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In geometrically frustrated (GF) magnets, conventional long-range order is suppressed due to the presence of primitive triangular structural units, and the nature of the ensuing ground state remains elusive. One class of candidate states, extensively sought in experiments and vigorously studied theoretically, is the quantum spin liquid (QSL), a magnetically disordered state in which all spinsparticipate in a quantum-coherent many-body state. Randomly located impurities, present in all materials, may prevent QSL formation and instead lead to the formation of a spin-glass state. In this article, we review available data on the specific heat, magnetic susceptibility, and neutron scattering in GF materials. Such data show that a pure GF magnet possesses a characteristic ‘‘hidden energy scale’’ significantly exceeded by the other microscopic energy scales in the material. When cooled down to a temperature below the hidden energy scale, a GF material develops significant short-range order that dominates its properties and, in particular, dictates the spin-glass transition temperature for experimentally accessible impurity densities. We review the manifestations of short-range order in the commonly observed thermodynamic quantities in GF materials, possible scenarios for the hidden energy scale, and related open questions. 

Environmentally benign, highly stable oxides exhibiting desirable optical properties and high near-IR reflectance are being researched for their potential application as pigments. Mg1−xMxV2O6 (M = Mn, Cu, Co, or Ni) oxides with brannerite-type structures were synthesized by the conventional solid-state reaction method to study their optical properties. These series exhibit structural transitions from brannerite (C2/m) to distorted brannerite (P1¯) and NiV2O6-type (P1¯) structures. The average color of Mg1−xMxV2O6 compounds varies from reddish-yellow to brown to dark brown. The L*a*b* color coordinates reveal that Mg1−xCuxV2O6 and Mg1−xNixV2O6 show more red hues in color with x = 0.4 and x = 0.5, respectively. The UV–Vis diffuse reflectance spectra indicate a possible origin for these results include the ligand-to-metal charge transfer (O2− 2p-V5+ 3d), metal-to-metal charge transfer (from Mn2+ 3d/Cu2+ 3d/Co2+ 3d/Ni2+ 3d to V5+ 3d), band gap transitions, and d–d transitions. Magnetic property measurements revealed antiferromagnetic behavior for the compounds Mg1−xMxV2O6 (M = Mn, Cu, Co, and Ni), and an oxidation state of +2 for the M ions was deduced from their Curie–Weiss behavior. The system Mg1−xMnxV2O6 has a NIR reflectance in the range between 40% and 70%, indicating its potential to be utilized in the pigment industry. 

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.