- Email: [email protected]
Pressure variations of the 5f magnetism in UH3
Journal Pre-proofs Pressure variations of the 5f magnetism in UH3 J. Prchal, V. Buturlim, J. Valenta, M. Dopita, M. Divis, I. Turek, L. Kyvala, D. Legut, L. Havela PII: DOI: Reference:
S0304-8853(19)32272-3 https://doi.org/10.1016/j.jmmm.2019.165993 MAGMA 165993
To appear in:
Journal of Magnetism and Magnetic Materials
Received Date: Revised Date: Accepted Date:
2 July 2019 8 October 2019 15 October 2019
Please cite this article as: J. Prchal, V. Buturlim, J. Valenta, M. Dopita, M. Divis, I. Turek, L. Kyvala, D. Legut, L. Havela, Pressure variations of the 5f magnetism in UH3, Journal of Magnetism and Magnetic Materials (2019), doi: https://doi.org/10.1016/j.jmmm.2019.165993
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
© 2019 Published by Elsevier B.V.
Pressure variations of the 5f magnetism in UH3 J. Prchal1, V. Buturlim1, J. Valenta1, M. Dopita1, M. Divis1, I. Turek1, L. Kyvala2, D. Legut2, L. Havela1 1
Department of Condensed Matter Physics, Faculty of Mathematics and Physics, Charles University, Ke Karlovu 5, 121 16 Prague 2, Czech Republic 2 IT4Innovations, VSB-Technical University of Ostrava, 17.listopadu 2172/15, 708 00 Ostrava, Czech Republic Abstract Pressure variations of the Curie temperature of the 5f ferromagnet -UH3 were studied using the Mo-alloyed hydride (UH3)0.82Mo0.18, which is stable in air and has very similar TC and magnetization per U atom. By means of ac magnetic susceptibility a linear decrease of TC was observed for pressures up to 3.2 GPa. The coefficient dTC/dp = -2.05 K/GPa gives dlnTC/dp = 1/T*dTC/dp ≈ -0.011 GPa-1. This value is smaller than expected for a 5f-band ferromagnet with relatively short U-U distances and suggests that UH3 may be more localized than expected. Among AnX compounds, similar dependence was found e.g. for US. Revisiting existing data on lattice elasticity for -UH3, bulk modulus B ≈ 100 GPa can be assumed, leading to dlnTC/dlnV = 1.1. Experimental data are confronted with results of GGA+U electronic structure calculations. Plausible values of direct Coulomb U and Hund’s exchange J are deduced. The lattice compression was found to reduce predominantly the orbital moments.
Keywords: Uranium hydrides; Ferromagnetism; Bulk modulus; High pressures; Ab initio calculations
1. INTRODUCTION Magnetic properties of uranium systems are affected by the open 5f shell, which is the characteristic of the actinide series. The 5f electronic states tend to the localization, analogous to 4f states in lanthanides, for heavy actinides. On the other hand, 5f states in light actinides (up to plutonium with atomic number Z = 94) can be involved in metallic bonds, i.e. itinerant, and they resemble more transition metals, albeit with a strong spin-orbit interaction. In a broad crossover region, the degree of localization cannot be simply deduced from experimental observables, as no single property gives a clear quantification of the regime of the 5f states. Not only that there is no simple way to interpolate between the description using the Bloch waves and atomic wave functions, but a higher level of complexity can arise, leading to non-trivial emergent phases as unusual types of magnetism, sometimes coexisting with anomalous superconductivity, charge density waves, etc. As some of measurable properties point to the 5f itinerant states, while other may evoke their localization, it is common to use the term of dual nature of the 5f states [1,2]. One of fundamental difficulties is that neither theoretical physics nor ab initio calculations can decide about the situation of the 5f states in such a complex regime. The reason is that differences of total energy between localized and Bloch-like 5f wave functions can be in the critical region very small, and the two situations cannot be safely treated on the same theoretical footing. Experimental data related to bulk and spectroscopic properties remain as necessary reference, guiding the calculations by providing a firm ground as well as stimulation by discoveries of new unexpected phenomena. Recent experimental effort in the field of light actinides has been naturally focused on materials exhibiting some of the exotic properties. The family of heavy fermion materials with record high effective masses of electrons at the Fermi level has been studied since 1980s [3]. The analogy with Ce-based heavy fermions led fast to a recognition on importance of electron-electron correlations, which sometimes yield superconductivity instead of more expected magnetic order. Several decades of research led to a recognition that such unconventional superconductivity just at the verge of magnetic order is rather a rule than an exception [4,5]. Very important in these efforts were studies under high pressure, used as a tool to tune magnetism to its suppression [6,7]. Now vast majority of experimental findings were collected, as to actinides, for U-based systems. Np and especially Pu, which is just at the localization threshold as a pure element, are more difficult to handle due to safety and security constraints. On the opposite side of the spectrum of U-based materials, where magnetism is rather stable, high pressure has been used to characterize its volume variations. In the limit of a band magnetism, a lattice compression due to applied pressure leads to a band broadening. The density of states at the Fermi level, N(EF), then typically decreases, which projects into reduction of ordered magnetic moments and ordering temperatures. In a case of localized magnetism, the moments are insensitive to commonly achievable pressure of several GPa, while their interaction can vary somewhat as a function of interatomic distance. Somewhere between the two limits a new type of regime was observed. Applying pressure the critical temperature starts first to increase dramatically, reaching a broad maximum and then turning down. Such a type of behavior can be qualitatively understood in a two-band model, in which the 5f states constituting magnetic moments interact predominately via more extended states. The coupling depends on the mutual hybridization, which becomes stronger at high pressures, but too strong hybridization tends to wash out the 5f moments, and magnetism is eventually suppressed. Such behavior has been indeed found at materials exhibiting local 5f
moments, i.e. ordered moments comparable with effective moments in the paramagnetic state. Typical examples among binaries are UGa2 [8] or UTe [9]. Certain complications arise due to the fact that the explicit variable modifying magnetism is the pressure-induced change of crystal lattice, not the pressure itself. In low-symmetry structures, the response to hydrostatic pressure can be strikingly anisotropic [10], and a crystal can even expand in one direction despite overall volume compression, prescribed by thermodynamics [11]. Such uncertainty naturally falls away if the material maintains the cubic symmetry at all pressures applied. However, even then it is essential for quantification of the pressure impact to know at least the bulk modulus if not all the whole equation of state, yielding the volume-pressure dependence. Uranium hydride, UH3, which forms in two cubic forms, the transient phase -UH3 and stable -UH3, was among the first 5f ferromagnets discovered [12]. Structure details can be found in [13]. Despite many decades of research there has been only limited basic information collected, clearly due to the pyrophoricity, which did not allow application of common experimental techniques. Its position among other U-based systems is anomalous. Magnetism typically appears for the U-U spacing exceeding the Hill limit, 340-360 pm [14]. In -UH3, some of the U atoms are only 330 pm apart, but ferromagnetism with rather high TC ≈ 165 K places it out of the known systematics. The fact that its transient form -UH3 with quite different structure has the same TC as well as magnetic moments (≈ 1.0 B/U in both cases) [15] is also rather unusual for any itinerant magnetic material, which would be the first choice when trying to classify UH3 on the basis of the short U-U distances, dU-U. An influence of electron-electron correlations, becoming prominent with the progressing 5f localization, was also speculated on the basis of photoelectron spectroscopy [16]. On the other hand, the only existing high-pressure experiment [17] exhibits a fast decrease of TC, which was interpreted as signature of itinerant 5f magnetism. This experiment reached, however, only the pressure of 0.8 GPa. Although one would not expect a pronounced non-linearity of TC(p) on such small pressure scale, ref. [17] exhibits a strong downward curvature, which can be interpreted e.g. due to chemical interaction of the sensitive hydride with environment. Later development showed that uranium hydrides can be, however, prepared with small alloying of certain transition metals, which does not shift dramatically TC and U values, but the material is much more stable to oxidation, and even larger monolithic pieces can be obtained is some cases [15,18]. This opened an avenue for much easier experimental studies, including application of high pressure. Here we describe the work performed with the material of nominal composition (UH3)0.82Mo0.18. Its Curie temperature approximately determined from low-field dc susceptibility was TC ≈ 187 K [19].
2. EXPERIMENTAL The hydride was synthesized from the arc melted alloy U0.82Mo0.18, checked to have the proper bcc structure by X-ray diffraction (XRD). The ingot was placed to a reactor. After evacuation by a hydrocarbon-free pumping to 10-4 Pa the system was pressurized at room temperature by pure H2 gas obtained from a LaNi5 bed. The pressure of ≈ 10 MPa was maintained for 100 hours and then gradually released. After such procedure the material becomes brittle, but monolithic piece of several mm3 can be extracted and carefully used for further studies. XRD proved the nanocrystalline structure of the β-UH3 type. Very small grain size of the order of several
nm is most likely due to fast activation of hydride formation but a slow grain growth, impeded by the Mo atoms. The material structure was in addition analyzed by a Pair Distribution Function analysis (at ESRF Grenoble, ID22, using the photon energy 80 keV). Results, published in the context of other types of hydrides [20], demonstrate that Mo occupies the position of U in the βUH3 crystal lattice. As the H concentration per one unit cell is somewhat reduced and the ratio of 3 H atoms per 1 U atom (determined by programmed desorption in a closed volume) is approximately obeyed, the formula (UH3)0.82Mo0.18 is appropriate at least for not very high Mo concentrations. The lattice parameter, determined also using the ID22 data, shows a slight decrease as a function of Mo concentration, yielding a = 664.5 pm at T = 300 K [20]. This value coincides with the a-value reported by regular XRD for pure -UH3 [13]. As none of fundamental electronic properties differ significantly among both phases and their alloyed varieties, one can take results obtained for (UH3)0.82Mo0.18 as relevant for -UH3 and to some extent also for -UH3. The measurement of ac magnetic susceptibility under hydrostatic pressure was performed using a home-made miniature detection coils set containing one layer of detection coil of 50+50 turns (for the detection and compensation part) and additional two excitation layers of 200 turns. The strength of ac excitation field can change to some extent with the geometrical factors inside the cell (dependent on applied pressure), but is approximately 0.5 mT. The excitation frequency 81 Hz was used. This set was placed into a hybrid two-layered CuBe/NiCrAl clamped pressure cell (C&T Factory Co., Ltd.) with a highest nominal pressure of 3 GPa [21]. Daphne oil 7373 was used as a pressure-transmitting medium [22] and thermally stabilized manganin wire was used to determine the pressure inside the cell at room temperature. The pressure difference between the room- and the lowest measured temperature of the Daphne 7373 oil inside the pressure cell is p ≈ 0.2 GPa and remains similar all over the used range of pressures. The cell was cooled by the closed-cycle refrigerator (Janis Research & Sumitomo Heavy Industries) from room temperature down to T = 3 K. The ac-susceptibility signal was detected using the SR830 lock-in amplifier (Stanford Research).
