The low temperature magnetic phase transitions in $\mathrm{Ba}{\mathrm{V}}_{10}{\mathrm{O}}_{15}$ at $\sim 40\mathrm{K}$ and $\sim 25\mathrm{K}$ are investigated in detail. The topology of the V sublattice, which consists of linked ${\mathrm{V}}_{10}$ clusters formed by four tetrahedra sharing edges and corners, leads to geometric magnetic frustration and a depression of the ordering temperature characterized by the frustration index, $f=\mid \theta \mid ∕T_c\sim 30$. Specific heat data show the coexistence of both long range and short range magnetic order at low temperature. The position of a $\lambda$ peak, identified with $T_c$ for long range antiferromagnetic order, depends on the ${\mathrm{V}}^{2+}∕{\mathrm{V}}^{3+}$ ratio and varies from $43.0\mathrm{K}\text{to}41.6\mathrm{K}$ for samples with the highest ${\mathrm{V}}^{2+}$ content but is suppressed to zero for highly oxidized samples. A broad maximum in the specific heat occurs at $\sim 25\mathrm{K}$ and is present in all samples regardless of the level of oxidation. For samples with a well defined $T_c$, estimates of the entropy removal over the range $5\mathrm{K}\text{to}55\mathrm{K}$ are only 11% of that expected for $8{\mathrm{V}}^{3+}(S=1)$ and $2{\mathrm{V}}^{2+}(S=3∕2)$ ions per formula unit, suggesting the presence of considerable short-range order. Neutron diffraction data support the presence of long range antiferromagnetic (AF) order with $T_c\sim 40\mathrm{K}$. The magnetic structure below $T_c$ is complex: there are five crystallographically independent vanadium ions in the unit cell, leading to 40 magnetic ions in the crystal unit cell and 80 spins per magnetic cell. Furthermore, the magnetic structure is of the multi-$k$ type involving the two unrelated wave vectors $\mathbf{k}=\left(000\right)$ and $\mathbf{k}=(1∕200)$. Zero field muon spin relaxation data show spin freezing below $30\mathrm{K}$. ac susceptibility results are anomalous. Two peaks, at $\sim 0\mathrm{K}$ and $\sim 25\mathrm{K}$ are seen in ${\chi }^{\prime }$ but the maxima are frequency independent as is the prominent maximum in ${\chi }^{″}$ near $25\mathrm{K}$, behavior atypical of spin glasses. Ti-doped samples, $\mathrm{Ba}{\mathrm{V}}_{10-x}{\mathrm{Ti}}_x{\mathrm{O}}_{15}$, show remarkable results as only 5% Ti doping is sufficient to destroy the AF long range order and induce conventional spin glass behavior in the dc and ac susceptibility, with freezing temperatures ranging from $15\mathrm{K}–5\mathrm{K}$ for doping levels from 5% to 50%. The frustration indices reach enormous values to $f=130$ for $x=3$. The spin glass state is quenched for 70% Ti doping and only paramagnetic behavior is seen.

• Received 12 December 2005

DOI:https://doi.org/10.1103/PhysRevB.74.024426