Magnetic transitions in the spin-52frustrated magnetBiMn2PO6and strong lattice softening inBiMn2PO6andBiZn2PO6below 200 K

Abstract

The crystallographic, magnetic, and thermal properties of polycrystalline $\mathrm{Bi}{\mathrm{Mn}}_{2}{\mathrm{PO}}_{6}$ and its nonmagnetic analog $\mathrm{Bi}{\mathrm{Zn}}_{2}{\mathrm{PO}}_{6}$ are investigated by x-ray diffraction, magnetization $M$, magnetic susceptibility $\ensuremath{\chi}$, heat capacity ${C}_{p}$, and $^{31}\mathrm{P}$ nuclear magnetic resonance (NMR) measurements versus applied magnetic field $H$ and temperature $T$ as well as by density-functional band theory and molecular-field calculations. Both compounds show a strong monotonic lattice softening on cooling, where the Debye temperature decreases by a factor of two from ${\ensuremath{\Theta}}_{\mathrm{D}}\ensuremath{\sim}650$ K at $T=300$ K to ${\ensuremath{\Theta}}_{\mathrm{D}}\ensuremath{\sim}300$ K at $T=2$ K. The $\ensuremath{\chi}(T)$ data for $\mathrm{Bi}{\mathrm{Mn}}_{2}{\mathrm{PO}}_{6}$ above 150 K follow a Curie-Weiss law with a Curie constant consistent with a Mn${}^{+2}$ spin $S=5/2$ with $g$ factor $g=2$ and an antiferromagnetic (AFM) Weiss temperature ${\ensuremath{\theta}}_{\mathrm{CW}}\ensuremath{\simeq}\ensuremath{-}78$ K. The $\ensuremath{\chi}$ data indicate long-range AFM ordering below ${T}_{\mathrm{N}}\ensuremath{\simeq}30$ K, confirmed by a sharp $\ensuremath{\lambda}$-shaped peak in ${C}_{\mathrm{p}}(T)$ at 28.8 K. The magnetic entropy at 100 K extracted from the ${C}_{\mathrm{p}}(T)$ data is consistent with spin $S=5/2$ for the Mn${}^{+2}$ cations. The band-theory calculations indicate that $\mathrm{Bi}{\mathrm{Mn}}_{2}{\mathrm{PO}}_{6}$ is an AFM compound with dominant interactions ${J}_{1}/{k}_{\mathrm{B}}\ensuremath{\simeq}6.7$ K and ${J}_{3}/{k}_{\mathrm{B}}\ensuremath{\simeq}5.6$ K along the legs and rungs of a Mn two-leg spin-ladder, respectively. However, sizable and partially frustrating interladder couplings lead to an anisotropic three-dimensional magnetic behavior with long-range AFM ordering at ${T}_{\mathrm{N}}\ensuremath{\simeq}30$ K observed in the $\ensuremath{\chi}$, ${C}_{\mathrm{p}}$, and NMR measurements. A second magnetic transition at $\ensuremath{\approx}$10 K is observed from the $\ensuremath{\chi}$ and NMR measurements but is not evident in the ${C}_{\mathrm{p}}$ data. The ${C}_{\mathrm{p}}$ data at low $T$ suggest a significant contribution from AFM spin waves moving in three dimensions and the absence of a spin-wave gap. A detailed analysis of the NMR spectra indicates commensurate magnetic order between 10 and 30 K, while below 10 K additional features appear that may arise from an incommensurate modulation and/or spin canting. The commensurate order is consistent with microscopic density functional calculations that yield a collinear N\'eel-type AFM spin arrangement both within and between the ladders, despite the presence of multiple weak interactions frustrating this magnetic structure of the Mn spins. Frustration for AFM ordering and the one-dimensional spatial anisotropy of the three-dimensional spin interactions are manifested in the frustration ratio $f=|{\ensuremath{\theta}}_{\mathrm{CW}}|/{T}_{\mathrm{N}}\ensuremath{\simeq}2.6$, indicating a suppression of ${T}_{\mathrm{N}}$ from 68 K in the absence of these effects to the observed value of about 30 K in $\mathrm{Bi}{\mathrm{Mn}}_{2}{\mathrm{PO}}_{6}$.