= Solution
Assume $u>0$, as required for the stable quartic model, and retain the stated domain $t>0$. For the <opposite-axis quadratic anisotropy of a vector order parameter>, fix the magnitude $\rho$. Then the anisotropy lowers the energy most by putting all <magnetization> along component 1 if $r<0$ and component 2 if $r>0$. Component 3 has positive quadratic coefficient $t$ and cannot lower the uniform minimum. Minimizing the remaining amplitude gives
$$
\boxed{\begin{array}{c|c|c}
\text{region}&\text{uniform equilibrium magnetization}&f_{\min}\\\hline
r<-t&\bigl(\pm\sqrt{-(t+r)/(4u)},0,0\bigr)&-(t+r)^2/(16u)\\
-t\leq r\leq t&(0,0,0)&0\\
r>t&\bigl(0,\pm\sqrt{(r-t)/(4u)},0\bigr)&-(t-r)^2/(16u)
\end{array}}
$$
The component-1 and component-2 ordered regions each break a discrete sign symmetry, giving two easy-axis orientations rather than a sphere of equivalent directions. To check stability, in the component-1 minimum the longitudinal curvature is $-2(t+r)>0$, while the two transverse curvatures are $-2r>0$ and $-r>0$. The component-2 case similarly has longitudinal curvature $-2(t-r)$ and transverse curvatures $2r,r$, all positive in its region. The disordered state is stable exactly when $t\pm r\geq0$.
Both boundaries $r=-t$ and $r=t$ are continuous, second-order mean-field transitions: the selected component vanishes with a square root, and the first derivatives of the minimum <free energy> agree across the boundary. In the stipulated upper half-plane $t>0$, the two ordered phases are separated by a disordered wedge. There is no direct first-order boundary between them in that domain. Extrapolating a phase boundary through $t<0$ would answer a different, larger phase-diagram question.
\Image[/past-exam-of-the-theoretical-physics-major-option-course-of-the-university-of-oxford/2015-anisotropic-vector-landau-phase-diagram.png]
{title=Uniform anisotropic ferromagnet phase diagram in the specified t-positive half-plane}
{description=Original saddle-point phase diagram for positive quartic coupling. The two continuous transition rays enclose the disordered region; the two outer regions select different easy axes.}
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