Magnetic phase diagram of YbCo${}_2$Si${}_2$ derived from magnetization measurements

We report on high-resolution dc-magnetization $M$ measurements on a high-quality single crystal of YbCo${}_2$Si${}_2$. $M$ was measured down to 0.05 K and in fields up to 3 T, with the magnetic field oriented along the crystallographic directions $\left[100\right]$, $\left[110\right]$, and $\left[001\right]$ of the tetragonal structure. In a small field ${\mu }_{0}H=0.1$ T two antiferromagnetic (AFM) phase transitions have been detected at $T_N=1.75$ K and $T_L=0.9$ K, in the form of a sharp cusp and a sudden drop in $\chi =M/H$. These signatures confirm that the phase transitions are second order at $T_N$ and first order at $T_L$. The AFM order is completely suppressed by fields as high as ${\mu }_0{H}_N\left(0\right)=1.9$, 1.88, and 2.35 T for $H\parallel \left[100\right]$, $\left[110\right]$, and $\left[001\right]$, respectively. At these fields, $M$ reaches its saturation values $M_s(H\parallel \left[100\right])\approx 1.4{\mu }_B$ and $M_s(H\parallel \left[001\right])\approx 0.68{\mu }_B$, which match quite well those calculated for the ${\Gamma }_7$ ground state proposed in C. Klingner, C. Krellner, M. Brando, C. Geibel, and F. Steglich [New J. Phys. 13, 083024 (2011)] and which confirm the trivalent state of the Yb ions in YbCo${}_2$Si${}_2$. We have derived the $H$-$T$ phase diagrams along the three crystallographic directions from isothermal and isofield measurements. Four AFM regions can be identified for $H$ parallel to $\left[100\right]$ and $\left[110\right]$, which are separated by first- and second-order phase-transition lines, showing anisotropy in the basal plane. For $H$ parallel to $\left[001\right]$ only two AFM phases have been observed. The phase boundary $T_N\left(H\right)$, which separated the AFM phase from the paramagnetic one, can be well described by the empirical relation ${[H_N\left(T\right)/H_N\left(0\right)]}^n+{[T/T_N\left(0\right)]}^n=1$ with $n$ close to 2.

Figure 1

Magnetic susceptibility $\chi =M/H$, plotted as a function of $T$, in external magnetic fields applied along three crystallographic directions. The curves at different fields have been offset for clarity. $T_N$ denotes the upper AFM transition temperature, and $T_L$ denotes the lower one. $T_N^{\prime }$ defines the temperature down to which the susceptibility stays constant below $T_N$, thereafter decreasing. The arrows indicate the evolution of the transition temperatures with increasing magnetic field.

Figure 2

Uniform susceptibility plotted as a function of $T^4$ to emphasize the behavior below the lower AFM transition temperature $T_L$ (indicated by arrows).

Figure 3

Top panel: $M$ vs $H$ at four selected temperatures with $H\parallel \left[100\right]$. $H_N$ denotes the critical field associated with the transition at $T_N$. In the inset we zoom on the metamagnetic-like transitions to emphasize the hysteresis loop at 0.05 K; the arrows indicate the field sweep direction. In the bottom panels, the derivative of the isothermal magnetization is plotted at 0.5, 0.65, and 0.8 K. The two metamagnetic-like transitions visible at 0.5 K join each other to become one at 0.65 K and split again at 0.8 K. This feature is clearer in $dM/dH$ (bottom panels). We have associated the fields $H_N^{\prime }$ and $H_L$ with the transitions at $T_N^{\prime }$ and $T_L$, respectively.

Figure 4

Top panel: $M$ vs $H$ at three selected temperatures with $H\parallel \left[110\right]$. Bottom panels: $dM/dH$ vs $H$ at the same three temperatures. $H_N$ and $H_N^{\prime }$ denote the critical fields associated with the transitions at $T_N$ and $T_N^{\prime }$, respectively.

Figure 5

Top panel: $M$ vs $H$ at six selected temperatures with $H\parallel \left[001\right]$. Bottom panel: $dM/dH$ vs $H$ at the same six temperatures. $H_N$ and $H_L$ denote the critical fields associated with the transitions at $T_N$ and $T_L$, respectively. The arrows indicate the evolution of the critical fields with increasing temperature.

Figure 6

Magnetic phase diagram of YbCo${}_2$Si${}_2$ with $H\parallel \left[100\right]$, $\left[110\right]$, and $\left[001\right]$. The square and circle points have been extracted from isofield and isothermal measurements of $M$, respectively. PM indicates the paramagnetic region, while AFM indicates the antiferromagnetic one. The four different AFM phases are labeled from I to IV. The solid lines represent phase transition lines at which the propagation vector $\mathbf{Q}$ changes, whereas the dashed lines mark the reorientation of the moments. The border between the PM and the AFM regions has been fitted with the empirical curve ${[H_N\left(T\right)/H_N\left(0\right)]}^n+{[T/T_N\left(0\right)]}^n=1$, where $T_N\left(0\right)=1.77$ K, ${\mu }_0{H}_N\left(0\right)=1.9$, 1.88, and 2.35 T, and $n=1.9$, 1.78, and 1.94 for $H\parallel \left[100\right]$, $\left[110\right]$, and $\left[001\right]$, respectively.

Figure 7

Temperature dependence of the ac susceptibility ${\chi }^{\prime }\left(T\right)$ measured at different external magnetic fields. The arrows indicate the maximum observed only at high fields. The inset shows the magnetic phase diagram with $H\parallel \left[100\right]$ in which we have included the points extracted from the maxima of ${\chi }^{\prime }\left(T\right)$. The temperature scale was cut to optimize the drawing space.