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Register a new userCharacteristic signatures of quantum criticality driven by geometrical frustration
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Geometrical frustration describes situations where interactions are incompatible with the lattice geometry and stabilizes exotic phases such as spin liquids. Whether geometrical frustration of magnetic interactions in metals can induce unconventional quantum critical points is an active area of research. We focus on the hexagonal heavy fermion metal CeRhSn where the Kondo ions are located on distorted kagome planes stacked along the c axis. Low-temperature specific heat, thermal expansion and magnetic Gruneisen parameter measurements prove a zero-field quantum critical point. The linear thermal expansion, which measures the initial uniaxial pressure derivative of the entropy, displays a striking anisotropy. Critical and noncritical behaviors along and perpendicular to the kagome planes, respectively, prove that quantum criticality is driven by geometrical frustration. We also discovered a spin-flop-type metamagnetic crossover. This excludes an itinerant scenario and suggests that quantum criticality is related to local moments in a spin-liquid like state.
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Dimensionality is a critical factor in determining the properties of solids and is an apparent built-in character of the crystal structure. However, it can be an emergent and tunable property in geometrically frustrated spin systems. Here, we study the spin dynamics of the tetrahedral cluster antiferromagnet, pharmacosiderite, via muon spin resonance and neutron scattering. We find that the spin correlation exhibits a two-dimensional characteristic despite the isotropic connectivity of tetrahedral clusters made of spin 5/2 Fe3+ ions in the three-dimensional cubic crystal, which we ascribe to two-dimensionalisation by geometrical frustration based on spin wave calculations. Moreover, we suggest that even one-dimensionalisation occurs in the decoupled layers, generating low-energy and one-dimensional excitation modes, causing large spin fluctuation in the classical spin system. Pharmacosiderite facilitates studying the emergence of low-dimensionality and manipulating anisotropic responses arising from the dimensionality using an external magnetic field.
Quantum electrodynamics in 2+1 dimensions is an effective gauge theory for the so called algebraic quantum liquids. A new type of such a liquid, the algebraic charge liquid, has been proposed recently in the context of deconfined quantum critical points [R. K. Kaul {it et al.}, Nature Physics {bf 4}, 28 (2008)]. In this context, we show by using the renormalization group in $d=4-epsilon$ spacetime dimensions, that a deconfined quantum critical point occurs in a SU(2) system provided the number of Dirac fermion species $N_fgeq 4$. The calculations are done in a representation where the Dirac fermions are given by four-component spinors. The critical exponents are calculated for several values of $N_f$. In particular, for $N_f=4$ and $epsilon=1$ ($d=2+1$) the anomalous dimension of the Neel field is given by $eta_N=1/3$, with a correlation length exponent $ u=1/2$. These values change considerably for $N_f>4$. For instance, for $N_f=6$ we find $eta_Napprox 0.75191$ and $ uapprox 0.66009$. We also investigate the effect of chiral symmetry breaking and analyze the scaling behavior of the chiral holon susceptibility, $G_chi(x)equiv<bar psi(x)psi(x)bar psi(0)psi(0)>$.
Localized spins and itinerant electrons rarely coexist in geometrically-frustrated spinel lattices. We show that the spinel CoV2O4 stands at the crossover from insulating to itinerant behavior and exhibits a complex interplay between localized spins and itinerant electrons. In contrast to the expected paramagnetism, localized spins supported by enhanced exchange couplings are frustrated by the effects of delocalized electrons. This frustration produces a non-collinear spin state and may be responsible for macroscopic spin-glass behavior. Competing phases can be uncovered by external perturbations such as pressure or magnetic field, which enhance the frustration.
Hexagonal CeRhSn with paramagnetic $4f$ moments on a distorted Kagome lattice displays zero-field quantum critical behavior related to geometrical frustration. We report high-resolution thermal expansion and magnetostriction measurements under multiextreme conditions such as uniaxial stress up to 200 MPa, temperatures down to 0.1 K and magnetic fields up to 10 T. Under uniaxial stress along the $a$-direction, quantum criticality disappears and a complex magnetic phase diagram arises with a sequence of phases below 1.2 K and fields between 0 and 3 T ($parallel a$). Since the Kondo coupling increases with stress, which alone would stabilize paramagnetic behavior in CeRhSn, the observed order arises from the release of geometrical frustration by in-plane stress.
Exotic physics often emerges around quantum criticality in metallic systems. Here we explore the nature of topological phase transitions between 3D double-Weyl semimetals and insulators (through annihilating double-Weyl nodes with opposite chiralities) in the presence of Coulomb interactions. From renormalization-group (RG) analysis, we find a non-Fermi-liquid quantum critical point (QCP) between the double-Weyl semimetals and insulators when artificially neglecting short-range interactions. However, it is shown that this non-Fermi-liquid QCP is actually unstable against nematic ordering when short-range interactions are correctly included in the RG analysis. In other words, the putative QCP between the semimetals and insulators is preempted by emergence of nematic phases when Coulomb interactions are present. We further discuss possible experimental relevance of the nematicity-preempted QCP to double-Weyl candidate materials HgCr2Se4 and SrSi2.
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