Spin structure and magnetic phase transitions in ${\mathrm{TbBaCo}}_2{\mathrm{O}}_{5.5}$

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 $a_p\times 2a_p\times 2a_p,Pmmm$ $(Z=2)$, where $a_p$ is parameter of perovskite cell, contains about 32% of the phase $a_p\times a_p\times 2a_p,Pmmm$ $(Z=1)$ with statistical distribution of oxygen over the apical sites. The other sample is a single phase $a_p\times 2a_p\times 2a_p,Pmmm$ $(Z=2)$ 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 $T=265\mathrm{K}$ unambiguously indicates the phase $2a_p\times 2a_p\times 2a_p,Pmma$ $(Z=4)$. At $T_N\approx 290\mathrm{K}$, the spins order with the wave vector ${\mathbf{k}}_{19}=0$ (phase 1). At $T_1\approx 255\mathrm{K}$, a magnetic transition takes place to the phase 2 with ${\mathbf{k}}_{22}={\mathbf{b}}_3∕2$. The extinction law of magnetic reflections below $T_2\approx 170\mathrm{K}$ evidences that the crystal structure changes to $2a_p\times 2a_p\times 4a_p,Pcca$ $(Z=8)$. 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 $M_0=0.30\left(3\right){\mu }_B∕\mathrm{Co}$ at $T=260\mathrm{K}$ is due to ferrimagnetic ordering of the moments $M_{\mathrm{Py}1}=0.46\left(9\right){\mu }_B$ and $M_{\mathrm{Py}2}=-1.65\left(9\right){\mu }_B$ in pyramidal sites (Dzyaloshinskii-Moriya canting is forbidden by symmetry). The moments in the nonequivalent octahedral sites are: $M_{\mathrm{Oc}1}=-0.36\left(9\right){\mu }_B$, $M_{\mathrm{Oc}2}=0.39\left(9\right){\mu }_B$. At $T=230\mathrm{K}$, $M_{\mathrm{Py}1}=0.28\left(8\right){\mu }_B$, $M_{\mathrm{Py}2}=1.22\left(8\right){\mu }_B$, $M_{\mathrm{Oc}1}=1.39\left(8\right){\mu }_B$, $M_{\mathrm{Oc}2}=-1.52\left(8\right){\mu }_B$. At $T=100\mathrm{K}$, $M_{\mathrm{Py}1}=1.76\left(6\right){\mu }_B$, $M_{\mathrm{Py}2}=-1.76{\mu }_B$, $M_{\mathrm{Oc}1}=3.41\left(8\right){\mu }_B$, $M_{\mathrm{Oc}2}=-1.47\left(8\right){\mu }_B$. The moment values together with the ligand displacements are used to analyze the spin-state/orbital ordering in the low-temperature phase.

Figure 1

(a) Unit cell of the layered perovskite $R{\mathrm{BaCo}}_2{\mathrm{O}}_{5.5}$. Open small circles show the crystallographic positions, which can be partially occupied by the ${\mathrm{O}}^{2-}$ ions. (b) Unit cell $a_p\times a_p\times 2a_p$ that has been found at partial occupancies of the apical oxygen sites.

Figure 2

Temperature dependence of magnetization measured in the field 1 T for the sample I. Thin line shows contamination of ${\mathrm{Tb}}^{3+}$. Field dependence in the maximum of magnetization is shown in the inset.

Figure 3

Temperature dependence of magnetization measured in the field 0.1 T for sample II. In addition to the main maximum at 260 K, the second weak maximum can be noticed at 180 K.

Figure 4

Isotherms of magnetization measured at some characteristic temperatures for sample II.

Figure 5

Diffraction pattern from sample I measured on the DMC diffractometer at the same temperature as that in Fig. 6 below. Positions of the Bragg reflections $(h,k,l)$ for the phase $a_p\times 2a_p\times 2a_p$, unrecognized reflections (???) and a superstructure peak $(1∕3,0,0)$ are indicated by arrows. A fit of the $(1∕3,0,0)$ peak by a Lorentzian is shown in the inset.

Figure 6

Diffraction pattern from sample I above $T_N$. The best fit by two phases, $2a_p\times 2a_p\times 2a_p\left(Pmmm\right)$ and $a_p\times a_p\times 2a_p\left(Pmmm\right)$.

Figure 7

Diffraction patterns from sample II collected on DMC diffractometer with a temperature step of 10 K. Indices are given for the unit cell $2a_p\times 2a_p\times 4a_p$.

Figure 8

Intensity temperature dependence of reflections (1,1,2), (0,0,1), and (1,1,1). Indices are given for the unit cell $2a_p\times 2a_p\times 4a_p$.

Figure 9

Differential diffraction patterns: (a) $I\left(265\mathrm{K}\right)\text{–}I\left(300\mathrm{K}\right)$ sample I; (b) $I\left(260\mathrm{K}\right)\text{–}I\left(308\mathrm{K}\right)$ sample II; (c), (d) $I\left(250\mathrm{K}\right)\text{–}I\left(265\mathrm{K}\right)$ sample I. Miller indices are given for the unit cell $2a_p\times 2a_p\times 4a_p$. The curve is a guide to the eye for (a), (b) and the best fit for (c), (d).

Figure 10

Ordering of the ${\mathrm{Co}}^{3+}$ moments ${\mathbf{M}}_N$ in three phases of ${\mathrm{TbBaCo}}_2{\mathrm{O}}_{5.53\left(1\right)}$: (a) ferrimagnetic phase 1 at $T=260\mathrm{K}$; (b) antiferromagnetic phase 2 at $T=230\mathrm{K}$; (c) antiferromagnetic phase 3 at $T=100\mathrm{K}$. The circles shadowing and the arrows lengths reflect the different moment value. The vectors ${\mathbf{a}}_1,{\mathbf{a}}_2,{\mathbf{a}}_3$ define the chemical unit cell for each phase. Calculated (grey bars) and experimental intensities (aa), (bb), (cc) correspond to the structures (a), (b), (c). For experimental values the following symbols are used: (aa) $엯-h=2n+1$, $●-h=2n$; (bb) $▵-h=2n+1$, $◻-h=2n$; (cc) $엯-h=2n+1$, $l=2n$, $▵-h=2n+1$, $l=2n+1$, $◻-h=2n$, $l=2n+1$. Indexing is always in the unit cell (c) $-a_3\approx 4a_p$.

Figure 11

Asymmetric part of the unit cell $2a_p\times 2a_p\times 4a_p$ with nonequivalent pyramidal (Py1, Py2) and octahedral (Oc1, Oc2) ${\mathrm{Co}}^{3+}$ ions. The ligands (${\mathrm{O}}^{2-}$ ions O1, O2, O3, O4, O5, O61, O62) are shown by small black circles. The unit cell origin is at $x=-1∕4$, $y=0$, $z=-z_{\mathrm{Py}1}$.