Tricritical phenomena at the Fréedericksz transition in ferronematic liquid crystals

Within the continuum theory we study the magnetic segregation effects in ferronematics, i.e., suspensions of monodomain magnetic particles in nematic liquid crystals. Orientational and concentrational distributions in a ferronematic layer are obtained as functions of a magnetic field strength for different values of material parameters. Tricritical behavior of the Fréedericksz transition in ferronematics induced by magnetic field is revealed. It is found out that this transition can be either first- or second-order transition depending on the segregation degree. We derive the analytical expression for the tricritical segregation parameter, determining the phase-transition character change. The dependence of birefringence on the external magnetic field and the segregation parameter is studied.

Figure 1

Ferronematic layer in a magnetic field $\mathbf{H}$.

Figure 2

Fréedericksz field $h_c$ in FN as a function of the coupling energy $\sigma$: $b=0.1$, quadrupolar mode; $b=1$, intermediate mode; $b=10$, dipolar mode; dashed line, Fréedericksz field $h_c^{LC}=\pi$ in pure LCs.

Figure 3

Tricritical segregation parameter ${\varkappa }^{\ast }$ as a function of coupling energy $\sigma$ for (a) quadrupolar mode $b=0.1$ and (b) dipolar mode $b=10$.

Figure 4

(a) The angle ${\phi }_0$ of the director orientation and (b) the angle ${\psi }_0$ of the magnetization orientation in the middle of the layer as functions of a magnetic field strength $h$ for $\sigma =10$, $k=1.56$, $b=10$, and different values of the segregation parameter $\varkappa$. Here ${\varkappa }^{\ast }$ is the tricritical segregation parameter, $h_t\approx 3.72$ is the magnetic field strength of the equilibrium phase transition, $h_c^{LC}=\pi$, and $h_c\approx 4.91$ (dashed lines correspond to the metastable state).

Figure 5

(a) Orientational and (b) concentrational distributions within the ferronematic layer for $\sigma =10$, $k=1.56$, $b=10$, $\varkappa =5$, and different magnetic field strengths $h$. In this case ${\varkappa }^{\ast }\approx 2.07$ and $h_c\approx 4.91$.

Figure 6

(a) Orientational and (b) concentrational distributions within the ferronematic layer for $\sigma =10$, $k=1.56$, $b=10$, $\varkappa =0.1$, and different magnetic field strengths $h$. In this case ${\varkappa }^{\ast }\approx 2.07$, $h_c\approx 4.91$, and $h_t\approx 3.72$.

Figure 7

Field dependence of reduced phase lag $\delta /{\delta }_0$ in FN layer for $\sigma =10$, $k=1.56$, $b=10$, and $\xi =0.2$. Here ${\delta }_0\approx 1.24\times 2\pi \text{rad}$, $h_c\approx 4.91$, and $h_t\approx 3.72$ (dashed line corresponds to the metastable state).