Impact of orbital degrees of freedom on geometrical frustration in the kagome-like magnet ${\text{SrV}}_x{\text{Ga}}_{12-x}{\text{O}}_{19}$

We studied kagome-like magnets, ${\text{SrV}}_x{\text{Ga}}_{12-x}{\text{O}}_{19}$ with ${\text{V}}^{3+}$ ($3d^2$ in the triply degenerate $t_{2g}$ states), as a geometrically frustrated spin system with orbital degrees of freedom. We observed a suppression of low-temperature spin entropy and an anomalous contraction of the V triangles on the kagome lattice, which can be regarded as the V trimerization with spin-singlet formation. This result, which is in clear contrast to their ${\text{Cr}}^{3+}$ $\left(3d^3\right)$ analogs exhibiting a spin-liquid behavior, indicates a substantial impact of orbitals on geometrically frustrated magnets.

Figure 1

(Color online) (a) Inverse magnetic susceptibility of ${\text{SrV}}_x{\text{Ga}}_{12-x}{\text{O}}_{19}$ per V mole with various values of $x$ at 0.1 T. The dashed line indicates the result of the fitting for $x=8$ by the sum of one Curie-Weiss term and one spin-gap term. The inset shows the $x$ dependence of a Curie constant per V mole below 50 K. (b) Magnetic susceptibility data of $x=8$ (a solid line) and the fitting result (a dashed line, barely seen because it follows the solid line) by the sum of a Curie-Weiss term (a dot-dot-dashed line) and two spin-gap terms (each by dashed lines and the sum by a dot-dashed line.) (c) Schematic picture of the arrangement of the V ions in ${\text{SrV}}_x{\text{Ga}}_{12-x}{\text{O}}_{19}$.

Figure 2

(Color online) (a) Specific heat of ${\text{SrV}}_x{\text{Ga}}_{12-x}{\text{O}}_{19}$ and ${\text{SrCr}}_8{\text{Ga}}_4{\text{O}}_{19}$ per formula-unit $\left({\text{SrV}}_x{\text{Ga}}_{12-x}{\text{O}}_{19}\right)$ mole. (b) Magnetic specific heat per V (or Cr) mole divided by temperature for ${\text{SrV}}_x{\text{Ga}}_{12-x}{\text{O}}_{19}$ and ${\text{SrCr}}_8{\text{Ga}}_4{\text{O}}_{19}$.

Figure 3

(Color online) (a) Synchrotron x-ray powder diffraction patterns (plus marks) and Rietveld refinement patterns (solid lines) of ${\text{SrV}}_8{\text{Ga}}_4{\text{O}}_{19}$ at 800 K with $\lambda =0.7778\text{Å}$. The vertical marks indicate the position of Bragg peaks, and the solid line at the bottom corresponds to the difference between observed and calculated intensities. Small closed circles and triangles are those from nonmagnetic impurity phases (${\text{Sr}}_3{\text{V}}_2{\text{O}}_8$ and ${\text{Sr}}_{10}{\text{V}}_6{\text{O}}_{25}$). The inset is the expanded figure at higher angles $2\theta =50–70°$. [(b) and (c)] Temperature dependence of $a$ and $c$ lattice constants normalized to the values at 800 K.

Figure 4

(Color online) (a) V-V (Ga-Ga) bond length on triangle A (open symbols) and B (closed symbols) for ${\text{SrV}}_x{\text{Ga}}_{12-x}{\text{O}}_{19}$. (b) Kagome lattice with two inequivalent triangles, A and B. (c) Orbital ordering of the $t_{2g}$ states ($xy$, $yz$, and $zx$ states) for three V ions on triangle B.