The LiHo_xY_{1-x}F_4 magnetic material in a transverse magnetic
field B_x perpendicular to the Ising spin direction has long been used
to study tunable quantum phase transitions in pure and random disordered systems.
We first present analytical and numerical evidences for the validity of an effective spin-1/2
approach to the description of a general dipolar spin
glass model with strong uniaxial Ising anisotropy and subject to weak
B_x.
We relate this toy model to the LiHo_xY_{1-x}F_4 transverse field Ising material.
We show that an effective spin-1/2
model is able to capture both the qualitative and quantitative aspects of the
physics at small B_x.
After confirming the validity of the effective spin-1/2 approach, we show that the field-induced magnetization along the
x direction,
combined with the local random dilution-induced
destruction of crystalline mirror symmetries
generates, via the predominant dipolar interactions between Ho^{3+} ions,
random fields along the Ising z direction.
This identifies LiHo_xY_{1-x}F_4 in B_x as a new
random field Ising system.
We show that the random fields explain the smearing
of the nonlinear susceptibility at the spin glass transition
with increasing B_x.
In this thesis, we also investigate the phase diagram of non-diluted LiHoF_4 in the presence of B_x, by performing
Monte-Carlo simulations. A previous quantum Monte Carlo (QMC) simulation found that even for small B_x where quantum fluctuations are small, close to the classical critical
point, there is a discrepancy between experiment and the QMC results. We revisit this problem, focusing on
weak B_x close to the classical T_c, using an alternative approach. For small B_x, by applying a so-called cumulant
expansion, the quantum fluctuations around the classical T_c are taken into account perturbatively. We derived an effective
perturbative classical Hamiltonian, on which MC simulations are performed. With this method we
investigate different proposed sources of uncertainty which can affect the numerical results.
We fully reproduce the previous QMC results at small B_x. Unfortunately, we find that
none of the modifications to the microscopic Hamiltonian that we explore are able to provide a B_x-T phase diagram compatible with the experiments in the small
semi-classical B_x regime.
| Identifer | oai:union.ndltd.org:WATERLOO/oai:uwspace.uwaterloo.ca:10012/3888 |
| Date | January 2008 |
| Creators | Tabei, Seyed Mohiaddeen Ali |
| Source Sets | University of Waterloo Electronic Theses Repository |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
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