Doped bilayer antiferromagnets: Hole dynamics on both sides of a magnetic ordering transition

Abstract

The two-layer square lattice quantum antiferromagnet with spins 1 2 shows a magnetic orderdisorder transition at a critical ratio of the interplane to intraplane couplings. We investigate the dynamics of a single hole in a bilayer antiferromagnet described by a t−J Hamiltonian. To model the spin background we propose a ground-state wave function for the undoped system which covers both magnetic phases and includes transverse as well as longitudinal spin fluctuations. The photoemission spectrum is calculated using the spin-polaron picture for the whole range of the ratio of the magnetic couplings. This allows for the study of the hole dynamics of both sides of the magnetic order-disorder transition. For small interplane coupling we find a quasiparticle with properties known from the single-layer antiferromagnet, e.g., the dispersion minimum is at (±π/2, ±π/2). For large interplane coupling the hole dispersion is similar to that of a free fermion (with reduced bandwidth). The cross-over between these two scenarios occurs inside the antiferromagnetic phase which indicates that the hole dynamics is governed by the local environment of the hole.

Single-hole dynamics in the half-filled two-dimensional Kondo-Hubbard model

“…In the large U/t limit this leads to a bilayer spin model which has been considered by Vojta and Becker [17]. The authors arrive at a similar conclusion namely that hole dynamics are governed by local spin environment.…”

Magnetic properties and spin waves of bilayer magnets in a uniform field

“…This ansatz contains two subsequent unitary transformations of the singlet product state |φ 0 (5): the λ term creates a spin-density-wave condensate with ordering vector Q and quantization axis in x direction [thus explicitely breaking the U(1) symmetry of the z axis rotation], the µ term introduces canting and a non-zero z magnetization into this state. For µ = 0 and Q = (π, π) which corresponds to J > 0 and B = 0, this wavefunction reduces to a state interpolating between the singlet and the Néel state; it has been recently used to describe the dynamics of holes doped into a bilayer system [31]. A finite external field B larger than the spin gap will lead to a finite uniform magnetization described by finite µ; for large B the system is driven into a fully polarized state with λ → ∞ and µ = 1.…”

“…In the case of µ = 0 the Hamiltonian reduces to the Hamiltonian derived for the zero-field case [31]. It can be seen that H 1 contains creation, hopping, and conversion terms of the three types of excitations {t ix ,t iy ,t iz }.…”

“…The (generalized) singlet is assumed to fully condense, s = 1. It is known from the zero-field case [14,31] that this approximation is controlled by the existence of a small parameter, namely the density of (generalized) triplet excitations t † iαt iα . With this in mind, all terms of the Hamiltonian containing more than two excitation operatorst iα will be neglected.…”

“…We start with the uniform and staggered magnetizations which are obtained as expection values of the corresponding spin operators gered magnetization in the zero-field case has been calculated earlier (see Fig 2 of Ref [31]); it shows a good overall agreement with the series expansion data of Ref [13] if plotted as function of (J /J ⊥ )/(J /J ⊥ ) c -the critical coupling ratio itself is underestimated in the independent boson approach as discussed above.…”