Field Induced Magnetic States in Holmium Tetraboride

A study of the zero field and field induced magnetic states of the frustrated rare earth tetraboride, HoB$_4$, has been carried out using single crystal neutron diffraction complemented by magnetisation measurements. In zero field, HoB$_4$ shows magnetic phase transitions at $T_{\mathrm{N1}}$ = 7.1 K to an incommensurate state with a propagation vector ($\delta$, $\delta$, $\delta'$), where $\delta$ = 0.02 and $\delta'$ = 0.43 and at $T_{\mathrm{N2}}$ = 5.7 K to a non-collinear commensurate antiferromagnetic structure. Polarised neutron diffraction measurements in zero field have revealed that the incommensurate reflections, albeit much reduced in intensity, persist down to 1.5 K despite antiferromagnetic ordering at 5.7 K. At lower temperatures, application of a magnetic field along the $c$-axis initially re-establishes the incommensurate phase as the dominant magnetic state in a narrow field range, just prior to HoB$_4$ ordering with an up-up-down ferrimagnetic structure characterised by the $(h,k,\frac{1}{3})$-type reflections between 18 and 24 kOe. This field range is marked by the previously reported $M/M_{\mathrm{sat}}$= $\frac{1}{3}$ magnetisation plateau, which we also see in our magnetisation measurements. The region between 21 and 33 kOe is characterised by the increase in the intensity of the antiferromagnetic reflections, such as (100), the maximum of which coincides with the appearance of the narrow magnetisation plateau with $M/M_{\mathrm{sat}}\approx$ $\frac{3}{5}$. Further increase of the magnetic field results in the stabilisation of a polarised state above 33 kOe, while the incommensurate reflections are clearly present in all fields up to 59 kOe. We propose the $H-T$ phase diagram of HoB$_4$ for the $H \parallel c$ containing both stationary and transitionary magnetic phases which overlap and show significant history dependence.