3. RESULTS AND DISCUSSION One of convenient techniques to detect small changes of TC in a ferromagnet is measurement of ac susceptibility, ac. Uranium systems as materials with a significant magnetic anisotropy exhibit very sharp peak of ac in conjunction with the phase transition. The peak appears due to an interplay of magnetization increase with decreasing T and freezing the moments due to magnetic anisotropy. For low driving ac fields magnetization becomes “frozen” few Kelvins below TC, as soon as the width of hysteresis curve exceeds the amplitude of the driving magnetic field. Hence the peak position, T = 173 K, does not really coincide with TC in a ferromagnet. A real TC value could be closer to the inflection point on the high-temperature slope of the peaks, plotted in Fig.1, which gives ≈ 180 K in low pressures. The shape of the peaks, however, does not change with pressure, which gives the opportunity to use the temperatures of the sharp maxima, giving better relative precision for the TC determination. We can estimate from the data that the maxima appear 10-15 K below the actual TC-value. Here we plot the real part of ac(T), i.e. the component in-phase with the driving field. The imaginary component, expressing the dissipation, has very similar T dependence (not shown here), but its values are two orders of magnitude smaller, hence more affected by data scatter.
2.8
(UH3)0.82Mo0.18
Re (arb.u.)
2.6
p = 0.3 GPa
2.4 2.2 2.0 p = 3.2 GPa
1.8 1.6 0
50
100
150
200
250
T (K) Fig. 1: Real part of ac susceptibility, ac(T), for (UH3)0.82Mo0.18 in the lowest and highest pressure applied.
Figs. 1 and 2 clearly demonstrate that TC is systematically shifted towards lower temperatures with increasing pressure. Fig. 3 reveals that both temperatures of the ac(T) maxima and TC determined (with a larger uncertainty) from the inflection points follow a linear function of applied pressure. The value of TC extrapolated to p = 0, TC(0) = 180.3 K, while Tmax = 173.4 K. The pressure derivatives given by the slope of the straight lines in Fig. 3 can be evaluated as dTC/dp = 1.87 K/GPa and dTmax/dp = -2.05 K/GPa. It is generally assumed that the logarithmic derivative dlnTC/dp = 1/T*dTC/dp ≈ -0.011 GPa-1 has a more profound meaning than the pressure derivative itself. The important message is that this number is actually more than twice smaller than that given in the paper [17], -0.024 GPa-1. The value dlnTC/dp = -0.011 GPa-1 is in absolute value also by a factor of 3 lower than another U compound with similar TC ≈ 160 K, UFe2 [23]. However, UFe2 has a significant contribution of the Fe-3d magnetism, therefore we later compare with purely 5f magnetic systems.
Re (arb.u.)
2.8 2.6
(UH3)0.82Mo0.18
p1 p2 p3 p4 p5
2.4 2.2
= 0.3 = 1.0 = 1.7 = 2.4 = 3.2
GPa GPa GPa GPa GPa
2.0 1.8 1.6 150
160
170
180
190
200
T (K) Fig. 2: Detailed pressure variations of real part of ac susceptibility, ac(T), for (UH3)0.82Mo0.18. Some of the data were vertically shifted for a better clarity.
182 180
Tmax, TC (K)
178
TC
176 174 172 Tmax
170 168 166 164
0
1
2
3
4
p (GPa) Fig.3: Pressure variations of TC and Tmax for (UH3)0.82Mo0.18 determined as described in the text.
The negative pressure derivative of TC could be actually expected on the basis of thermodynamics at ambient pressure. The reason is the sizeable spontaneous magnetostriction, found from the temperature dependence of lattice parameter, and estimated as s = 3.2*10-3 for (UH3)0.85Zr0.15 representing the -UH3 structure or 2.2*10-3 for (UH3)0.96Mo0.04 (TC ≈ 180 K), representing -UH3 [19], which can be attributed to the larger spin moment in the ferromagnetic state than in the paramagnetic state, described by the Disordered Local Moment (DLM) picture. On the quantitative level, the well-known Ehrenfest’s relation for the second-order phase transition states that dTC/dp = 3VTC/Cp, where is the difference between the linear thermal expansion coefficient below and above the transition (9.2*10-6 K-1 is practically identical for - and -UH3 [19]), V is the molar volume (23*10-6 m3), and Cp, is the step of specific heat at the transition (-10 J/mol K for -UH3 [13]). Such parameters would give dTC/dp ≈ -34 K/GPa, which is one order of magnitude more than found in reality. This discrepancy can mean that the effective inter-site exchange coupling actually increases at elevated pressures, while the magnetostriction, driven by the spin moments, decreases. For a comparison with other materials it is desirable to relate the variations of TC not to pressure, but also to the actual volume change. For such analysis it is necessary to know the bulk modulus B. To our best knowledge, there has been so far published only one structure study of UH3 under high pressure [24], which proved the phase stability at least up to 29 GPa and deduced a rather low value of the bulk modulus B = 33±5 GPa, obtained from the fitting using a full equation of state over extended pressure range. This is in a striking disagreement with calculated bulk modulus values using various ab initio methods, which give as a rule values close to or exceeding 100 GPa. For example, B = 104 GPa for -UH3 and 144 GPa for -UH3 was obtained using the VASP code within Generalized Gradient Approximation (GGA) [25], or B = 110 GPa in Local Density Approximation (LDA) and 116 GPa in LDA+U for -UH3 and 128 GPa (LDA) and 120 GPa (LDA+U) for -UH3, when using rather high Coulomb interaction parameter U = 4 eV [26]. Using GGA + U with U = 2 eV gave B = 97 GPa for -UH3 [27]. Finally, using the Local Spin Density Approximation (LSDA) within the FPLO code, B = 101 GPa was obtained for -UH3 [15]. A certain evidence can be deduced also from the synthesis of U-polyhydrides at very high hydrogen pressures, performed in a diamond anvil cell, giving diffraction data of both UH3 phases before they actually transform into the polyhydrides. An attempt to analyse several experimental points given in [28] yields B ≈ 110 GPa for -UH3 and ≈160 GPa for -UH3, hinting that the values of B much below 100 GPa are unlikely. Revisiting experimental data from [24] in the pressure range of few GPa, where V(p) is approximately linear, we also obtain B ≈ 100 GPa. Hence we can calculate dlnTc/dlnV ≈ 1.1 if a plausible value B ≈ 100 GPa is taken. Here we naturally also neglect any temperature dependence of B. For comparison (see Tab. 1) we included well documented cases of cubic materials (NaCl structure type), so as to avoid ambiguities with possible anisotropic compressibilities and anisotropic reactions of magnetism on a lattice compression. The choice involves a typical band antiferromagnet UN [29-31], US with higher TC and presumably more local-moment system [32], and UAs, where TN already increases with pressure [34], and we can deduce the 5f states character shifted towards the localization. material UN US UH3 UAs
Type of order AF F F AF
TC,N [K] 53 [29] 180 [32] 180 127 [34]
dlnTC,N/dp B [GPa] dlnTC,N/dlnV [GPa-1] -0.1 [29] 203 [30] 19 [31] -0.012 [32] 92 [33] 1.1 [32] -0.011 ≈100 1.1 +0.020 [34] 101 [35] -2.0
Tab. 1: Comparison of properties of UH3 with diverse U compounds, all cubic, crystalizing with the NaCl structure type. The data without reference are based on the present work or calculated by us on the basis of other parameters. If we map UH3 onto the group of NaCl structure compounds, it would be located somewhere close to US, i.e. far from the itinerant magnetism limit. This is quite remarkable if we consider the U-U distances, which are 387 pm for US (407 pm for UAs, 345 pm for UN) in a contrast with 331 pm and 360 pm for - and -UH3, respectively. Uranium trihydride clearly reaches such degree of localization at much smaller U-U distances. The specific impact of the U-H bonding on the 5f states, not only the volume expansion, is the vital ingredient in the hydrides. As stated previously, we can assume that the 6d-1s hybridization reducing the 5f-6d hybridization, has the decisive role [15]. A question remains what is the real pressure dependence of U magnetic moments () in UH3. Existing data covering the pressure range below 1 GPa [17] indicate a linear decrease dln/dp = -0.016 GPa-1. As this value represents a faster decrease than for TC it can indeed mean that the fast decay of moments is partly compensated by a stronger effective inter-site coupling, induced by the volume compression. Although the data in ref. [17] do not show any non-linearity (surprizingly observed for TC), it would be desirable to explore the fine variations of magnetization over a larger pressure range. Such experiment, however, requires also high magnetic fields because of a slow approach to saturation, which needs a careful data analysis. Moreover, one has to keep in mind that although dlndlnTC is expected to be close to 1 in itinerant magnetic systems [36], U-based materials have the magnetization with a dominant orbital moment component (antiparallel to the spin component), while the exchange driven phenomena will depend predominantly on spin, which can considerably distort the ratio dlndlnTC It is naturally interesting to probe the compressed state by ab initio calculations which may suggest tendencies in variations of magnetic moments. The ordering temperatures as one of finite temperature properties are much more involved and cannot be deduced in a straightforward way. Although results of fully relativistic GGA computations give reasonable agreement as to the equilibrium volume [15], the obtained size of total magnetic moments if close to 0 due to almost complete cancellation of spin and orbital parts. As this result is far from the bulk magnetization corresponding to ≈ 1 B/U, we employed the GGA+U scheme. Our calculations were performed using the projected augmented wave (PAW) potentials as implemented in the VASP code [37]. For the exchange–correlation effects, Generalized Gradient Approximation (GGA) as parametrized by the Perdew, Burke and Ernzerhof (PBE) functional [38] was utilized simultaneously with the Hubbard model in the rotationally invariant approach [39] for uranium 5f-electrons. Spin-orbit coupling (SOC) was included, as well. Although the necessity to choose the values of the direct Coulomb and Hund’s exchange parameters U and J means in a strict sense a loss of the parameter-free ab initio nature, the successful choice of U and J values can provide an additional information on the interactions in a particular system. Here we took as a figure of merit the agreement of equilibrium volume for - and -UH3 and UH2, as well as the total magnetic moments. Because of the experimental uncertainty, we could not take the equilibrium bulk modulus as one of the benchmark parameters. Testing the merit of the GGA+U calculations on the landscape of all meaningful values of parameters of U and J, we found that the combination U = 0.5 eV, J = 0.5 eV, can be used as a reasonable basis.
