Metamagnetic transition in single-crystalline UIr\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{2}$$\end{document}2Si\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{2}$$\end{document}2

A single crystal of the ternary uranium silicide UIr\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{2}$$\end{document}2Si\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{2}$$\end{document}2 was studied by means of of X-ray diffraction, magnetization, heat capacity and electrical transport measurements. The studied compound orders antiferromagnetically at the Néel temperature of 5.5 K and undergoes a metamagnetic transition at 1.8 K in a field of 1.52 T. The metamagnetic transition has a spin-flop character.

cated that the prepared crystal was homogeneous and single phase.The EDX analysis yielded the composition to be U-18.7(6)at.%, Ir-37.9(5)at.%, Si-43.3(5) at.%, which corresponds to the formula U 0.9±0.1 Ir 1.9±0.1 Si 2.2±0.1 close to the nominal one, with an excess of Si.
X-ray diffraction measurements performed on a single crystal of UIr 2 Si 2 confirmed that the compound crystallizes with the tetragonal primitive CaBe 2 Ge 2 -type unit cell (space group P4/nmm).Although the crystal structure is centrosymmetric, the U atoms are located in a non-centrosymmetric position C 4v (4mm in Hermann- Mauguin notation).The crystal structure of UIr 2 Si 2 is shown in Fig. 1a.To refine the crystal structure, a two-step approach was employed.First, the initial assumption that all crystallographic positions were fully occupied was made.Then, a slight crystallographic disorder was introduced, the presence of which is reflected in other physical properties, as discussed below.It should be recalled that the previous reports revealed crystallographic disorder in UIr 2 Si 2 due to understoichiometry of Ir 18 .
Four models of the crystal structure of UIr 2 Si 2 were considered: (i) deficiency of both Ir and Si atoms at the 2c positions, (ii) deficiency of Ir and Si at the 2c position with some admixture of Si at the Ir 2c site and not fully occupied Si position, (iii) slight mixing of Ir and Si at the 2c atomic positions with the assumption that composition of the crystal is a nominal one, (iv) small admixture of Si at the Ir 2c position.All these models are reasonable and give very similar refinement parameters.However, owing to the EDX reasults, that show an excess of Si, the model (iv), which gives the largest excess of Si, was considered as the most probable.The details of the refinement and the obtained crystallographic data are given in Tables 1, 2, and 3.   Low-field properties.Figure 1b shows the temperature dependence of the inverse molar magnetic susceptibility, χ −1 (T) of UIr 2 Si 2 measured in a magnetic field of 0.1 T applied parallel and perpendicular to the c axis of the tetragonal unit cell.It is noteworthy that the variation measured along the c axis is strongly bent at lower temperatures and, remarkably, two χ(T) curves cross each other at about 60 K.Such a behavior, marking changes in magnetocrystalline anisotropy, has been reported previously for this compound 14 .Interestingly, it was also observed for UIrSi 3 , which crystallizes with a closely related crystal structure 23 .Above 50 K, both variations fol- low a modified Curie-Weiss (MCW) law: , where µ eff is the magnetic effective moment, θ P stands for the paramagnetic Curie temperature, and χ 0 is the temperature independent Pauli-like susceptibil- ity.The least-square fitting of the formula to the experimental data yielded χ 0 = 9 × 10 −4 emu/mol, µ eff = 2.17 µ B , and θ P = −75 K for H a , and χ 0 = 1.4 × 10 −3 emu/mol, µ eff = 1.5 µ B , and θ P = −12 K for H c .The µ eff is much smaller than those predicted for free U 3+ and U 4+ ions (3.62 and 3.58 µ B , respectively), which can be ascribed to crystal field effects and possibly also partial delocalization of U 5f electrons.θ P is nega- tive and has a large absolute value similar to those reported previously 19 .The low-temperature dependencies of the magnetic susceptibility of single-crystalline UIr 2 Si 2 , are shown in the lower inset of Fig. 1b.The compound exhibits a distinct magnetocrystalline anisotropy with the magnetization component measured along the c axis being distinctly larger than that taken along the a axis.This result is in agreement with the previous reports 14,18 and the neutron diffraction experiments 19 .At low temperatures, both χ(T) variations show maxima signaling the onset of the antiferromagnetic ordering.Below the Néel temperature, χ c does not decrease monotonically, but forms a shallow minimum followed by a slight upturn.Such a feature is not expected for simple antiferromagnets and may indicate more complicated magnetic structure in UIr 2 Si 2 than reported before 19 .Very similar behavior of the magnetic susceptibility was observed also by Vernière 18 .The Néel temperature determined as the inflection points on the χT(T) variations 24 equals 5.5 K (see the upper inset to Fig. 1b), i.e within the reported previously range (4.9-6 K) 14,18 .
The temperature dependencies of the electrical resistivity of single-crystalline UIr 2 Si 2 , ρ (T) and ρ ⊥ (T) , meas- ured with the electric current flowing along and perpendicular to the c axis, respectively, are shown in Fig. 1c.The resistivity shows a distinct anisotropy with the component measured along the four-fold axis being much larger than that measured perpendicular to it.This feature is characteristic of UT 2 M 2 compounds that adapt the CaBe 2 Ge 2 -type structure 25 .Closely related intermetallics crystallizing with the ThCr 2 Si 2 -type unit cell show a dif- ferent anisotropy with smaller resistivity along the tetragonal axis 25 .At room temperature, ρ � = 400 µ� cm and ρ ⊥ = 240 µ� cm .With decreasing temperature ρ initially increases, undergoes a broad maximum at 80 K and then decreases down to 2 K.In turn, ρ ⊥ decreases monotonically down to the lowest temperatures.A significant feature of both ρ(T) components is a rather high magnitude of the residual resistivity, being ρ � = 309 µ� cm and ρ ⊥ = 95 µ� cm at 2 K.The residual resistivity ratio RRR defined as ρ(300 K)/ρ(2 K) equals to 1.3 and 2.5 for j c and j ⊥ c , respectively.Large values of ρ(2 K) and thus small values of RRR can be linked to the atomic disorder at the Ir/Si positions in the studied crystal.As shown in the inset to Fig. 1c, at low temperatures both resistivity components form a knee-like anomaly associated with the magnetic ordering.The Néel temperature defined as the inflection points of these curves is equal to 5.3 K for both directions of the electric current.This value is very close to that obtained from the magnetic susceptibility data.
Figure 1d presents the temperature dependence of the specific heat of UIr 2 Si 2 , C p (T) .At room temperature, C p is nearly saturated at a value of 120 J mol −1 K −1 , which is close to the theoretical Dulong-Petit limit 3nR = 125 J mol −1 K −1 (where n = 5 is the number of atoms per molecule and R represents the universal gas constant).The onset of the antiferromagnetic state manifests itself as a distinct -like anomaly (see the lower inset to the figure).As can be inferred from the upper inset to Fig. 1d, the specific heat data can be well described below T N by the formula C p = γ T + βT 3 , where the first term represents the electronic contribution and the second one is the sum of the contributions due to antiferromagnetic magnons and phonons.The least-square fitting of the above equation to the experimental data yielded the parameters γ = 292 J mol −1 K −2 and β = 5.8 The value of γ is very close to that reported in the literature 14,19 .Its enhanced magnitude can be attributed to strong electronic correlations but may also result from the atomic disorder in the crystal structure of UIr 2 Si 2 revealed in the X-ray diffraction experiment and supported by the electrical resistivity data.

