Competition between the inter- and intra-sublattice interactions in ${\mathrm{Yb}}_2{\mathrm{V}}_2{\mathrm{O}}_7$

We studied the magnetic properties of single-crystal ${\mathrm{Yb}}_2{\mathrm{V}}_2{\mathrm{O}}_7$ using dc and ac susceptibility measurements, elastic and inelastic neutron-scattering measurements, and linear spin-wave theory. The experimental data show a ferromagnetic ordering of ${\mathrm{V}}^{4+}$ ions at 70 K, a short-range ordering of ${\mathrm{Yb}}^{3+}$ ions below 40 K, and finally a long-range noncollinear ordering of ${\mathrm{Yb}}^{3+}$ ions below 15 K. With external magnetic field oriented along the [111] axis, the Yb sublattice experiences a spin flop transition related to the “three-in one-out” spin structure. By modeling the spin-wave excitations, we extract the Hamiltonian parameters. Our results confirm that although the extra inter-sublattice Yb-V interactions dramatically increase the Yb ordering temperature to 15 K, the intra-sublattice Yb-Yb interactions, based on the pyrochlore lattice, still stabilize the Yb ions' noncollinear spin structure and spin flop transition.

Figure 1

(a) Temperature dependence of the dc susceptibility $\chi \left(T\right)$ measured with ${\mu }_{0}H=0.05\mathrm{T}$. Blue circles: Calculated temperature dependence of magnetization $M\left(T\right)$ of the Yb sublattice. (b) Temperature dependence of the real ${\chi }^{\prime }$ and imaginary ${\chi }^{\prime \prime }$ parts of the ac susceptibility measured under ${\mu }_0{H}_{\mathrm{ac}}=4.2e-4$ T with different frequencies. The ${\chi }^{\prime \prime }$ data are offset by each other. (c) Temperature dependence of the (002) and (004) Bragg peak intensity obtained from single-crystal neutron-diffraction experiments. Three ordering temperatures (70, 40, and 15 K) are marked as dashed lines. (d) The elastic channel ($-0.1\le \Delta E\le 0.1\mathrm{meV}$) of the neutron-scattering data collected at MACS for $T=1.5$ K and (e) $T=40$ K; the (002) Bragg peak position is highlighted with a green circle. Error bars in the figure represent one standard deviation.

Figure 2

The spin configuration of the ${\mathrm{Yb}}^{3+}$ and ${\mathrm{V}}^{4+}$ sublattices in (a) zero field and (b) with an applied magnetic field along the [111] axis after the spin flop transition.

Figure 3

The dc magnetization of ${\mathrm{Yb}}_2{\mathrm{V}}_2{\mathrm{O}}_7$ measured at 60 and 0.6 K with external magnetic field applied along three different axis [111], [110], and [100]. $M_{c3}$ represents the saturation moment measured at 0.6 K.

Figure 4

Field dependence of (a) the dc magnetization $M$ measured at 0.6 K and (b) its derivative. (c) Field dependence of the real part of ac susceptibility (${\mu }_0{H}_{\mathrm{ac}}$ = $4.2e-4$ T) measured at 20 mK. The data are offset by each other. (d) Field dependence of the magnetic torque measured with $H$ $\parallel$ [111] and its derivative. The external field $H$ is applied along the [111], [110], and [100] axes. Two critical fields 0.15 and0.4 T are indicated by the dashed lines, and $M_{c1},M_{c2}$ represent the moments at corresponding fields. $M_{c3}$ represents the moment measured at 5 T in Fig. 3.

Figure 5

Lower panels: the measured inelastic neutron scattering $S$(Q,$\omega$) at 1.5 K, sliced along various directions in the HHL plane. Upper panels: the corresponding calculated $S$(Q,$\omega$) convoluted with a Gaussian of full width 0.15 meV (chosen to meet the spin-wave width observed) adopting the exchange parameters in the main text (r.l.u. stands for reciprocal-lattice unit).