Magnetization and magnetic phase diagrams of a spin-1/2 ferrimagnetic diamond chain at low temperature

We used the Jordan–Wigner transform and the invariant eigenoperator method to study the magnetic phase diagram and the magnetization curve of the spin-1/2 alternating ferrimagnetic diamond chain in an external magnetic field at finite temperature. The magnetization versus external magnetic field curve exhibits a 1/3 magnetization plateau at absolute zero and finite temperatures, and the width of the 1/3 magnetization plateau was modulated by tuning the temperature and the exchange interactions. Three critical magnetic field intensities H_(CB), H_(CE) and H_(CS) were obtained, in which the H_(CB) and H_(CE) correspond to the appearance and disappearance of the 1/3 magnetization plateau, respectively, and the higher H_(CS) correspond to the appearance of fully polarized magnetization plateau of the system. The energies of elementary excitation ωσ,k(σ = 1, 2, 3) present the extrema of zero at the three critical magnetic fields at 0 K, i.e., [hω_(3,k)(HCB)]_(min)= 0, [hω_(2,k)(H_(CE))]_(max)= 0 and [hω _(2,k)(H_(CS))]_(min)= 0, and the magnetic phase diagram of magnetic field versus different exchange interactions at 0 K was established by the above relationships. According to the relationships between the system's magnetization curve at finite temperatures and the critical magnetic field intensities, the magnetic field-temperature phase diagram was drawn. It was observed that if the magnetic phase diagram shows a three-phase critical point, which is intersected by the ferrimagnetic phase, the ferrimagnetic plateau phase, and the Luttinger liquid phase, the disappearance of the1/3 magnetization plateau would inevitably occur. However, the 1/3 magnetization plateau would not disappear without the three-phase critical point. The appearance of the 1/3 magnetization plateau in the low temperature region is the macroscopic manifestations of quantum effect.     

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.     

Quantum effects in a half-polarized pyrochlore antiferromagnet

We study quantum effects in a spin-3/2 antiferromagnet on the pyrochlore lattice in an external magnetic field, focusing on the vicinity of a plateau in the magnetization at half the saturation value, observed in CdCr2O4 and HgCr2O4. Our theory, based on quantum fluctuations, predicts the existence of a symmetry-broken state on the plateau, even with only nearest-neighbor microscopic exchange. This symmetry-broken state consists of a particular arrangement of spins polarized parallel and antiparallel to the field in a 3:1 ratio on each tetrahedron. It quadruples the lattice unit cell, and reduces the space group from Fd3m to P4(3)32. We also predict that for fields just above the plateau, the low-temperature phase has transverse spin order, describable as a Bose-Einstein condensate of magnons. Other comparisons to and suggestions for experiments are discussed.     

Magnetization plateaus and sublattice ordering in easy-axis kagome lattice antiferromagnets

We study kagome lattice antiferromagnets where the effects of easy-axis single-ion anisotropy (D) dominates over the Heisenberg exchange J. For S> or =3/2, virtual quantum fluctuations help lift the extensive classical degeneracy. We demonstrate the presence of a one-third magnetization plateau for a broad range of magnetic fields J3/D2 < or = B < or = JS along the easy axis. The fully equilibrated system at low temperature on this plateau develops an unusual nematic order that breaks sublattice rotation symmetry but not translation symmetry; however, extremely slow dynamics associated with this ordering is expected to lead to glassy freezing of the system on intermediate time scales.     

Quantum Phase Diagram of an Exactly Solved Mixed Spin Ladder

We investigate the quantum phase diagram of the exactly solved mixed spin-(1/2,1) ladder via the thermodynamic Bethe ansatz (TBA). In the absence of a magnetic field the model exhibits three quantum phases associated with su(2), su(4), and su(6) symmetries. In the presence of a strong magnetic field, there is a third and full saturation magnetization plateaux within the strong antiferromagnetic rung coupling regime. Gapless and gapped phases appear in turn as the magnetic field increases. For weak rung coupling, the fractional magnetization plateau vanishs and the model undergoes new quantum phase transitions. However, in the ferromagnetic coupling regime, the system does not have a third saturation magnetization plateau. The critical behaviour in the vicinity of the critical points is also derived systematically using the TBA.     

