Magnetic phase diagram of the dimerized spin S = 1/2 ladder

The ground-state magnetic phase diagram of a spin S=1/2 two-leg ladder with alternating rung exchange J_⊥(n)=J_⊥[1 + (-1)ⁿ δ] is studied using the analytical and numerical approaches. In the limit where the rung exchange is dominant, we have mapped the model onto the effective quantum sine-Gordon model with topological term and identified two quantum phase transitions at magnetization equal to the half of saturation value from a gapped to the gapless regime. These quantum transitions belong to the universality class of the commensurate-incommensurate phase transition. We have also shown that the magnetization curve of the system exhibits a plateau at magnetization equal to the half of the saturation value. We also present a detailed numerical analysis of the low energy excitation spectrum and the ground state magnetic phase diagram of the ladder with rung-exchange alternation using Lanczos method of numerical diagonalizations for ladders with number of sites up to N = 28. We have calculated numerically the magnetic field dependence of the low-energy excitation spectrum, magnetization and the on-rung spin-spin correlation function. We have also calculated the width of the magnetization plateau and show that it scales as δ^ν, where critical exponent varies from ν = 0.87±0.01 in the case of a ladder with isotropic antiferromagnetic legs to ν = 1.82±0.01 in the case of ladder with ferromagnetic legs. Obtained numerical results are in an complete agreement with estimations made within the continuum-limit approach.     

Quantum Oscillations of Magnetization in Antiferromagnetic Semimetals on a Triangular Lattice

The specific features of magnetization in antiferromagnetic semimetals with a low charge carrier density on a triangular lattice in a high magnetic field are studied. It is demonstrated that the well-known plateau in the magnetic field dependence of the magnetization manifesting itself in the subsystem of localized S = 1/2 spins is actually not strictly horizontal but has a slight positive slope. It is found that an abrupt change in the frequency of quantum oscillations of the magnetization in the itinerant subsystem should be observed at the magnetic field values corresponding to the edges of this plateau owing to the strong s–d(f) exchange coupling.     

Ladders in a magnetic field: a strong coupling approach

We show that non-frustrated and frustrated ladders in a magnetic field can be systematically mapped onto an XXZ Heisenberg model in a longitudinal magnetic field in the limit where the rung coupling is the dominant one. This mapping is valid in the critical region where the magnetization goes from zero to saturation. It allows one to relate the properties of the critical phase (H _c ¹, H _c ², the critical exponents) to the exchange integrals and provide quantitative estimates of the frustration needed to create a plateau at half the saturation value for different models of frustration. Received: 7 May 1998 / Revised and Accepted: 10 July 1998     

MaxEnt and dynamical information

The presence of a quantum critical point can significantly affect the thermodynamic properties of a material at finite temperatures. This is reflected, e.g., in the entropy landscape S(T, c) in the vicinity of a quantum critical point, yielding particularly strong variations for varying the tuning parameter c such as magnetic field. In this work we have studied the thermodynamic properties of the quantum compass model in the presence of a transverse field. The specific heat, entropy and cooling rate under an adiabatic demagnetization process have been calculated. During an adiabatic (de)magnetization process temperature drops in the vicinity of a field-induced zero-temperature quantum phase transitions. However close to field-induced quantum phase transitions we observe a large magnetocaloric effect.     

Magnetization plateaus and supersolid phases in an extended Shastry–Sutherland model

New magnetization plateaus and supersolid phases are identified in an extended Shastry–Sutherland model – with additional longer range interactions and exchange anisotropy – over a wide range of interaction parameters and an applied magnetic field. The model is appropriate for describing the low energy properties of some members of the rare earth tetraborides. Using a plaquette representation and exact mapping of ground state configurations in the Ising limit, supplemented by large scale quantum Monte Carlo simulations to include the effects of exchange interactions, we have identified several magnetization plateaus and associated spin supersolid phases. Our methods enable us to elucidate the underlying structure and mechanism of formation of the supersolid phases, thus gaining deeper understanding into their emergence from competing interactions. Additionally, in this regime we find evidence of a fractional plateau at 1∕9 saturation magnetization, which may hold the clue to understanding the fractional plateau in TmB₄ that exhibits magnetic hysteresis.     

