Saturated Ferromagnetic State Research Articles

Exceptional spectrum and dynamic magnetization

A macroscopic effect can be induced by a local non-Hermitian term in a many-body system, when it manifests simultaneously level coalescence of a full real degeneracy spectrum, leading to exceptional spectrum. In this paper, we propose a family of systems that support such an intriguing property. It is generally consisted of two arbitrary identical Hermitian sub-lattices in association with unidirectional couplings between them. We show exactly that all single-particle eigenstates coalesce in pairs even only single unidirectional coupling appears. It means that all possible initial states obey the exceptional dynamics, resulting in some macroscopic phenomena, which never appears in a Hermitian system. As an application, we study the dynamic magnetization induced by complex fields in an itinerant electron system. It shows that an initial saturated ferromagnetic state at half-filling can be driven into its opposite state according to the dynamics of high-order exceptional point. Any Hermitian quench term cannot realize a steady opposite saturated ferromagnetic state. Numerical simulations for the dynamical processes of magnetization are performed for several representative situations, including lattice dimensions, global random and local impurity distributions. It shows that the dynamic magnetization processes exhibit universal behavior.

Frustrated magnetism in the layered triangular lattice materials K2Co(SeO3)2 and Rb2Co(SeO3)2

A study of the layered triangular lattice materials ${\mathrm{K}}_{2}\mathrm{Co}{({\mathrm{SeO}}_{3})}_{2}$ and ${\mathrm{Rb}}_{2}\mathrm{Co}{({\mathrm{SeO}}_{3})}_{2}$ is reported. These isostructural compounds crystallize in the trigonal space group $R\ensuremath{-}3m$ (No. 166). The magnetic $\mathrm{C}{\mathrm{o}}^{2+}$ ions form a spin-1/2 triangular lattice and display strongly frustrated magnetism. We find no evidence in the susceptibility or heat capacity for in-plane ordering of the spins; rather the in-plane inverse susceptibility is typical of that seen for frustrated magnets. At around 10 K, a ferromagnetic component appears in the magnetic susceptibility perpendicular to the triangular planes. The heat capacity at low applied fields does not show sharp features, but in larger applied fields a sharp ferromagneticlike transition appears. Field- and direction-dependent magnetization measurements at 2 K indicate that both materials have a magnetic easy axis perpendicular to the triangular planes. The magnetic properties are sensitive to the field applied perpendicular to the triangular planes, which induces a metamagnetization transition at 0.75 T. Spin polarization develops along with the increasing out-of-plane field, resulting in a saturated ferromagnetic state at high fields. In contrast, the magnetic properties are resistant to the in-plane field. Our results suggest that these materials are embodiments of Ising spins on triangular lattices with easy-axis anisotropy.

Dynamic magnetization in non-Hermitian quantum spin systems

We report a global effect induced by the local complex field, associated with the spin-exchange interaction. High-order exceptional point up to ($N+1$)-level coalescence is created at the critical local complex field applied to the $N$-size quantum spin chain. The ($N+1$)-order coalescent level is a saturated ferromagnetic ground state in the isotropic spin system. Remarkably, the final state always approaches the ground state for an arbitrary initial state with any number of spin flips; even if the initial state is orthogonal to the ground state. Furthermore, the switch of macroscopic magnetization is solely driven by the time and forms a hysteresis loop in the time domain. The retentivity and coercivity of the hysteresis loop mainly rely on the non-Hermiticity. Our findings highlight the cooperation of non-Hermiticity and the interaction in quantum spin system, suggest a dynamical framework to realize magnetization, and thus pave the way for the non-Hermitian quantum spin system.

Signature of the ferromagnetic (T = 0) transition in real space and time

A detailed study of the spatio-temporal dynamics in several Hubbard clusters at zero temperature is performed. Small systems of two and three electrons, which could be considered representative systems of Nagaoka's, Mielke's and Tasaki's ferromagnetism, are investigated using a combination of analytical and numerical exact diagonalization techniques. The results raise the possibility that spin-dependent localization is correlated in real space and real time with the transition to a saturated ferromagnetic state. The long-time average of the expectation value of the center of mass coordinates for electrons with spin up does not coincide with that for electrons with spin down at the transition. The reason for this is that the long-time averages of the probabilities are different for states in which the spins of one system are exchanged with another. The physical origin of itinerant ferromagnetism is discussed.

