High-temperature magnetism and crystallography of a ${\mathrm{YCrO}}_3$ single crystal

Magnetization measurements and time-of-flight neutron powder-diffraction studies on the high-temperature (300–980 K) magnetism and crystal structure (321–1200 K) of a pulverized ${\mathrm{YCrO}}_3$ single crystal have been performed. Temperature-dependent inverse magnetic susceptibility coincides with a piecewise linear function with five regimes, with which we fit a Curie-Weiss law and calculate the frustration factor $f$. The fit results indicate a formation of magnetic polarons between 300 and 540 K and a very strong magnetic frustration. By including one factor $\eta$ that represents the degree of spin interactions into the Brillouin function, we can fit well the applied-magnetic-field dependence of magnetization. No structural phase transition was observed from 321 to 1200 K. The average thermal expansions of lattice configurations ($a$, $b$, $c$, and V) obey well the $\mathrm{Gr}\ddot{\mathtt{u}}\mathrm{neisen}$ approximations with an anomaly appearing around 900 K, implying an isosymmetric structural phase transition, and display an anisotropic character along the crystallographic $a$, $b$, and $c$ axes with the incompressibility $K_0^a>K_0^c>K_0^b$. It is interesting to find that at 321 K, the local distortion size $\mathrm{\Delta }$(O2) $\approx 1.96\mathrm{\Delta }$(O1) $\approx 4.32\mathrm{\Delta }$(Y) $\approx 293.89\mathrm{\Delta }$(Cr). Based on the refined Y-O and Cr-O bond lengths, we deduce the local distortion environments and modes of Y, Cr, O1, and O2 ions. Especially, the Y and O2 ions display obvious atomic displacement and charge subduction, which may shed light on the dielectric property of the ${\mathrm{YCrO}}_3$ compound. Additionally, by comparing Kramers ${\mathrm{Mn}}^{3+}$ with non-Kramers ${\mathrm{Cr}}^{3+}$ ions, it is noted that being a Kramers or non-Kramers ion can strongly affect the local distortion size, whereas, it may not be able to change the detailed distortion mode.

Figure 1

(a) Measured magnetization (M) of chromium ions in single-crystal ${\mathrm{YCrO}}_3$ compound (circles) with an increase of temperature at ${\mu }_{0}H=0.3\mathrm{T}$ ($\sim 40008$ circles overlap each other so most of the error bars are embedded into the symbols). The solid line is a fit by Eq. (1) as described in the text. (b) Corresponding inverse magnetic susceptibility ${\chi }^{-1}$ (circles) of chromium ions in single-crystal ${\mathrm{YCrO}}_3$ compound versus temperature. The solid line indicates a CW behavior of the data as described by Eq. (2) from 300 to 980 K, which was extrapolated to ${\chi }^{-1}=0$ (dashed line) to show the PM Curie temperatures ${\theta }_{\mathtt{CW}}$.

Figure 2

(a) Inverse magnetic susceptibility ${\chi }^{-1}$ (circles) of chromium ions in single-crystal ${\mathrm{YCrO}}_3$ compound versus temperature. The solid lines indicate CW behaviors of the data as described by Eq. (2) at respective temperature regimes of 300–400 K and 750–980 K. They were extrapolated down to ${\chi }^{-1}=0$ (dash-dotted lines) to show the PM Curie temperatures ${\theta }_{\mathtt{CW}}$ and up to 1020 K (dash-dotted line). The fit results are listed in Table 1. (b) Inverse magnetic susceptibility ${\chi }^{-1}$ (circles) of chromium ions in single-crystal ${\mathrm{YCrO}}_3$ compound versus temperature. The solid lines indicate CW behaviors of the data as described by Eq. (2) at respective temperature regimes of 300–400 K, 400–540 K, 540–640 K, 640–750 K, and 750–980 K. They were extrapolated to ${\chi }^{-1}=0$ (dashed lines) to show the PM Curie temperatures ${\theta }_{\mathtt{CW}}$. The fit results are listed in Table 1.

Figure 3

Measured magnetization per chromium ion in single-crystal ${\mathrm{YCrO}}_3$ compound (circles) as a function of applied magnetic fields up to 14 T at 300, 500, 700, and 900 K. The dashed lines are fits to Eqs. (3). See detailed analysis in the text. Error bars are standard deviations and embedded into the circles because collected data points ($\sim 1600$) at respective temperatures overlap each other.

Figure 4

Observed (circles) and calculated (solid lines) time-of-flight neutron powder-diffraction patterns of a pulverized ${\mathrm{YCrO}}_3$ single crystal, collected on the POWGEN diffractometer (SNS, USA) at 321, 750, and 1200 K. The vertical bars mark the positions of nuclear Bragg reflections (space group $Pmnb$). The lower curves represent the difference between observed and calculated patterns.

Figure 5

Crystal structure (space group $Pmnb$) with one unit cell (solid line) of the ${\mathrm{YCrO}}_3$ single crystal within the present experimental accuracy at the studied temperature regime of 321–1200 K. The solid balls were labeled as Y, Cr, O1, and O2 ions, respectively.

