Frustration of square cupola in Sr(TiO)Cu${}_4$(PO${}_4$)${}_4$

Abstract

The structural and magnetic properties of the square-cupola antiferromagnet Sr(TiO)Cu${}_4$(PO${}_4$)${}_4$ are investigated via x-ray diffraction, magnetization, heat capacity, and ${}^{31}$P nuclear magnetic resonance experiments on polycrystalline samples, as well as density-functional band-structure calculations. The temperature-dependent unit cell volume could be described well using the Debye approximation with the Debye temperature of ${\theta }_{\mathrm{D}}\simeq$ 550~K. Magnetic response reveals a pronounced two-dimensionality with a magnetic long-range-order below $T_{\mathrm{N}}\simeq 6.2$~K. High-field magnetization exhibits a kink at $1/3$ of the saturation magnetization. Asymmetric ${}^{31}$P NMR spectra clearly suggest strong in-plane anisotropy in the magnetic susceptibility, as anticipated from the crystal structure. From the ${}^{31}$P NMR shift vs bulk susceptibility plot, the isotropic and axial parts of the hyperfine coupling between ${}^{31}$P nuclei and the Cu${}^{2+}$ spins are calculated to be $A_{\mathrm{hf}}^{\mathrm{iso}}\simeq 6539$ and $A_{\mathrm{hf}}^{\mathrm{ax}}\simeq 952$~Oe/${\mu }_{\mathrm{B}}$, respectively. The low-temperature and low-field ${}^{31}$P NMR spectra indicate a commensurate antiferromagnetic ordering. Frustrated nature of the compound is inferred from the temperature-dependent ${}^{31}$P NMR spin-lattice relaxation rate and confirmed by our microscopic analysis that reveals strong frustration of the square cupola by next-nearest-neighbor exchange couplings.

arXiv comment11 pages, 13 figures, 1 table, Phys. Rev. B (Accepted, 2018)

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• Microscopic Magnetism of A(TiO)Cu4(PO4)4 (A = Ba, Pb, Sr): 31P and 63,65Cu NMR Study
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