Metamagnetic transition. Figure 2a presents the magnetic field dependencies of the magnetization σ (H)
of the UIr 2 Si 2 single crystal measured at constant temperature of 2 K in a magnetic field applied along two Table 3. Anisotropic thermal displacement parameters for the atoms in UIr 2 Si 2 (in 10 −3 Å 2 ).The anisotropic displacemant factor exponent takes the form: principal directions.The variation taken along the a axis, σ a (H) , being the hard magnetic direction, is straight- linear up to a limiting field of 14 T. In contrast, the magnetization measured with the magnetic field applied along the c axis, σ c (T) , shows a rapid increase near 1.5 T, indicating a metamagnetic phase transition.Remark- ably, σ c (T) does not tend to saturate in strong magnetic fields, and at 14 T attains a value that corresponds to the magnetic moment of 0.43 µ B .This is much larger than the magnetic moment of 0.1 µ B /U atom revealed for UIr 2 Si 2 by neutron diffraction 19 .It has been suspected that magnetic field splits the excited crystal field dou- blet, located close to the ground state, and such a mixing with the excited crystal field level leads to enhanced magnetism 20 .Extrapolation of the σ a (H) and σ c (H) variations beyond investigated field range results in crossing near 80 T, that can be considered as a rough estimation of the magnetocrystalline anisotropy field.This value is similar to the magnetocrystalline anisotropy field of 59 T, derived for a closely related compound UIrSi 3 23 .
Figure 2b shows the magnetization data taken at 1.8 K in magnetic field in the range 1-2 T applied parallel to the four-fold axis.The left and right insets to the figure show the first and second order field derivatives of the magnetization dσ/dT and dσ 2 /d 2 T , respectively, taken with increasing magnetic field.As can be seen, the σ (H) variations do not overlap and show a very narrow hysteresis marking the first order of the transition, as expected for metamagnets 26 .The critical field H c1 was defined as an inflection point on the σ (H) variation (note a maximum in the first order derivative dσ/dH ) and amounts to 1.52 T. At the dσ/dH curve, above the maximum, there can be observed a distinct bump that can be linked to a slight kink in σ (H) occuring near 1.85 T (note a minimum in the second-order derivative).Such a feature suggests a spin-flop character of the metamagnetic transition, in agreement with the relatively small magnetic anisotropy in UIr 2 Si 2 .In stronger fields another phase transition, to the field-induced paramagnetic phase, can be expected, where the alignment of the magnetic moments changes continuously towards the easy direction 26,27 .
Figure 2c presents the magnetization isotherms measured at different temperatures.The inset shows the field derivatives of the magnetization.For each isotherm, the critical field H c1 was defined as a maximum in dσ/dH , while H c2 was defined as a kink on the σ (H) variation (an inflection point in dσ/dH above the hump).It was The lower inset shows the low- temperature region.The arrow marks the magnetic phase transition temperature.The upper inset presents the data plotted as C/T(T 2 ) .The solid line is a linear fit described in the text.
found that H c1 hardly depends on temperature up to 4 K, and then slightly decreases.In stronger fields, H c2 does not change up to 4.7 K, and cannot be identified at higher temperatures.The σ (H) variation measured at 6 K does not show any anomalies, and is typical of paramagnets.The so-determined values of the critical fields are plotted on a magnetic phase diagram presented in Fig. 3d.
Figure 2d shows the temperature dependencies of the magnetic susceptibility χ(T) measured in different mag- netic fields applied along the c axis.With increasing field up to 1 T, the maximum associated with the magnetic ordering shifts slightly towards lower temperatures, as expected for antiferromagnets.At stronger fields, above the metamagnetic transition field, the susceptibility increases down to the lowest temperatures measured, and does not show any anomaly.The Néel temperature, determined as a maximum on the d (χT)/dT variation (see the inset to Fig. 2c), is equal to 5.5 K for a magnetic field of 0.01 T. It hardly changes up to 0.5 T, and decreases down to 5 K for 1 T. The so-obtained data were added to Fig. 3d.
The low-temperature dependencies of the specific heat of UIr 2 Si 2 taken in zero and finite magnetic fields applied along the c axis are presented in Fig. 3a.With increasing field the -like maximum associated with the magnetic ordering shifts towards lower temperatures, broadens, and becomes smaller, in a manner typical of antiferromagnets.In a field of 1.5, that is the critical field of the metamagnetic transition, the maximum is superimposed on a broad hump.In stronger magnetic fields, this hump shifts towards higher temperatures, as expected for field-polarized paramagnets.The Néel temperature, defined as the maximum in the C p (T) variation, gradually shifts towards lower temperatures with increasing the magnetic field strength, and at 1.3 T T N is equal to 4.92 K.These data have also been included in the phase diagram shown in Fig. 3d.
The magnetic phase transitions in UIr 2 Si 2 are also well seen in the electrical transport data.Figure 3b, c present the field dependencies of the magnetoresistivity of the studied crystal, defined as measured with the magnetic field applied along the c axis and electric current j flowing parallel and perpendicular to the c axis, respectively.As can be seen in Fig. 3b, with increasing magnetic field, the transverse www.nature.com/scientificreports/magnetoresistivity �ρ/ρ ⊥ 0 measured below T N initially slightly decreases.The spin-flop transition manifests itself as a sudden drop in �ρ/ρ ⊥ 0 , down to a value of −11 % at 2 K in a field of 3 T.The critical field H c1 can be deter- mined for each isotherm by inspecting the field derivatives of the magnetoresistivity (cf. the inset to Fig. 3b).Generally, H c1 does not change much up to 4 K.It should be noted that no clear signature of the upper critical field H c2 is seen in the resistivity data.In the paramagnetic state, the transverse magnetoresistivity decreases monotonically over the entire field range and does not show any feature, as expected for paramagnets.
As apparent from Fig. 3c, the longitudinal magnetoresistivity �ρ/ρ 0 (H) is much smaller than the transverse one.The metamagnetic phase transition manifests itself as a maximum in �ρ/ρ 0 (H) .The variation measured at 2 K shows a distinct feature of 0.25 % at µ 0 H c1 = 1.5 T. Interestingly, at 3 K, the magnitude of the maximum associated with the metamagnetic transition increases up to 0.9%.Further increase of temperature results in decrease of the maximum.The feature marking H c1 remains almost temperature independent up to 4.25 K.In the paramagnetic region, the longitudinal magnetoresistivity does not show any anomaly, alike �ρ/ρ ⊥ 0 (H) .The so-obtained data points were added to Fig. 3d.

