Abstract
We present the experimental phase diagram of LiHo${}_{x}$Er${}_{1\ensuremath{-}x}$F${}_{4}$, a dilution series of dipolar-coupled model magnets. The phase diagram was determined using a combination of ac susceptibility and neutron scattering. Three unique phases in addition to the Ising ferromagnet LiHoF${}_{4}$ and the $XY$ antiferromagnet LiErF${}_{4}$ have been identified. Below $x=0.86$, an embedded spin-glass phase is observed, where a spin glass exists within the ferromagnetic structure. Below $x=0.57$, an Ising spin glass is observed consisting of frozen needlelike clusters. For $x\ensuremath{\sim}0.3--0.1$, an antiferromagnetically coupled spin glass occurs. A reduction of ${T}_{C}(x)$ for the ferromagnet is observed which disobeys the mean-field predictions that worked for LiHo${}_{x}$Y${}_{1\ensuremath{-}x}$F${}_{4}$.
Highlights
When combinations of disorder and frustration are present in a magnetic system, the so-called spin-glass state can arise
We present the experimental phase diagram of LiHoxEr1-xF4, a dilution series of dipolar-coupled model magnets
The phase diagram was determined using a combination of ac susceptibility and neutron scattering
Summary
When combinations of disorder and frustration are present in a magnetic system, the so-called spin-glass state can arise. Two independent groups reach the conclusion that the presence of a transverse field induces random fields which destroy true spin-glass order.13,14,16 It has been demonstrated that the observed nonlinear susceptibility is consistent with this spin-glass-like state. We establish a phase diagram with several striking features compared both to LiHoxY1-xF4 and to simple mean-field (MF) expectations for LiHoxEr1-xF4: (a) The spin-glass region is greatly extended, both in terms of x and in temperature, up to a maximum Tf > 0.5 K; (b) TC for ferromagnetic order decreases faster than for Y dilution and in contrast to MF predictions; (c) the antiferromagnetic order found in pure LiErF4 is destroyed by just 10% of Ho. The experimentally determined phase diagram for. The final section is dedicated to discussion of the results in a more general context and conclusions
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