Magnetism in polymorphic phases: Case of ${\text{PrIr}}_2{\text{Si}}_2$

We have pursued a comparative study of magnetism in the two polymorphic phases of ${\text{PrIr}}_2{\text{Si}}_2$ in order to demonstrate how magnetism is influenced by changing the crystallographic symmetry while the chemical composition remains conserved. For this purpose we have prepared single crystals of the $\alpha$ and $\beta$ phase of ${\text{PrIr}}_2{\text{Si}}_2$, and measured magnetization, ac susceptibility, specific heat, and electrical resistivity as functions of temperature and magnetic field and performed neutron-diffraction experiments in magnetic field. We have confirmed that the $\beta$ phase remains paramagnetic down to 2 K whereas the $\alpha$ phase exhibits ordering of the Pr magnetic moments at temperatures lower than $T_N=45.5\text{K}$. We have found two different magnetic structures: the first a longitudinal sine-modulated structure with a magnetic propagation vector $\mathit{k}=\left(005/6\right)$ at temperatures $23.7<T<45.5\text{K}$ and the second a simple antiferromagnetic structure with $\mathit{k}=\left(001\right)$ for $T<23.7\text{K}$. The phases can be destabilized by applying a magnetic field along the $c$ axis while they remain intact if the magnetic field is applied along the $a$ axis. In both magnetic phases, the ${\text{Pr}}^{3+}$ ion has a stable magnetic moment of $3.2{\mu }_B$. Another striking difference in magnetism between the $\alpha$ and $\beta$ phase of ${\text{PrIr}}_2{\text{Si}}_2$ is observed in the type of magnetocrystalline anisotropy, easy axis (easy plane) in the $\alpha$ phase ($\beta$ phase). The different anisotropy types for the $\alpha$ and $\beta$ phase are corroborated by results obtained from first-principles crystal-field calculations based on density-functional theory.

Figure 1

The specific heat of ${\text{LaIr}}_2{\text{Si}}_2$. The lines represent the best fit due to electronic and phonon contribution as described in the text.

Figure 2

The magnetic part of the specific heat of $\beta {\text{-PrIr}}_2{\text{Si}}_2$ plotted together with the calculated corresponding magnetic entropy. The solid line in the figure represents the best fit due to the Schottky contribution.

Figure 3

The inverse susceptibility of the $\beta$ phase. The lines represent the best fit with the Curie-Weiss law.

Figure 4

The magnetization curves of the $\beta$ phase measured up to 40 T at $T=4.2\text{K}$. The line represents the best fit according to Eq. (5) in the main text.

Figure 5

The low-temperature detail of the resistivity of $\beta {\text{-PrIr}}_2{\text{Si}}_2$.

Figure 6

The magnetic part of the specific heat of $\alpha {\text{-PrIr}}_2{\text{Si}}_2$ plotted together with the calculated corresponding magnetic entropy.

Figure 7

The low-temperature detail of the $\alpha$-phase specific heat shows the upturn caused by the nuclear contribution to the specific heat. The line represents the best fit using the Eq. (7).

Figure 8

ac susceptibility of $\alpha {\text{-PrIr}}_2{\text{Si}}_2$ measured with driving frequency of 1000 Hz with a driving field amplitude of 0.001 T applied along the $c$ axis. The upturn of the data for temperatures below 5 K is probably the impurity effect.

Figure 9

The inverse susceptibility of the $\alpha$ phase. The lines represent the best fit with the Curie-Weiss law.

Figure 10

High-field experiment on the mixed single-crystal sample (approximately 76.7% of $\alpha$ phase, and 23.3% of $\beta$ phase). The field was applied along the $c$ axis, which is common for both phases. To simplify the figure, we have plotted only representative curves. The solid line represents the recalculated data for 100% of the $\alpha$ phase.

Figure 11

Comparative neutron powder patterns for the $\alpha {\text{-PrIr}}_2{\text{Si}}_2$. The peak at $62.9°$ is from the (111) reflection of the aluminum sample holder.

Figure 12

Final Rietveld fit to the $\alpha {\text{-PrIr}}_2{\text{Si}}_2$ data at (a) 1.5 K and (b) 30 K. The observed data are circles, the fit a solid line, and the difference curve is plotted below. The tick marks show the allowed reflections.

Figure 13

The integrated intensity of $\left(-1-11\right)$ magnetic reflection with respect to temperature and to applied magnetic field.

Figure 14

The raw data scans from the single-crystal neutron-diffraction experiment on the $\alpha$ phase. The position $\omega =9°$, $2\theta =51.6°$ is the diffraction position for the $\left(-1-11\right)$ reflection. (a) The ZFC data obtained at $B=6\text{T}$. The mask on the 2D detector was centered to $51.6°$ in $2\theta$. (b) The same scans as in (a) but the mask on the 2D detector was centered to $50.4°$. (c) The FC data obtained at $B=6\text{T}$. The mask on the 2D detector was centered to $51°$ in $2\theta$. To keep the figure simple, only representative scans are plotted.

Figure 15

The low-temperature detail of the resistivity of $\alpha {\text{-PrIr}}_2{\text{Si}}_2$: (a) $i\parallel a$; $B\parallel c$; (b) $i\parallel c$; $B\parallel a$.

Figure 16

The transverse magnetoresistivity of $\alpha {\text{-PrIr}}_2{\text{Si}}_2$ in the experimental configuration $i\parallel a$; $B\parallel c$. The lines are guides for the eye.

Figure 17

The phase diagram of the $\alpha$ phase for the magnetic field applied along the $c$ axis constructed using the specific-heat data (squares), $M\left(T\right)$ data (circles), static field $M\left(B\right)$ data (both types of triangles), and pulsed magnetic field data (diamonds). The lines are only guides for the eye.