Pairwise entanglement and critical behavior of an anisotropic ferrimagnetic spin chain

We studied the quantum phase transition revealed to occur in the ferrimagnetic mixed-spin (S,s)=(1,1/2) chain with positive crystal-field anisotropy D under an external magnetic field by using concepts from quantum information theory such as pairwise entanglement and purity, incorporated into the density matrix renormalization group algorithm. In this system, a magnetization plateau appears at 1/3 of the saturation magnetization for all values of D except for a critical value Dc where it vanishes. We obtained this value Dc=1.11445±0.00065 within the thermodynamic limit as local minima of the pairwise entanglement and the purity. Moreover, using this procedure we were able to investigate the second-order (or continuous) character of the quantum phase transition.     

Quantum Phase Transition and Magnetocaloric Effect in a Tetrameric Chain with Three-Spin Interaction

We investigate the quantum phase transition (QPT) and magnetocaloric effect (MCE) of a tetrameric chain with three-spin interaction using Green's function theory. The magnetization and gap analysis reveals a variety of quantum phases tuned by magnetic field and three-spin interaction, which can open up an energy gap, giving rise to the occurrence of zero magnetization plateau. However, strong three-spin couplings causing strong frustration will destroy the intermediate 1/2 plateau with emergence of a new gapless phase between two cusps. It favors achieving an enhanced MCE at the critical fields, where the minima of isoentropes as well as the valley-peak structure of Grüneisen ratio, signaling the accumulation of entropy, lead to cooling via adiabatic (de)magnetization processes. It is also found that the temperature dependence of specific heat combined with Grüneisen ratio can testify various quantum phases explicitly.     

Exact solution and magnetic properties of an anisotropic spin ladder

We study an integrable two-leg spin-1/2 ladder with an XYZ-type rung interaction. The exact rung states and rung energies are obtained for the anisotropic rung coupling in the presence of a magnetic field. The magnetic properties are analyzed at both zero and finite temperatures via the thermodynamic Bethe ansatz and the high-temperature expansion. According to different couplings in the anisotropic rung interaction, there are two cases in which a gap opens, where the ground state involves one or two components in the absence of a magnetic field. We obtain the analytic expressions of all critical fields for the field-induced quantum phase transitions (QPT). The anisotropic rung interaction leads to such effects as separated magnetizations and susceptibilities in different directions, lowered inflection points, and remnant weak variation of the magnetization after the last QPT.Received: 21 May 2004, Published online: 30 September 2004PACS: 75.10.Jm Quantized spin models - 75.30.Kz Magnetic phase boundaries (including magnetic transitions, metamagnetism, etc.) - 75.40.Cx Static properties (order parameter, static susceptibility, heat capacities, critical exponents, etc.)     

The magnetization of PrFeAsO0.60F0.12 superconductor

The magnetization of the PrFeAsO_0.60F_0.12 polycrystalline sample has been measured as functions of temperature and magnetic field (H). The observed total magnetization is the sum of a superconducting irreversible magnetization and a paramagnetic magnetization. Analysis of dc susceptibility χ(T) in the normal state shows that the paramagnetic component of magnetization comes from the Pr³⁺ magnetic moments. The intragrain critical current density (J_L) derived from the magnetization data is large. The J_L(H) curve displays a second peak which shifts towards the high-field region with decreasing temperature. In the low-field region, a plateau up to a field H^* followed by a power law H^?5/8 behavior of J_L(H) is the characteristic of the strong pinning. A vortex phase diagram for the present superconductor has been obtained from the magnetization and resistivity data.     

