Spin structure and magnetic phase transitions inTbBaCo2O5.5

Abstract

Spin ordering in ${\mathrm{TbBaCo}}_{2}{\mathrm{O}}_{5.5}$ and its temperature transformation reproducible for two differently synthesized samples are studied. One of the ceramic samples, in addition to the main phase ${a}_{p}\ifmmode\times\else\texttimes\fi{}2{a}_{p}\ifmmode\times\else\texttimes\fi{}2{a}_{p},\phantom{\rule{0.3em}{0ex}}Pmmm$ $(Z=2)$, where ${a}_{p}$ is parameter of perovskite cell, contains about 32% of the phase ${a}_{p}\ifmmode\times\else\texttimes\fi{}{a}_{p}\ifmmode\times\else\texttimes\fi{}2{a}_{p},\phantom{\rule{0.3em}{0ex}}Pmmm$ $(Z=1)$ with statistical distribution of oxygen over the apical sites. The other sample is a single phase ${a}_{p}\ifmmode\times\else\texttimes\fi{}2{a}_{p}\ifmmode\times\else\texttimes\fi{}2{a}_{p},\phantom{\rule{0.3em}{0ex}}Pmmm$ $(Z=2)$ with well defined octahedral and pyramidal sublattices. Treatment of neutron diffraction patterns of the double-phase sample itself gives a sophisticated spin structure. Knowing the spin structure of the single-phase sample, one can choose only proper magnetic lines, which give exactly the same results for both samples. The spin structure at $T=265\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ unambiguously indicates the phase $2{a}_{p}\ifmmode\times\else\texttimes\fi{}2{a}_{p}\ifmmode\times\else\texttimes\fi{}2{a}_{p},\phantom{\rule{0.3em}{0ex}}Pmma$ $(Z=4)$. At ${T}_{N}\ensuremath{\approx}290\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, the spins order with the wave vector ${\mathbf{k}}_{19}=0$ (phase 1). At ${T}_{1}\ensuremath{\approx}255\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, a magnetic transition takes place to the phase 2 with ${\mathbf{k}}_{22}={\mathbf{b}}_{3}∕2$. The extinction law of magnetic reflections below ${T}_{2}\ensuremath{\approx}170\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ evidences that the crystal structure changes to $2{a}_{p}\ifmmode\times\else\texttimes\fi{}2{a}_{p}\ifmmode\times\else\texttimes\fi{}4{a}_{p},\phantom{\rule{0.3em}{0ex}}Pcca$ $(Z=8)$. The wave vector of the spin structure becomes again ${\mathbf{k}}_{19}=0$ (phase 3). The basis functions of irreducible representations of the group ${G}_{\mathbf{k}}$ have been found. Using results of this analysis, the magnetic structure in all phases is determined. The spins are always parallel to the $\mathbf{x}$ axis, and the difference is in the values and the mutual orientation of the moments in the ordered nonequivalent pyramidal or octahedral positions. Spontaneous moment ${M}_{0}=0.30(3){\ensuremath{\mu}}_{B}∕\mathrm{Co}$ at $T=260\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ is due to ferrimagnetic ordering of the moments ${M}_{\mathrm{Py}1}=0.46(9){\ensuremath{\mu}}_{B}$ and ${M}_{\mathrm{Py}2}=\ensuremath{-}1.65(9){\ensuremath{\mu}}_{B}$ in pyramidal sites (Dzyaloshinskii-Moriya canting is forbidden by symmetry). The moments in the nonequivalent octahedral sites are: ${M}_{\mathrm{Oc}1}=\ensuremath{-}0.36(9){\ensuremath{\mu}}_{B}$, ${M}_{\mathrm{Oc}2}=0.39(9){\ensuremath{\mu}}_{B}$. At $T=230\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, ${M}_{\mathrm{Py}1}=0.28(8){\ensuremath{\mu}}_{B}$, ${M}_{\mathrm{Py}2}=1.22(8){\ensuremath{\mu}}_{B}$, ${M}_{\mathrm{Oc}1}=1.39(8){\ensuremath{\mu}}_{B}$, ${M}_{\mathrm{Oc}2}=\ensuremath{-}1.52(8){\ensuremath{\mu}}_{B}$. At $T=100\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, ${M}_{\mathrm{Py}1}=1.76(6){\ensuremath{\mu}}_{B}$, ${M}_{\mathrm{Py}2}=\ensuremath{-}1.76{\ensuremath{\mu}}_{B}$, ${M}_{\mathrm{Oc}1}=3.41(8){\ensuremath{\mu}}_{B}$, ${M}_{\mathrm{Oc}2}=\ensuremath{-}1.47(8){\ensuremath{\mu}}_{B}$. The moment values together with the ligand displacements are used to analyze the spin-state/orbital ordering in the low-temperature phase.