Magnetic structure and excitations in BaV$_{10}$O$_{15}$

Recently, new type of frustrated magnets, BaV$_{10}$O$_{15}$ and SrV$_{10}$O$_{15}$, were found to exhibit interesting physics due to the magnetic V$^{2.8+}$ ions with mixed valence. Using elastic and inelastic neutron scattering measurements we have examined the magnetic structure and excitations of BaV$_{10}$O$_{15}$. Magnetic excitations show highly dispersive two modes along c axis. Furthermore, two excitations are dispersionless along the a-axis. And very interestingly, along the b-axis one excitation is dispersionless while the other is strongly dispersive. Magnetic ground state of BaV$_{10}$O$_{15}$ was studied using neutron powder diffraction data, which order below 45 K with magnetic wave vector Q$_{\mathrm{m}}=$(1/2 0 0). Here we present the possible magnetic structures of BaV$_{10}$O$_{15}$ using representation analysis, which can explain both the magnetic diffraction data and the basic features of the magnetic excitations observed in different directions. Linear spinwave calculations were also performed to shed light in understanding an effective spin hamiltonian for this system.