Ferromagnetism and electronic structure of ${\text{TmB}}_2$

The magnetic properties and electronic structure of thulium diboride were investigated as it is a magnetically unknown phase between ferromagnetic (FM) $RE{\text{B}}_2$ $\left(RE=\text{Tb},\text{Dy},\text{Ho},\text{Er}\right)$ and antiferromagnetic ${\text{YbB}}_2$. ${\text{TmB}}_2$ adopts the ${\text{AlB}}_2$-type crystal structure $\left(P6/mmm\right)$ with $a=3.26016\left(5\right)\text{Å}$ and $c=3.75351\left(8\right)\text{Å}$ and exhibits long-range FM order with the specific heat $C_p$ exhibiting a peak at $T_C=7.2\text{K}$ at the Curie temperature. A Curie-Weiss fit of the magnetic susceptibility yielded ${\mu }_{\text{eff}}=7.49{\mu }_B/\text{Tm}$ $\left({\text{Tm}}^{3+}\right)$ and weak FM interactions. A Schottky anomaly in $C_p$ was used to investigate crystal electric field (CEF) effects. From a measurement of $C_p\left(T\right)$ of the isostructural ${\text{LuB}}_2$ the magnetic entropy $S_{\text{mag}}$ of ${\text{TmB}}_2$ is determined. The ordered state of the Tm ions involves three CEF levels. Electronic-structure calculations, performed within the local spin density approximation, indicate a Ruderman-Kittel-Kasuya-Yoshida-type mechanism for the magnetic order. With respect to the total energy, ferromagnetic order is found to be more stable than the $A$-type antiferromagnetically ordered state, in agreement with the experiment.

Figure 1

Crystal structure determination of ${\text{TmB}}_2$: (top) X-ray powder-diffraction pattern. Calculated (line) and experimental (points) data are shown together with the difference plot and calculated peak positions (ticks). (bottom) View of the crystal structure along [001]. Three-bonded boron atoms form graphitelike layers with $d\left(\text{B-B}\right)=1.882\text{Å}$.

Figure 2

(Color online) Temperature dependence of the (a) magnetic susceptibility at 100 Oe (dots), 1 kOe (crosses), and 10 kOe (open squares) and (b) inverse magnetic susceptibility at 10 kOe of ${\text{TmB}}_2$. In (a) both zero-field-cooled (zfc) and field-cooled (fc) curves are plotted for 100 Oe, while the fc curve is plotted for 1 kOe and the zfc curve for 10 kOe. The line in (b) indicates the $50\text{K}\ge T\ge 400\text{K}$ fit to the Curie-Weiss law: $1/\chi =\left(T-{\theta }_{\text{CW}}\right)/C$, yielding $C=7.0\text{emu}\text{K}/\text{mol}$ and ${\theta }_{\text{CW}}=4.8\text{K}$. The arrow indicates the start of the visible deviation at $\approx 30\text{K}$.

Figure 3

Magnetization of ${\text{TmB}}_2$ at 1.8 K for a sample which was aligned in paraffin at 90 kOe (circles) and a randomly oriented fixed sample (crosses).

Figure 4

Temperature dependence of the specific heat $C_p$ of ${\text{TmB}}_2$ and ${\text{LuB}}_2$. The arrows indicate $T_C=7.2\text{K}$ and the hump commencing below 30 K.

Figure 5

Temperature dependence of the magnetic specific heat $C_{\text{mag}}$ and entropy $S_{\text{mag}}$ of ${\text{TmB}}_2$. The line depicts the extrapolation of $C_{\text{mag}}$ below 1.9 K, which was determined by fitting the $1.97\text{K}\le T\le 6.2\text{K}$ data by a power-law function to obtain parameters of $B{T}^{\alpha }$ $\left(B=0.358\text{J}{\text{K}}^{-1}{\text{mol}}^{-1},\alpha =1.80\right)$.

Figure 6

Temperature dependence of the specific heat $C_p\left(T,H\right)$ in various magnetic fields for ${\text{TmB}}_2$. 0 Oe (closed circles), 10 kOe (crosses), 20 kOe (open triangles), 40 kOe (closed triangles), 60 kOe (closed squares), and 90 kOe (open circles).

Figure 7

(Color) Electronic density of states (DOS) for ${\text{TmB}}_2$. Total DOS is shown together with the contributions of thulium and boron for spin-polarized states (top). DOS of ${\text{TmB}}_2$ excluding $f$ states compared with total DOS of ${\text{YB}}_2$ (middle). Total DOS of ${\text{TmB}}_2$ plotted with $\text{B}\left(2p\right)$ and $\text{Tm}\left(5d\right)$ contributions (bottom).