Magnetic resonance spectroscopy on the spin-frustrated magnets ${\mathrm{YBaCo}}_{3}M{\mathrm{O}}_7$ ($M$=Al, Fe)

We present experimental results of combined electron spin resonance (ESR) and nuclear magnetic resonance (NMR) measurements on single crystals of the Swedenborgite-type compounds ${\mathrm{YBaCo}}_{3}M{\mathrm{O}}_7$ ($M$=Al, Fe). The magnetic lattice of these materials can be described as stacks of strongly geometrically frustrated kagome layers built up of ${\mathrm{Co}}^{2+}$ ($S=3/2$) ions. Due to the Co-$M$ site intermixing, there are $M$-type defects in the kagome planes as well as magnetic Co ions at the interplanar positions. Previous investigations revealed large antiferromagnetic (AFM) Curie-Weiss temperatures in both compounds. Yet no AFM long-range order but a spin glass behavior at low temperatures has been observed. Using ${}^{27}\mathrm{Al}$ NMR as well as ${\mathrm{Co}}^{2+}$ and ${\mathrm{Fe}}^{3+}$ ESR spin probes that are sensitive to local magnetic properties at different crystallographic sites, we have identified two magnetic subsystems in both compounds and have studied their distinct properties. In particular in the case of ${\mathrm{YBaCo}}_3{\mathrm{AlO}}_7$, we have observed a gradual development of the spin correlations in the two-dimensional (2D) kagome planes containing nonmagnetic Al defects and the establishment of a 3D frozen glasslike spin state of the interplanar Co ions at lower temperatures. We have found that despite a strong dependence of the ordering temperature in the kagome layers on the type of the $M$ ion (magnetic or nonmagnetic), the final 3D static ground state sets in at rather similar temperatures. We argue that the peculiar spin dynamics and a disordered magnetic ground state of the studied compounds result from the interplay of strong magnetic frustration and intrinsic structural disorder arising due to the intersite mixing of Co and $M$ atoms.

Figure 1

A perspective view of the atomic structure of ${\mathrm{YBaCo}}_{3}M{\mathrm{O}}_7$ ($M=\mathrm{Al}$, Fe). The bonding lines between the metals and oxygen atoms show the oxygen interrelation of Y and Ba. The kagome plane is highlighted with thick lines between the 6c light blue sites. The 2a blue sites connect the planes. The hexagonal unit cell is marked with a thin green line. Metal ions at 2a and 6c sites are surrounded by four oxygen ligands each, forming axially symmetric tetrahedra around the 2a sites (dark blue colored) and distorted tetrahedra around the 6c sites (light blue colored). On the right side are the next metal surroundings for both crystallographic sites 2a and 6c.

Figure 2

Experimental ${}^{27}\mathrm{Al}$ NMR spectrum at the fields ${\mu }_{0}H=3$ T (top) and 7.7 T (bottom) in the paramagnetic state at $T=120$ K (symbols). The spectra are modeled with two contributions: the blue-colored signal (right-slanted hatching lines) is the signal from ${}^{27}\mathrm{Al}$ at the regular position (${\mathrm{Al}}_{\mathrm{R}}$), and the red-colored signal (left-slanted hatching lines) is the one from ${}^{27}\mathrm{Al}$ in the kagome plane (${\mathrm{Al}}_{\mathrm{D}}$), respectively. The black solid line represents the sum of the two contributions.

Figure 3

Experimental ${}^{27}\mathrm{Al}$ NMR signal at a field ${\mu }_{0}H=7.7$ T at different selected temperatures (symbols). The modeled contributions from ${}^{27}\mathrm{Al}$ at the regular interplane position (${\mathrm{Al}}_{\mathrm{R}}$) and at the defect position in the kagome plane (${\mathrm{Al}}_{\mathrm{D}}$) are shown by the blue-colored right-slanted hatching lines and the red-colored left-slanted hatching lines, respectively. The black solid line represents the sum of the two contributions.

Figure 4

${}^{27}\mathrm{Al}$ NMR lineshifts vs the bulk static susceptibility $\chi$ at fields of 3 and 7.7 T (circles and triangles, respectively) for the ${}^{27}\mathrm{Al}$ nuclei at the regular ${\mathrm{Al}}_{\mathrm{R}}$ position (main panel, open symbols) and at the defect ${\mathrm{Al}}_{\mathrm{D}}$ position (inset, closed symbols). The lines are linear fits (see the text).

