Magnetic-field–temperature phase diagram of alternating ferrimagnetic chains: Spin-wave theory from a fully polarized vacuum

Abstract

Quantum critical (QC) phenomena can be accessed by studying quantum magnets under an applied magnetic field (B). The QC points are located at the endpoints of magnetization plateaus and separate gapped and gapless phases. In one dimension, the low-energy excitations of the gapless phase form a Luttinger liquid (LL), and crossover lines bound insulating (plateau) and LL regimes, as well as the QC regime. Alternating ferrimagnetic chains have a spontaneous magnetization at T = 0 and gapped excitations at zero field. Besides the plateau at the fully polarized (FP) magnetization; due to the gap, there is another magnetization plateau at the ferrimagnetic (FRI) magnetization. We develop spin-wave theories to study the thermal properties of these chains under an applied magnetic field: one from the FRI classical state, and other from the FP state, comparing their results with quantum Monte Carlo data. We deepen the theory from the FP state, obtaining the crossover lines in the T vs. B low-T phase diagram. In particular, from local extreme points in the susceptibility and magnetization curves, we identify the crossover between an LL regime formed by excitations from the FRI state to another built from excitations of the FP state. These two LL regimes are bounded by an asymmetric dome-like crossover line, as observed in the phase diagram of other quantum magnets under an applied magnetic field.

Lieb and hole-doped ferrimagnetism, spiral, resonating valence-bond states, and phase separation in large-U AB 2 Hubbard chains

“…Since the dispersive modes preserve the local triplet bond, they are identical to those found in the spin-1/2 -spin-1 chains [62][63][64][65]. These chains also exhibit interesting field-induced Luttinger liquid behavior [66]. Now, our aim is to obtain the leading corrections to LSWT, i.e., second-order spin-wave theory to the GS energy, sublattice magnetizations and Lieb GS total spin per unit cell.…”

The role of density-dependent magnon hopping and magnon-magnon repulsion in ferrimagnetic spin-(1/2, $S$) chains in a magnetic field

“…We have shown in Ref. [64] that this problem can be overcome, even for finite T , by introducing an effective chemical potential µ to the upper band, in a way similar to Takahashi's solution to the ferromagnetic linear chain [84]. In particular, µ → −J = −2sJ as T → 0, such that the overall effect of µ at T = 0 is the suppression of the upper band.…”

“…Furthermore, rich phase diagrams are observed through doping [46][47][48][49][50] or adding geometric frustration [51][52][53][54][55][56][57][58] to the ferrimagnetic models. In particular, ferrimagnetic spin-(1/2, S) chains under an applied magnetic field present magnetization plateaus at m = S − 1/2 (ferrimagnetic plateau) and m = S + 1/2 (saturation plateau), where m is the magnetization per unit cell [59][60][61][62][63][64]. On the experimental side, the onedimensional magnetic phase of a variety of bimetallic compounds was shown to be modeled by spin-(1/2, S) ferrimagnetic chains [65][66][67][68][69][70].…”

“…Since spin-(s, S) ferrimagnetic chains have a longranged ordered ground state, linear and interacting spinwave theory [72] from the classical ferrimagnetic state was used to characterize their low-energy magnetic excitations, mainly through the Holstein-Primakoff formalism [59,60,[73][74][75][76][77][78]. Furthermore, linear spin-wave theory from the fully polarized state [64] gives good results for the gapped and gapless phases of spin-(1/2, S) chains in a magnetic field.…”

Quantum Phase Transition of a Quantum Mixed Spin Chain by Employing Density Matrix Renormalization Group Method

“…Interestingly, more complicated cases can appear if one introduces inhomogeneities into the quantum spin chains. In general, quantum mixed spin chains possess two types of inhomogeneities, [16,17] the alternation of coupling strengths and spin magnitudes within a unit cell, and have attracted a great interest for their exotic low-energy physics, like the magnetization plateau and Luttinger liquid shown in various ferrimagnetic Heisenberg chains, [18][19][20] the Kosterlitz-Thouless and Gaussian criticalities recently studied in the mixed spin-(1∕2, 5∕2, 1∕2) Heisenberg branched chain, [21,22] and the quantum spin liquid phases appeared in the mixed spin-1 and spin-1∕2 Heisenberg octahedral chain. [23] Additionally, these mixed spin chains are also of experimental interest and have several realistic realizations.…”