Conclusions
The silicide UIr 2 Si 2 crystallizes with a locally non-centrosymmetric tetragonal crystal structure of the CaBe 2 Ge 2 type.The compound orders antiferromagnetically below the Néel temperature of 5.5 K.The antiferromagnetic phase transition manifests itself as a maximum in the magnetic susceptibility, a knee-like anomaly in the electrical resistivity and a distinct -like anomaly in the specific heat.UIr 2 Si 2 shows relatively small magnetic anisotropy with the easy magnetic direction oriented along the c axis.The magnetic properties are fairly robust in magnetic fields up to 14 T applied along the a axis of the tetragonal unit cell.On the contrary, the compound undergoes a metamagnetic transition in fields applied along the c axis.At 1.8 K, the critical field is about 1.5 T. This transition gives rise to distinct features in the low-temperature field dependencies of the magnetization and the magnetoresistance.Furthermore, in magnetic fields stronger than 1.5 T, the temperature variations of the magnetization and the heat capacity distinctly change their character.
Combining the data from the magnetization, specific heat, electrical resistivity, and magnetoresistivity measurements, the magnetic phase diagram of UIr 2 Si 2 was constructed, which is presented in Fig. 3d.In zero field, the investigated crystal was found to order antiferromagnetically at T N = 5.5 K. Below the Néel temperature, the field-induced metamagnetic transition to the spin-flop state was established, followed by another transition to the field-induced paramagnetic phase.At 1.8 K, the critical fields are relatively small being µ 0 H c1 = 1.52 T and µ 0 H c2 = 1.85 T at 1.8 K.
The magnetic phase diagram derived for UIr 2 Si 2 can be compared with that obtained for a closely related compound UIrSi 3 .The latter crystallizes with a similar crystal structure, also being derivative of the BaAl 4 -type, in which the U atoms are located at a non-centrosymmetric position 23,28 .The magnetic anisotropy in the latter compound is similar, with the easy magnetic direction along the c axis.Also the magnetocrystalline anisotropy field estimated for both compounds has similar values.UIrSi 3 orders antiferromagnetically at T N = 41.7 K , which is much larger than T N of UIr 2 Si 2 .At low temperatures, UIrSi 3 undergoes a first-order metamagnetic transition, characterized by rather small critical field, compared to its T N (7.3 T at 2 K).At the critical field, the measured physical characteristics show wide hysteresis loops (different from UIr 2 Si 2 ), which narrow and shift towards lower fields with increasing magnetic field strength.With increasing temperature, the character of the transition changes to the second order, and a tricritical point in the phase diagram occurs at T = 28 K and µ 0 H = 5.8 T.

