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43219-AC10
Frustrated Magnetism as a Problem of Coupled Spin Chains

Oleg Starykh, University of Utah

My research activities this year, partially supported by PRF award,

can be separated into 3 major projects. Brief description of these projects

is given below.

1) Inelastic neutron scattering in spatially anisotropic triangular

lattice antiferromagnet Cs2CuCl4 . This unusual material was considered

to represent our best chance for the spin-liquid ground state

just a few years ago. However, it is understood now that its ground state

in ordered spiral, albeit with a rather small value of site magnetization.

Nonetheless, the excitations above this ordered state are very unusual:

most of the spectral weight, observed via inelastic neutron scattering, is

concentrated in a broad continuum of excitations. This continuum extends

for momentum transfers along both chain and inter-chain directions, which

is very unusual. Strong variation of the continuum spectral weight with

the transverse (with respect to the chain direction) momentum was

interpreted by many researchers as a ``proof" of two-dimensional nature

of spin excitations and led to a number of exotic scenarios.

We, instead, decided to approach the nature of spin excitations from

one-dimensional perspective and check whether spinons that constitute

the continuum in a two-dimensional magnet can be understood as

descendants of well-understood one-dimensional spinons, a.k.a. domain walls.

By restricting the Hilbert space of the problem to that expressed by exact

eigenstates of the Heisenberg chain, we derive an effective Schrodinger

equation in momentum space. The main feature of this equation is that

inter-chain exchange J'(k) plays the role of potential energy. Depending on

the two-dimensional momentum k, three distinct behaviors are possible:

(a) J'(k) < 0 leads to attraction between spinons resulting in delta-function peak below the continuum; (b) J'(k) > 0 describes repulsion and results

in upward shift of spectral weight towards the upper edge; (c) J'(k) = 0 corresponds to non-interacting spinons with the structure factor identical

to that of decoupled chains.

We find that all three behaviors are seen in the experimental data by

Coldea and collaborators. Moreover, by using experimentally determined

values for the two main exchanges (J = 0.374 meV and J'= 0.128 meV)

we were able to explain ALL major experimental features with no fitting

parameters at all. The agreement is of such quality that it makes

us conclude that our novel approach provides the most consistent,

direct and unbiased explanation of the ten-year old puzzle presented

by Cs2CuCl4 . This work, done is collaboration with Masanori Kohno and

Leon Balents is currently available as arXiv:0706.2012 and has been

accepted for publication in Nature Physics (2007).

2) Interplay of spin-orbit and strong Coulomb interactions in quantum

dots and wires.

This is the continuation of the spintronics project began last year

in collaboration with Dr. Dr. Suhas Gangadharaiah (who is partially

supported by PRF award as a postdoctoral researcher) and my graduate

student Mr. Jianmin Sun. We consider two single-electron quantum dots,

electron motion in which is subject to the spin-orbit interaction of Rashba

type, coupled by Coulomb interaction. We find that even in the limit of

large separation between the dots, when the exchange spin interaction

(which is determined by the overlap of the wave functions) is exponentially

small, the spins of the electrons are strongly correlated. This comes about

from the interaction-induced correlation of the orbital motion of two electrons

which, in turn, induces correlations between their spins via the single-particle

spin-orbit coupling. This novel non-exchange coupling between the spins

can be described as an extension of the well-known van der Waals

interaction. It describes ferromagnetic coupling of Ising type, with the strength

of interaction following 1/R6 with inter-dot separation R.

Despite the simplicity of the calculation, this non-exchange mechanism

of spin interaction has not been discussed in the literature yet, to the best

of our knowledge. We believe that it may be the crucial missing ingredient

for understanding magnetic properties of electron Wigner crystals. Most

of experimental realizations of those are done in MOSFET geometry,

which guaranties strong structure-inversion-asymmetry and, as a result,

significant spin-orbital interaction.

3) Competition between Dzyaloshinskii-Moriya (DM) interaction and

magnetic (Zeeman) field.

Here we study how uniform DM interaction, which is present in many,

if not all, experimental realizations of Heisenberg spin-1/2 chains,

competes with the magnetic field. The competition is keen when direction

of the magnetic field is perpendicular to the DM axis. Strong magnetic field

then results in staggered long-range magnetic order along the orthogonal

to the applied field direction. Weak (in comparison with the DM coupling

strength) magnetic field leads to no order. We analyze the transition

between these two limits with the help of bosonization technique

and perturbative renormalization group calculations.

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