Compound -UH3 -UH3 (UH3)0.82Mo0.18 UH2
6c 2a 6c 2a
aexp (pm) 416.0
acalc (pm) 417.1
S (B)
L (B)
U (B)
-2.01
3.04
1.03
664.4
667.7
664 *
649.9
536 **
531.6
-2.03 -1.98 -1.7 -1.8 -1.99
2.80 2.38 2.7 2.2 2.96
0.77 0.40 1.0 0.4 0.97
Bcalc (GPa) 87 91 104 75
*Data from total scattering experiment **Data from a thin film Tab. 2: Calculated equilibrium lattice parameter acalc (bulk modulus Bcalc, and spin, orbital, and total magnetic moments per U atom. Two different U sites in the -UH3 structure are distinguished. (UH3)0.82Mo0.18 is emulated by the -UH3 structure with a Mo atom replacing U in the one of the two 2a positions, which makes also the individual magnetic moments at the 6c positions somewhat different. The table gives an average value. Two different U sites in -UH3 yield somewhat different uranium moments. This fact agrees with previous computational results [40], although no support for a difference has been found by neutron diffraction [13]. A moderate increase of U (up to 2 eV) allows to reproduce the lattice parameters, but the spin magnetic moments exceed orbital ones, which is for U-compounds unrealistic [41]. For the above-mentioned specific choice U = J, the spherically-symmetric terms in the “+U” part of the rotationally invariant GGA+U functional are set to zero, and remaining spin and orbitally dependent GGA+U terms include just the orbital polarization (OP) [42] and spin-flips beyond the level given by the density functional approximation. The situation can be assumed as the OP limit of GGA+U, and guarantees that the 5f states are not split off from the Fermi level EF, maintaining the Sommerfeld coefficient enhanced from ≈10 mJ/mol K2 in -U to ≈30 mJ/mol K2 in UH3 [43]. The 5f presence at EF was actually also indicated by photoelectron spectroscopy [16]. Tab. 2 demonstrates that the explicit inclusion of Mo in one of the 2a U positions and relaxing the structure (the concentration corresponds to 1/8 = 12.5 % Mo, 7/8 = 87.5% U) does not change much the U moments or B, providing a good basis for using the alloyed U-Mo hydride as a model material for -UH3. Further details of results of ab initio calculations can be seen in Figs. 4 and 5, depicting variations of total energy as a function of volume, giving the calculated equilibrium volume. A simple analysis for -UH3 with smaller unit cell demonstrates that using the scalar relativistic GGA approximation gives about 2% overbinding, including the spin-orbit interaction reduces the misfit to 1.1%. This is both considerably better than using the conventional LSDA approximation (not shown here) with 11% overbinding and much stiffer lattice. The effect of magnetism for -UH3 is shown on Fig.5, where a non-magnetic (forced paramagnetic) state is compared with the ferromagnetic state both for GGA and GGA + U (U = J = 0.5 eV) case. The absence of uranium moments leads to a volume collapse, the calculated equilibrium volumes are 6% and 4.5%, respectively, below the experimental value. Allowing for the ferromagnetic ordering with the (111) direction of moments, which gives the lowest total energy, gives the equilibrium volume 2% below the experimental value for GGA and 1.5% above it for GGA +U, both with spin orbit coupling. Compressing the -UH3 lattice to estimate the moment variations under pressure leads to a reduction of both S and L. The calculations for the volume corresponding to the pressure of 3.2 GPa show that orbital moments are more pressure sensitive. The decrease of L by 4% and of S by 2% gives the total moment reduced by ≈10%. This is actually more than if estimated magnetization
variations at low pressures [17] would be extrapolated to 3.2 GPa. Such procedure would show about 5% decrease from the respective zero-pressure value. Pressure variations of magnetization, or even its spin and orbital component, accessible via X-ray magnetic circular dichroism experiment, would be an important test of the relevance of the calculations with respect of details of 5f magnetism. For precise determination of ordered U moments the slow approach of saturation is, however, the fact needing a special care. In particular high magnetic fields are needed.
-2.1769
-5.9864
-UH3 scalar relativistic GGA
E - E0 (eV/f.u.)
-2.2109
-6.0204
-2.2449 -6.0544 -2.2789 -6.0884 -2.3129 -6.1224
-2.3469 -UH GGA with SOC 3 -2.3810
0.88
0.92
0.96
1.00
1.04
1.08
-6.1565
V/V0
Fig. 4: Total energy variations of -UH3 as a function of unit cell volume for the scalar relativistic GGA calculations (using WIEN2k package with PBE functional) for the scalar relativistic approximation and with spin-orbit coupling.
0.7
E - E0 (eV/f.u.)
0.6 0.5
GGA+U - NM
0.4 GGA - NM
0.3 0.2 0.1 0.0
GGA - FM
GGA+U - FM
-0.1 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15
V/V0 Fig. 5: Total energy variations of -UH3 as a function of unit cell volume for the fully relativistic GGA and GGA+ U calculations (using VASP code with PBE functional) for the ferromagnetic and non-magnetic state. The energies were normalized (by proper choice of E0) to give the E – E0 = 0 in the ferromagnetic states and energies for the GGA and GGA + U cannot be directly compared. The energy differences between the respective ferromagnetic and non-magnetic states are physically meaningful. The lines represent the Birch-Murnaghan fits, yielding the bulk modulus B = 96 GPa for ferromagnetic GGA case. Including U and J makes the lattice somewhat softer (B = 91 GPa) while the overbinding in the absence of U magnetic moments gives a higher B-values (108 GPa for GGA + U and 117 GPa for GGA).
4. CONCLUSIONS The high-pressure ac susceptibility study revealed that the Curie temperature of UH3 is reduced linearly under applied hydrostatic pressure up to 3.2 GPa. The rate of the decrease, -1.87 K/GPa, is lower than expected for a 5f itinerant system. Critical evaluation of existing elastic properties suggests the bulk modulus around 100 GPa, i.e. UH3 does not have the extremely soft lattice as reported in the past. This allowed us to estimate dlnTC/dlnV ≈ 1.1, which is close to e.g. US. We can therefore deduce a significant 5f localization tendencies, rather unexpected for short UU distances. Acknowledgements This work was supported by the Czech Science Foundation under the grant no. 18-02344S. A part of the theoretical research was supported by the grant no. 17-27790S. We acknowledge support by
the projects CZ.02.1.01/0.0/0.0/15_003/0000485 and CZ.02.1.01/0.0/0.0/16_013/0001791 within the Operational programme Research Development and Education financed by ERDF. Experiments were partly performed in MGML (http://mgml.eu), which is supported within the program of Czech Research Infrastructures (project no. LM2018096). References [1] J. Lee, M. Matsuda, J.A. Mydosh, I. Zaliznyak, A.I. Kolesnikov, S. Süllow, J.P. C. Ruff, G.E. Granroth, Dual Nature of Magnetism in a Uranium Heavy-Fermion System. Phys. Rev. Lett. 121 (2018) 057201. DOI: 10.1103/PhysRevLett.121.057201. [2] G. Zwicknagl, 5f Electron correlations and core level photoelectron spectra of Uranium compounds, Phys. Stat. Sol. B 250 (2013) 634-637. DOI 10.1002/pssb.201200732. [3] H.R. Ott and Z. Fisk, Heavy-electron actinide materials, in: Handbook on the Physics and Chemistry of the Actinides, vol. 5, A.J. Freeman and G.H. Lander, eds., North-Holland, Amsterdam 1987, pp. 85-225. [4] D. Aoki, J. Flouquet, Ferromagnetism and Superconductivity in Uranium Compounds. J. Phys. Soc. Jpn. 81 (2012) 011003. DOI: 10.1143/JPSJ.81.011003. [5] G. Koutroulakis, H. Yasuoka, P.H. Tobash, J.N. Mitchell, E.D. Bauer, J. D. Thompson, Extended Nuclear Quadrupole Resonance Study of the Heavy-Fermion Superconductor PuCoGa5, Phys. Rev. B 94 (2016) 165115. DOI: 10.1103/PhysRevB.94.165115. [6] V. Taufour, D. Aoki, G. Knebel, and J. Flouquet, Tricritical Point and Wing Structure in the Itinerant Ferromagnet UGe2. Phys. Rev. Lett. 105 (2010) 217201. DOI: https://doi.org/10.1103/PhysRevLett.105.217201. [7] L. Havela, A.V. Kolomiets, A.V. Andreev, J.-C. Griveau, F. Honda, Z. Arnold: Extended stability range of the non-Fermi liquid phase in UCoAl, J. Phys.: Condens. Matter. 30 (2018) 385601. DOI: 10.1088/1361-648X/aada59. [8] A.V. Kolomiets, J.-C. Griveau, J. Prchal, A.V. Andreev, L. Havela: Variations of magnetic properties of UGa2 under pressure, Phys.Rev. B 91 (2015) 064405. DOI: 10.1103/PhysRevB.91.064405. [9] Q.G. Sheng, B.R. Cooper, Pressure-induced magnetic ordering effects in correlated-electron uranium mon ochalcogenides, J. Mag. Mag. Mater. 164 (1996) 335-344. DOI: 10.1016/S03048853(96)00409-X. [10] L. Havela, M. Diviš, V. Sechovský, A.V. Andreev. F. Honda, G. Oomi, Y. Méresse, S. Heathman: U ternaries with ZrNiAl structure - lattice properties, J.Alloys Comp. 322 (2001) 7-13. DOI: 10.1016/S0925-8388(01)01176-8 [11] S. Mašková, A.M. Adamska, L. Havela, N.-T.H. Kim-Ngan, J. Przewoźnik, S. Daniš, K. Kothapalli, A.V. Kolomiets, S. Heathman, H. Nakotte, H. Bordallo: Lattice anisotropy in uranium ternary compounds: UTX, J. Alloys Comp. 522 (2012) 130-135. DOI: 10.1016/j.jallcom.2012.01.122.