Doping control of realization of an extended Nagaoka ferromagnetic state from the Mott state

Inspired by the Nagaoka ferromagnetism, we propose an itinerant model to study the transition between the Mott singlet state and a ferromagnetic state by emulating a doping process in finite lattices. In the Nagaoka ferromagnetism, the total spin of the system takes the maximum value when an electron is removed from the half-filled system. To incorporate a procedure of the electron removal, our model contains extra sites as a reservoir of electrons, and the chemical potential of the reservoir controls the distribution of electrons. As a function of the chemical potential, the system exhibits ground-state phase transitions among various values of the total spin, including a saturated ferromagnetic state due to the Nagaoka mechanism at finite hole density. We discuss the nature of the ferromagnetism by measuring various physical quantities, such as the distribution of electrons, the spin correlation functions, the magnetization process in the magnetic field, and also the entanglement entropy.

Neutron diffraction and scattering study of the weak ferromagnetism inNaFe4Sb12skutterudite

A structural and magnetic investigation of ${\mathrm{NaFe}}_{4}{\mathrm{Sb}}_{12}$ with filled skutterudite structure is carried out by means of powder neutron diffraction and magnetization measurements in order to investigate the magnetic ground state of this compound. The existence of an ordered magnetic moment on the Fe site of $\ensuremath{\approx}0.6{\ensuremath{\mu}}_{B}$/Fe atom is in good agreement with magnetization data. The ratio between the number of spins in the paramagnetic state and in the saturated ferromagnetic state is $\ensuremath{\approx}1.7$, indicating some degree of delocalization of the Fe magnetic moment in ${\mathrm{NaFe}}_{4}{\mathrm{Sb}}_{12}$. Theoretical density-functional calculations of real-space spin-density maps are performed and compared to the experimental findings of weak ferromagnetism in ${\mathrm{NaFe}}_{4}{\mathrm{Sb}}_{12}$ (${T}_{C}\ensuremath{\approx}83$ K). Diffuse magnetic scattering with polarized neutrons revealed that a localized moment exists in the paramagnetic phase which decreases with increasing temperature. The results are discussed in the light of comparison with other intermetallic compounds.

Phase diagram of a two-dimensional square lattice of magnetic particles with perpendicular anisotropy

The ground state of an array of small single-domain magnetic particles having perpendicular anisotropy and forming a square two-dimensional lattice is studied in the presence of a magnetic field. The stability of some basic states with respect to nonuniform perturbations is analyzed in a linear approximation, and analytical model calculations and numerical simulation are used for an analysis. The entire set of states at various anisotropy constants and magnetic fields is considered when a field is normal to the array plane. Two main classes of states are possible for an infinite system, namely, collinear and noncollinear states. For collinear states, the magnetic moments of all particles are normal to the array plane. At a sufficiently high anisotropy, a wide class of collinear states exists. At low fields, a staggered antiferromagnetic order of magnetic moments takes place. An increase in the magnetic field causes an unsaturated state, and this state transforms into a saturated (ferromagnetic) state with a parallel orientation of the magnetic moments of all particles at a sufficiently high field. At a lower anisotropy, the ground state of the system is represented by noncollinear states, which include a complex four-sublattice structure for the components of the magnetic moments in the array plane and a nonzero projection of the magnetic moments of the particles onto the field direction. A phase diagram is plotted for the states of an array of anisotropic magnetic particles in the anisotropy constant-magnetic field coordinates. For a finite array of particles, sample boundaries are shown to play a significant role, which is particularly important for noncollinear states. As a result of the effect of the boundaries at a moderate field or anisotropy, substantially heterogeneous noncollinear states with a heterogeneity size comparable with the sample size can appear in the system.