Methods
A single crystal of UIr 2 Si 2 was grown by the Czochralski pulling technique in an ultra-pure Ar atmosphere using a tetra-arc furnace (GES Corporation).The starting components were high-purity elements (U-3N,Ir-3N, and Si-6N).The obtained crystal was a rod of approximately 4 mm in diameter and 15 mm in length.
The crystal homogeneity was checked by energy dispersive X-ray spectroscopy analysis performed on an FEI scanning electron microscope equipped with an EDAX Genesis XM4 spectrometer.
The Oxford X'Calibur four-circle single-crystal diffractometer, equipped with a CCD camera and graphitemonochromated MoKα radiation ( = 0.71073 Å), was used to collect X-ray diffraction data at room temperature from a single crystal with dimensions of 0.08 × 0.07 × 0.05 mm.The data collection and reduction were performed with CrysAlis PRO software (1.171.39.46 and 1.171.41.93a,Rigaku Oxford Diffraction, 2018 and 2020).Absorption was corrected based on Gaussian integration over a multifaceted crystal model.The structure was solved by direct methods and refined using the SHELX-2014 crystallographic software package 29 in cooperation with the graphical user interface of Olex2 30 .
Magnetic properties measurements were performed in the temperature range 1.8-300 K in magnetic fields up to 7 T using a Quantum Design MPMS-7 superconducting quantum interference device (SQUID) magnetometer, and up to 14 T employing a Quantum Design PPMS-14 platform equipped with a vibrating sample magnetometer.The heat capacity was measured in the temperature interval 2-300 K and in magnetic fields up to 5 T, using a relaxation technique.The temperature and magnetic field variations of the electrical resistivity were studied from 2 to 300 K, in magnetic fields up to 14 T, employing a standard ac four-probe method.For these measurements a Quantum Design PPMS-9 and PPMS-14 platforms were employed.