[12] R. Troc, W. Suski, The discovery of the ferromagnetism in U(H,D)3: 40 years later, J. Alloys Comp. 219 (1995) 1-5. DOI: 10.1016/0925-8388(94)05062-7. [13] I. Grenthe, J. Drozdynski, T. Fujino, E.C. Buck, T.E. Albrecht-Schmitt, S.F. Wolf, Uranium, in: The Chemistry of the Actinide and Transactinide Elements, 3rd Edition, J.J. Katz, J.R. Morss, N. Edelstein, J. Fuger, eds., Springer 2006, pp. 253-698. [14] H.H. Hill, The early “actinides”: The periodic system’s f electron transition metal series, in: Plutonium 1970 and Other Actinides, ed. W.N. Miner (AIME 1970), pp 1-19. [15] I. Tkach, M. Paukov, D. Drozdenko, M. Cieslar, B. Vondráčková, Z. Matěj, D. Kriegner, A.V. Andreev, N.-T.H. Kim-Ngan, I. Turek, M. Diviš, and L. Havela: Electronic properties of α-UH3 stabilized by Zr , Phys.Rev. B 91 (2015) 115116. DOI: 10.1103/PhysRevB.91.115116. [16] T. Gouder, R. Eloirdi, F. Wastin, E. Colineau, J. Rebizant, D. Kolberg, and F. Huber, Electronic structure of UH3 thin films prepared by sputter deposition, Phys. Rev. B 70 (2004) 235108. DOI: 10.1103/PhysRevB.70.235108. [17] A.V. Andreev, S.M. Zadvorkin, M.I. Bartashevich, T. Goto, J. Kamarád, Z. Arnold, H. Drulis, Magnetic and magnetoelastic properties of β-UH3, J. Alloys Comp. 267 (1998) 32-36. https://doi.org/10.1016/S0925-8388(97)00531-8. [18] I. Tkach, S. Mašková, Z. Matěj, N.-T. H. Kim-Ngan, A. V. Andreev, L. Havela, Ferromagnetism with TC=200 K in the amorphous 5f compound UH3Mo0.18, Phys. Rev. B 88 (2013) 060407(R). DOI: 10.1103/PhysRevB.88.060407 [19] L. Havela, M. Paukov, I. Tkach, Z. Matěj, D. Kriegner, S. Mašková, B. Vondráčková, M. Prachařová, I. Turek, M. Diviš, M. Cieslar, D. Drozdenko, N.-T.H. Kim-Ngan, A.V. Andreev, UH3-based ferromagnets: New look an an old material, J. Mag. Mag. Mater. 400 (2016) 130-136. DOI: 10.1016/j.jmmm.2015.07.053. [20] L. Havela, M. Paukov, I. Tkach, V. Buturlim, Z. Matej, S. Maskova, I. Turek, M. Divis, D. Drozdenko, M. Cieslar, M. Dopita, Z. Molcanova, M. Mihalik, Strong 5f Ferromagnetism in UH3Based Materials, 1 (2016) 2987-2992. DOI: 10.1557/adv.2016.287. [21] N. Fujiwara, T. Matsumoto, K. Koyama-Nakazawa, A. Hisada, Y. Uwatoko, Fabrication and efficiency evaluation of a hybrid NiCrAl pressure cell up to 4 GPa, Rev. Sci. Instrum. 78 (2007) 073905. DOI: 10.1063/1.2757129. [22] K. Murata, H. Yoshino, H. O. Yadav, Y. Honda, N. Shirakawa, Pt resistor thermometry and pressure calibration in a clamped pressure cell with the medium, Daphne 7373, Rev. Sci. Instrum., 68 (1997) 2490-2493. DOI: 10.1063/1.1148145. [23] J.J.M. Franse, Itinerant-electron magnetism studied in high-magnetic field and high-pressure experiments, J. Mag. Mag. Mater. 31-34 (1983) 819-828. [24] I. Halevy, S. Sahov, S. Zalkind, M. Brill, I. Yaar, High pressure study of -UH3 crystallographic and electronic structure, J. Alloys Comp. 370 (2004) 59-64. DOI: 10.1016/j.jallcom.2003.09.124. [25] Ch.D. Taylor, T. Lookman, and R.S. Lillard, Ab initio calculations of the uranium-hydrogen system: Thermodynamics, hydrogen saturation of -U and phase-transformation to UH3, Acta Materialia 58 (2010) 1045-1055. DOI: 10.1016/j.actamat.2009.10.021. [26] Y. Zhang, B. Wang, Y. Lu, Y. Yang, P. Zhang, Electronic, mechanical and thermodynamic properties of -UH3: A comparative study by using the LDA and LDA+U approaches, J. Nucl. Mater. 430 (2012) 137-141. DOI: 10.1016/j.jnucmat.2012.07.002. [27] C. Zhang, H. Jiang, H.-L. Shi, G.-H. Zhong, Y.-H. Su, Mechanical and thermodynamic properties of -UH3 under pressure, J. Alloys Comp. 604 (2014) 171-174. DOI: 10.1016/j.jallcom.2014.03.071.
[28] I.A. Kruglov, A.G. Kvashnin, A.F. Goncharov, A.R. Oganov,.S. Lobanov, N. Holtgrewe, S. Jiang, V. Prakapenka, E. Greenberg, A.V. Yanilkin, Uranium polyhydrides at moderate pressures: Prediction, synthesis, and expected superconductivity, Sci.Adv. 4 (2018) eaat9776. DOI: 10.1126/sciadv.aat9776. [29] J.M. Fournier, J. Beille, C.-H. de Novion, Magnetic properties of UN under pressure, J. Phys. Colloq. 40 (1979) C4-32-C4-33. DOI: 10.1051/jphyscol:1979411. [30] J. Staun Olsen, L. Gerward, U. Benedict, A new high-pressure phase of uranium nitride studied by X-ray-diffraction and synchrotron radiation, J.Appl. Crystallography 18 (1985) 37-41. https://doi.org/10.1107/S0021889885009736. [31] J.M. Fournier, J. Beille, A. Boeuf, C. Vettier, A. Wedgwood, Magnetic structure of UN under pressure, Physica 102B (1980) 282-284. DOI: 10.1016/0378-4363(80)90174-6. [32] C.Y. Huang, R.J. Laskowski, C.E. Olsen, J.L. Smith, High pressure study of ferromagnetic US, J. Phys. Colloq.40 (1979) C4-26-C4-27. DOI: 10.1051/jphyscol:1979408. [33] J. Staun Olsen S. Steenstrup, L. Gerward, U. Benedict, C. Spirlet, G.D. Andretti, High-pressure X-ray diffraction experiments on US using synchrotron radiation, J. Less Common Met. 98 (1984) 291-300. https://doi.org/10.1016/0022-5088(84)90302-3. [34] I.N. Goncharenko, J.-M. Mignot, V.A. Somenkov, J. Rossat-Mignod, O. Vogt, Magnetic phase diagram of UAs at very high pressures up to 50 kbar, Physica B199&200 (1994) 625-627. [35] J.M. Léger, I. Vedel, A.M. Redon, J. Rossat-Mignod, O. Vogt, High-pressure X-ray studies of UAs and UTe, Solid Sate Commun. 66 (1988) 1173-1176. DOI: 10.1016/0038-1098(88)91127-1. [36] J.M. Fournier, Pressure effects on the magnetic properties of actinide intermetallics, Physica 130B (1985) 268-277. [37] G. Kresse and J. Furthmueller, Phys. Rev. B 54 (1996) 11169-11186. DOI: 10.1103/PhysRevB.54.11169. [38] J.P. Perdew, K. Burke, M. Ernzerhof, Generalized Gradient Approximation made simple, Phys. Rev. Lett. 77 (1996), 3865−3868. DOI: 10.1103/PhysRevLett.77.3865. [39] A.I. Liechtenstein, V.I. Anisimov, J. Zaanen, Phys. Rev. B 52 (1995) R5467-R5470. DOI: 10.1103/PhysRevB.52.R5467. [40] Ch.D. Taylor, Characterizing electronic structure motifs in -UH3. Phys. Rev. B 82 (2010) 224408. DOI: 10.1103/PhysRevB.82.224408. [41] F. Wilhelm, J.P. Sanchez, A. Rogalev, Magnetism of uranium compounds probed by XMCD spectroscopy, J. Phys. D: Appl. Phys. 51 (2018) 333001. DOI: 10.1088/1361-6463/aacf7d. [42] A. Shick, V. Janis, V. Drchal, W. Pickett, Spin and orbital magnetic state of UGe2 under pressure, Phys. Rev. B 70 (2004) 134506. DOI: 10.1103/PhysRevB.70.134506. [43] J.W. Ward, L.E. Cox, J.L. Smith, G.R. Stewart, J.H. Wood, J.Phys.(Paris) 40 (1979) C4-15. DOI: 10.1051/jphyscol:1979403.
We state hereby that none of the authors has any conflict of interests related to the matter of publishing the paper Pressure variations of the 5f magnetism in UH3 .
