Field-induced magnetic states in holmium tetraboride

A study of the zero field and field induced magnetic states of the frustrated rare earth tetraboride ${\mathrm{HoB}}_4$ has been carried out using single crystal neutron diffraction complemented by magnetization measurements. In zero field, ${\mathrm{HoB}}_4$ shows magnetic phase transitions at $T_{\mathrm{N}1}=7.1$ K to an incommensurate state with a propagation vector $(\delta ,\delta ,{\delta }^{\prime })$, where $\delta =0.02$ and ${\delta }^{\prime }=0.43$ and at $T_{\mathrm{N}2}=5.7$ K to a noncollinear commensurate antiferromagnetic structure. Polarized 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 ${\mathrm{HoB}}_4$ ordering with an up-up-down ferrimagnetic structure characterized by the $\left(hk\frac{1}{3}\right)$-type reflections between 18 and 24 kOe. This field range is marked by the previously reported $M/M_{\mathrm{sat}}=\frac{1}{3}$ magnetization plateau, which we also see in our magnetization measurements. The region between 21 and 33 kOe is characterized by the increase in the intensity of the antiferromagnetic reflections, such as (100), the maximum of which coincides with the appearance of the narrow magnetization plateau with $M/M_{\mathrm{sat}}\approx \frac{3}{5}$. Further increase of the magnetic field results in the stabilization of a polarized 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 ${\mathrm{HoB}}_4$ for the $H\parallel c$ containing both stationary and transitionary magnetic phases which overlap and show significant history dependence.

Figure 1

(a) The Shastry-Sutherland lattice, (b) projection of ${\mathrm{HoB}}_4$ structure along the tetragonal $c$ axis. The Ho ions form a lattice that topologically maps to the Shastry-Sutherland lattice. Solid bonds correspond to the nearest neighbor interaction $J$, while the dashed bonds are the next nearest neighbor interaction $J^{\prime }$.

Figure 2

Single crystal neutron diffraction maps of $\left(h0l\right)$ plane for ${\mathrm{HoB}}_4$ measured using the D7 diffractometer. The non-spin-flip (left column) and spin-flip (right column) channels at different temperature are shown: (a) 10 K, paramagnetic phase, (b) 6.5 K, IT incommensurate phase, and (c) 1.5 K, low-temperature antiferromagnetic phase.

Figure 3

Line of cuts of the $z$ polarization intensity maps at 10, 6.5, and 1.5 K for the $\left[H0L\right]$ direction, where (a) $L=1.0\pm 0.1$ and (b) $L=0.43\pm 0.10$.

Figure 4

Temperature dependent magnetic susceptibility in increasing fields applied along $H\parallel c$. Zero-field transition temperatures are indicated by the arrows. The inset shows the inverse susceptibility for $H=1$ kOe.

Figure 5

Evolution of (top panel) fractional and (middle panel) integer $\left(hkl\right)$ reflections intensities with magnetic field compared to (bottom panel) the magnetization curve for the magnetic field ramping up at $T=2$ K. There are four stationary magnetic structures, colored in gray and labeled as phases I, II, III, and IV, in which magnetization remains almost constant, while the white regions are transitionary structures in which magnetization is rapidly changing. The dashed line corresponds to a narrow transitionary state between phases II and III.

Figure 6

Temperature dependence of the intensity incommensurate reflection $\left(2.021.020.43\right)$ in different fields. A stabilization of the incommensurate phase is observed at 20 kOe, while a decrease of the low temperature intensity with increasing field is observed. Each curve is sequentially offset by 1100 counts.

Figure 7

Comparison of the calculated and observed intensity for the incommensurate phase re-established at $T=2.0$ K in an applied field of 17.5 kOe. The model for the zero-field incommensurate structure was used to calculate the intensity.

Figure 8

Field dependence of the intensity of $\left(21\frac{1}{3}\right)$ reflection at different temperatures. Filled symbols correspond to ramping the field up, empty symbols correspond to ramping the field down. The temperature increase between $T=1.8$ and 4 K causes a visible shift of the magnetic phase corresponding to $\frac{1}{3}$-magnetization plateau to lower fields.

Figure 9

Comparison of the calculated and observed intensity for phase II corresponding to the $\frac{1}{3}$-magnetization plateau. An up-up-down ferrimagnetic phase along the $c$ axis was used to calculate the intensity. The proposed magnetic structure is shown in the inset.

Figure 10

Magnetic phase diagram of ${\mathrm{HoB}}_4$ constructed from neutron diffraction data for different reflections (squares, filled circles, triangles, and diamonds) and magnetization (empty circles) measurements. All field dependent measurements were made by ramping the field up. The labeling of different magnetic structures is consistent with the one used in Fig. 5 for $T=2$ K, however, with the increased temperature the magnetic phases tend to overlap. The separation between the stationary and transitionary phases also becomes less obvious on heating, with the transitionary phases II+IT and II+III occupying large portions of the phase diagram.