Experimental realization of a spin-1/2 triangular-lattice Heisenberg antiferromagnet

We report the results of magnetization and specific heat measurements on Ba{3}CoSb{2}O{9}, in which the magnetic Co{2+} ion has a fictitious spin 1/2, and provide evidence that a spin-1/2 Heisenberg antiferromagnet on a regular triangular lattice is actually realized in Ba{3}CoSb{2}O{9}. We found that the entire magnetization curve including the one-third quantum magnetization plateau is in excellent quantitative agreement with the results of theoretical calculations. We also found that Ba{3}CoSb{2}O{9} undergoes a three-step transition within a narrow temperature range.     

Nature of the spin dynamics and 1/3 magnetization plateau in azurite

We present a specific heat and inelastic neutron scattering study in magnetic fields up into the 1/3 magnetization plateau phase of the diamond chain compound azurite Cu3(CO3)2(OH)2. We establish that the magnetization plateau is a dimer-monomer state, i.e., consisting of a chain of S=1/2 monomers, which are separated by S=0 dimers on the diamond chain backbone. The effective spin couplings Jmono/kB=10.1(2) K and Jdimer/kB=1.8(1) K are derived from the monomer and dimer dispersions. They are associated to microscopic couplings J1/kB=1(2) K, J2/kB=55(5) K and a ferromagnetic J3/kB=-20(5) K, possibly as result of dz2} orbitals in the Cu-O bonds providing superexchange (SE) pathways with JSE=6.5 K.     

Cascade of Magnetic Field Induced Spin Transitions in LaCoO_{3}

We present magnetization and magnetostriction studies of LaCoO_{3} in magnetic fields approaching 100?T. In contrast with expectations from single-ion models, the data reveal two distinct first-order transitions and well-defined magnetization plateaus. The magnetization at the higher plateau is only about half the saturation value expected for spin-1 Co^{3+} ions. These findings strongly suggest collective behavior induced by interactions between different electronic configurations of Co^{3+} ions. We propose a model that predicts crystalline spin textures and a cascade of four magnetic phase transitions at high fields, of which the first two account for the experimental data.     

反对称Spin-1/2阻挫钻石链的基态和磁化行为研究

对含有次近邻节点自旋交换耦合的自旋-1/2伊辛-海森伯钻石链体系进行了研究,利用矩阵对角化和传递矩阵方法对基态磁相和宏观热力学量进行了严格求解,重点探讨了所有交换耦合均为反铁磁耦合时,体系节点伊辛自旋间次近邻相互作用的影响.研究结果表明次近邻节点伊辛自旋存在反铁磁耦合时会增强系统的阻挫效应,引入破坏平移对称性的经典亚铁磁相,使基态呈现出上上上下上上的自旋构型以及磁化曲线新颖的2/3磁化平台,丰富了体系的基态相图和宏观磁性行为.     

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.     

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.     

Magnetically induced phase transitions in LaCoO<Subscript>3</Subscript> in fields of up to 500 T

The differential magnetization of LaCoO₃ in magnetic fields of up to 500 T has been measured at a temperature of 4.2 K. The magnetization curve reveals several features which suggest a complex pattern of the transition of LaCoO₃ from the low-spin state to the high-spin state. The magnetic moment starts to grow in fields above 50 T to reach a plateau in the 130–240-T region, after which the magnetic moment continues to rise up to saturation in fields ∼500 T.     

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.     

