Moment canting and domain effects in antiferromagnetic ${\mathrm{DyRh}}_2{\mathrm{Si}}_2$

A combined experimental and theoretical study of the layered antiferromagnetic compound ${\mathrm{DyRh}}_2{\mathrm{Si}}_2$ in the ${\mathrm{ThCr}}_2{\mathrm{Si}}_2$-type structure is presented. The heat capacity shows two transitions upon cooling: The first one at the Néel temperature $T_{\mathrm{N}}=55\mathrm{K}$ and a second one at $T_{\mathrm{N}2}=12\mathrm{K}$. Using magnetization measurements, we study the canting process of the Dy moments upon changing the temperature and can assign $T_{\mathrm{N}2}$ to the onset of the canting of the magnetic moments towards the [100] direction away from the $c$ axis. Furthermore, we found that the field dependence of the magnetization is highly anisotropic and shows a two-step process for $H\parallel 001$. We used a mean-field model to determine the crystalline electric field as well as the exchange interaction parameters. Our magnetization data together with the calculations reveal a moment orientation close to the [101] direction in the tetragonal structure at low temperatures and fields. Applying photoemission electron microscopy, we explore the (001) surface of the cleaved ${\mathrm{DyRh}}_2{\mathrm{Si}}_2$ single crystal and visualize Si- and Dy-terminated surfaces. Our results indicate that the Si-Rh-Si surface protects the deeper lying magnetically active Dy layers and is thus attractive for investigation of magnetic domains and their properties in the large family of ${\mathrm{LnT}}_2{\mathrm{Si}}_2$ materials.

Figure 1

Magnetic properties of ${\mathrm{DyRh}}_2{\mathrm{Si}}_2$. (a) Magnetic susceptibility at 1 T for three different field directions. An enlarged view of the low-temperature data is shown in the inset (b) for the in-plane fields. Solid lines result from the CEF model. (c) CEF-split $4f$ levels with each level being doubly degenerate. The ground state in the PM phase is an almost pure ($99\%$) $M_J=13/2$ state.

Figure 2

(a) Field dependence of the magnetization per ${\mathrm{Dy}}^{3+}$ at $T=1.8\mathrm{K}$ measured with $H\parallel 100$ (black), $H\parallel 110$ (blue), and $H\parallel 001$ (red). The simulated data are shown by gray, light-blue, and brown lines. (b) For $H\parallel 100$ and $H\parallel 110$, a reorientation of magnetic domains and a metamagnetic transition occur at small fields. Insets (c) and (d) for $H\parallel 001$, $M\left(H\right)$ shows a small hysteresis around the critical fields ${\mu }_0{H}_1^{001}$ and ${\mu }_0{H}_2^{001}$.

Figure 3

Temperature-dependent susceptibility for the three main symmetry directions with ${\mu }_{0}H=0.01\mathrm{T}$. In the inset, a schematic drawing of the experimental setup is shown for $H\perp 001$ of the sample $s$.

Figure 4

Inverse susceptibility measured at ${\mu }_{0}H=1\mathrm{T}$. Solid gray and black lines indicate the region of the Curie-Weiss fit above $150\mathrm{K}$.

Figure 5

${\mu }_{0}H\text{−}T$ phase diagram for $H\parallel 001$. In ${\mathrm{DyRh}}_2{\mathrm{Si}}_2$, upon increasing the field, the magnetic configuration changes in two steps from $+-+-$ (AFM I) to $+++-$ (AFM II) before reaching the $++++$ field-polarized (FP) state. Upon increasing the temperature, the paramagnetic (PM) state is reached. Red circles mark transitions extracted from $M\left(H\right)$ data and triangles were extracted from ${\chi }_{\mathrm{mol}}\left(T\right)$. Brown diamonds and stars show the result of the simulation of $M\left(H\right)$ and ${\chi }_{\mathrm{mol}}\left(T\right)$.

Figure 6

Comparison of the low-field behavior of $\mathbf{M}·\mathbf{H}/H^2$ vs ${\left({\mu }_{0}H\right)}^2$ at $T=1.8\mathrm{K}$ for increasing $H$ along the three main symmetry directions.

Figure 7

$\mathbf{M}·\mathbf{H}/H^2$ versus ${\mu }_{0}H$ for $H\parallel 100$. Below $10\mathrm{K}$, a strong change of slope and a small AFM hysteresis occur which indicates the reorientation of magnetic domains.

Figure 8

${\mu }_{0}H\text{−}T$ phase diagram for $H\parallel 110$. Circles mark transitions extracted from $M\left(H\right)$ data and triangles were extracted from ${\chi }_{\mathrm{mol}}\left(T\right)$. Diamonds show the results of the simulations.

Figure 9

(a) Heat capacity of ${\mathrm{DyRh}}_2{\mathrm{Si}}_2$ and ${\mathrm{LuRh}}_2{\mathrm{Si}}_2$ [35]. (b) $C/T$ versus $T^2$ of ${\mathrm{DyRh}}_2{\mathrm{Si}}_2$ does not show linear behavior below $10\mathrm{K}$, which hinders the determination of the Sommerfeld coefficient and hints at a magnon contribution to the heat capacity below $T_{\mathrm{N}2}$. (c) The magnetic part of the heat capacity, $C^{4f}$, was determined by using the nonmagnetic reference ${\mathrm{LuRh}}_2{\mathrm{Si}}_2$ [gray symbols in (b)].

Figure 10

Magnetic entropy, $S^{4f}$, of ${\mathrm{DyRh}}_2{\mathrm{Si}}_2$. The experimental data were obtained from $C^{4f}$ after subtracting the data of the nonmagnetic reference (gray solid line). The simulation is shown in black.

Figure 11

Normalized resistivity of ${\mathrm{DyRh}}_2{\mathrm{Si}}_2$.

Figure 12

Spectromicroscopic insight into the surface terminations of ${\mathrm{DyRh}}_2{\mathrm{Si}}_2$. (a) Representative XPEEM image showing a $(20\times 20)\mu {\mathrm{m}}^2$ area of the (001) surface from a cleaved ${\mathrm{DyRh}}_2{\mathrm{Si}}_2$ single crystal at a temperature of 30 K using a photon energy of 170 eV. The image results from integration over kinetic energies of the photoelectrons ranging from 150 to 170 eV. Bright and dark regions reflect surface areas with Dy and Si terminations, respectively. (b) Dy $4f$ photoemission spectra derived from the bright and dark areas in the XPEEM image that are highlighted by red and cyan squares, respectively. (c) Calculated $M_J$-dependent Dy $4f$ spectra for the geometry of the XPEEM measurements. The calculated spectrum that shows the best agreement with the experimental one taken from the Si surface is highlighted in cyan.