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Register a new userOne- and three-dimensional quantum phase transitions and anisotropy in Rb$_{2}$Cu$_{2}$Mo$_{3}$O$_{12}$
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Single crystal samples of the frustrated quasi one-dimensional quantum magnet Rb$_{2}$Cu$_{2}$Mo$_{3}$O$_{12}$ are investigated by magnetic, thermodynamic, and electron spin resonance (ESR) measurements. Quantum phase transitions between the gapped, magnetically ordered and fully saturated phases are observed. Surprisingly, the former has a distinctive three-dimensional character, while the latter is dominated by one-dimensional quantum spin fluctuations. The entire $H$-$T$ phase diagram is mapped out and found to be substantially anisotropic. In particular, the lower critical fields differ by over 50% depending on the direction of applied field, while the upper ones are almost isotropic, as is the magnetization above saturation. The ESR spectra are strongly dependent on field orientation and point to a helical structure with a rigidly defined spin rotation plane.
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Dielectric and magnetic properties have been studied for poly-crystalline samples of quasi-one-dimensional frustrated spin-1/2 system Rb$_{2}$(Cu$_{1-x}$M$_{x}$)$_{2}$Mo$_{3}$O$_{12}$(M=Ni and Zn) which does not exhibit a three-dimensional magnetic transition due to quantum spin fluctuation and low dimensionality. A broad peak in the magnetic susceptibility - temperature curves originated from a short range helical ordering at low temperature is suppressed by the Ni and Zn substitution for Cu sites. The capacitance is found to anomalously increase with decreasing T below ~50 K, which is also suppressed by the impurity doping. The behavior of the anomalous capacitance component is found to be strongly connected with that of the magnetic susceptibility for Rb$_{2}$(Cu$_{1-x}$M$_{x}$)$_{2}$Mo$_{3}$O$_{12}$ which indicates that the low-temperature dielectric response is driven by the magnetism.
A single-crystal sample of the frustrated quasi one-dimensional quantum magnet Cs$_{2}$Cu$_{2}$Mo$_{3}$O$_{12}$ is investigated by magnetic and thermodynamic measurements.A combination of specific heat and magnetic torque measurements maps out the entire $H$-$T$ phase diagram for three orientations.Remarkably, a new phase emerges below the saturation field, irrespective of the crystal orientation. It is suggested that the presaturation phase represents spin-nematic order or other multi-magnon condensate. The phase diagrams within the long-range ordered dome are qualitatively different for each geometry. In particular, multiple transitions are identified in the field along the chain direction.
We have investigated magnetic properties of Rb$_2$Cu$_2$Mo$_3$O$_{12}$ powder. Temperature dependence of magnetic susceptibility and magnetic-field dependence of magnetization have shown that this cuprate is a model compound of a one-dimensional spin-1/2 Heisenberg system with ferromagnetic first-nearest-neighbor (1NN) and antiferromagnetic second-nearest-neighbor (2NN) competing interactions (competing system). Values of the 1NN and 2NN interactions are estimated as $J_1 = -138$ K and $J_2 = 51$ K ($alpha equiv J_2 / J_1 = -0.37$). This value of $alpha$ suggests that the ground state is a spin-singlet incommensurate state. In spite of relatively large $J_1$ and $J_2$, no magnetic phase transition appears down to 2 K, while an antiferromagnetic transition occurs in other model compounds of the competing system with ferromagnetic 1NN interaction. For that reason, Rb$_2$Cu$_2$Mo$_3$O$_{12}$ is an ideal model compound to study properties of the incommensurate ground state that are unconfirmed experimentally.
We present the muon spin relaxation/rotation spectra in the multiferroic compound (Cu,Zn)$_{3}$Mo$_{2}$O$_{9}$. The parent material Cu$_{3}$Mo$_{2}$O$_{9}$ has a multiferroic phase below $T_{rm N}$ = 8.0 K, where the canted antiferromagnetism and the ferroelectricity coexist. The asymmetry time spectra taken at RIKEN-RAL pulsed muon facility show a drastic change at $T_{rm N}$. At low temperatures the weakly beating oscillation caused by the static internal magnetic fields in the antiferromagnetic phase was observed in Cu$_{3}$Mo$_{2}$O$_{9}$ and the lightly ($0.5%$) Zn-doped sample. From the fitting of the oscillating term, we obtain the order parameter in these samples: ferromagnetic moment in two sublattices of antiferromagnet. In the heavily ($5.0%$) Zn-doped sample, the muon-spin oscillation is rapidly damped. The frequency-domain spectrum of this sample suggests a formation of magnetic superstructure.
From experimental and theoretical analyses of magnetic and specific-heat properties, we present the complete magnetic phase diagram of the quasi-one-dimensional antiferromagnet Cu(N$_2$H$_5$)$_2$(SO$_4$)$_2$. On cooling and at zero magnetic field this compound enters a one-dimensional regime with short-range magnetic correlations, marked by a broad maximum in the specific heat and magnetic susceptibility at $T_mathrm{max}sim 2,mathrm{K}$, followed by an ordered antiferromagnetic phase below $T_mathrm{N}sim 1,mathrm{K}$ induced by small interchain couplings. The intermediate-temperate one-dimensional regime can be modeled using exact quantum-transfer-matrix calculations, which perfectly describe the nonmonotonic behavior of T_max as a function of the magnetic field, giving $J = 4.25,mathrm{K}$ for the intrachain exchange parameter. The analysis of magnetic specific-heat and susceptibility data at low temperature indicates that the interchain exchange couplings are an order of magnitude smaller than the coupling inside the chains.
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