Magnetic anisotropy and evolution of ground-state domain structures in bccFe81Ni19/Co(001)superlattices

The magnetic anisotropy and evolution of striped magnetic domain structures in bcc ${\text{Fe}}_{81}{\text{Ni}}_{19}/\text{Co}(001)$ superlattices with the total thickness ranging from 85 to 1370 nm has been studied by magneto-optical Kerr effect and magnetic force microscopy. At a thickness of about 85 nm [25 bilayers (BL)] the domains appear as stripe domains, typical for perpendicular anisotropy films, with the weak cubic anisotropy of the in-plane magnetization component stabilizing the stripe direction. The magnetic domain period strongly depends on the thickness of the superlattice. As the thickness increases, the equilibrium magnetization orients at oblique angles with respect to the film plane and continuously varies with the thickness from in-plane to out-of-plane. We first apply a simple phenomenological model which correctly predicts the transition from in-plane to out-of-plane magnetization as well as increasing domain period and saturation field with increasing BL number. The results indicate the presence of partial flux-closure domains at the film surface with the tilt angle continuously varying with the superlattice thickness. By solving a linearized Landau--Lifshitz equation together with Maxwell's equations in magnetostatic approximation for samples consisting of up to 1000 individual layers, we calculate the spin-wave dispersion and determine the stability conditions for the saturated ferromagnetic state. From these results the dependence of the saturation field on the number of layers is inferred and agrees well with the experiment. The uniaxial bulk anisotropy is attributed to distortions along the $c$ axis and the results further show evidence for the presence of an easy-plane interface anisotropy in these samples.

Magnetic phase transitions in the two-dimensional frustrated quantum antiferromagnetCs2CuCl4

We report magnetization and specific heat measurements in the two-dimensional frustrated spin-$1∕2$ Heisenberg antiferromagnet ${\mathrm{Cs}}_{2}\mathrm{Cu}{\mathrm{Cl}}_{4}$ at temperatures down to $0.05\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and high magnetic fields up to $11.5\phantom{\rule{0.3em}{0ex}}\mathrm{T}$ applied along $a$, $b$, and $c$ axes. The low-field susceptibility $\ensuremath{\chi}(T)\ensuremath{\simeq}M∕B$ shows a broad maximum around $2.8\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ characteristic of short-range antiferromagnetic correlations and the overall temperature dependence is well described by high temperature series expansion calculations for the partially frustrated triangular lattice with $J=4.46\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and ${J}^{\ensuremath{'}}∕J=1∕3$. At much lower temperatures $(\ensuremath{\leqslant}0.4\phantom{\rule{0.3em}{0ex}}\mathrm{K})$ and in in-plane field (along $b$ and $c$ axes) several new intermediate-field ordered phases are observed in between the low-field incommensurate spiral and the high-field saturated ferromagnetic state. The ground state energy extracted from the magnetization curve shows strong zero-point quantum fluctuations in the ground state at low and intermediate fields.

Ferromagnetism in the Hubbard model on a two-leg ladder with interchain Coulomb repulsion

We investigate the ground-state magnetic properties of the Hubbard model on a two-leg ladder with interchain Coulomb repulsion. When both the on-site and the interchain Coulomb repulsions are infinitely large, we show exactly that the model exhibits saturated ferromagnetism in the ground states for the electron filling factor 1/4<n<½. The explicit expression of the saturated ferromagnetic ground state is also obtained. By using numerical calculations, we find that ferromagnetism remains stable for sufficiently large values of these interactions, and that the interchain Coulomb repulsion induces tendencies to ferromagnetism, especially on the 1/4-filling side for small values of the interchain hopping parameter.

Slave fermions and the infinite-UAnderson lattice above quarter-filling: Ferromagnetic spin excitations and antiferromagnetic instabilities at low electron count

We extend our earlier formulation for the Anderson lattice (using auxiliary fermions and bosons to represent the charge and spin, respectively) to calculate the spin wave excitation spectrum for a wide range of model parameters in one and two dimensions. We show that, for the case of nearest neighbor conduction electron hopping, the compensated spin state obtained in mean-field theory is bounded at an upper conduction electron concentration (where the spin wave velocity vanishes) and at a lower concentration (close to quarter-filling) by an antiferromagnetic instability, signaled by a vanishing spin wave energy at the appropriate zone boundary. In addition, the range of stable compensated ferromagnetism vanishes as the local f-level energy passes through the bottom of the band (from below). This suggests that only the Kondo regime where the f level lies well below the Fermi level shows a saturated ferromagnetic state.

