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When J1 =264 K and J2 =-143 K, a ground state in the zero magnetic field is one of the ST =0 states and is expressed as | 02, SzT =0 = C01 (| - ++ + | ++ - - | -+-+ - | +-+- ) + C02 (| -+-+ + | +-+- - | + - + - | -++- ) = C01 (| -+ - | +- ) α2 (| -+ - | +- ) α4 + C02 (| -+ - | +- ) α1 (| -+ - | +- ) α3. The two coefficients are C01 =1/ 3+ (-1+4j+2 1-2j+4 j2) 2 and C02 = (2-4j-2 1-2j+4 j2) /2 3+ (-1+4j+2 1-2j+4 j2) 2. The first term in | 02, SzT =0 is a product of a singlet state in the α2 pair and a singlet state in the α4 pair. The second term is a product of a singlet state in the α1 pair and a singlet state in the α3 pair. The ground state is singlet. Therefore, we cannot determine whether Cu1 spins [S2 and S3 in Fig. 1] and Cu2 spins [S1 and S4 in Fig. 1] have magnetic moments or not.
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When J1 =264 K and J2 =-143 K, a ground state in the zero magnetic field is one of the ST =0 states and is expressed as | 02, SzT =0 = C01 (| - ++ + | ++ - - | -+-+ - | +-+- ) + C02 (| -+-+ + | +-+- - | + - + - | -++- ) = C01 (| -+ - | +- ) α2 (| -+ - | +- ) α4 + C02 (| -+ - | +- ) α1 (| -+ - | +- ) α3. The two coefficients are C01 =1/ 3+ (-1+4j+2 1-2j+4 j2) 2 and C02 = (2-4j-2 1-2j+4 j2) /2 3+ (-1+4j+2 1-2j+4 j2) 2. The first term in | 02, SzT =0 is a product of a singlet state in the α2 pair and a singlet state in the α4 pair. The second term is a product of a singlet state in the α1 pair and a singlet state in the α3 pair. The ground state is singlet. Therefore, we cannot determine whether Cu1 spins [S2 and S3 in Fig. 1] and Cu2 spins [S1 and S4 in Fig. 1] have magnetic moments or not.
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