Figure 6

Temperature dependence of the lattice constants, $a$, b, and $c$, of the pulverized ${\mathrm{YCrO}}_3$ single crystal (void symbols), which was extracted from our FullProf [36] refinements based on the time-of-flight neutron powder-diffraction data collected on POWGEN diffractometer (SNS, USA) between 321 and 1200 K. The solid lines are theoretical estimates of the variation of structural parameters at the respective temperature regimes of 321–900 K and 900–1200 K, using the $\mathrm{Gr}\ddot{\mathtt{u}}\mathrm{neisen}$ model [Eqs. (4) and (5)] with Debye temperature ${\theta }_{\mathtt{D}}$ = 580 K and extrapolated to the entire temperature range of 321–1200 K (dashed lines). Error bars are standard deviations obtained from our FullProf [36] refinements in the Pmnb symmetry.

Figure 7

Temperature-dependent unit-cell volume, V, of the ${\mathrm{YCrO}}_3$ single crystal (void symbols). This was extracted from our FullProf [36] refinements based on the time-of-flight neutron powder-diffraction data collected on POWGEN diffractometer (SNS, USA) between 321 and 1200 K. The solid lines are theoretical estimates of the variation of V within respective temperature regimes using the $\mathrm{Gr}\ddot{\mathtt{u}}\mathrm{neisen}$ model [Eqs. (4) and (5)] with Debye temperature ${\theta }_{\mathtt{D}}$ = 580 K and extrapolated to the whole temperature range (dashed lines). Error bars are standard deviations obtained from our FullProf [36] refinements in the Pmnb symmetry.

Figure 8

Temperature-dependent bond lengths of Cr-O1, Cr-O21, and Cr-O22 as well as the averaged bond length of Cr-O, i.e., $<\mathrm{Cr}\text{−}\mathrm{O}>$, of the single-crystal ${\mathrm{YCrO}}_3$ compound (void symbols). This was extracted from our time-of-flight neutron powder-diffraction study. Error bars are standard (for the Cr-O1, Cr-O21, and Cr-O22 bond lengths)/combined (for the Cr-O bond length) deviations. Solid lines are linear fits.

Figure 9

Lengths of Y-O11, Y-O12, Y-O21, and Y-O22 bonds of the single-crystal ${\mathrm{YCrO}}_3$ compound versus temperature varying from 321 to 1200 K (void symbols), which was extracted from our time-of-flight neutron powder-diffraction study. Error bars are standard deviations. Solid lines are linear fits.

Figure 10

Temperature variation of the distortion parameter, $\mathrm{\Delta }$, of Y, Cr, O1, and O2 ions of the single-crystal ${\mathrm{YCrO}}_3$ compound (void symbols), calculated by Eq. (6) from the refined structural parameters between 321 and 1200 K. Error bar is root means square deviation. The solid/dashed lines are tentative linear fits.

Figure 11

Local pentahedron environment of Y ions in the single-crystal ${\mathrm{YCrO}}_3$ compound, which was extracted based on our FullProf refinements [36]. The Y, O11, O12, O21, and O22 ions are labeled as displayed. Detailed bond lengths of Y-O11, Y-O12, Y-O21 ($\times 2$), and Y-O22 ($\times 2$) are listed in Table 2. The arrows sitting on the Y-O bonds schematically show the deduced pentahedron distortion configuration.

Figure 12

(a) Local octahedral environment of Cr ion in the single-crystal ${\mathrm{YCrO}}_3$ compound, which was extracted based on our FullProf refinements [36]. The arrows drawn through the oxygen ions ($2\times \mathrm{O}1$, $2\times \mathrm{O}21$, and $2\times \mathrm{O}22$) schematically show the deduced octahedral distortion mode. Representative refined bond lengths of Cr-O1, Cr-O21, and Cr-O22 at 321, 750, and 1200 K are listed in Table 2. (b) In such octahedral geometry, we schematically drew the approximate $3d_{yz}$ orbital shape in real space.

Figure 13

Local tetrahedral environments of O1 (a) and O2 (b) ions in the single-crystal ${\mathrm{YCrO}}_3$ compound, which was extracted based on our FullProf refinements [36]. The Y, Cr, O1, and O2 ions are labeled as displayed. Detailed bond lengths of O1-Cr ($\times 2$), O1-Y, O2-Cr, and O2-Y at 321 K were marked. The arrows sitting on the O-Y and O-Cr bonds schematically show the deduced tetrahedral distortion modes.

Figure 14

Temperature variation of the bond valence states (BVSs) of Y, Cr, O1, and O2 ions in the single-crystal ${\mathrm{YCrO}}_3$ compound, calculated from our refined structural parameters between 321 and 1200 K by the FullProf Suite [36]. For a clear comparsion, we also calculated the average BVSs of O1 and O2 ions, i.e., (O1 $+$ O2)/2. Error bars are combined standard deviations.

Figure 15

Temperature variation of the isotropic thermal parameters, B, of Y, Cr, and O1/O2 ions in the single-crystal ${\mathrm{YCrO}}_3$ compound. During our FullProf [36] refinements, we constrained the B sizes of O1 and O2 ions to the same value. Error bars are standard deviations.