Evolution of Heterogeneous Antiferromagnetic State in URu₂Si₂: Study of Hydrostatic-Pressure, Uniaxial-Stress and Rh-Dope Effects

Abstract

We have investigated the nature of the competition between hidden order and antiferromagnetic (AF) order in URu2Si2 by performing the neutron scattering experiments under hydrostatic-pressure P , uniaxial-stress σ, and Rh-substitution conditions. Hidden order observed at ambient pressure in pure URu2Si2 is found to be replaced by the AF order by applying P , σ along the tetragonal basal plane, and by doping Rh. We discuss these experimental results on the basis of the crystalline strain calculations, and suggest that this phase transition is generated by the 0.1% increase of the tetragonal c/a ratio. We have also found that the magnetic excitation observed in the hidden order phase vanishes in the AF phase. We show that this variation can be qualitatively explained by assuming the hidden order parameter to be quadrupole.KEYWORDS: heavy-electron system, URu2Si2, hidden order, inhomogeneous magnetism, neutron scattering IntroductionThe ternary tetragonal compound URu 2 Si 2 is a well known heavy-electron system that shows a peculiar ordered phase below T o = 17.5 K and an unconventional superconductivity below T c ∼ 1.2 K.1-3) The phase transition at T o is associated with clear anomalies in bulk properties including specific heat, magnetic susceptibility and electrical resistivity, whose shapes indicate that the gap is formed in parts of the Fermi surfaces of the heavy quasi-particles below T o . The elastic neutron scattering experiments [4][5][6][7][8][9] revealed that the type-I antiferromagnetic (AF) order develops below ∼ T o . However, the magnitude of the AF moment µ o is found to be extremely small (∼ 0.03 µ B /U), which is hard to account for the large bulk anomalies at T o such as the specific-heat jump (∆C/T o ∼ 300 mJ/K 2 mol). Furthermore, the internal field associated with µ o is never observed in the 29 Si-NMR experiments.10) The inconsistency among these experiments has been puzzling many researchers for about 20 years, i.e., whether the intrinsic order parameter is the weak AF moment or some unidentified "hidden" degree of freedom. So far various ideas for the order parameter have been proposed: the AF moment with highly reduced g values, 11-15) quadrupole order, [16][17][18][19][20] octupole order, 21,22) valence transition, 23) uranium dimers, 24) unconventional spin density wave, 25, 26) charge current order, 27) and helicity order.

Electronic Tuning in URu2Si2 Through Ru to Pt Chemical Substitution

“…(Zhu et al, 2010;Luo et al, 2013). Instead of this, temperature-dependent magnetic susceptibility, electrical resistivity, heat capacity, and high-field magnetoresistivity measurements reveal striking similarities to earlier reported phase diagrams in which tuning effectively adds electrons (Amitsuka et al, 1988;Dalichaouch et al, 1990a;Miyako et al, 1991;Kawarazaki et al, 1994;Yokoyama et al, 2004;Yokoyama and Amitsuka, 2007;Gallagher et al, 2016a;Gallagher et al, 2016b). In particular, the HO phase boundary is rapidly suppressed and abruptly collapses before x ≈ 0.03.…”

“…Finally, magnetic order with an antiferromagnetic character emerges and strengthens for 0.06 ≲ x ≲ 0.19, although it is distinct from what is seen for other tuning series (Amitsuka et al, 1988;Dalichaouch et al, 1990a;Miyako et al, 1991;Kawarazaki et al, 1994;Yokoyama et al, 2004;Yokoyama and Amitsuka, 2007;Gallagher et al, 2016a;Gallagher et al, 2016b;Rahn et al, 2021). These results provide evidence that although Ru → Pt, Rh and Si → P chemical substitutions are each distinct in their own way, they nonetheless provide semiunified tuning in URu 2 Si 2 that is likely connected to charge doping.…”

“…This is distinct from what is seen in other substitution series (e.g., Si → P (Gallagher et al, 2016a;Gallagher et al, 2016b) and Ru → Fe (Kanchanavatee et al, 2011)), where hidden order hosts SC even for chemically substituted specimens. The reason for the absence of SC is not clear, but it may suggest that, instead of enabling a smooth suppression of hidden order, Pt substitution stabilizes a magnetic phase that is similar to the antiferromagnetism that is seen at low x in the Ru → Rh series (Dalichaouch et al, 1990a;Amitsuka et al, 1988;Miyako et al, 1991;Kawarazaki et al, 1994;Yokoyama et al, 2004;Yokoyama and Amitsuka, 2007) or the parasitic small moment antiferromagnetism that occurs due to defects in the parent compound (Niklowitz et al, 2010). Recent results also suggest that antiferromagnetism intervenes in the Si → P substitution series at the boundary of the hidden order phase (Chappell et al, 2020).…”

“…A productive strategy for addressing these questions has been to perturb the electronic state and structure using tuning parameters such as applied pressure (McElfresh et al, 1987;Motoyama et al, 2003;Hassinger et al, 2008;, magnetic fields (De Boer et al, 1986;Nieuwenhuys, 1987;Kim et al, 2003a;Kim et al, 2003b), and chemical substitution (Amitsuka et al, 1988;Dalichaouch et al, 1989;Dalichaouch et al, 1990a;Dalichaouch et al, 1990b;Miyako et al, 1991;Kawarazaki et al, 1994;Yokoyama et al, 2004;Bauer et al, 2005;Jeffries et al, 2007;Yokoyama and Amitsuka, 2007;Butch and Maple, 2009;Kanchanavatee et al, 2011;Kanchanavatee et al, 2014;Das et al, 2015;Ran et al, 2016;Wilson et al, 2016). Applied pressure (McElfresh et al, 1987;Motoyama et al, 2003;Hassinger et al, 2008; and isoelectronic chemical substitution at the Ru site [Ru → Fe, Os (Kanchanavatee et al, 2011;Kanchanavatee et al, 2014;Das et al, 2015;Ran et al, 2016;Wilson et al, 2016)] produce similar results: as the hybridization strength increases, HO is first enhanced, and then it is converted to antiferromagnetism (LMAFM).…”

“…Superconductivity is only observed within the HO region. Nonisoelectronic substitution at the Ru site is less straightforward: Ru → Mn, Tc, Re substitution (Dalichaouch et al, 1989;Dalichaouch et al, 1990a;Dalichaouch et al, 1990b;Bauer et al, 2005;Jeffries et al, 2007;Butch and Maple, 2009; (effectively removing electrons) suppresses HO and stabilizes complex ferromagnetism, while Ru → Rh, Ir (Amitsuka et al, 1988;Dalichaouch et al, 1990a;Miyako et al, 1991;Kawarazaki et al, 1994;Yokoyama et al, 2004;Yokoyama and Amitsuka, 2007) (effectively adding electrons) suppresses HO, stabilizes a region with no long range magnetic order, and eventually gives rise to a new antiferromagnetically ordered state. More recently, studies have shown that Si → P substitution produces a similar phase diagram (Gallagher et al, 2016a;Gallagher et al, 2016b;Chappell et al, 2020).…”