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arXiv:cond-mat/9907258 · Physical Review Letters

Doping-Induced Magnetization Plateaus

Holger Frahm, Constantin Sobiella

Published Dec 27, 1999• 17 citations
arXivHTMLPDF

Abstract

The low-temperature magnetization process of antiferromagnetic spin- $S$ chains doped with mobile spin- $(S\ensuremath{-}1/2)$ carriers is studied in an exactly solvable model. For sufficiently high magnetic fields the system is in a metallic phase with a finite gap for magnetic excitations. In this phase, which exists for a large range of carrier concentrations $x$, the zero-temperature magnetization is determined by $x$ alone. This leads to plateaus in the magnetization curve at a tunable fraction of the saturation magnetization. The critical behavior at the edges of these plateaus is studied in detail.

DOI
10.1103/physrevlett.83.5579

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The low-temperature magnetization process of antiferromagnetic spin- SSS chains doped with mobile spin- (S\ensuremath−1/2)(S\ensuremath{-}1/2)(S\ensuremath−1/2) carriers is studied in an exactly solvable model. For sufficiently high magnetic fields the system is in a metallic phase with a finite gap for magnetic excitations. In this phase, which exists for a large range of carrier concentrations xxx, the zero-temperature magnetization is determined by xxx alone. This leads to plateaus in the magnetization curve at a tunable fraction of the saturation magnetization. The critical behavior at the edges of these plateaus is studied in detail.
Hubbard chains with periodically modulated coupling constants in a magnetic field exhibit gaps at zero temperature in their magnetic and charge excitations in a variety of situations. In addition to fully gapped situations (plateau in the magnetization curve and charge gap), we have shown [Phys. Lett. A 268, 418 (2000)] that plateaus also appear in the presence of massless modes, leading to a plateau with a magnetization m whose value depends continuously on the filling n. Here we detail and extend the arguments leading to such doping-dependent magnetization plateaus. First we analyze the low-lying excitations using Abelian bosonization. We compute the susceptibility and show that due to the constraint of fixed n, it vanishes at low temperatures (thus leading to a magnetization plateau) even in the presence of one massless mode. Next we study correlation functions and show that one component of the superconducting order parameter develops quasi-long-range order on a doping-dependent magnetization plateau. We then use perturbation theory in the on-site repulsion U to compute the width of these plateaus up to first order in U. Finally, we compute ground state phase diagrams and correlation functions by Lanczos diagonalization of finite clusters, confirming the presence of doping-dependent plateaus and their special properties.
We study a spin chain and a three-dimensional spin lattice with ground states given by a product of spin-singlet nearest-neighbor pairs. In a magnetic field, the ground state and low-lying states are a mixture of spin singlets and spin-polarized triplets; these states are highly degenerate. When the lattice is distorted, hopping terms are introduced which lift the degeneracy. For particular parameter ranges, the magnetization versus magnetic-field curve exhibits spin plateaus, when the excited states are separated from the ground state by a spin gap. At a critical point, the plateau and the corresponding gap vanish. This spin system is embedded in a more general interacting electron system, and when doped, the charged carriers are found to bind in pairs.
We discuss zero-temperature quantum spin chains in a uniform magnetic field, with axial symmetry. For integer or half-integer spin, SSS, the magnetization curve can have plateaus and we argue that the magnetization per site mmm is topologically quantized as $n(S\ensuremath{-}m)\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\mathrm{integer}$ at the plateaus, where nnn is the period of the ground state. We also discuss conditions for the presence of the plateau at those quantized values. For S=3/2S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3/2S=3/2 and m=1/2m\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2m=1/2, we study several models and find two distinct types of massive phases at the plateau. One of them is argued to be a ``Haldane gap phase'' for half-integer SSS.
Plateaus can be observed in the zero-temperature magnetization curve of quantum spin systems at rational values of the magnetization. In one dimension, the appearance of a plateau is controlled by a quantization condition for the magnetization which involves the length of the local spin and the volume of a translational unit cell of the ground state. We discuss examples of geometrically frustrated quantum spin systems with large (in general unbounded) periodicities of spontaneous breaking of translational symmetry in the ground state. In two dimensions, we discuss the square, triangular and Kagomé lattices using exact diagonalization (ED) for up to N = 40 sites. For the spin-1/2 XXZ model on the triangular lattice we study the nature and stability region of a plateau at one third of the saturation magnetization. The Kagomé lattice gives rise to particularly rich behaviour with several plateaus in the magnetization curve and a jump due to local magnon excitations just below saturation.
In this thesis the low temperature properties of an exactly solvable anti-ferromagnetic spin S = 1 chain doped with mobile spin S = 1 =2 impurities will be considered.The doped spin S = 1 chain is a generalization of the super-symmetric t-J model and interpolates between the isotropic spin S = 1 =2 HEISENBERG model and the spin S = 1 TAKHTAJAN-BABUJIAN chain for the completely doped case and vanishing impurity concentration x h = 0 respectively.Within the framework of the Quantum Inverse Scattering Method the doped spin S = 1 chain can be built from a gl(2j1)-invariant solution of the graded YANG-BAXTER equation corresponding to the atypical [1] + -representation of the super-algebra gl(2j1).The associated transfer matrix is diagonalized by means of a nested algebraic BETHE ansatz.Using a generalized fusion procedure the Hamiltonian and it's eigenvalues are constructed.By applying TAKAHASHI's string hypothesis we deduce in the third part the thermodynamic BETHE ansatz equations.Performing the low temperature limit we can determine ground state properties and the phase diagram depending on an external magnetic field H and the impurity concentration x h .The system shows spin-charge separation.We also examine the magnetic properties of the model.For sufficiently high magnetic fields and finite impurity concentration we find a new metallic phase with a finite gap for the magnetic excitations.In this phase the magnetization curve shows a plateau that is only a fraction of the saturation magnetization and can be tuned by the impurity concentration x h .The critical behavior near the edges of the plateau is also analyzed.To study the dynamical properties e.g. the low lying magnetic excitations we calculate the Finite Size Correction of the model.Using predictions of Conformal Field Theory we can identify the effective low temperature theories as well as the scaling dimensions which determine the asymptotic behavior of the correlation functions at criticality.In the plateau phase no magnetic excitations are found to exist.