Quantum Oscillations in Magnetic Field Induced Antiferromagnetic Phase of Underdoped Cuprates : Application to Ortho-II YBa2Cu3O6.5

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The small parameters η 1 \eta_{1} and η 2 \eta_{2} in g s x ⁡ ( y ) g_{s}^{x(y)} and g s z g_{s}^{z} are given by η 1 = 2 X / ( 1 − δ 2 + 4 m 0 2 ) 2 \eta_{1}=2X/(1-\delta^{2}+4m_{0}^{2})^{2} , η 2 = 8 m 0 2 ( 2 X 1 + X 1 2 ) / ( 8 m 0 2 + X 2 ) \eta_{2}=8m_{0}^{2}(2X_{1}+X_{1}^{2})/(8m_{0}^{2}+X_{2}) , X = δ 2 ( Δ 2 − χ 2 ) + 4 m 0 2 X 2 + X 2 2 / 4 X=\delta^{2}\left(\Delta^{2}-\chi^{2}\right)+4m_{0}^{2}X_{2}+X_{2}^{2}/4 , X 2 = χ 2 + Δ 2 X_{2}=\chi^{2}+\Delta^{2} , and X 1 = 3 X 2 ( 1 − δ ) 2 / [ ( 1 − δ 2 + 4 m 0 2 ) ( 1 + η 1 ) 3 ] X_{1}=3X_{2}(1-\delta)^{2}/[(1-\delta^{2}+4m_{0}^{2})(1+\eta_{1})^{3}]
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