Compensation Point Phenomena in a Transverse Ising Antiferromagnet: Unconventional Effects of an Applied Magnetic Field

Abstract

The thermal variations of magnetizations in a transverse Ising antiferromagnet consisting of two magnetic (A and B) layers are examined by the use of the effective-field theory with correlations, applying a magnetic field p. Particular attentions are paid to the systems with a compensation point in the zero applied field (p = 0.0), when crystallographically equivalent conditions between the A and B layers are broken. We find some characteristic phenomena, such as the possibility of more than one compensation point induced by a finite applied magnetic field and the thermally induced first-order transition.

Appendix

The coefficients A _n and B _n (n = 1–15) of coupled Eqs. (7) and (8) are given by

$$\begin{array}{@{}rcl@{}} A_{1} &=&{\cosh}^{3}\left( A \right) \sinh \left( A \right)\cosh^{\text{2}}(C)F_{A} \left( {x+H} \right)\vert_{x=0} \\ A_{2} &=&{\cosh}^{4}\left( A \right)\sinh \left( C \right)\cosh\left( C \right) F_{\mathrm{A}} \left( {x+H} \right)\vert_{x=0} \\ A_{3} &=&{\cosh}\left( A\right)\sinh^{3}\left( A \right)\cosh_{2} \left( C \right)F_{\mathrm{A}} \left( {x+H} \right)\vert_{x=0} \\ A_{4} &=&{\cosh}^{2}\left( A \right)\sinh^{2}\left( A \right)\sinh\left( C \right)\cosh\left( C \right)F_{\mathrm{A}} \left( {x+H} \right)\vert_{x=0} \\ A_{5}&=&{\cosh}^{3}\left( A \right)\sinh\left( A \right)\sinh^{2}\left( C \right) F_{\mathrm{A}} \left( {x+H} \right)\vert_{x=0} \\ A_{6}&=&{\sinh}^{4}\left( A \right)\sinh\left( C \right)\cosh\left( C \right)F_{\mathrm{A}} \left( {x+H} \right)\vert_{x=0} \\ A_{7}&=&{\cosh}\left( A \right)\sinh^{3}\left( A \right)\sinh^{2}\left( C \right)F_{\mathrm{A}} \left( {x+H} \right)\vert_{x=0} \\ A_{8}&=&{\cosh}^{4}\left( A \right)\cosh^{2}\left( C \right) F_{\mathrm{A}} \left( {x+H} \right)\vert_{x=0} \\ A_{9} &=&{\cosh}^{2}\left( A \right)\sinh^{2}\left( A \right)\cosh^{2}\left( C \right) F_{\mathrm{A}} \left( {x+H} \right)\vert_{x=0} \\ A_{10} &=&{\cosh}^{3}\left( A \right)\sinh\left( A \right)\sinh\left( C \right)\cosh\left( C \right) F_{\mathrm{A}} \left( {x+H} \right)\vert_{x=0} \\ A_{11} &=&{\cosh}^{4}\left( A \right)\cosh^{2}\left( C \right) F_{\mathrm{A}} \left( {x+H} \right)\vert_{x=0} \\ A_{12} &=&{\sinh}^{4}\left( A \right)\cosh^{2}\left( C \right) F_{\mathrm{A}} \left( {x+H} \right)\vert_{x=0} \\ A_{13} &=&{\cosh}\left( A \right)\sinh^{3}\left( A \right)\sinh\left( C \right)\cosh\left( C \right)F_{\mathrm{A}} \left( {x+H} \right)\vert_{x=0} \\ A_{14} &=&{\cosh}^{2}\left( A \right)\sinh^{2}\left( A \right)\sinh^{2}\left( C \right) F_{\mathrm{A}} \left( {x+H} \right)\vert_{x=0} \\ A_{15} &=&{\sinh}^{4}\left( A \right)\sinh^{2}\left( C \right) F_{\mathrm{A}} \left( {x+H} \right)\vert_{x=0} \end{array} $$

(10)

and

$$\begin{array}{@{}rcl@{}} B_{1} &=&{\cosh}^{3}\left( B \right)\sinh\left( B \right)\cosh^{2}\left( C \right)F_{\mathrm{B}} \left( {x+H} \right)|_{x=0} \\ B_{2} &=&{\cosh}^{4}\left( B \right)\sinh \left( C \right)\cosh \left( C \right) F_{\mathrm{B}} \left( {x+H} \right)|_{x=0} \\ B_{3} &=&{\cosh}\left( B \right)\sinh^{3}\left( B \right)\cosh_{2} \left( C \right) F_{\mathrm{B}} \left( {x+H} \right)|_{x=0} \\ B_{4} &=&{\cosh}^{2}\left( B \right)\sinh^{2}\left( B \right)\sinh\left( C \right)\cosh\left( C \right) F_{\mathrm{B}} \left( {x+H} \right)|_{x=0} \\ B_{5} &=&{\cosh}^{3}\left( B \right)\sinh \left( B \right)\sinh^{2}\left( C \right)F_{\mathrm{B}} \left( {x+H} \right)|_{x=0} \\ B_{6} &=&{\sinh}^{4}\left( B \right)\sinh\left( C \right)\cosh\left( C \right)F_{\mathrm{B}} \left( {x+H} \right)|_{x=0} \\ B_{7} &=&{\cosh}\left( B \right)\sinh^{3}\left( B \right)\sinh^{2}\left( C \right)F_{\mathrm{B}} \left( {x+H} \right)|_{x=0} \\ B_{8} &=&{\cosh}^{4}\left( B \right)\cosh^{2}\left( C \right) F_{\mathrm{B}} \left( {x+H} \right)|_{x=0} \\ B_{9} &=&{\cosh}^{2}\left( B \right)\sinh^{2}\left( B \right)\cosh^{2}\left( C \right)F_{\mathrm{B}} \left( {x+H} \right)|_{x=0} \\ B_{10} &=&{\cosh}^{3}\left( B \right)\sinh\left( B \right)\sinh\left( C \right)\cosh\left( C \right)F_{\mathrm{B}} \left( {x+H} \right)|_{x=0} \\ B_{11} &=&{\cosh}^{4}\left( B \right)\cosh^{2}\left( C \right)F_{\mathrm{B}} \left( {x+H} \right)|_{x=0} \\ B_{12} &=&{\sinh}^{4}\left( B \right)\cosh^{2}\left( C \right)F_{\mathrm{B}} \left( {x+H} \right)|_{x=0} \\ B_{13} &=&{\cosh}\left( B \right)\sinh^{\text{3}}\left( B \right)\sinh\left( C \right)\cosh\left( C \right)\text{}F_{\mathrm{B}} \left( {x+H} \right)|_{x=0} \\ B_{14} &=&{\cosh}^{2}\left( B \right)\sinh^{2}\left( B \right)\sinh^{2}\left( C \right)\text{}F_{\mathrm{B}} \left( {x+H} \right)|_{x=0} \\ B_{15}& =&{\sinh}^{4}\left( B \right)\sinh^{2}\left( C \right)\text{}F_{\mathrm{B}} \left( {x+H} \right)|_{x=0} \end{array} $$

(11)

where these coefficients can be easily calculated by using the mathematical relation exp(a D)F(x) = F(x + a).