Magnetic susceptibility and magnetization showed that A2Cu2Mo3O12 (A=Rb or Cs) includes a one-dimensional spin-1∕2 Heisenberg system with ferromagnetic first-nearest-neighbor (1NN) and antiferromagnetic second-nearest-neighbor (2NN) competing exchange interactions (competing system). Values of the 1NN and 2NN interactions are estimated as J1=−138K and J2=51K for A=Rb or J1=−93K and J2=33K for A=Cs. Rb2Cu2Mo3O12 is a suitable compound to study the competing system with ferromagnetic J1, because other interactions are small. The value of J2∕J1 indicates that Rb2Cu2Mo3O12 has a spin-singlet incommensurate ground state.
Investigation of the magnetism of Cu 3 Mo 2 O 9 single crystal, which has antiferromagnetic ͑AF͒ linear chains interacting with AF dimers, reveals an AF second-order phase transition at T N = 7.9 K. Although weakferromagnetic-like behavior appears at lower temperatures in low magnetic fields, complete remanent magnetization cannot be detected down to 0.5 K. However, a jump is observed in the magnetization below weakferromagnetic ͑WF͒ phase transition at T c Ӎ 2.5 K when a tiny magnetic field along the a axis is reversed, suggesting that the coercive force is very weak. A component of magnetic moment parallel to the chain forms AF long-range order ͑LRO͒ below T N , while a perpendicular component is disordered above T c at zero magnetic field and forms WF-LRO below T c . Moreover, the WF-LRO is also realized by applying magnetic fields even between T c and T N . These results are explainable by both magnetic frustration among symmetric exchange interactions and competition between symmetric and asymmetric Dzyaloshinskii-Moriya exchange interactions.
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