Highlights
Curie temperature of beta-UH3 decreases with pressure to 3.2 GPa. The linear decrease approx. -2 K/GPa is linear and weaker than assumed before The decrease indicates intermediate 5f delocalization Basic features are captured by GGA+U method.
S0304-8853(19)32272-3 https://doi.org/10.1016/j.jmmm.2019.165993 MAGMA 165993
To appear in:
Journal of Magnetism and Magnetic Materials
Received Date: Revised Date: Accepted Date:
2 July 2019 8 October 2019 15 October 2019
Please cite this article as: J. Prchal, V. Buturlim, J. Valenta, M. Dopita, M. Divis, I. Turek, L. Kyvala, D. Legut, L. Havela, Pressure variations of the 5f magnetism in UH3, Journal of Magnetism and Magnetic Materials (2019), doi: https://doi.org/10.1016/j.jmmm.2019.165993
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
© 2019 Published by Elsevier B.V.
Pressure variations of the 5f magnetism in UH3 J. Prchal1, V. Buturlim1, J. Valenta1, M. Dopita1, M. Divis1, I. Turek1, L. Kyvala2, D. Legut2, L. Havela1 1
Department of Condensed Matter Physics, Faculty of Mathematics and Physics, Charles University, Ke Karlovu 5, 121 16 Prague 2, Czech Republic 2 IT4Innovations, VSB-Technical University of Ostrava, 17.listopadu 2172/15, 708 00 Ostrava, Czech Republic Abstract Pressure variations of the Curie temperature of the 5f ferromagnet -UH3 were studied using the Mo-alloyed hydride (UH3)0.82Mo0.18, which is stable in air and has very similar TC and magnetization per U atom. By means of ac magnetic susceptibility a linear decrease of TC was observed for pressures up to 3.2 GPa. The coefficient dTC/dp = -2.05 K/GPa gives dlnTC/dp = 1/T*dTC/dp ≈ -0.011 GPa-1. This value is smaller than expected for a 5f-band ferromagnet with relatively short U-U distances and suggests that UH3 may be more localized than expected. Among AnX compounds, similar dependence was found e.g. for US. Revisiting existing data on lattice elasticity for -UH3, bulk modulus B ≈ 100 GPa can be assumed, leading to dlnTC/dlnV = 1.1. Experimental data are confronted with results of GGA+U electronic structure calculations. Plausible values of direct Coulomb U and Hund’s exchange J are deduced. The lattice compression was found to reduce predominantly the orbital moments.
Keywords: Uranium hydrides; Ferromagnetism; Bulk modulus; High pressures; Ab initio calculations
1. INTRODUCTION Magnetic properties of uranium systems are affected by the open 5f shell, which is the characteristic of the actinide series. The 5f electronic states tend to the localization, analogous to 4f states in lanthanides, for heavy actinides. On the other hand, 5f states in light actinides (up to plutonium with atomic number Z = 94) can be involved in metallic bonds, i.e. itinerant, and they resemble more transition metals, albeit with a strong spin-orbit interaction. In a broad crossover region, the degree of localization cannot be simply deduced from experimental observables, as no single property gives a clear quantification of the regime of the 5f states. Not only that there is no simple way to interpolate between the description using the Bloch waves and atomic wave functions, but a higher level of complexity can arise, leading to non-trivial emergent phases as unusual types of magnetism, sometimes coexisting with anomalous superconductivity, charge density waves, etc. As some of measurable properties point to the 5f itinerant states, while other may evoke their localization, it is common to use the term of dual nature of the 5f states [1,2]. One of fundamental difficulties is that neither theoretical physics nor ab initio calculations can decide about the situation of the 5f states in such a complex regime. The reason is that differences of total energy between localized and Bloch-like 5f wave functions can be in the critical region very small, and the two situations cannot be safely treated on the same theoretical footing. Experimental data related to bulk and spectroscopic properties remain as necessary reference, guiding the calculations by providing a firm ground as well as stimulation by discoveries of new unexpected phenomena. Recent experimental effort in the field of light actinides has been naturally focused on materials exhibiting some of the exotic properties. The family of heavy fermion materials with record high effective masses of electrons at the Fermi level has been studied since 1980s [3]. The analogy with Ce-based heavy fermions led fast to a recognition on importance of electron-electron correlations, which sometimes yield superconductivity instead of more expected magnetic order. Several decades of research led to a recognition that such unconventional superconductivity just at the verge of magnetic order is rather a rule than an exception [4,5]. Very important in these efforts were studies under high pressure, used as a tool to tune magnetism to its suppression [6,7]. Now vast majority of experimental findings were collected, as to actinides, for U-based systems. Np and especially Pu, which is just at the localization threshold as a pure element, are more difficult to handle due to safety and security constraints. On the opposite side of the spectrum of U-based materials, where magnetism is rather stable, high pressure has been used to characterize its volume variations. In the limit of a band magnetism, a lattice compression due to applied pressure leads to a band broadening. The density of states at the Fermi level, N(EF), then typically decreases, which projects into reduction of ordered magnetic moments and ordering temperatures. In a case of localized magnetism, the moments are insensitive to commonly achievable pressure of several GPa, while their interaction can vary somewhat as a function of interatomic distance. Somewhere between the two limits a new type of regime was observed. Applying pressure the critical temperature starts first to increase dramatically, reaching a broad maximum and then turning down. Such a type of behavior can be qualitatively understood in a two-band model, in which the 5f states constituting magnetic moments interact predominately via more extended states. The coupling depends on the mutual hybridization, which becomes stronger at high pressures, but too strong hybridization tends to wash out the 5f moments, and magnetism is eventually suppressed. Such behavior has been indeed found at materials exhibiting local 5f
moments, i.e. ordered moments comparable with effective moments in the paramagnetic state. Typical examples among binaries are UGa2 [8] or UTe [9]. Certain complications arise due to the fact that the explicit variable modifying magnetism is the pressure-induced change of crystal lattice, not the pressure itself. In low-symmetry structures, the response to hydrostatic pressure can be strikingly anisotropic [10], and a crystal can even expand in one direction despite overall volume compression, prescribed by thermodynamics [11]. Such uncertainty naturally falls away if the material maintains the cubic symmetry at all pressures applied. However, even then it is essential for quantification of the pressure impact to know at least the bulk modulus if not all the whole equation of state, yielding the volume-pressure dependence. Uranium hydride, UH3, which forms in two cubic forms, the transient phase -UH3 and stable -UH3, was among the first 5f ferromagnets discovered [12]. Structure details can be found in [13]. Despite many decades of research there has been only limited basic information collected, clearly due to the pyrophoricity, which did not allow application of common experimental techniques. Its position among other U-based systems is anomalous. Magnetism typically appears for the U-U spacing exceeding the Hill limit, 340-360 pm [14]. In -UH3, some of the U atoms are only 330 pm apart, but ferromagnetism with rather high TC ≈ 165 K places it out of the known systematics. The fact that its transient form -UH3 with quite different structure has the same TC as well as magnetic moments (≈ 1.0 B/U in both cases) [15] is also rather unusual for any itinerant magnetic material, which would be the first choice when trying to classify UH3 on the basis of the short U-U distances, dU-U. An influence of electron-electron correlations, becoming prominent with the progressing 5f localization, was also speculated on the basis of photoelectron spectroscopy [16]. On the other hand, the only existing high-pressure experiment [17] exhibits a fast decrease of TC, which was interpreted as signature of itinerant 5f magnetism. This experiment reached, however, only the pressure of 0.8 GPa. Although one would not expect a pronounced non-linearity of TC(p) on such small pressure scale, ref. [17] exhibits a strong downward curvature, which can be interpreted e.g. due to chemical interaction of the sensitive hydride with environment. Later development showed that uranium hydrides can be, however, prepared with small alloying of certain transition metals, which does not shift dramatically TC and U values, but the material is much more stable to oxidation, and even larger monolithic pieces can be obtained is some cases [15,18]. This opened an avenue for much easier experimental studies, including application of high pressure. Here we describe the work performed with the material of nominal composition (UH3)0.82Mo0.18. Its Curie temperature approximately determined from low-field dc susceptibility was TC ≈ 187 K [19].
2. EXPERIMENTAL The hydride was synthesized from the arc melted alloy U0.82Mo0.18, checked to have the proper bcc structure by X-ray diffraction (XRD). The ingot was placed to a reactor. After evacuation by a hydrocarbon-free pumping to 10-4 Pa the system was pressurized at room temperature by pure H2 gas obtained from a LaNi5 bed. The pressure of ≈ 10 MPa was maintained for 100 hours and then gradually released. After such procedure the material becomes brittle, but monolithic piece of several mm3 can be extracted and carefully used for further studies. XRD proved the nanocrystalline structure of the β-UH3 type. Very small grain size of the order of several
nm is most likely due to fast activation of hydride formation but a slow grain growth, impeded by the Mo atoms. The material structure was in addition analyzed by a Pair Distribution Function analysis (at ESRF Grenoble, ID22, using the photon energy 80 keV). Results, published in the context of other types of hydrides [20], demonstrate that Mo occupies the position of U in the βUH3 crystal lattice. As the H concentration per one unit cell is somewhat reduced and the ratio of 3 H atoms per 1 U atom (determined by programmed desorption in a closed volume) is approximately obeyed, the formula (UH3)0.82Mo0.18 is appropriate at least for not very high Mo concentrations. The lattice parameter, determined also using the ID22 data, shows a slight decrease as a function of Mo concentration, yielding a = 664.5 pm at T = 300 K [20]. This value coincides with the a-value reported by regular XRD for pure -UH3 [13]. As none of fundamental electronic properties differ significantly among both phases and their alloyed varieties, one can take results obtained for (UH3)0.82Mo0.18 as relevant for -UH3 and to some extent also for -UH3. The measurement of ac magnetic susceptibility under hydrostatic pressure was performed using a home-made miniature detection coils set containing one layer of detection coil of 50+50 turns (for the detection and compensation part) and additional two excitation layers of 200 turns. The strength of ac excitation field can change to some extent with the geometrical factors inside the cell (dependent on applied pressure), but is approximately 0.5 mT. The excitation frequency 81 Hz was used. This set was placed into a hybrid two-layered CuBe/NiCrAl clamped pressure cell (C&T Factory Co., Ltd.) with a highest nominal pressure of 3 GPa [21]. Daphne oil 7373 was used as a pressure-transmitting medium [22] and thermally stabilized manganin wire was used to determine the pressure inside the cell at room temperature. The pressure difference between the room- and the lowest measured temperature of the Daphne 7373 oil inside the pressure cell is p ≈ 0.2 GPa and remains similar all over the used range of pressures. The cell was cooled by the closed-cycle refrigerator (Janis Research & Sumitomo Heavy Industries) from room temperature down to T = 3 K. The ac-susceptibility signal was detected using the SR830 lock-in amplifier (Stanford Research).
