Origin of the net magnetic moment in ${\mathrm{LaCoO}}_3$

We use polarized neutron scattering to characterize the Bragg scattering intensity below $T_C=89.5$ K at the (1,0,0) pseudocubic nuclear Bragg point of ${\mathrm{LaCoO}}_3$. Upon cooling in a field (FC), a net magnetic moment is apparent in Bragg scattering intensity, just as it was in previous magnetization measurements. Critical behavior associated with the net moment near $T_C$ upon cooling in small applied fields rapidly rounds with increasing field strength. We show, using a mean-field calculation, that this net moment can develop in a metastable state that forms upon FC, even when all the interactions in the system are antiferromagnetic.

Figure 1

Polarized neutron intensity of the (1 0 0) pseudocubic Bragg scattering vs $T$ for both the spin-flip (SF) and non-spin-flip (NSF) configurations after subtracting the background (BG) determined from fits for $145<T<200$ K, as described in the main text. The counting times for the SF and NSF data were 45 and 5 minutes, respectively.

Figure 2

The difference between the SF and NSF intensities vs $T$, The NSF intensity is normalized by the spin-flip ratio of 9.8 and both the SF and NSF intensities had backgrounds subtracted as described in Fig. 1. The curve represents Eq. (1) with $T_C=89.5$ K, $A=59.0$, $\beta =0.88$, $B=0$, and $C=0$.

Figure 3

The ($h$ 0 0) magnetic scattering intensity at $T=4$ and 50 K for crystal B, obtained by subtracting the intensity with the neutron polarization perpendicular to $\vec{Q}$ ($I_{\text{VF-SF}}$), which is in the vertical to the scattering plane, from the intensity with the polarization parallel to $\vec{Q}$ ($I_{\text{HF-SF}}$). The curves are fits with the background set to zero and with $A=248$ and 186 counts per 90 minutes for $T=4$ and 50 K, respectively, using the HWHM of 0.0075 r.l.u. determined from the (1 0 0) nuclear scattering peak.

Figure 4

The primitive rhombohedral LCO cell showing La ions (green) at the center and corners and two Co ions (blue) along with their oxygen octahedra. The rhombohedron is elongated along the line containing the two Co ions. The red lines connecting four La ions represents one of three possible twinning planes in the pseudocubic representation, each one containing four La ions at the rhombohedron corners and the central La ion, but no Co ions.

Figure 5

A chain of Co ions crossing a twin interface, represented by the vertical line at the center. The upper figure shows blue ions representing a chain of Co ions that is nearly perpendicular to the twin plane in a crystallite to the right of the twin plane. Each Co is in the center of an oxygen octahedron (red). The gold-colored Co ions, surrounded by their oxygen octahedra (white), are from the crystallite to the left of the twin interface. The bi-colored oxygen is on the twin interface and is shared by both chains. The lower figure is the same as the upper one except that the chain from the left is extended into the right crystallite to emphasize the small misalignment of the two chains. The Co-O-Co angles are near ${163}^{\circ }$ except across the twin interface, where half the bond angles are near ${165}^{\circ }$ and half near ${161}^{\circ }$, in an alternating pattern.

Figure 6

The pattern of ions in one plane adjacent to the twin interface with strongly antiferromagnetic bonds across the interface (dark) alternating ions with nonmagnetic bonds (light) across the interface. The angles associated with the bonds across the interface (perpendicular to the page, but not shown) are next to the associated Co ions. All bond angles in the plane shown are ${163}^{\circ }$, as are all other angles for bonds that do not traverse the twin interface. Note that in the LCO crystal, multiple orientations of the interface exist because of the possible twins throughout the crystal.

Figure 7

A side view of the twin interface where only the strong antiferromagnetic bonds are shown spanning the interface (shown in the shaded region). The nonmagnetic bonds are not shown. The La ions are also not shown for clarity, including those that lie on the twin boundary. The two planes of Co ions are parallel. The bicolored oxygens are on the twin interface and are shared by oxygen octahedra from each of the two twin domains. Because of the twinning in LCO, such interfaces will be oriented in various directions and any field applied to the LCO crystal will, in general, have varying components along different octahedral axes.

