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Register a new userNuclear and Magnetic Structures of the Frustrated Quantum Antiferromagnet Barlowite, Cu$_{4}$(OH)$_{6}$FBr
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Barlowite, Cu$_{4}$(OH)$_{6}$FBr, has attracted much attention as the parent compound of a new series of quantum spin liquid candidates, Zn$_{x}$Cu$_{4-x}$(OH)$_{6}$FBr. While it is known to undergo a magnetic phase transition to a long-range ordered state at $T_{N} = 15$ K, there is still no consensus over either its nuclear or magnetic structures. Here, we use comprehensive powder neutron diffraction studies on deuterated samples of barlowite to demonstrate that the only space group consistent with the observed nuclear and magnetic diffraction at low-temperatures is the orthorhombic $Pnma$ space group. We furthermore conclude that the magnetic intensity at $T < T_{N}$ is correctly described by the $Pn^prime m^prime a$ magnetic space group, which crucially allows the ferromagnetic component observed in previous single-crystal and powder magnetisation measurements. As such, the magnetic structure of barlowite resembles that of the related material clinoatacamite, Cu$_{4}$(OH)$_{6}$Cl$_{2}$, the parent compound of the well-known quantum spin liquid candidate hebertsmithite, ZnCu$_{3}$(OH)$_{6}$Cl$_{2}$.
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We have systematically studied the magnetic properties of Cu$_{4-x}$Zn$_x$(OH)$_6$FBr by the neutron diffraction and muon spin rotation and relaxation ($mu$SR) techniques. Neutron-diffraction measurements suggest that the long-range magnetic order and the orthorhombic nuclear structure in the $x$ = 0 sample can persist up to $x$ = 0.23 and 0.43, respectively. The temperature dependence of the zero-field (ZF) $mu$SR spectra provide two characteristic temperatures, $T_{A0}$ and $T_{lambda}$. Comparison between $T_{A0}$ and $T_M$ from previously reported magnetic-susceptibility measurements suggest that the former comes from the short-range interlayer-spin clusters that persist up to $x$ = 0.82. On the other hand, the doping level where $T_{lambda}$ becomes zero is about 0.66, which is much higher than threshold of the long-range order, i.e., $sim$ 0.4. Our results suggest that the change in the nuclear structure may alter the spin dynamics of the kagome layers and a gapped quantum-spin-liquid state may exist above $x$ = 0.66 with the perfect kagome planes.
Barlowite Cu$_4$(OH)$_6$FBr shows three-dimensional (3D) long-range antiferromagnetism, which is fully suppressed in Cu$_3$Zn(OH)$_6$FBr with a kagome quantum spin liquid ground state. Here we report systematic studies on the evolution of magnetism in the Cu$_{4-x}$Zn$_x$(OH)$_{6}$FBr system as a function of $x$ to bridge the two limits of Cu$_4$(OH)$_6$FBr ($x$=0) and Cu$_3$Zn(OH)$_6$FBr ($x$=1). Neutron-diffraction measurements reveal a hexagonal-to-orthorhombic structural change with decreasing temperature in the $x$ = 0 sample. While confirming the 3D antiferromagnetic nature of low-temperature magnetism, the magnetic moments on some Cu$^{2+}$ sites on the kagome planes are found to be vanishingly small, suggesting strong frustration already exists in barlowite. Substitution of interlayer Cu$^{2+}$ with Zn$^{2+}$ with gradually increasing $x$ completely suppresses the bulk magnetic order at around $x$ = 0.4, but leaves a local secondary magnetic order up to $xsim 0.8$ with a slight decrease in its transition temperature. The high-temperature magnetic susceptibility and specific heat measurements further suggest that the intrinsic magnetic properties of kagome spin liquid planes may already appear from $x>0.3$ samples. Our results reveal that the Cu$_{4-x}$Zn$_x$(OH)$_6$FBr may be the long-thought experimental playground for the systematic investigations of the quantum phase transition from a long-range antiferromagnet to a topologically ordered quantum spin liquid.
The effect of chemical substitution on the ground state of the geometrically frustrated antiferromagnet CsCrF$_4$ has been investigated through a neutron powder diffraction experiment. Magnetic Fe-substituted CsCr$_{0.94}$Fe$_{0.06}$F$_{4}$ and nonmagnetic Al-substituted CsCr$_{0.98}$Al$_{0.02}$F$_{4}$ samples are measured, and magnetic Bragg peaks are clearly observed in both samples. Magnetic structure analysis revealed a 120$^{circ}$ structure having a magnetic propagation vector $mathbf{k}_{rm mag}=(0,0,1/2)$ in CsCr$_{0.94}$Fe$_{0.06}$F$_{4}$. For CsCr$_{0.98}$Al$_{0.02}$F$_{4}$, a quasi-120$^{circ}$ structure having $mathbf{k}_{rm mag}=(1/2,0,1/2)$ is formed. It is notable that the identified magnetic structure in CsCr$_{0.94}$Fe$_{0.06}$F$_{4}$ belongs to a different phase of ground states from those in CsCr$_{0.98}$Al$_{0.02}$F$_{4}$ and the parent CsCrF$_{4}$. These results suggest that the Fe-substitution strongly influences the ground state of CsCrF$_{4}$.
Spin-waves e.g. magnons are the conventional elementary excitations of ordered magnets. However, other possibilities exist. For instance, magnon bound-states can arise due to attractive magnon-magnon interactions and drastically impact the static and dynamic properties of materials. Here, we demonstrate a zoo of distinct multi-magnon quasiparticles in the frustrated spin-1 triangular antiferromagnet FeI$_2$ using time-domain terahertz spectroscopy. The energy-magnetic field excitation spectrum contains signatures of one-, two-, four- and six-magnon bound-states, which we analyze using an exact diagonalization approach for a dilute gas of interacting magnons. The two-magnon single-ion bound states occur due to strong anisotropy and the preponderance of even higher order excitations arises from the tendency of the single-ion bound states to themselves form bound states due to their very flat dispersion. This menagerie of tunable interacting quasiparticles provides a unique platform in a condensed matter setting that is reminiscent of the few-body quantum phenomena central to cold-atom, nuclear, and particle physics experiments.
We systematically study the low-temperature specific heats for the two-dimensional kagome antiferromagnet, Cu$_{3}$Zn(OH)$_6$FBr. The specific heat exhibits a $T^{1.7}$ dependence at low temperatures and a shoulder-like feature above it. We construct a microscopic lattice model of $Z_2$ quantum spin liquid and perform large-scale quantum Monte Carlo simulations to show that the above behaviors come from the contributions from gapped anyons and magnetic impurities. Surprisingly, we find the entropy associated with the shoulder decreases quickly with grain size $d$, although the system is paramagnetic to the lowest temperature. While this can be simply explained by a core-shell picture in that the contribution from the interior state disappears near the surface, the 5.9-nm shell width precludes any trivial explanations. Such a large length scale signifies the coherence length of the nonlocality of the quantum entangled excitations in quantum spin liquid candidate, similar to Pippards coherence length in superconductors. Our approach therefore offers a new experimental probe of the intangible quantum state of matter with topological order.
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