3. RESULTS AND DISCUSSION One of convenient techniques to detect small changes of TC in a ferromagnet is measurement of ac susceptibility, ac. Uranium systems as materials with a significant magnetic anisotropy exhibit very sharp peak of ac in conjunction with the phase transition. The peak appears due to an interplay of magnetization increase with decreasing T and freezing the moments due to magnetic anisotropy. For low driving ac fields magnetization becomes “frozen” few Kelvins below TC, as soon as the width of hysteresis curve exceeds the amplitude of the driving magnetic field. Hence the peak position, T = 173 K, does not really coincide with TC in a ferromagnet. A real TC value could be closer to the inflection point on the high-temperature slope of the peaks, plotted in Fig.1, which gives ≈ 180 K in low pressures. The shape of the peaks, however, does not change with pressure, which gives the opportunity to use the temperatures of the sharp maxima, giving better relative precision for the TC determination. We can estimate from the data that the maxima appear 10-15 K below the actual TC-value. Here we plot the real part of ac(T), i.e. the component in-phase with the driving field. The imaginary component, expressing the dissipation, has very similar T dependence (not shown here), but its values are two orders of magnitude smaller, hence more affected by data scatter.
2.8
(UH3)0.82Mo0.18
Re (arb.u.)
2.6
p = 0.3 GPa
2.4 2.2 2.0 p = 3.2 GPa
1.8 1.6 0
50
100
150
200
250
T (K) Fig. 1: Real part of ac susceptibility, ac(T), for (UH3)0.82Mo0.18 in the lowest and highest pressure applied.
Figs. 1 and 2 clearly demonstrate that TC is systematically shifted towards lower temperatures with increasing pressure. Fig. 3 reveals that both temperatures of the ac(T) maxima and TC determined (with a larger uncertainty) from the inflection points follow a linear function of applied pressure. The value of TC extrapolated to p = 0, TC(0) = 180.3 K, while Tmax = 173.4 K. The pressure derivatives given by the slope of the straight lines in Fig. 3 can be evaluated as dTC/dp = 1.87 K/GPa and dTmax/dp = -2.05 K/GPa. It is generally assumed that the logarithmic derivative dlnTC/dp = 1/T*dTC/dp ≈ -0.011 GPa-1 has a more profound meaning than the pressure derivative itself. The important message is that this number is actually more than twice smaller than that given in the paper [17], -0.024 GPa-1. The value dlnTC/dp = -0.011 GPa-1 is in absolute value also by a factor of 3 lower than another U compound with similar TC ≈ 160 K, UFe2 [23]. However, UFe2 has a significant contribution of the Fe-3d magnetism, therefore we later compare with purely 5f magnetic systems.
Re (arb.u.)
2.8 2.6
(UH3)0.82Mo0.18
p1 p2 p3 p4 p5
2.4 2.2
= 0.3 = 1.0 = 1.7 = 2.4 = 3.2
GPa GPa GPa GPa GPa
2.0 1.8 1.6 150
160
170
180
190
200
T (K) Fig. 2: Detailed pressure variations of real part of ac susceptibility, ac(T), for (UH3)0.82Mo0.18. Some of the data were vertically shifted for a better clarity.
182 180
Tmax, TC (K)
178
TC
176 174 172 Tmax
170 168 166 164
0
1
2
3
4
p (GPa) Fig.3: Pressure variations of TC and Tmax for (UH3)0.82Mo0.18 determined as described in the text.
The negative pressure derivative of TC could be actually expected on the basis of thermodynamics at ambient pressure. The reason is the sizeable spontaneous magnetostriction, found from the temperature dependence of lattice parameter, and estimated as s = 3.2*10-3 for (UH3)0.85Zr0.15 representing the -UH3 structure or 2.2*10-3 for (UH3)0.96Mo0.04 (TC ≈ 180 K), representing -UH3 [19], which can be attributed to the larger spin moment in the ferromagnetic state than in the paramagnetic state, described by the Disordered Local Moment (DLM) picture. On the quantitative level, the well-known Ehrenfest’s relation for the second-order phase transition states that dTC/dp = 3VTC/Cp, where is the difference between the linear thermal expansion coefficient below and above the transition (9.2*10-6 K-1 is practically identical for - and -UH3 [19]), V is the molar volume (23*10-6 m3), and Cp, is the step of specific heat at the transition (-10 J/mol K for -UH3 [13]). Such parameters would give dTC/dp ≈ -34 K/GPa, which is one order of magnitude more than found in reality. This discrepancy can mean that the effective inter-site exchange coupling actually increases at elevated pressures, while the magnetostriction, driven by the spin moments, decreases. For a comparison with other materials it is desirable to relate the variations of TC not to pressure, but also to the actual volume change. For such analysis it is necessary to know the bulk modulus B. To our best knowledge, there has been so far published only one structure study of UH3 under high pressure [24], which proved the phase stability at least up to 29 GPa and deduced a rather low value of the bulk modulus B = 33±5 GPa, obtained from the fitting using a full equation of state over extended pressure range. This is in a striking disagreement with calculated bulk modulus values using various ab initio methods, which give as a rule values close to or exceeding 100 GPa. For example, B = 104 GPa for -UH3 and 144 GPa for -UH3 was obtained using the VASP code within Generalized Gradient Approximation (GGA) [25], or B = 110 GPa in Local Density Approximation (LDA) and 116 GPa in LDA+U for -UH3 and 128 GPa (LDA) and 120 GPa (LDA+U) for -UH3, when using rather high Coulomb interaction parameter U = 4 eV [26]. Using GGA + U with U = 2 eV gave B = 97 GPa for -UH3 [27]. Finally, using the Local Spin Density Approximation (LSDA) within the FPLO code, B = 101 GPa was obtained for -UH3 [15]. A certain evidence can be deduced also from the synthesis of U-polyhydrides at very high hydrogen pressures, performed in a diamond anvil cell, giving diffraction data of both UH3 phases before they actually transform into the polyhydrides. An attempt to analyse several experimental points given in [28] yields B ≈ 110 GPa for -UH3 and ≈160 GPa for -UH3, hinting that the values of B much below 100 GPa are unlikely. Revisiting experimental data from [24] in the pressure range of few GPa, where V(p) is approximately linear, we also obtain B ≈ 100 GPa. Hence we can calculate dlnTc/dlnV ≈ 1.1 if a plausible value B ≈ 100 GPa is taken. Here we naturally also neglect any temperature dependence of B. For comparison (see Tab. 1) we included well documented cases of cubic materials (NaCl structure type), so as to avoid ambiguities with possible anisotropic compressibilities and anisotropic reactions of magnetism on a lattice compression. The choice involves a typical band antiferromagnet UN [29-31], US with higher TC and presumably more local-moment system [32], and UAs, where TN already increases with pressure [34], and we can deduce the 5f states character shifted towards the localization. material UN US UH3 UAs
Type of order AF F F AF
TC,N [K] 53 [29] 180 [32] 180 127 [34]
dlnTC,N/dp B [GPa] dlnTC,N/dlnV [GPa-1] -0.1 [29] 203 [30] 19 [31] -0.012 [32] 92 [33] 1.1 [32] -0.011 ≈100 1.1 +0.020 [34] 101 [35] -2.0
Tab. 1: Comparison of properties of UH3 with diverse U compounds, all cubic, crystalizing with the NaCl structure type. The data without reference are based on the present work or calculated by us on the basis of other parameters. If we map UH3 onto the group of NaCl structure compounds, it would be located somewhere close to US, i.e. far from the itinerant magnetism limit. This is quite remarkable if we consider the U-U distances, which are 387 pm for US (407 pm for UAs, 345 pm for UN) in a contrast with 331 pm and 360 pm for - and -UH3, respectively. Uranium trihydride clearly reaches such degree of localization at much smaller U-U distances. The specific impact of the U-H bonding on the 5f states, not only the volume expansion, is the vital ingredient in the hydrides. As stated previously, we can assume that the 6d-1s hybridization reducing the 5f-6d hybridization, has the decisive role [15]. A question remains what is the real pressure dependence of U magnetic moments () in UH3. Existing data covering the pressure range below 1 GPa [17] indicate a linear decrease dln/dp = -0.016 GPa-1. As this value represents a faster decrease than for TC it can indeed mean that the fast decay of moments is partly compensated by a stronger effective inter-site coupling, induced by the volume compression. Although the data in ref. [17] do not show any non-linearity (surprizingly observed for TC), it would be desirable to explore the fine variations of magnetization over a larger pressure range. Such experiment, however, requires also high magnetic fields because of a slow approach to saturation, which needs a careful data analysis. Moreover, one has to keep in mind that although dlndlnTC is expected to be close to 1 in itinerant magnetic systems [36], U-based materials have the magnetization with a dominant orbital moment component (antiparallel to the spin component), while the exchange driven phenomena will depend predominantly on spin, which can considerably distort the ratio dlndlnTC It is naturally interesting to probe the compressed state by ab initio calculations which may suggest tendencies in variations of magnetic moments. The ordering temperatures as one of finite temperature properties are much more involved and cannot be deduced in a straightforward way. Although results of fully relativistic GGA computations give reasonable agreement as to the equilibrium volume [15], the obtained size of total magnetic moments if close to 0 due to almost complete cancellation of spin and orbital parts. As this result is far from the bulk magnetization corresponding to ≈ 1 B/U, we employed the GGA+U scheme. Our calculations were performed using the projected augmented wave (PAW) potentials as implemented in the VASP code [37]. For the exchange–correlation effects, Generalized Gradient Approximation (GGA) as parametrized by the Perdew, Burke and Ernzerhof (PBE) functional [38] was utilized simultaneously with the Hubbard model in the rotationally invariant approach [39] for uranium 5f-electrons. Spin-orbit coupling (SOC) was included, as well. Although the necessity to choose the values of the direct Coulomb and Hund’s exchange parameters U and J means in a strict sense a loss of the parameter-free ab initio nature, the successful choice of U and J values can provide an additional information on the interactions in a particular system. Here we took as a figure of merit the agreement of equilibrium volume for - and -UH3 and UH2, as well as the total magnetic moments. Because of the experimental uncertainty, we could not take the equilibrium bulk modulus as one of the benchmark parameters. Testing the merit of the GGA+U calculations on the landscape of all meaningful values of parameters of U and J, we found that the combination U = 0.5 eV, J = 0.5 eV, can be used as a reasonable basis.