Superfluid spiral state of quantum ferrimagnets in a magnetic field

We study the phase diagram of one-dimensional quantum ferrimagnets by using a numerical exact diagonalization of a finite size system along with a field-theoretical non-linear $\sigma$ model of the quantum ferrimagnets at zero temperature and its effective description in the presence of the external magnetic field in terms of the quantum XY-model. The low- and the high-field phases correspond respectively to the classical N\'eel and the fully polarized ferromagnetic states where in the intermediate magnetic field ($h_{c1} < h < h_{c2}$), it is an XXZ+h model with easy plane anisotropy, which possess the spiral (superfluid) states that carry the dissipationless spin-supercurrent. We derive the critical exponents, and then will study the stability of the XY spiral state against these spin-supercurrents and the hard axis fluctuations. We will show a first order phase transition from the easy plane spiral state to a saturated ferromagnetic state occurs at $h=h_{c2}$ if the spin-supercurrent reaches to its critical value.

Electron Correlations in the Nagaoka State on the Square Lattice -Three-Body Correlations-

A three-body scattering theory previously proposed by one of the present authors is developed to be applied to the saturated ferromagnetic state in the two-dimensional Hubbard model. The single-particle Green's function is calculated by taking account of the multiple scattering between two electrons and one hole. Several limiting cases are discussed and the relation to the variational principle is examined. The importance of the three-body correlation is demonstrated in comparison with the results of the ladder approximation. A possible phase boundary for the Nagaoka ground state is presented for the square lattice, which improves the previous variational results.

Existence of Saturated Ferromagnetic and Spiral States in 1D Lieb-Ferrimagnetic Models away from Half-Filling

In order to study conditions for the appearance of ferromagnetism in a wide filling region, we investigate numerically three types of one-dimensional Lieb-ferrimagnetic Hubbard models: a periodic diamond (PD) chain, a periodic alternately-attached leg (PAAL) chain and an open diamond (OD) chain. All of these models have a flat band (or equivalently, degenerate single-electron eigenvalues). The PD and OD chains commonly have a local-loop structure. Nagaoka's theorem holds only in the PD chain. At half-filling, it have been rigorously proven that all of these models are ferrimagnet. Away from half-filling, however, quite different magnetic properties are found. In the fillings 1/3< rho_e <1/2, the ground state of the PD chain for a infinitely-large U is the extended ferromagnetic state, that is, the saturated ferromagnetic state or the spiral state for odd or even number of electrons, respectively. In the PAAL chain, on the other hand, there is no magnetic order. Thus, the flat band is found to be not a sufficient condition of the extended ferromagnetic state. We find, moreover, that the saturated ferromagnetism appears in the OD chain, although the Nagaoka theorem does not hold on this chain. This indicates that the local-loop structure plays an important role on the appearance of the extended ferromagnetic state.

Electron spectrum and stability of the saturated ferromagnetic state in a Hubbard model with strong correlations

A Hubbard model with infinite Coulomb repulsion is studied in a many-electron operator representation. A picture of the density of states is constructed using expressions for the one-particle Green’s functions of first order in 1/z. Its behavior is studied near the Fermi level, especially Condon effects. The stability of saturated ferromagnetism is examined. The corresponding critical current carrier densities are found for semielliptical and rectangular seed densities of state, and for square and cubic lattices. These results are compared with earlier work.

The singlet state in the Hubbard model with U=∞

We discuss, in connection with the problem of the ground state in the Hubbard model with U=∞, the normal (nonmagnetic) N-state of a system over the entire range of electron concentrations n≤1. It is found that in a one-particle approximation, e.g., in the generalized Hartree-Fock approximation, the energy e0(n) of the N-state is lower than the energy eFM(n) of a saturated ferromagnetic state for all values of n. Using the random phase approximation we calculate the dynamical magnetic susceptibility and show that the N-state is stable for all values of n. A formally exact representation is derived for the mass operator of the one-particle electron Green’s function, and its expression in the self-consistent Born approximation is obtained. We discuss the first Born approximation and show that when correlations are taken into account, the attenuation vanishes on the Fermi surface and the electron distribution function at T=0 acquires a Migdal discontinuity, whose magnitude depends on n. The energy of the N-state in this approximation is still lower than eFM(n) for n<1. We show that the spin correlation functions are isotropic, which is a characteristic feature of the singlet states of the system. We calculate the spin correlation function for the nearest neighbors in the zeroth approximation as a function of n. Finally, we conclude that the singlet state of the system in the thermodynamic limit is the ground state.

