The authors consider the model \[ \frac{\partial\psi(\mathbf{r},t)}{\partial t}=\omega+\frac{1}{4\pi}\int_{\mathbb{S}^2}G(\mathbf{r},\mathbf{r}')\sin{[\psi(\mathbf{r}',t)-\psi(\mathbf{r},t)-\alpha]} d\mathbf{r}' \] describing the evolution of the phase \(\psi(\mathbf{r},t)\) of an oscillator at position \(\mathbf{r}\) on the unit sphere at time \(t\). The nonlocal coupling function is \[ G(\mathbf{r},\mathbf{r}')=\cos{\gamma}+\frac{\kappa}{4}(3\cos{(2\gamma)}+1) \] where \(\kappa\) is a parameter and \(\gamma\) is the great circle distance between points \(\mathbf{r}\) and \(\mathbf{r}'\). Their main finding is the existence of a stable stripe-core mixed spiral chimera state, in which two spiral waves separated by a stripe-type region of incoherent oscillators on the equator rotate around phase-randomized cores at the poles; these spirals are in anti-phase to each other. Such a state can exist only when \(\kappa\neq 0\). The authors use the Ott/Antonsen ansatz to describe the evolution of the system and largely analytically determine the existence and stability of this and other states such as the two-core spiral state and the incoherent state, exploring the \((\alpha,\kappa)\) plane. Numerical simulations of a discretisation of the phase model are shown, which agree with the analysis given.