Breakdown of an intermediate plateau in the magnetization process of anisotropic spin-1 Heisenberg dimer: Theory vs. experiment

The magnetization process of the spin-1 Heisenberg dimer model with the uniaxial or biaxial single-ion anisotropy is particularly investigated in connection with recent experimental high-field measurements performed on the single-crystal sample of the homodinuclear nickel(II) compound [Ni₂(Medpt)₂(μ-ox)(H₂O)₂](ClO₄)₂·2H₂O (Medpt=methyl-bis(3-aminopropyl)amine). The results obtained from the exact numerical diagonalization indicate a striking magnetization process with a marked spatial dependence on the applied magnetic field for arbitrary but finite single-ion anisotropy. It is demonstrated that the field range, which corresponds to an intermediate magnetization plateau emerging at a half of the saturation magnetization, basically depends on a single-ion anisotropy strength as well as a spatial orientation of the applied field. The breakdown of the intermediate magnetization plateau is discussed at length in relation to the single-ion anisotropy strength.     

Unconventional magnetic phase diagram of cuprate superconductor La2−xSrxCuO4 at quantum critical point x=1/9

We propose a new magnetic phase diagram of La_2?xSr_xCuO₄ around a quantum critical point x=1/9 based on field-cooled magnetization measurements and critical fittings. A new phase boundary T_m2(H) is discovered which buries deeply below the first order vortex melting line in the vortex solid phase. The coupling between superconductivity and antiferromagnetism is found to be attractive below T_m2(H) while repulsive above. The attractive coupling between superconducting order and static antiferromagnetic order provides compelling experimental evidence that the antiferromagnetism microscopically coexists and collaborates with the high temperature superconductivity in cuprates.     

Magnetic properties of the spin S = 1/2 Heisenberg chain with hexamer modulation of exchange

We consider the spin-1/2 Heisenberg chain with alternating spin exchange in the presence of additional modulation of exchange on odd bonds with period 3. We study the ground state magnetic phase diagram of this hexamer spin chain in the limit of very strong antiferromagnetic (AF) exchange on odd bonds using the numerical Lanczos method and bosonization approach. In the limit of strong magnetic field commensurate with the dominating AF exchange, the model is mapped onto an effective XXZ Heisenberg chain in the presence of uniform and spatially modulated fields, which is studied using the standard continuum-limit bosonization approach. In the absence of additional hexamer modulation, the model undergoes a quantum phase transition from a gapped phase into the only one gapless Lüttinger liquid (LL) phase by increasing the magnetic field. In the presence of hexamer modulation, two new gapped phases are identified in the ground state at magnetization equal to [Formula: see text] and [Formula: see text] of the saturation value. These phases reveal themselves also in the magnetization curve as plateaus at corresponding values of magnetization. As a result, the magnetic phase diagram of the hexamer chain shows seven different quantum phases, four gapped and three gapless, and the system is characterized by six critical fields which mark quantum phase transitions between the ordered gapped and the LL gapless phases.     

Magnetic catalysis and magnetic oscillations in the Nambu-Jona-Lasinio model

The phase structure of the four-dimensional Nambu-Jona-Lasinio model in the presence of a chemical potential μ and an external magnetic field H is investigated at comparatively small values of the bare coupling constant (G<G _c). It is shown that only for magnetic-field strengths in excess of some critical value H _c(μ) does the magnetic field induce a spontaneous breakdown of chiral symmetry. On the phase portrait of the model, there are infinitely many massless chiral-invariant phases; in addition, there is one massive phase characterized by spontaneously broken chiral invariance. It is because of this phase structure of the system that some physical features of its ground state, including magnetization, pressure, and particle density, oscillate as H → 0. Changes in the vacuum properties of the model are accompanied by first-or second-order phase transitions.     

Entanglement spectrum and magnetization plateaus in an S = 1 bond-alternative Heisenberg chain with single-ion anisotropy and magnetic field

Entanglement spectrum and quantum phase transitions (QPTs) in S = 1 bond-alternative antiferromagnetic Heisenberg chain with single-ion anisotropy and magnetic field are investigated by the infinite time-evolving block decimation (iTEBD) method. The combined effects of the single-ion anisotropy and magnetic field have been discussed, and a rich ground-state phase diagram is obtained. We find that the single-ion anisotropy is advantageous to the stability of the 1/2 magnetization plateau. Both entanglement entropy and entanglement spectrum, as two model-independent measures, are capable of describing all the QPTs. Especially, doubly degenerate entanglement spectrum on even bond is observed in the 1/2 plateau phase. Besides constant spontaneous magnetization, three magnetization plateaus (M ^z = 0, 1/2, and 1) are found to have constant entanglement entropy, entanglement spectrum, and nearest-neighbor correlation. In addition, all the QPTs in such a model have been determined to belong to the second-order category.     

