

Quantum simulation of antiferromagnetic spin chains in an optical lattice

Understanding exotic forms of magnetism in quantum mechanical systems is a central goal of modern condensed matter physics, with implications for systems ranging from high-temperature superconductors to spintronic devices. Simulating magnetic materials in the vicinity of a quantum phase transition is computationally intractable on classical computers, owing to the extreme complexity arising from quantum entanglement between the constituent magnetic spins. Here we use a degenerate Bose gas of rubidium atoms confined in an optical lattice to simulate a chain of interacting quantum Ising spins as they undergo a phase transition. Strong spin interactions are achieved through a site-occupation to pseudo-spin mapping. As we vary a magnetic field, quantum fluctuations drive a phase transition from a paramagnetic phase into an antiferromagnetic phase. In the paramagnetic phase, the interaction between the spins is overwhelmed by the applied field, which aligns the spins. In the antiferromagnetic phase, the interaction dominates and produces staggered magnetic ordering. Magnetic domain formation is observed through both in situ site-resolved imaging and noise correlation measurements. By demonstrating a route to quantum magnetism in an optical lattice, this work should facilitate further investigations of magnetic models using ultracold atoms, thereby improving our understanding of real magnetic materials.

Magnetic circular dichroism in two-photon absorption and depth-resolved magnetic microscopy

The magnetic circular dichroism (MCD) for the $1s\ensuremath{\rightarrow}3d$ two-photon excitation is calculated for a relativistic one-electron atom in an external magnetic field. The MCD in two-photon absorption is of the same order of magnitude as the MCD for the $2p\ensuremath{\rightarrow}3d$ one-photon excitation for the model. Because the MCD in one-photon absorption is well known in nature, this indicates that the MCD in two-photon absorption should be observable experimentally for real magnetic materials. It is suggested to combine the MCD effect with the well-established two-photon microscopy in the infrared and optical regime to establish a depth-resolved magnetic microscopy, with interesting potential applications for magnetic semiconductors or biological systems with paramagnetic centers.

Using the reduced Preisach vector model to predict the cut angle influence in Si-Fe steels

In this paper, we present and discuss the use of a reduced Preisach vector model (RVPM) as a numerical tool for the analysis of the influence of the cut angle in the magnetic behavior of laminated Fe-Si steels. The model parameters can be deduced by measurements along the easy and hard axis, and the families of hysteresis loops and virgin curves for the same Si-Fe sheet, cut at different angles with respect to the rolling direction can be derived. In particular, we present a simplified identification procedure based on the assumption that the material is single-quadrant medium along the principal axes. Results seem to indicate that the hypothesis of factorizable Preisach function is not compatible with the real magnetic materials.

Ferromagnetic Kondo-lattice model

We present a many-body approach to the electronic and magnetic properties of the (multiband) Kondo-lattice model with ferromagnetic interband exchange. The coupling between itinerant conduction electrons and localized magnetic moments leads, on the one hand, to a distinct temperature-dependence of the electronic quasiparticle spectrum and, on the other hand, to magnetic properties, as e.~g.the Curie temperature T_C or the magnon dispersion, which are strongly influenced by the band electron selfenergy and therewith in particular by the carrier density. We present results for the single-band Kondo-lattice model in terms of quasiparticle densities of states and quasiparticle band structures and demonstrate the density-dependence of the self-consistently derived Curie temperature. The transition from weak-coupling (RKKY) to strong-coupling (double exchange) behaviour is worked out. The multiband model is combined with a tight-binding-LMTO bandstructure calculation to describe real magnetic materials. As an example we present results for the archetypal ferromagnetic local-moment systems EuO and EuS. The proposed method avoids the double counting of relevant interactions and takes into account the correct symmetry of atomic orbitals.

The Ising model and real magnetic materials

The factors that make certain magnetic materials behave similarly to corresponding Ising models are reviewed. Examples of extensively studied materials include Dy(C2H5SO4)3.9H2) (DyES), Dy3Al5O12 (DyAlG), DyPO4, Dy2Ti2O7, LiTbF4, K2CoF4, and Rb2CoF4. Various comparisons between theory and experiment for these materials are examined. The agreement is found to be generally very good, even when there are clear differences between the ideal Ising model and the real materials. In a number of experiments behavior has been observed that requires extensions of the usual Ising model. These include the effects of long range magnetic dipole interactions, competing interaction effects in field-induced phase transitions, induced staggered field effects and frustration effects, and dynamic effects. The results show that the Ising model and real magnetic materials have provided an unusually rich and productive field for the interaction between theory and experiment over the past 40 years.

Surface and interface excitations for bilayer Ising-model systems in a transverse field (abstract)

We present some calculations for the surface and interface excitations (spin waves) in layered solid structures which may be represented by the Ising model in a transverse magnetic field. In particular, we consider a two-medium system consisting of a ferromagnetic thin film on a semi-infinite substrate of another ferromagnetic material. By generalizing previous results for a single semi-infinite medium,1,2 we show that there may be excitations localized near the surface and interface of the coupled magnetic system, depending on the parameters of the model. We deduce dispersion relations for these surface and interface spin waves, as well as for the quantized (or ‘‘standing’’) bulk spin waves in the thin film, including the effects of relaxational damping of the modes. For nonzero values of the transverse field, the formalism can be applied at temperatures above and below the critical temperatures in the two media. Although our theory provides a description of some real anisotropic magnetic materials when placed in a transverse magnetic field, it is also of wider applicability within a pseudo-spin formalism for certain order–disorder ferroelectrics and Jahn–Teller systems.

Exact Diagonalization Study of Real Materials

ABSTRACTWe report some recent developments in theoretical modeling of real 3d magnetic materials, particularly interface and ultrathin-film structures. We focus on many-body correlation effects and describe the method of modeling realistic strongly correlated electron systems using and going beyond die local-density-approximation single-particle electronic structures. Group-theoretical techniques and high-performance computing facilities are systematically used in this work. Fundamental spectroscopic properties of several prototypical 3d transition-metal systems have been obtained and new features induced by many-body correlation have been discovered. Results will be presented and discussed.

Influence of cutting strains and magnetic anisotropy of electrical steel on the air gap flux distribution of an induction motor

This paper describes an iterative algorithm for the simulation of various real magnetic materials in a small induction motor and their influence on the flux distribution in the air gap. Two standard materials, fully-, and semi-processed steel strips were used. The nonlinearity of the magnetization curve, the influence of cutting strains and magnetic anisotropy are also considered. All these influences bring out the facts that the uniformly rotated and sine form exitation causes a nonuniformly rotated and deformed magnetic field in the air gap of the machine and that the magnetization current is winding place dependent.

Easy-axis antiferromagnets with intermediate anisotropy

The easy-axis Heisenberg antiferromagnet in a longitudinal field is studied for the case of anisotropy strengths in the intermediate range. In the low-anisotropy limit the system is known to have a spin-flop phase and a bicritical point; for large anisotropy it may become an Ising-like metamagnet with a tricritical point. Mean-field predictions for the system are reviewed, and it is pointed out that a class of real magnetic materials, namely certain alkylammonium metal halides with weak antiferromagnetic coupling, may be candidates for intermediate behaviour, having both a spin-flop phase and a tricritical point. Next, the problem of bicritical to tricritical crossover is considered in a renormalisation-group context. For the cases of uniaxial and orthorhombic anisotropy, it is found that the biconical fixed point of Nelson, Kosterlitz and Fisher controls the behaviour of the system at the multicritical point that arises when the bi- and tricritical points coincide.