In this thesis, anisotropic Heisenberg magnets with arbitrary spin are investigated within the second-order Green-function theory. Three models are considered. First, the second-order Green-fuction theory for one-dimensional and two-dimensional Heisenberg ferromagnets with arbitrary spin S in a magnetic field is developed. For the determination of the introduced vertex parameters sum rules, higher-derivative sum rules, and regularity conditions are derived, and the equality of the isothermal and the longitudinal uniform static Kubo susceptibilities is required. Thermodynamic quantities, such as the specific heat, magnetic susceptibility, transverse and longitudinal correlation lengths are calculated. Empirical formulas describing the dependence of the position and height of the susceptibility maximum on the magnetic field are given. An anomal behavior of the longitudinal correlation length is observed. The appearance of two maxima in the temperature dependence of the specific heat is discussed. Further, as an example of a system with an anisotropy in the spin space, the S=1 ferromagnetic chain with easy-axis single-ion anisotropy is studied. Justified by the up-down symmetry of the model with respect to $S_i^z -> -S_i^z$, $\\langle S_i^z \\rangle=0$ is set. Two different ways of the determination of the introduced vertex parameters are presented. The transverse nearest-neighbor correlation function, spin-wave spectrum and longitudinal correlation length are analyzed. The effects of the single-ion anisotropy on the transverse and longitudinal uniform static susceptibilities as well as on the appearance of two maxima in the temperature dependence of the specific heat are examined. Finally, as examples of spatial anisotropic spin systems,layered Heisenberg ferromagnets and antiferromagnets with arbitrary spin are studied within the rotation-invariant Green-function theory. The long-range order is described by the condensation term, which is determined from the requirement that in the ordered state the static susceptibility has to diverge at the ordering wave vector. For determination of the introduced vertex parameters, the sum rule and the isotropy condition are used and also assumptions regarding the temperature dependence of some parameters are made. The main focus is put on the calculation of the specific heat, the Curie temperature, and the Néel temperature in dependence on the interlayer coupling and the spin-quantum number. Empirical formulas describing the dependence of the transition temperatures on the ratio of interlayer and intralayer couplings are given. For all three models, the results of the Green-function theory are compared to available results of exact approaches (Quantum Monte Carlo, exact diagonalization, Bethe-ansatz method) and to available experimental data.

ABSTRACT The phase transition of the antiferromagnetic-torsional XY model is studied with molecular dynamics. In the process of releasing energy, we find a minimally stable state. The minimally stable state indicates the process of disordered state to ordered state when the 2nd phase transition was derived. The temperature of phase transition for the iferromagnetic-torsional XY model is lower than that for the antiferromagnetic XY model. A increase of the coefficient J2 will delay the temperature of phase transition for the antiferromagnetic-torsional XY model .

This thesis presents studies of the low energy properties of nseveral frustrated spin-1/2 Heisenberg antiferromagnets using various analytic and computational methods. The models studied include the union jack model, the alternating Heisenberg chain, the Heisenberg bilayer model, and the spin-Peierls model. The union jack model is a Heisenberg antiferromagnetic spin model with frustration, and is analyzed using spin-wave theory. For small values of the frustrating coupling $\alpha$, the system is N{\' e}el ordered, while for large $\alpha$ the frustration is found to induce a canted phase. Spin wave theory with second order corrections finds the critical coupling at $\alpha \simeq 0.645$,which agrees quantitatively with series expansion results. No intermediate spin-liquid phase is found to exist between the two phases. The alternating Heisenberg chain is studied using an alternative triplet-wave expansion formalism for dimerized spin systems, modification of the ??bond operator?? formalism of Sachdev and Bhatt. Projection operators are used to confine the system to the physical subspace, rather than constraint equations. Comparisons are made with the results of dimer series expansions and exact diagonalization. The S=1/2 Heisenberg bilayer spin model at zero temperature is studied in the dimerized phase using analytic triplet-wave expansions and dimer series expansions. The occurrence of two-triplon bound states in the S=0 and S=1 channels, and antibound states in the S=2 channel, is predicted with triplet-wave theory and confirmed by series expansions. All bound states are found to vanish at or before the critical coupling separating the dimerized phase from the N{\' e}el phase. The critical behavior of the total and single-particle static transverse structure factors is also studied by series expansion methods and found to conform with theoretical expectations. The Heisenberg spin-Peierls model with dispersive, gapless phonons is studied with Density Matrix Renormalization Group methods. We investigate the zero temperature properties of the model using the crossover method. The calculations were found to converge poorly and no conclusive results could be found using this method. An analysis of the convergence problems and the discovery of an anomalous triplet ground state is presented in this chapter.