Compound -UH3 -UH3 (UH3)0.82Mo0.18 UH2
6c 2a 6c 2a
aexp (pm) 416.0
acalc (pm) 417.1
S (B)
L (B)
U (B)
-2.01
3.04
1.03
664.4
667.7
664 *
649.9
536 **
531.6
-2.03 -1.98 -1.7 -1.8 -1.99
2.80 2.38 2.7 2.2 2.96
0.77 0.40 1.0 0.4 0.97
Bcalc (GPa) 87 91 104 75
*Data from total scattering experiment **Data from a thin film Tab. 2: Calculated equilibrium lattice parameter acalc (bulk modulus Bcalc, and spin, orbital, and total magnetic moments per U atom. Two different U sites in the -UH3 structure are distinguished. (UH3)0.82Mo0.18 is emulated by the -UH3 structure with a Mo atom replacing U in the one of the two 2a positions, which makes also the individual magnetic moments at the 6c positions somewhat different. The table gives an average value. Two different U sites in -UH3 yield somewhat different uranium moments. This fact agrees with previous computational results [40], although no support for a difference has been found by neutron diffraction [13]. A moderate increase of U (up to 2 eV) allows to reproduce the lattice parameters, but the spin magnetic moments exceed orbital ones, which is for U-compounds unrealistic [41]. For the above-mentioned specific choice U = J, the spherically-symmetric terms in the “+U” part of the rotationally invariant GGA+U functional are set to zero, and remaining spin and orbitally dependent GGA+U terms include just the orbital polarization (OP) [42] and spin-flips beyond the level given by the density functional approximation. The situation can be assumed as the OP limit of GGA+U, and guarantees that the 5f states are not split off from the Fermi level EF, maintaining the Sommerfeld coefficient enhanced from ≈10 mJ/mol K2 in -U to ≈30 mJ/mol K2 in UH3 [43]. The 5f presence at EF was actually also indicated by photoelectron spectroscopy [16]. Tab. 2 demonstrates that the explicit inclusion of Mo in one of the 2a U positions and relaxing the structure (the concentration corresponds to 1/8 = 12.5 % Mo, 7/8 = 87.5% U) does not change much the U moments or B, providing a good basis for using the alloyed U-Mo hydride as a model material for -UH3. Further details of results of ab initio calculations can be seen in Figs. 4 and 5, depicting variations of total energy as a function of volume, giving the calculated equilibrium volume. A simple analysis for -UH3 with smaller unit cell demonstrates that using the scalar relativistic GGA approximation gives about 2% overbinding, including the spin-orbit interaction reduces the misfit to 1.1%. This is both considerably better than using the conventional LSDA approximation (not shown here) with 11% overbinding and much stiffer lattice. The effect of magnetism for -UH3 is shown on Fig.5, where a non-magnetic (forced paramagnetic) state is compared with the ferromagnetic state both for GGA and GGA + U (U = J = 0.5 eV) case. The absence of uranium moments leads to a volume collapse, the calculated equilibrium volumes are 6% and 4.5%, respectively, below the experimental value. Allowing for the ferromagnetic ordering with the (111) direction of moments, which gives the lowest total energy, gives the equilibrium volume 2% below the experimental value for GGA and 1.5% above it for GGA +U, both with spin orbit coupling. Compressing the -UH3 lattice to estimate the moment variations under pressure leads to a reduction of both S and L. The calculations for the volume corresponding to the pressure of 3.2 GPa show that orbital moments are more pressure sensitive. The decrease of L by 4% and of S by 2% gives the total moment reduced by ≈10%. This is actually more than if estimated magnetization
variations at low pressures [17] would be extrapolated to 3.2 GPa. Such procedure would show about 5% decrease from the respective zero-pressure value. Pressure variations of magnetization, or even its spin and orbital component, accessible via X-ray magnetic circular dichroism experiment, would be an important test of the relevance of the calculations with respect of details of 5f magnetism. For precise determination of ordered U moments the slow approach of saturation is, however, the fact needing a special care. In particular high magnetic fields are needed.
-2.1769
-5.9864
-UH3 scalar relativistic GGA
E - E0 (eV/f.u.)
-2.2109
-6.0204
-2.2449 -6.0544 -2.2789 -6.0884 -2.3129 -6.1224
-2.3469 -UH GGA with SOC 3 -2.3810
0.88
0.92
0.96
1.00
1.04
1.08
-6.1565
V/V0
Fig. 4: Total energy variations of -UH3 as a function of unit cell volume for the scalar relativistic GGA calculations (using WIEN2k package with PBE functional) for the scalar relativistic approximation and with spin-orbit coupling.
0.7
E - E0 (eV/f.u.)
0.6 0.5
GGA+U - NM
0.4 GGA - NM
0.3 0.2 0.1 0.0
GGA - FM
GGA+U - FM
-0.1 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15
V/V0 Fig. 5: Total energy variations of -UH3 as a function of unit cell volume for the fully relativistic GGA and GGA+ U calculations (using VASP code with PBE functional) for the ferromagnetic and non-magnetic state. The energies were normalized (by proper choice of E0) to give the E – E0 = 0 in the ferromagnetic states and energies for the GGA and GGA + U cannot be directly compared. The energy differences between the respective ferromagnetic and non-magnetic states are physically meaningful. The lines represent the Birch-Murnaghan fits, yielding the bulk modulus B = 96 GPa for ferromagnetic GGA case. Including U and J makes the lattice somewhat softer (B = 91 GPa) while the overbinding in the absence of U magnetic moments gives a higher B-values (108 GPa for GGA + U and 117 GPa for GGA).
4. CONCLUSIONS The high-pressure ac susceptibility study revealed that the Curie temperature of UH3 is reduced linearly under applied hydrostatic pressure up to 3.2 GPa. The rate of the decrease, -1.87 K/GPa, is lower than expected for a 5f itinerant system. Critical evaluation of existing elastic properties suggests the bulk modulus around 100 GPa, i.e. UH3 does not have the extremely soft lattice as reported in the past. This allowed us to estimate dlnTC/dlnV ≈ 1.1, which is close to e.g. US. We can therefore deduce a significant 5f localization tendencies, rather unexpected for short UU distances. Acknowledgements This work was supported by the Czech Science Foundation under the grant no. 18-02344S. A part of the theoretical research was supported by the grant no. 17-27790S. We acknowledge support by
the projects CZ.02.1.01/0.0/0.0/15_003/0000485 and CZ.02.1.01/0.0/0.0/16_013/0001791 within the Operational programme Research Development and Education financed by ERDF. Experiments were partly performed in MGML (http://mgml.eu), which is supported within the program of Czech Research Infrastructures (project no. LM2018096). References [1] J. Lee, M. Matsuda, J.A. Mydosh, I. Zaliznyak, A.I. Kolesnikov, S. Süllow, J.P. C. Ruff, G.E. Granroth, Dual Nature of Magnetism in a Uranium Heavy-Fermion System. Phys. Rev. Lett. 121 (2018) 057201. DOI: 10.1103/PhysRevLett.121.057201. [2] G. Zwicknagl, 5f Electron correlations and core level photoelectron spectra of Uranium compounds, Phys. Stat. Sol. B 250 (2013) 634-637. DOI 10.1002/pssb.201200732. [3] H.R. Ott and Z. Fisk, Heavy-electron actinide materials, in: Handbook on the Physics and Chemistry of the Actinides, vol. 5, A.J. Freeman and G.H. Lander, eds., North-Holland, Amsterdam 1987, pp. 85-225. [4] D. Aoki, J. Flouquet, Ferromagnetism and Superconductivity in Uranium Compounds. J. Phys. Soc. Jpn. 81 (2012) 011003. DOI: 10.1143/JPSJ.81.011003. [5] G. Koutroulakis, H. Yasuoka, P.H. Tobash, J.N. Mitchell, E.D. Bauer, J. D. Thompson, Extended Nuclear Quadrupole Resonance Study of the Heavy-Fermion Superconductor PuCoGa5, Phys. Rev. B 94 (2016) 165115. DOI: 10.1103/PhysRevB.94.165115. [6] V. Taufour, D. Aoki, G. Knebel, and J. Flouquet, Tricritical Point and Wing Structure in the Itinerant Ferromagnet UGe2. Phys. Rev. Lett. 105 (2010) 217201. DOI: https://doi.org/10.1103/PhysRevLett.105.217201. [7] L. Havela, A.V. Kolomiets, A.V. Andreev, J.-C. Griveau, F. Honda, Z. Arnold: Extended stability range of the non-Fermi liquid phase in UCoAl, J. Phys.: Condens. Matter. 30 (2018) 385601. DOI: 10.1088/1361-648X/aada59. [8] A.V. Kolomiets, J.-C. Griveau, J. Prchal, A.V. Andreev, L. Havela: Variations of magnetic properties of UGa2 under pressure, Phys.Rev. B 91 (2015) 064405. DOI: 10.1103/PhysRevB.91.064405. [9] Q.G. Sheng, B.R. Cooper, Pressure-induced magnetic ordering effects in correlated-electron uranium mon ochalcogenides, J. Mag. Mag. Mater. 164 (1996) 335-344. DOI: 10.1016/S03048853(96)00409-X. [10] L. Havela, M. Diviš, V. Sechovský, A.V. Andreev. F. Honda, G. Oomi, Y. Méresse, S. Heathman: U ternaries with ZrNiAl structure - lattice properties, J.Alloys Comp. 322 (2001) 7-13. DOI: 10.1016/S0925-8388(01)01176-8 [11] S. Mašková, A.M. Adamska, L. Havela, N.-T.H. Kim-Ngan, J. Przewoźnik, S. Daniš, K. Kothapalli, A.V. Kolomiets, S. Heathman, H. Nakotte, H. Bordallo: Lattice anisotropy in uranium ternary compounds: UTX, J. Alloys Comp. 522 (2012) 130-135. DOI: 10.1016/j.jallcom.2012.01.122.