Figure 8

Mean-field exchange interactions. $S_a$ and $S_m$ are on one side of the twin interface and $S_b$ and $S_n$ are on the other. The $S_a$ and $S_m$ each have four neighbors, each with interaction strength $j$. $S_a$ and $S_b$ interact with strength $J$ and $S_m$ and $S_n$ do not directly interact with each other.

Figure 9

The ground-state maps for $J=0$, with $\mathrm{\Delta }=0.8$ (left) and 1.0 (right). The case $\mathrm{\Delta }=0.8$ agrees well with previous studies [24, 25] and the case $\mathrm{\Delta }=1.0$ is isotropic, as in the model developed for the LCO twin interface. For $\mathrm{\Delta }=0.8$, both the antiferromagnetic (AF) state with moments along $H$ and the biconical states (BC1 and BC2) are clearly visible, as is the paramagnetic (PM) state that appears at high fields. For $\mathrm{\Delta }=1.0$, the antiferromagnetic state is absent, as is expected.

Figure 10

The ground-state configuration for $J/\left(4j\right)=2/3$ for the moments along $H$ applied in the $z$ direction for the four types of spin as a function of $H$ and $F$ (top) calculated by minimizing the energy in Eq. (2) and the moments of each component parallel (left) and perpendicular (right) of the spins as a function of $H$ along cuts at $F/\left(4j\right)=-0.67$, 0, and 0.67 (bottom). Biconical states (BC) similar to those in Fig. 9 are observed as well as an intermediate state between the biconical state and the paramagnetic state for $F>0$.

Figure 11

The ground-state configuration for $J/\left(4j\right)=-2/3$ for the moments along $H$ applied in the $z$ direction for the four types of spin as a function of $H$ and $F$ (top) calculated by minimizing the energy in Eq. (2) and the moments of each component parallel (left) and perpendicular (right) of the spins as a function of $H$ along cuts at $F/\left(4j\right)=-0.67$, 0 and $-0.67$ (bottom). A biconical state (BC) is observed for $F>0$.

Figure 12

The ground-state configuration with $J=J/\left(4j\right)=2/3$, similar to that shown in Fig. 10 except that the oxygen octahedra are tilted with respect to $z$ in an alternating pattern as described in the text. A biconical-like (BC) state is observed for both $F>0$ and $F<0$.

Figure 13

The average moments of each spin component as well as the net moment $T_z$ along $H$ and $T_{xy}$ perpendicular to $H$, where $H$ is an applied field equivalent to $H_z=20$ Oe for FC and ZFC with $J/\left(4j\right)=2/3$ and $F/\left(4j\right)=-0.67$, 0, and 0.67. In the ZFC procedure, the system is started in its ground state at low temperature. All interactions are antiferromagnetic.

Figure 14

The behavior of the moments near $T_{\mathrm{eq}}$ for $J/\left(4j\right)=2/3$, showing the polarization of the sublattices for FC and ZFC as well as the energy for FC and ZFC. The smooth growth of the weak FC ferrimagnetic moment contrasts to sharp SF transition observed in ZFC.

Figure 15

The average moments of each spin component as well as the net moment $T_z$ along $H$ and $T_{xy}$ perpendicular to $H$, where $H$ is an applied field equivalent to $H_z=20$ Oe for FC and ZFC with $J/\left(4j\right)=-2/3$ and $F/\left(4j\right)=-0.67$, 0, and 0.67. The interactions are all antiferromagnetic except between $S_a$ and $S_b$ which is ferromagnetic.

Figure 16

The net moment $M$ and $H/M$ vs $T$ upon FC for several fields with $J/\left(4j\right)=2/3$ and $F/\left(4j\right)=-0.67$, 0, and 0.67.