This thesis presents studies of the low energy properties of nseveral frustrated spin-1/2 Heisenberg antiferromagnets using various analytic and computational methods. The models studied include the union jack model, the alternating Heisenberg chain, the Heisenberg bilayer model, and the spin-Peierls model. The union jack model is a Heisenberg antiferromagnetic spin model with frustration, and is analyzed using spin-wave theory. For small values of the frustrating coupling $\alpha$, the system is N{\' e}el ordered, while for large $\alpha$ the frustration is found to induce a canted phase. Spin wave theory with second order corrections finds the critical coupling at $\alpha \simeq 0.645$,which agrees quantitatively with series expansion results. No intermediate spin-liquid phase is found to exist between the two phases. The alternating Heisenberg chain is studied using an alternative triplet-wave expansion formalism for dimerized spin systems, modification of the ??bond operator?? formalism of Sachdev and Bhatt. Projection operators are used to confine the system to the physical subspace, rather than constraint equations. Comparisons are made with the results of dimer series expansions and exact diagonalization. The S=1/2 Heisenberg bilayer spin model at zero temperature is studied in the dimerized phase using analytic triplet-wave expansions and dimer series expansions. The occurrence of two-triplon bound states in the S=0 and S=1 channels, and antibound states in the S=2 channel, is predicted with triplet-wave theory and confirmed by series expansions. All bound states are found to vanish at or before the critical coupling separating the dimerized phase from the N{\' e}el phase. The critical behavior of the total and single-particle static transverse structure factors is also studied by series expansion methods and found to conform with theoretical expectations. The Heisenberg spin-Peierls model with dispersive, gapless phonons is studied with Density Matrix Renormalization Group methods. We investigate the zero temperature properties of the model using the crossover method. The calculations were found to converge poorly and no conclusive results could be found using this method. An analysis of the convergence problems and the discovery of an anomalous triplet ground state is presented in this chapter.

Title: Optical and magneto-optical spectroscopy of materials with antiferro- magnetic interaction Author: Bc. Katarína Križanová Department: Institute of Physics of Charles University Supervisor: RNDr. Jakub Zázvorka, Ph.D., Institute of Physics of Charles University Abstract: One of the goals of spintronic research is the efficient external con- trol of magnetic moment. Non-collinear antiferromagnets in the antiperovskite structure, such as Mn3NiN, show a piezomagnetic effect that can be used to utilize these materials in applications. In the strain free state, the material ex- hibit zero net magnetic moment. Using strain induced by a lattice constant mismatch between the thin layer and a substrate on which the thin film is applied on a non-zero net magnetic moment can be registered. Magneto-optical Kerr effect spectroscopy is used to investigate the non-collinear magnetic thin films. The effect of two substrate layers with resulting opposite sign of strain influencing the magnetic ordering of the antiperovskite material is studied with respect to sample temperature. Results show comparable spectral dependence with opposite sign of the Kerr effect caused by the opposite direc- tion of net magnetization moments. Ellipsometry measurements depending on sample orientation are performed to study the material...

