Spontaneous lattice distortion and crystal field effects in HoB 4

The tetraboride HoB 4 crystallizes in a tetragonal structure (space group P 4/ mbm ), with the Ho atoms realizing a Shastry-Sutherland lattice. It orders antiferromagnetically at T N1 = 7 . 1 K and undergoes further magnetic transition at T N2 = 5 . 7 K. The complex magnetic structures are attributed to competing order parameters of magnetic and quadrupolar origin with significant magnetoelastic coupling. Here, we investigate the response of the lattice of HoB 4 across the antiferromagnetic phase transitions by using low-temperature powder x-ray diffraction and ultrasound-velocity measurements, supported by crystal electric field (CEF) calculations. Below T N2 , the crystal structure of HoB 4 changes to monoclinic (space group P 2 1 / b ) as a macroscopic manifestation of the quadrupolar ordering. Between 300 and 3.5 K, the total distortion amplitude is 0.46 Å and the relative volume change is 3 . 5 × 1 0 − 3 . This structural phase transition is compatible with the huge softening of the modulus C 44 observed around T N2 due to ferroquadrupolar order. A lattice instability developing immediately below T N1 is seen consistently in x-ray and ultrasound data. CEF analysis suggests a quasi-degenerated ground state for the Ho 3 + ions in this system. • The tetragonal structure of HoB 4 ( P 4/ mbm ) remains stable down to T N2 = 5.7 K. • Below T N2 , the crystal structure of HoB 4 changes to monoclinic (space group P 2 1 / b ). • The lattice instability coincides with strong softening of modulus C 44 around T N2 . • The structural transition is the manifestation of quadrupolar ordering below T N2 .