Figure 5

Time dependence of the ${}^{27}\mathrm{Al}$ stimulated spin echo decay at $T=21$ K (symbols). The solid line is a fit to Eq. (6).

Figure 6

Longitudinal relaxation rate $T_1^{-1}$ of ${}^{27}\mathrm{Al}$ nuclei as a function of temperature measured at the fields of 7.7 (main panel) and 3 T (inset). Open symbols correspond to the fast relaxing component of $T_1^{-1}$ and filled symbols denote the slow relaxing component, respectively. Red solid lines are fits with the critical exponent (see discussion in Sec. 4). Due to technical limitations, it was difficult to measure long relaxation times. The upper limit for the corresponding slow relaxation rates is marked with stars. Lines connecting the data points are guides for the eye.

Figure 7

HF-ESR on ${\mathrm{YBaCo}}_3{\mathrm{AlO}}_7$. Top: Spectra for several temperatures at a fixed frequency of 302 GHz. For comparison, spectra were normalized to signal intensity at zero field after subtraction of a linear background. Bottom: frequency vs resonance field dependence $\nu \left(H_{\mathrm{res}}\right)$. The solid line is the fit of the data and the dashed lines show to the uncertainty range.

Figure 8

HF-ESR on ${\mathrm{YBaCo}}_3{\mathrm{FeO}}_7$: spectra at $\nu =166$ GHz for several temperatures. A linear background was subtracted from the signals and an admixture of dispersion signal to the line was corrected. Afterwards, spectra were normalized to the extremum and shifted vertically for clarity.

Figure 9

HF-ESR on ${\mathrm{YBaCo}}_3{\mathrm{FeO}}_7$. (Top) Frequency resonance field dependence $\nu \left(H_{\mathrm{res}}\right)$ for different temperatures and orientations. A comparison of $\nu \left(H_{\mathrm{res}}\right)$ measured on ${\mathrm{YBaCo}}_3{\mathrm{AlO}}_7$ (open triangles) and ${\mathrm{YBaCo}}_3{\mathrm{FeO}}_7$ (filled circles) is shown in the inset. (Bottom) Temperature dependence of the linewidth $\mathrm{\Delta }H$ for two orientations measured at different frequencies.

Figure 10

${}^{27}\mathrm{Al}$ NMR linewidth $\mathrm{\Delta }H\left(T\right)$ normalized to the measurement field vs the macroscopic susceptibility $\chi \left(T\right)$ at the fields of 3 (circles) and 7.7 T (triangles). Open symbols (main panel) correspond to ${\mathrm{Al}}_{\mathrm{R}}$ sites in between the kagome planes, filled symbols (inset) to ${\mathrm{Al}}_{\mathrm{D}}$ sites in the kagome planes, respectively. Lines are linear fits.

Figure 11

Temperature dependence of ${}^{27}\mathrm{Al}$ NMR linewidths $\mathrm{\Delta }H\left(T\right)$ normalized to the measurement field at fields 3 (circles) and 7.7 T (triangles). Open symbols correspond to the signal from ${{}^{27}\mathrm{Al}}_{\mathrm{R}}$ nuclei at the regular interplane positions (main panel) and closed symbols to the signal from ${{}^{27}\mathrm{Al}}_{\mathrm{D}}$ nuclei in the kagome planes (inset). Solid lines are the respective fits $\mathrm{\Delta }H\sim {\varepsilon }^{\gamma }$ (see the text).

Figure 12

Temperature dependence of the ${{}^{27}\mathrm{Al}}_{\mathrm{D}}$ NMR linewidth at the fields of 3 (left scale, filled circles) and 7.7 T (right scale, filled triangles) for the ${\mathrm{Al}}_{\mathrm{D}}$ site in the kagome planes plotted as a function of the reduced temperature $(T_{\mathrm{f}1}-T)/T_{\mathrm{f}1}$ with $T_{\mathrm{f}1}=40$ K. Solid line is a fit to the data $\mathrm{\Delta }H\sim {[(T_{\mathrm{f}1}-T)/T_{\mathrm{f}1}]}^{\beta }$ (see the text).