Electro-nuclear quantum phase transition in TmVO ₄

Hyperfine interactions couple nuclear and electronic degrees of freedom. The present work explores how hyperfine coupling within the Tm ions in TmVO 4 single crystals affects an electronic ferroquadrupole ordered ground state and its associated field-tuned quantum phase transition. As temperature is progressively reduced through the hyperfine energy scale, the nuclear moments reduce the critical field for the electronic order, resulting in a dramatic back-bending of the phase boundary delineating the ferroquadrupole order. This behavior is well described by a single-ion semiclassical mean-field model down to approximately 50 mK. Analysis of the effective Hamiltonian leads to a prediction of spontaneous nuclear magnetic order mediated by 4 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>f</mml:mi> </mml:math> electrons, which in principle persists with the application of orthogonal antisymmetric strain, yielding a proposed electro-nuclear tetracritical point.