Transport of spin angular momentum (spin currents) in magnetic thin films is important for non-volatile spin-based memory devices and other emerging information technology applications. It is especially important to understand how a spin current propagates across interfaces and how a spin current interacts with magnetic moments. The great interest in devices based on ferromagnetic metals generated intensive theoretical and experimental studies on the basic physics of spin currents for the last few decades. Of particular interest recently is the so-called "pure" electronic spin current, which is carried by electrons and yet unaccompanied by net charge flow, in part because of the prospect of transporting spin with minimal Joule heating. However, in contrast to ferromagnetic metals, spin transport in antiferromagnetic metals, which are promising materials for next-generation magnetic information technology, is not well understood yet. This dissertation addresses the mechanisms of transport by pure spin current in thin-film multilayers incorporating metals with antiferromagnetic order. We focus on two specific materials: (1) CoGd alloys with ferrimagnetic sublattices, which resemble antiferromagnets near the compensation composition, and (2) elemental antiferromagnetic Cr, which can be grown as epitaxial films and hence serve as a model system material. For both the CoGd and Cr studies, spin-valve-like structures of NiFe/Cu/CoGd and NiFe/Cu/Cr/CoFe are prepared to conduct ferromagnetic resonance spin pumping experiments. Precessing magnetization in the NiFe "spin source" pumps a transverse spin current to the adjacent layers. We measure the loss of the spin angular momentum in the "spin sink" layer by measuring the broadening of the resonance linewidth, i.e., the non-local damping enhancement, of the spin source. The antiparallel magnetic moments of Co and Gd sublattices partially cancel out the dephasing of a transverse spin current, thereby resulting in a long spin dephasing length of ≈ 5-6 nm near the magnetic compensation point. We find evidence that the spin current interacts somewhat more strongly with the itinerant transition-metal Co magnetism than the localized rare-earth-metal Gd magnetism in the CoGd alloy. We also examine spin transport via structurally clean antiferromagnetic Cr, epitaxially grown with BCC crystal order. We observe strong spin reflection at the Cu/Cr interface, which is surprising considering that thin layers of Cu and Cr individually are transparent to spin currents carried by electrons. Further, our results indicate other combinations of electrically conductive elemental metals (e.g., Cu/V) can form effective spin-reflecting interfaces. Overall, this thesis advances the basic understanding of spin transport in metallic thin films with and without magnetic order, which can aid the development of next generations of efficient spintronic devices. This work was supported in part by the National Science Foundation, Grant No. DMR-2003914. / Doctor of Philosophy / Manipulation of electronic flow, i.e., net charge flow, underlies modern electronic devices such as computers, mobile phones, and electric cars. However, the conventional charge transport inevitably results in wasted energy, due to resistive (Joule) heating in the devices. A new research area which uses the electron's spin has recently emerged, namely spintronics. Spintronics uses the spin of electrons rather than just the charge, thereby reducing the dependence on charge flow. The flow of spin angular momentum carried by electrons, i.e., "electronic spin current," underpins numerous phenomena in condensed matter physics. An important example is switching and excitation of magnetic order driven electrically by spin current rather than external magnetic field. Spin currents can interact not only with ferromagnetic order consisting of parallel magnetic moments – but also with antiferromagnetic order consisting of alternating magnetic moments that cancel the net magnetization of the material. Indeed, experiments from the last few years demonstrate the ability to rotate antiferromagnetic order (a.k.a. Néel vector) by spin current, which offers new physics not achievable in ferromagnets, such as ultrafast spin dynamics in the THz regime and superfluid spin transport analogous to superconducting electronic transport. However, interaction of a spin current with antiferromagnetic order is not well understood yet. The aim of this thesis is to build a better understanding of spin currents in antiferromagnetic metals. Specifically, we experimentally study basic spin-current physics in a ferrimagnet (CoGd) and an antiferromagnet (Cr). We choose CoGd because adjusting its chemical composition allows us to easily tune its magnetism from ferromagnet-like (uncompensated magnetization) to antiferromagnet-like (compensated magnetization). In antiferromagnet-like CoGd, we find that the oppositely oriented Co and Gd magnetic moments partially cancel the scrambling (dephasing) of spins, so that the spin current is able to propagate over a longer distance - about 3-4 times more than in ferromagnetic metals. The mechanisms behind the longer spin propagation is somewhat akin to the spin "rephasing" technique for lengthening the lifetime of spin-based qubits for quantum computers, but what is remarkable is that we observe this effect in rather disordered magnetic alloys at room temperature. In the other major project of this thesis, we investigate spin transport through multilayers that contain Cr, a structurally and chemically clean antiferromagnetic material. We find that Cr by itself is a good spin transmitter, i.e., effectively allowing a pure spin current to pass through. Surprisingly, when Cr and Cu (another good spin transmitter) are stacked together, we observe strong reflection of a pure spin current at the interface of Cr and Cu. We find that the antiferromagnetic order in Cr is not responsible for this peculiar spin reflection and that other pairs of spin-transmitting metals (for example, V and Cu) can form spin-reflecting interfaces as well. Our work shows an interesting example of "emergent" phenomena where the interface behaves in a way that is not intuitively expected from the properties of the constituent materials. The basic scientific findings from this thesis may help the development of more efficient information-technology devices that run on spin currents.

In this thesis, anisotropic Heisenberg magnets with arbitrary spin are investigated within the second-order Green-function theory. Three models are considered. First, the second-order Green-fuction theory for one-dimensional and two-dimensional Heisenberg ferromagnets with arbitrary spin S in a magnetic field is developed. For the determination of the introduced vertex parameters sum rules, higher-derivative sum rules, and regularity conditions are derived, and the equality of the isothermal and the longitudinal uniform static Kubo susceptibilities is required. Thermodynamic quantities, such as the specific heat, magnetic susceptibility, transverse and longitudinal correlation lengths are calculated. Empirical formulas describing the dependence of the position and height of the susceptibility maximum on the magnetic field are given. An anomal behavior of the longitudinal correlation length is observed. The appearance of two maxima in the temperature dependence of the specific heat is discussed. Further, as an example of a system with an anisotropy in the spin space, the S=1 ferromagnetic chain with easy-axis single-ion anisotropy is studied. Justified by the up-down symmetry of the model with respect to $S_i^z -> -S_i^z$, $\\langle S_i^z \\rangle=0$ is set. Two different ways of the determination of the introduced vertex parameters are presented. The transverse nearest-neighbor correlation function, spin-wave spectrum and longitudinal correlation length are analyzed. The effects of the single-ion anisotropy on the transverse and longitudinal uniform static susceptibilities as well as on the appearance of two maxima in the temperature dependence of the specific heat are examined. Finally, as examples of spatial anisotropic spin systems,layered Heisenberg ferromagnets and antiferromagnets with arbitrary spin are studied within the rotation-invariant Green-function theory. The long-range order is described by the condensation term, which is determined from the requirement that in the ordered state the static susceptibility has to diverge at the ordering wave vector. For determination of the introduced vertex parameters, the sum rule and the isotropy condition are used and also assumptions regarding the temperature dependence of some parameters are made. The main focus is put on the calculation of the specific heat, the Curie temperature, and the Néel temperature in dependence on the interlayer coupling and the spin-quantum number. Empirical formulas describing the dependence of the transition temperatures on the ratio of interlayer and intralayer couplings are given. For all three models, the results of the Green-function theory are compared to available results of exact approaches (Quantum Monte Carlo, exact diagonalization, Bethe-ansatz method) and to available experimental data.