Figure 1 .
Figure 1.(a) Crystal structure of UIr 2 Si 2 . (b) Temperature dependences of the reciprocal molar magnetic susceptibility of single crystalline UIr 2 Si 2 recorded in a magnetic field 0.1 T applied along a and c axes of the tetragonal unit cell.Solid line represents fit of the modified Curie-Weiss law.The lower inset shows the lowtemperature magnetic susceptibility data.The upper inset presents derivative curves d(χ T)/dT.(c) Temperature variation of the electrical resistivity of single-crystalline UIr 2 Si 2 measured with the electric current flowing along two main crystallgraphic directions.The inset presents low-temperature data.The arrows mark the Néel temperature.(d) Specific heat of UIr 2 Si 2 as a function of the temperature.The lower inset shows the low- temperature region.The arrow marks the magnetic phase transition temperature.The upper inset presents the data plotted as C/T(T 2 ) .The solid line is a linear fit described in the text.

Figure 2 .
Figure 2. (a) Magnetization of UIr 2 Si 3 measured as a function of the external magnetic field oriented along a and c axes of the tetragonal unit cell, at a constant temperature of 2 K.(b) The magnetization measured with increasing (full circles) and decreasing (open circles) magnetic field applied along the c axis, close to the magnetic transitions.Arrows mark H c1 and H c2 .Insets present first and second order field derivatives of the magnetization taken with increasing field.Arrows mark H c2 .(c) Field dependencies of the magnetization measured along the c axis with increasing and decreasing magnetic field (full and open symbols respectively) at several temperatures.The inset presents magnetic field derivatives of the magnetization.(d) Temperature dependencies the magnetic susceptibility measured at various magnetic fields oriented along the c axis.The inset presents the temperature derivatives ( dχ)T/dT.

Figure 3 .
Figure 3. (a) Specific heat of UIr 2 Si 2 measured at low temperatures with magnetic field applied along the c axis.(b) Magnetic field dependence of the transverse magnetoresistivity measures at different temperatures with j a and H c . (c) Longitudinal magnetoresistivity as a function of magnetic field measured at several temperatures with j H c .(d) Magnetic phase diagram of UIr 2 Si 2 .

Table 1 .
Crystallographic and structure refinement data for UIr 2 Si 2 .

Table 2 .
Atomic coordinates, atomic populations, and equivalent isotropic thermal displacement parameters for UIr 2 Si 2 .U eq is defined as one third of the trace of the orthogonalized U ij tensor.