[12] R. Troc, W. Suski, The discovery of the ferromagnetism in U(H,D)3: 40 years later, J. Alloys Comp. 219 (1995) 1-5. DOI: 10.1016/0925-8388(94)05062-7. [13] I. Grenthe, J. Drozdynski, T. Fujino, E.C. Buck, T.E. Albrecht-Schmitt, S.F. Wolf, Uranium, in: The Chemistry of the Actinide and Transactinide Elements, 3rd Edition, J.J. Katz, J.R. Morss, N. Edelstein, J. Fuger, eds., Springer 2006, pp. 253-698. [14] H.H. Hill, The early “actinides”: The periodic system’s f electron transition metal series, in: Plutonium 1970 and Other Actinides, ed. W.N. Miner (AIME 1970), pp 1-19. [15] I. Tkach, M. Paukov, D. Drozdenko, M. Cieslar, B. Vondráčková, Z. Matěj, D. Kriegner, A.V. Andreev, N.-T.H. Kim-Ngan, I. Turek, M. Diviš, and L. Havela: Electronic properties of α-UH3 stabilized by Zr , Phys.Rev. B 91 (2015) 115116. DOI: 10.1103/PhysRevB.91.115116. [16] T. Gouder, R. Eloirdi, F. Wastin, E. Colineau, J. Rebizant, D. Kolberg, and F. Huber, Electronic structure of UH3 thin films prepared by sputter deposition, Phys. Rev. B 70 (2004) 235108. DOI: 10.1103/PhysRevB.70.235108. [17] A.V. Andreev, S.M. Zadvorkin, M.I. Bartashevich, T. Goto, J. Kamarád, Z. Arnold, H. Drulis, Magnetic and magnetoelastic properties of β-UH3, J. Alloys Comp. 267 (1998) 32-36. https://doi.org/10.1016/S0925-8388(97)00531-8. [18] I. Tkach, S. Mašková, Z. Matěj, N.-T. H. Kim-Ngan, A. V. Andreev, L. Havela, Ferromagnetism with TC=200 K in the amorphous 5f compound UH3Mo0.18, Phys. Rev. B 88 (2013) 060407(R). DOI: 10.1103/PhysRevB.88.060407 [19] L. Havela, M. Paukov, I. Tkach, Z. Matěj, D. Kriegner, S. Mašková, B. Vondráčková, M. Prachařová, I. Turek, M. Diviš, M. Cieslar, D. Drozdenko, N.-T.H. Kim-Ngan, A.V. Andreev, UH3-based ferromagnets: New look an an old material, J. Mag. Mag. Mater. 400 (2016) 130-136. DOI: 10.1016/j.jmmm.2015.07.053. [20] L. Havela, M. Paukov, I. Tkach, V. Buturlim, Z. Matej, S. Maskova, I. Turek, M. Divis, D. Drozdenko, M. Cieslar, M. Dopita, Z. Molcanova, M. Mihalik, Strong 5f Ferromagnetism in UH3Based Materials, 1 (2016) 2987-2992. DOI: 10.1557/adv.2016.287. [21] N. Fujiwara, T. Matsumoto, K. Koyama-Nakazawa, A. Hisada, Y. Uwatoko, Fabrication and efficiency evaluation of a hybrid NiCrAl pressure cell up to 4 GPa, Rev. Sci. Instrum. 78 (2007) 073905. DOI: 10.1063/1.2757129. [22] K. Murata, H. Yoshino, H. O. Yadav, Y. Honda, N. Shirakawa, Pt resistor thermometry and pressure calibration in a clamped pressure cell with the medium, Daphne 7373, Rev. Sci. Instrum., 68 (1997) 2490-2493. DOI: 10.1063/1.1148145. [23] J.J.M. Franse, Itinerant-electron magnetism studied in high-magnetic field and high-pressure experiments, J. Mag. Mag. Mater. 31-34 (1983) 819-828. [24] I. Halevy, S. Sahov, S. Zalkind, M. Brill, I. Yaar, High pressure study of -UH3 crystallographic and electronic structure, J. Alloys Comp. 370 (2004) 59-64. DOI: 10.1016/j.jallcom.2003.09.124. [25] Ch.D. Taylor, T. Lookman, and R.S. Lillard, Ab initio calculations of the uranium-hydrogen system: Thermodynamics, hydrogen saturation of -U and phase-transformation to UH3, Acta Materialia 58 (2010) 1045-1055. DOI: 10.1016/j.actamat.2009.10.021. [26] Y. Zhang, B. Wang, Y. Lu, Y. Yang, P. Zhang, Electronic, mechanical and thermodynamic properties of -UH3: A comparative study by using the LDA and LDA+U approaches, J. Nucl. Mater. 430 (2012) 137-141. DOI: 10.1016/j.jnucmat.2012.07.002. [27] C. Zhang, H. Jiang, H.-L. Shi, G.-H. Zhong, Y.-H. Su, Mechanical and thermodynamic properties of -UH3 under pressure, J. Alloys Comp. 604 (2014) 171-174. DOI: 10.1016/j.jallcom.2014.03.071.
[28] I.A. Kruglov, A.G. Kvashnin, A.F. Goncharov, A.R. Oganov,.S. Lobanov, N. Holtgrewe, S. Jiang, V. Prakapenka, E. Greenberg, A.V. Yanilkin, Uranium polyhydrides at moderate pressures: Prediction, synthesis, and expected superconductivity, Sci.Adv. 4 (2018) eaat9776. DOI: 10.1126/sciadv.aat9776. [29] J.M. Fournier, J. Beille, C.-H. de Novion, Magnetic properties of UN under pressure, J. Phys. Colloq. 40 (1979) C4-32-C4-33. DOI: 10.1051/jphyscol:1979411. [30] J. Staun Olsen, L. Gerward, U. Benedict, A new high-pressure phase of uranium nitride studied by X-ray-diffraction and synchrotron radiation, J.Appl. Crystallography 18 (1985) 37-41. https://doi.org/10.1107/S0021889885009736. [31] J.M. Fournier, J. Beille, A. Boeuf, C. Vettier, A. Wedgwood, Magnetic structure of UN under pressure, Physica 102B (1980) 282-284. DOI: 10.1016/0378-4363(80)90174-6. [32] C.Y. Huang, R.J. Laskowski, C.E. Olsen, J.L. Smith, High pressure study of ferromagnetic US, J. Phys. Colloq.40 (1979) C4-26-C4-27. DOI: 10.1051/jphyscol:1979408. [33] J. Staun Olsen S. Steenstrup, L. Gerward, U. Benedict, C. Spirlet, G.D. Andretti, High-pressure X-ray diffraction experiments on US using synchrotron radiation, J. Less Common Met. 98 (1984) 291-300. https://doi.org/10.1016/0022-5088(84)90302-3. [34] I.N. Goncharenko, J.-M. Mignot, V.A. Somenkov, J. Rossat-Mignod, O. Vogt, Magnetic phase diagram of UAs at very high pressures up to 50 kbar, Physica B199&200 (1994) 625-627. [35] J.M. Léger, I. Vedel, A.M. Redon, J. Rossat-Mignod, O. Vogt, High-pressure X-ray studies of UAs and UTe, Solid Sate Commun. 66 (1988) 1173-1176. DOI: 10.1016/0038-1098(88)91127-1. [36] J.M. Fournier, Pressure effects on the magnetic properties of actinide intermetallics, Physica 130B (1985) 268-277. [37] G. Kresse and J. Furthmueller, Phys. Rev. B 54 (1996) 11169-11186. DOI: 10.1103/PhysRevB.54.11169. [38] J.P. Perdew, K. Burke, M. Ernzerhof, Generalized Gradient Approximation made simple, Phys. Rev. Lett. 77 (1996), 3865−3868. DOI: 10.1103/PhysRevLett.77.3865. [39] A.I. Liechtenstein, V.I. Anisimov, J. Zaanen, Phys. Rev. B 52 (1995) R5467-R5470. DOI: 10.1103/PhysRevB.52.R5467. [40] Ch.D. Taylor, Characterizing electronic structure motifs in -UH3. Phys. Rev. B 82 (2010) 224408. DOI: 10.1103/PhysRevB.82.224408. [41] F. Wilhelm, J.P. Sanchez, A. Rogalev, Magnetism of uranium compounds probed by XMCD spectroscopy, J. Phys. D: Appl. Phys. 51 (2018) 333001. DOI: 10.1088/1361-6463/aacf7d. [42] A. Shick, V. Janis, V. Drchal, W. Pickett, Spin and orbital magnetic state of UGe2 under pressure, Phys. Rev. B 70 (2004) 134506. DOI: 10.1103/PhysRevB.70.134506. [43] J.W. Ward, L.E. Cox, J.L. Smith, G.R. Stewart, J.H. Wood, J.Phys.(Paris) 40 (1979) C4-15. DOI: 10.1051/jphyscol:1979403.
We state hereby that none of the authors has any conflict of interests related to the matter of publishing the paper Pressure variations of the 5f magnetism in UH3 .
Highlights
Curie temperature of beta-UH3 decreases with pressure to 3.2 GPa. The linear decrease approx. -2 K/GPa is linear and weaker than assumed before The decrease indicates intermediate 5f delocalization Basic features are captured by GGA+U method.