Motivated by frustrated magnets and quasi-one-dimensional magnetic materials, we study the magnetic properties of one-dimensional (1D) Ising chains with nearest-neighbor (NN) and weaker next-to-nearest-neighbor (NNN) interactions in the presence of vacancy defects. The effect of a vacancy on the magnetic susceptibility of a spin chain is twofold: it reduces the length of the chain by an effective “vacancy size” and may also act as a free spin, a “quasispin,” with a Curie-type 𝜒_{quasi}=⟨𝑆^2⟩/𝑇 contribution to the susceptibility. In chains with antiferromagnetic short-range order, the susceptibility of vacancy-free chains is exponentially suppressed at low temperatures, and quasispins dominate the effect of impurities on the chains' magnetic properties. For chains with antiferromagnetic NN interactions, the quasispin matches the value ⟨𝑆^2⟩=1 of the Ising spins in the chain for ferromagnetic NNN interactions and vanishes for antiferromagnetic NNN interactions. For chains with ferromagnetic short-range order, quasispin effects are insignificant due to exponentially large low-temperature susceptibilities, and the dominant effect of a vacancy is effectively changing the length of the chain.
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Depletion-driven antiferromagnetic, paramagnetic, and ferromagnetic behavior in quasi-two-dimensional buckled colloidal solids
We investigate quasi-two-dimensional buckled colloidal monolayers on a triangular lattice with tunable depletion interactions. Without depletion attraction, the experimental system provides a colloidal analog of the well-known geometrically frustrated Ising antiferromagnet [Y. Han et al., Nature 456, 898–903 (2008)]. In this contribution, we show that the added depletion attraction can influence both the magnitude and sign of an Ising spin coupling constant. As a result, the nearest-neighbor Ising “spin” interactions can be made to vary from antiferromagnetic to para- and ferromagnetic. Using a simple theory, we compute an effective Ising nearest-neighbor coupling constant, and we show how competition between entropic effects permits for the modification of the coupling constant. We then experimentally demonstrate depletion-induced modification of the coupling constant, including its sign, and other behaviors. Depletion interactions are induced by rod-like surfactant micelles that change length with temperature and thus offer means for tuning the depletion attraction in situ. Buckled colloidal suspensions exhibit a crossover from an Ising antiferromagnetic to paramagnetic phase as a function of increasing depletion attraction. Additional dynamical experiments reveal structural arrest in various regimes of the coupling-constant, driven by different mechanisms. In total, this work introduces novel colloidal matter with “magnetic” features and complex dynamics rarely observed in traditional spin systems.
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- Award ID(s):
- 2003659
- PAR ID:
- 10421914
- Date Published:
- Journal Name:
- The Journal of Chemical Physics
- Volume:
- 158
- Issue:
- 19
- ISSN:
- 0021-9606
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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