Experimental observation of magnetic dimers in diluted ${\mathrm{Yb}:\mathrm{YAlO}}_3$

We present a comprehensive experimental investigation of Yb magnetic dimers in ${\mathrm{Yb}}_{0.04}{\mathrm{Y}}_{0.96}{\mathrm{AlO}}_3$, an Yb-doped yttrium aluminum perovskite ${\mathrm{YAlO}}_3$, by means of specific heat, magnetization, and high-resolution inelastic neutron scattering (INS) measurements. In our sample, the Yb ions are randomly distributed over the lattice and $\sim 7\%$ of Yb ions form quantum dimers due to nearest-neighbor antiferromagnetic coupling along the $c$ axis. At zero field, the dimer formation manifests itself in an appearance of an inelastic peak at $\mathrm{\Delta }\approx 0.2\mathrm{meV}$ in the INS spectrum and a Schottky-like anomaly in the specific heat. The structure factor of the INS peak exhibits a cosine modulation along the $L$ direction, in agreement with the $c$-axis nearest-neighbor intradimer coupling. A careful fitting of the low-temperature specific heat shows that the excited state is a degenerate triplet, which indicates a surprisingly small anisotropy of the effective Yb-Yb exchange interaction despite the low crystal symmetry and anisotropic magnetic dipole contribution, in agreement with previous reports for the Yb parent compound, ${\mathrm{YbAlO}}_3$ [L. Wu et al., Nat. Commun. 10, 698 (2019), L. S. Wu et al., Phys. Rev. B 99, 195117 (2019)], and in contrast to ${\mathrm{Yb}}_2{\mathrm{Pt}}_2\mathrm{Pb}$ [L. S. Wu et al., Science 352, 1206 (2016), W. J. Gannon et al., Nat. Commun. 10, 1123 (2019)]. The obtained results are precisely reproduced by analytical calculations for the Yb dimers.

Figure 1

Crystal structure and energy levels of Yb dimers in $\mathrm{Yb}:{\mathrm{YAlO}}_3$. (a) Orthorhombic perovskite $Pbnm$ crystal structure of ${\mathrm{Y}}_{1-x}{\mathrm{Yb}}_x{\mathrm{AlO}}_3$, where Yb form chain segments along the $c$ axis. (b) Calculated probability for Yb ions to form $n\text{−}\mathrm{mers}$ of different length; the ratio $\frac{n·P\left({\text{Yb}}_{n+1}\right)}{(n+1)·P\left({\text{Yb}}_n\right)}$ is constant and equal to the concentration of Yb, $x\approx 0.043$. (c) Effective spin-1/2 energy levels of the ground state doublet of an isolated ${\mathrm{Yb}}^{3+}$ ion and (d) splitting of the Yb dimer levels in the presence of $XXZ$ interaction, Eq. (1), and magnetic field, $B$.

Figure 2

Low-temperature specific heat of $\mathrm{Yb}:{\mathrm{YAlO}}_3$. (a) Temperature dependences of specific heat measured at different magnetic field ($B\parallel \left[100\right]$) along with the results of fitting using Eq. (9). (b) Specific heat taken at 0 T. Note that the $y$ scale is an order of magnitude smaller compared to panel (a). Blue and red lines show calculated specific heat of Yb subsystem taking into account only the dimer and the dimer plus trimer contributions using Eq. (7) and Eq. (8), respectively. (c) Energy splitting for ${\mathrm{Yb}}_1$ subsystem as a function of magnetic field extracted from the specific heat measurements and its linear fitting $E\left(B\right)=g{\mu }_{\mathrm{B}}BS$.

Figure 3

(a) Field dependence of magnetization measured at $T=2\mathrm{K}$ along [100] and [001] directions. Green solid line represents the fit of $M_a\left(B\right)$ with Brillouin function. (b) Angular dependence of magnetization in $ab$ plane measured at $B=7$ T and $T=2\mathrm{K}$. $0^{\circ }$ and ${90}^{\circ }$ correspond to $B\parallel b$ and $B\parallel a$, respectively. Red line shows the fit with Eq. (10).

Figure 4

Inelastic neutron scattering spectra of $\mathrm{Yb}:{\mathrm{YAlO}}_3$. (a) Energy spectrum measured at $T\approx 0.1\mathrm{K}$ and $E_i=1.55\mathrm{meV}$. The data were integrated within $H=0\pm 0.1$, $K=1\pm 0.5$, and $L=1\pm 0.5$. (b) Constant-energy cut along the $\left(00L\right)$ direction taken at $T\approx 2\mathrm{K}$ and $E_i=3.32\mathrm{meV}$. The data were integrated in energy window $\hslash \omega =[0.17$–$0.25]\mathrm{meV}$; $H=0\pm 0.1$, $K=0\pm 1$. (c) Intensity of the inelastic peak at $\mathbf{Q}=\left(001\right)$ as a function of temperature and its fit with Eq. (5). Error bars represent one standard deviation.

Figure 5

Inelastic neutron scattering spectra of $\mathrm{Yb}:{\mathrm{YAlO}}_3$. (a) Observed (top) and modeled (bottom) constant energy slice in $\left(0KL\right)$ scattering plane at $T\approx 2\mathrm{K}$ and $E_i=3.32\mathrm{meV}$. The data are integrated within the energy window $\hslash \omega =[0.17,0.25]\mathrm{meV}$; $H=0\pm 0.1$. (b) Observed (right) and modeled (left) spectra along the $\left(00L\right)$ direction at $T\approx 2\mathrm{K}$, $E_i=3.32\mathrm{meV}$; $K=0\pm 1$; $H=0\pm 0.1$.