Magnetically induced bistable behavior of ferronematic liquid crystals

In the framework of the modified model [S. V. Burylov and A. N. Zakhlevnykh, Phys. Rev. E 88, 012511 (2013)] of soft ferronematic liquid crystals, i.e., suspensions of needlelike ferroparticles in nematic solvents, we consider the ferronematic states with different mutual orientations of the director and magnetization. We study the transitions between states in an external magnetic field and show that these transitions are characterized by either continuous or discontinuous changes in the order parameter; i.e., they can be both the second-order and the first-order, respectively. In the latter case the magnetic field induced orientational hysteresis arises, which can be observed in experiments on the birefringence of ferronematic liquid crystals.

Figure 1

Orientational states of FN in an external magnetic field.

Figure 2

Unbounded FN in the external magnetic field (a); choice of the coordinate system (b).

Figure 3

Regions of existence of orientational states A, B, and C induced by magnetic field in the plane $\left(\omega ,\zeta \right).$ Symbols (1) and (2) show the character of equilibrium transitions between the states (first or second order). The tricritical curves ${\zeta }_{\parallel }\left(\omega \right)$ and ${\zeta }_{\perp }\left(\omega \right)$ are calculated with use of Eqs. (22) and (23). The curves ${\zeta }_{}^{*}\left(\omega \right)$ and ${\zeta }_{}^{**}\left(\omega \right)$ correspond to Eqs. (26) and (28).

Figure 4

Regions of existence of orientational states A, B, and C in the magnetic field $h$ for $\omega =0.1$ and $\zeta =0.1$: (a) free energy density of the states; (b) deviation angles of the director $\varphi$ and the magnetization unit vector $\psi .$

Figure 5

Regions of existence of orientational states A, B, and C in the magnetic field $h$ for $\omega =0.1$ and $\zeta =0.25$: (a) free energy density of the states; (b) deviation angles of the director $\varphi$ and the magnetization unit vector $\psi .$

Figure 6

Regions of existence of orientational states A and C in the magnetic field $h$ for $\omega =0.1$ and $\zeta =0.4$: (a) free energy density of the states; (b) deviation angles of the director $\varphi$ and the magnetization unit vector $\psi .$ In this case the state B can be only metastable.

Figure 7

The reduced value of birefringence $\left(\Delta n/n_0\right)$ as a function of the magnetic field $h$ for $\omega =0.1$ and $\zeta =0.25.$ Arrows show plots of $\left[\Delta n\left(h\right)/n_0\right],$ which can be observed in the experiment at the increasing and decreasing of magnetic field.

Figure 8

Qualitative type of hysteresis loop at the birefringence for the regions of the plane $\left(\omega ,\zeta \right),$ shown in Fig. 3: $-1\le \zeta <{\zeta }_{\parallel }$ (a), ${\zeta }_{\parallel }<\zeta <{\zeta }_{}^{*}$ (b), ${\zeta }_{}^{*}<\zeta <{\zeta }_{\perp }$ (c), ${\zeta }_{\perp }<\zeta <{\zeta }_{}^{**}$ (d), ${\zeta }_{}^{**}<\zeta <{\zeta }_{BS}$ (e).