Long-distance super-exchange and quantum magnetic relaxation in a hybrid metal–organic framework

The hybrid metal–organic framework [(CH3)2NH2]Fe(HCOO)3with a perovskite-like structure exhibits a variety of unusual magnetic behaviors at low temperatures. While the long-distance super-exchange through the Fe-O–CH-O–Fe exchange path leads to a canted antiferromagnetic ordering at TN～ 19 K, a second transition of magnetic blocking develops at TB～ 9 K. The stair-shaped magnetization hysteresis loops below TBresemble the behaviors of resonant quantum tunneling of magnetization in single-molecular quantum magnets. Moreover, the magnetic relaxation also exhibits several features of resonant quantum relaxation, such as the exponential law with a single characteristic relaxation time, and the nonmonotonic dependence of relaxation rate on the applied magnetic field with a much faster relaxation around the resonant fields. The origin of quantum tunneling behaviors in the [(CH3)2NH2]Fe(HCOO)3metal–organic framework is discussed in terms of magnetic phase separation due to the modification of hydrogen bonding on the long-distance super-exchange interaction.     

Low-temperature metastable states in a stacked triangular Ising antiferromagnet

We study low-temperature magnetization processes in a stacked triangular Ising antiferromagnet by Monte Carlo simulations. In increasing and decreasing magnetic fields we observe multiple steps and hysteresis corresponding to formation of different metastable states. Besides the equidistant threefold splitting of the 1/3 ferrimagnetic plateau, we additionally confirm a fourth plateau in the field-increasing branch and a sizable remanence when the field is decreased to zero. The newly observed plateau only appears at sufficiently low temperature and sufficiently large exchange interaction in the stacking direction. These observations reasonably reproduce low-temperatures measurements on the spin-chain compound Ca₃Co₂O₆.     

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.     

Induced random fields in the LiHoxY1-xF4 quantum Ising magnet in a transverse magnetic field

The LiHoxY1-xF4 magnetic material in a transverse magnetic field Bx x perpendicular to the Ising spin direction has long been used to study tunable quantum phase transitions in a random disordered system. We show that the Bx-induced magnetization along the x direction, combined with the local random dilution-induced destruction of crystalline symmetries, generates, via the predominant dipolar interactions between Ho3+ ions, random fields along the Ising z direction. This identifies LiHoxY1-xF4 in Bx as a new random field Ising system. The random fields explain the rapid decrease of the critical temperature in the diluted ferromagnetic regime and the smearing of the nonlinear susceptibility at the spin-glass transition with increasing Bx and render the Bx-induced quantum criticality in LiHoxY1-xF4 likely inaccessible.     

Paramagnetism and reentrant behavior in quasi-one-dimensional superconductors at high magnetic fields

The thermodynamics of quasi-one-dimensional superconductors in the presence of large magnetic fields is studied. When the quantum effects of the magnetic field are taken into account, several reentrant superconducting phases persist at very high fields. In the last reentrant phase the free-energy change, the specific-heat jump and the excess magnetization are estimated near the critical temperature. In particular, the excess magnetization is found to be paramagnetic as opposed to diamagnetic in weak fields and its sign is controlled by the slope of H_c2(T). We further generalize this result to the entire phase diagram (including all quantum phases) and to different physical systems using general thermodynamic relations which show that the sign of the excess magnetization ΔM of the superconducting state near H_c2(T) follows dH_c2(T)/dT. These relations provide a scenario for the evolution of the sign of ΔM from weak fields to strong fields.     

自旋为1/2的XY模型亚铁磁棱型链的物性和有序-无序竞争

利用不变本征算符法, 计算低温下自旋为1/2的XY模型一维亚铁磁棱型链系统的元激发谱, 讨论在此系统中不同的特殊情形下的元激发能量, 从而给出体系的三个临界磁场强度的解析解H_C1, H_C2, H_peak. 分析不同外磁场下 体系的磁化强度随温度的变化规律, 发现三个临界磁场强度的解析解H_C1, H_C2, H_peak是正确的, 并从三个元激发对磁化强度的贡献进行了说明. 低温下磁化强度随外磁场的变化呈现1/3磁化平台. 体系的磁化率随温度或者外磁场的变化都出现了双峰现象. 这说明双峰源于二聚体分子内电子自旋平行排列的铁磁交换作 用能和二聚体与单基体分子间电子自旋反平行排列的反铁磁交换作用能, 热无序能, 外磁场强度相关的自旋磁矩势能之间的竞争.