Lattice dependence of saturated ferromagnetism in the Hubbard model

We investigate the instability of the saturated ferromagnetic ground state (Nagaoka state) in the Hubbard model on various lattices in dimensions d=2 and d=3. A variational resolvent approach is developed for the Nagaoka instability both for U = infinity and for U < infinity which can easily be evaluated in the thermodynamic limit on all common lattices. Our results significantly improve former variational bounds for a possible Nagaoka regime in the ground state phase diagram of the Hubbard model. We show that a pronounced particle-hole asymmetry in the density of states and a diverging density of states at the lower band edge are the most important features in order to stabilize Nagaoka ferromagnetism, particularly in the low density limit.

New Saturated Ferromagnetism in the Flat-Band Hubbard Model in High Electron Filling

We investigate the magnetization of the ground state of the one-dimensional flat-band Hubbard model as a function of the electron filling, using exact diagonalization techniques. Our calculation shows that the systems with odd n holes added to half-filling bands for a sufficiently large U (the on-site Coulomb repulsion energy) have a saturated ferromagnetic ground state, which is nondegenerate except for the trivial spin degeneracy. Dependences of the critical value of U on the size and on λ (a parameter of the system) are also investigated. For all values of λ, it is found that the ground state is a saturated ferromagnetic state if U is sufficiently large. Moreover, we find that the critical U for the saturated ferromagnetic ground state is almost independent on the system size, at least, for the system near quarter-filling. These facts indicate that even if the system size go to infinity, the ferromagnetic ground state can be exist for a finite U .

Magnetism and structure of small clusters: An exact treatment of electron correlations.

The electronic, magnetic, and structural properties of small clusters are studied in the framework of the single-band Hubbard Hamiltonian. Results for various ground-state and excited-state many-body properties are presented, which were calculated exactly by means of Lanczos's numerical diagonalization method. A full geometry optimization is performed for N\ensuremath{\le}8 atoms by considering all possible nonequivalent cluster structures with fixed nearest-neighbor bond lengths. The most stable structure and the corresponding total spin S are obtained rigorously as a function of the Coulomb interaction strength U/t and number of electrons \ensuremath{\nu}. The resulting interplay between electron correlations, magnetism, and cluster structure is analyzed and the main trends as a function of N, U/t, and \ensuremath{\nu} are derived. The stability of cluster ferromagnetism is studied from two complementary points of view. First, for N\ensuremath{\le}8 and \ensuremath{\nu}=N+1, we determine exactly the stability of the ferromagnetic ground state with respect to electronic excitations and structural changes. It is shown that in small clusters the structural changes can be as important to the temperature dependence of the magnetization as the purely electronic excitations. Second, we determine the stability of the saturated ferromagnetic state with respect to single spin flips as a function of the band filling \ensuremath{\nu}/N. In this case a few selected larger clusters (7\ensuremath{\le}N\ensuremath{\le}43) in the strongly correlated limit (U/t\ensuremath{\rightarrow}+\ensuremath{\infty}) are considered. It is shown that the \ensuremath{\nu}/N dependence of the spin-flip energy \ensuremath{\Delta}${\mathrm{\ensuremath{\varepsilon}}}_{\mathrm{sf}}$ shows interesting electronic-shell-like oscillations, which reflect the characteristics of the single-particle energy-level structure and its dependence on the symmetry and size of the cluster. Finally, we conclude by discussing some of the limitations of the model together with relevant extensions. \textcopyright{} 1996 The American Physical Society.

Hubbard model and fullerenes: Stability of the Nagaoka state.

We prove numerically that the saturated ferromagnetic state in the Hubbard model with infinitely large Coulomb repulsion and one hole (Nagaoka state) is unstable for a fullerene cluster if the hopping integral is negative, and possibly stable if possible. We analyze the stability versus the variation of the ratio between the hopping values for the two types of carbon-carbon bonds. The results suggest the existence of ferromagnetism in doped fullerene when the electronic correlation leads to a large effective electron-electron interaction.