Spintronics is the study of mutual dependence of magnetization and electron transport, which forms a complementary picture in ferromagnetic (FM) materials. Recently, spintronics based on antiferromagnetic (AF) materials has been suggested. However, a systematic study is not yet available, and a complementary picture of the AF dynamics with electron transport is highly desired. By developing a microscopic theory, we predict the occurrence of spintronic phenomena both in bulk AF texture and on the interface of AF with normal metals. For the bulk, we find that the electron dynamics becomes adiabatic when the local staggered field is varying slowly over space and time, by which the spin-motive force and the reactive spin-transfer torque (STT) are derived as reciprocal effects. While the former generates a pure spin voltage across the texture, the latter can be used to drive AF domain wall and trigger spin wave excitation with lower current densities compared to FM materials. For the interface, by calculating how electrons scatter off a normal metal -antiferromagnet heterostructure, we derive the pumped spin and staggered spin currents in terms of the staggered order parameter, the magnetization, and their rates of change; the reactions of an incident spin current on the antiferromagnet is derived as STTs. These effects are applicable to both compensated and uncompensated interfaces with a similar order of magnitude. In contrast to FM materials, the direction of spin pumping is controlled by the circular polarization of driving microwave; and conversely, the chirality of AF spin wave is tunable by the direction of spin accumulation. / text

The high-frequency properties of coupled magnetic systems have been investigated using vector network analyzer ferromagnetic resonance (VNA-FMR) spectroscopy. SAF structures consist of two ferromagnetic layers separated by a non-magnetic spacer, coupled through the indirect exchange interaction. The ferromagnetic layers of our samples were composed of FeCoB separated by a layer of Ru. The thickness of Ru was varied in the range of 8 to 18 Å among the samples studied. Antiferromagnetic coupling can be quickly identified by the major hysteresis loop (MHL). A new way of displaying FMR data for these trilayer samples is presented which completely preserves the anisotropy effects while fully characterizing the angular dependence of FMR. The advantage of our representation is that the high-frequency data can be easily compared to the static switching behavior at any angle obtained through susceptibility measurements. Ferromagnetic resonance; Coupled; Synthetic antiferromagnet; Magnetization switching

In the geometrical spin frustrated systems, order-disorder phenomena are interesting, for their intrinsic fluctuation, complicated completing interactions, and lattice structure leading to many intrigue physical behavior. To clarify the mechanism of such systems, experiments under extreme conditions (diverse magnetic fields and hydrostatic pressures) are powerful tools to meet the needs. In this dissertation, two kind of interesting materials are investigated. One is quasi-1D double chain antiferromagnet NaV2O4, the other is cubic like ferrimagnet Cu2OSeO3. In the polycrystalline compound NaV2O4, it exhibits an antiferromagnetic transition TN at 140 K, together with two field dependence subphases at 1 T≤H≤5 T. The two characteristic temperature TN1 and TN2 are associated to two subphases, which is determined by the peak position in the derivative of magnetization with respect to temperature. Under magnetic field, TN and TN1 remain almost unchanged (linear behavior), while TN2 acts in a nonlinear behavior with the application of magnetic field. Further, TN1 and TN2 are found to decrease roughly linear with applied pressure, while TN2 follows a nonlinear relation with applied pressure. On the other hand, the cubic single crystal Cu2OSeO3 exhibits a ferrimagnetic transition at 58 K, which is shifting to high temperature range with increasing magnetic fields. The peak values (from the mutual inductance measurements) associated with the ferrimagnetic transitions also increase with applied hydrostatic pressures. Moreover, the spin-flipped transitions are observed below transition temperature at ambient and applied pressure (12.67 kbar). The measurements above strongly suggested the ferrimagnetic spin configurations order earlier, i.e. transition temperatures increase with applied magnetic fields and pressures. In summary, the investigated frustrated spin systems (NaV2O4 and Cu2OSeO3) behave with the same trend with applied magnetic fields and hydrostatic pressures. It is possibly induced by the external DC magnetic field and the structure change and/or deformation under pressure.