Evidence for an internal-field-induced spin-flop configuration in the extended kagome YBaCo${}_4$O${}_7$

The spin structure and spin dynamics in the extended kagome frustrated antiferromagnet YBaCo${}_4$O${}_7$ have been investigated using zero field and low applied field ${}^{59}$Co NMR. The YBaCo${}_4$O${}_7$ lattice is made up of bipyramid Co-ion units that form alternating planes of edge-sharing spin triangles and corner-sharing kagome spin triangles in an unusual exchange topology. Our low-temperature spin configuration results, based on hyperfine field orientations, are consistent with those from neutron scattering for the triangle spins which order antiferromagnetically below 106 K. For the kagome spins at low temperatures the static hyperfine fields are found to be oriented orthogonal to those of the triangle spins in a spin-flop configuration that is in disagreement with the neutron findings. Nuclear relaxation rate measurements made as a function of temperature show that inhomogeneous dynamic spin disorder occurs in kagome planes well below the Néel point.

Figure 1

${}^{59}$Co zero field NMR spectrum for a YBaCo${}_4$O${}_7$ polycrystalline sample at 2.4 K. The spectral peaks are identified by the valence states of the Co ions in kagome and triangular plane lattice sites. The inset shows the Co-ion lattice. The shaded areas depict the kagome planes.

Figure 2

${}^{59}$Co zero field NMR spectra obtained for a single crystal of YBaCo${}_4$O${}_7$ over the temperature range 4.8–20 K. The RF field is directed along the crystal $c$ axis. Spectral amplitudes have been scaled by $T$ to compensate for the Boltzmann factor. The observed decrease in scaled amplitudes with $T$ is attributed to spin dynamics in kagome planes.

Figure 3

ZF ${}^{59}$Co NMR spectral areas for a YBaCo${}_4$O${}_7$ single crystal versus angle θ between the RF field direction in the $ab$ plane and the crystal [110] axis. The full fitted curves are based on a model described in the text. The observed phase shift shows that kagome plane ${}^{59}$Co hyperfine fields (90 and 120 MHz) are orthogonal to those of the triangular plane (100 MHz). The inset shows model predictions based on the spin configuration from neutron diffraction (Ref. 9). While the NMR and neutron results agree for the triangle layers there are clear differences for the kagome layers.

Figure 4

${}^{59}$Co NMR spectra for a single crystal of YBaCo${}_4$O${}_7$ as a function of applied field ${\mu }_0\mathit{H}$, in the range 0–1.5 T, directed parallel to [110] in the $ab$ plane. The RF field ${\mathit{B}}_{\mathbf{1}}$ is directed along the $c$ axis. The major peaks at 90, 100, and 120 MHz in ZF are associated with the dominant (70$\%$) domain. The applied field induces a split Δ$f$ in the ZF 100 MHz component but not in the principal domain 90 or 120 MHz components. The split in the subsidiary peaks shown is due to the 30$\%$ of smaller domains as discussed in the text. Predicted unbroadened line spectra for the 1.5 T case are shown in the box region at the top of the figure. For the chosen orientation the frequencies of the various components are calculated as described in Sec. 3b. The inset gives a plot of Δ$f$ versus ${\mu }_{0}H$ which shows a linear relationship. The line drawn through the points has slope 10.03 MHz/T, the ${\gamma }_I$ value for ${}^{59}$Co.

Figure 5

${}^{59}$Co NMR spectra for a YBaCo${}_4$O${}_7$ single crystal in an applied field ${\mu }_0\mathit{H}=0.5$ T directed at three different orientations, $\theta =0^{\circ }$, $-$40° and $-$90°, with respect to [110]. For $\theta ={90}^{\circ }$ the K spin component (at 90 MHz in ZF) is split while for $\theta =0$° the T spin component (at 100 MHz in ZF) is split. This behavior shows that the T and K hyperfine fields are orthogonal to one another. At the intermediate orientation of 50° both spectral components split.

Figure 6

Angular dependence of the ${}^{59}$Co NMR spectral peak frequencies $f$, for the two principal components, 90 MHz K spins and 100 MHz T spins, for an YBaCo${}_4$O${}_7$ single crystal in ZF. The angle θ is measured from [110] in an applied field ${\mu }_{0}H=0.5$ T in the $ab$ plane. The spectral peak frequencies were obtained from Lorentzian multipeak fits to the spectra as described in the text. The upper two curves have the form $f=99.6+5\cos \left(\theta +\varphi \right)$ with phase shifts $\varphi =0$ and π, while the lower curves are given by $f=89+5\sin \left(\theta +\varphi \right)$ with phase shifts 0 and π. The rotation pattern shows that the K spin and T spin hyperfine fields are orthogonal to one another.

Figure 7

(a) Spin configuration for the T and K spins in YBaCo${}_4$O${}_7$ at 4 K as derived from the NMR hyperfine field measurements. Co ions in the T layers are represented in blue and those in the K layers in red while the inset in Fig. 7a shows the [110] crystal direction for a hexagonal primitive cell. It is suggested in the text that the K layer spin-flop configuration is induced by coupling to the AFM ordered T layer spins. (b) Spin configuration based on neutron diffraction results for a single crystal of YBaCo${}_4$O${}_7$ at 5 K as given in Ref. 9.

Figure 8

(a) ${}^{59}$Co spin-spin 1/$T_2$ and (b) spin-lattice 1/$T_1$ relaxation rates for polycrystalline YBaCo${}_4$O${}_7$ as a function of $T$, at 90, 100, and 120 MHz. Regions shown as I, II, and III exhibit markedly different behavior. Spin wave scattering dominates in relaxation in region I below 4 K. The straight lines shown in region I of (b) each have the form $1/T_1\propto T^3$ as predicted by theory (Ref. 17) for AFM systems. At higher $T$, in regions II and III, the rates reflect 2D dynamical spin disorder in kagome planes. The inset in (a) shows $t=0$ spin-echo amplitudes as a function of $T$. The full curve is Curie's law which gives a fit to the data below 4 K. The relaxation rate plateau from 4 to12 K is accompanied by changes in spectral linewidth as discussed in the text.

Figure 9

Magnetization $M$ versus $T$ plot for the single crystal YBaCo${}_4$O${}_7$ sample. Measurements were made using a SQUID magnetometer with the applied field firstly in the $ab$ plane close to the [110] direction and secondly parallel to the $c$ axis. The temperature $T_N$ marks the onset of long-range magnetic order as determined by neutron scattering while $T_R$ corresponds to a spin reordering transition. The dashed lines at 4 and 12 K indicate temperatures at which changes in the relaxation rates occur for increasing $T$ as shown in Fig. 8. The straight line drawn through the low-$T$ points for the $ab$ plane data shows the onset at 4 K of a change in the $ab$ plane magnetization behavior, from an initial gradual decrease with $T$ to an increasing trend which continues above 12 K.