On a quantum plateau of magnetization in metal-organic quasi-one-dimensional ferrimagnets

The possibility of realizing a quantum plateau of magnetization in [Mn(hfac)₂BNO_R] metal-organic compounds is investigated theoretically. A model of a one-dimensional ferrimagnetic chain (5/2, 1) is used for calculating the magnetization as a function of an external field by the method of discrete path integral representation (DPIR). Within this model, the coexistence of classical and quantum plateaus of magnetization is revealed. It is shown that the critical field H_c1 that destroys the classical plateau (ground-state magnetization) is determined by the optical gap in zero field, which is estimated by the matrix-product method and a numerical method of exact diagonalization (recursion method).     

Quantum Hall ferrimagnetism in lateral quantum dot molecules

We demonstrate the existence of ferrimagnetic and ferromagnetic phases in a spin phase diagram of coupled lateral quantum dot molecules in the quantum Hall regime. The spin phase diagram is determined from the Hartree-Fock configuration interaction method as a function of electron number N and magnetic field B. The quantum Hall ferrimagnetic phase corresponds to spatially imbalanced spin droplets resulting from strong interdot coupling of identical dots. The quantum Hall ferromagnetic phases correspond to ferromagnetic coupling of spin polarization at filling factors between nu=2 and nu=1.     

Kac-Moody symmetries of critical ground states

The symmetries of critical ground states of two-dimensional lattice models are investigated. We show how mapping a critical ground state to a model of a rough interface can be used to identify the chiral symmetry algebra of the conformal field theory that describes its scaling limit. This is demonstrated in the case of the six-vertex model, the three-coloring model on the honeycomb lattice, and the four-coloring model on the square lattice. These models are critical and they are described in the continuum by conformal field theories whose symmetry algebras are the su(2)_k=1, su(3)_k=1, and the su(4)_k=1 Kac-Moody algebra, respectively. Our approach is based on the Frenkel-Kac-Segal vertex operator construction of level-one Kac-Moody algebras.     

Zero temperature phase transitions in spin-ladders: Phase diagram and dynamical studies of Cu2(C5H12N2)2Cl4>

In a magnetic field, spin-ladders undergo two zero-temperature phase transitions at the critical fields H_c1 and H_c2. An experimental review of static and dynamical properties of spin-ladders close to these critical points is presented. The scaling functions, universal to all quantum critical points in one-dimension, are extracted from (a) the thermodynamic quantities (magnetization) and (b) the dynamical functions (NMR relaxation). A simple mapping of strongly coupled spin ladders in a magnetic field on the exactly solvable XXZ model enables to make detailed fits and gives an overall understanding of a broad class of quantum magnets in their gapless phase (between H_c1 and H_c2). In this phase, the low temperature divergence of the NMR relaxation demonstrates its Luttinger liquid nature as well as the novel quantum critical regime at higher temperature. The general behavior close these quantum critical points can be tied to known models of quantum magnetism. Received: 13 March 1998 / Received in final form and Accepted: 21 July 1998     

Magnetization reversal dependence on magnetic properties of a spin torque oscillator with in-plane anisotropy free layer and orthogonal polarizer

The effect of magnetic properties on magnetization dynamics is studied for a spin torque oscillator (STO) composed of a free layer with an in-plane magnetic anisotropy and a reference layer with a fixed out-of plane magnetization. A transition from damped to uniform oscillations is observed for a critical value of saturation magnetization M_S). In the uniform oscillations regime, the frequency is inversely proportional to M_S. Similarly, the critical current for achieving uniform oscillations is investigated as a function of free layer intrinsic properties. In a second part of the study, the magnetostatic field (H_m) from the reference layer is considered and it is revealed that the out-of plane component of magnetization has a strong dependence on H_m. For a particular configuration, H_m could reduce the out-of plane component maximizing thus the out-put signal of the STO.