Complex Landau-Ginzburg theory of the hidden order in URu2Si2

We develop a Landau-Ginzburg theory of the hidden-order phase and the local moment antiferromagnetic phase of URu2Si2. We unify the two broken symmetries in a common complex-order parameter and derive many experimentally relevant consequences such as the topology of the phase diagram in magnetic field and pressure. The theory accounts for the appearance of a moment under application of stress and the thermal expansion anomaly across the phase transitions. It identifies the low-energy mode which is seen in the hidden-order phase near the commensurate wave vector (0, 0, 1) as the pseudo-Goldstone mode of the approximate U(1) symmetry. Copyright c © EPLA, 2010 URu2Si2 is arguably the most intriguing heavy-fermion material and its electronic structure has continued to be the focus of intensive investigations. At 17.7K, it displays a phase transition to a phase for which, in spite of a large number of experimental efforts, the order parameter has not been identified and it is therefore referred to as hidden order (HO) [1]. Recent first-principles LDA+DMFT calculations showed that in the paramagnetic phase of URu2Si2, the local ground state of the 5f configuration, and its first-excited state are two singlets, |∅〉 and |1〉 of opposite symmetry under x and y reflection, separated by a crystal field splitting ∆. We proposed that the order parameter of the hiddenorder (HO) and local moment antiferromagnetic (LMA) phase is the excitonic mixing between the two lowestlying configurations of the f electrons [2]. The excitonic mixing of the two singlets is described by a complexorder parameter 〈X∅1(j)〉=ψj/2 = (ψ1,j + iψ2,j)/2, where X∅1(j) is the Hubbard operator |∅〉〈1| at site j. ψ2 is proportional to the magnetization along the z-axis in the material, while ψ1 is proportional to the hexadecapole operator (JxJy +JyJx)(J 2 x −J2 y ). The characteristic shape of the hexadecapole is shown in fig. 1(c). The presence of ψ1 does not break the time reversal symmetry, nor the tetragonal symmetry, but it does break the reflection symmetry along the x and y-axis. We identify the phase with nonzero ψ1 as the “hidden-order” phase, and the phase with nonzero ψ2 as the LMA phase. In this picture, (a)E-mail: [email protected] the LMA and the HO order parameters are intimately connected, and they are related by an internal rotation in parameter space. In this paper, we build on these insights from LDA+DMFT microscopic theory to construct a lowenergy phenomenological model, and to establish contact with many of the available experimental results on this material. Phenomenological theories of the Landau Ginzburg type for URu2Si2 have been developed before [3–5]. However an approximate symmetry between the LMA and and the HO phase has not been noticed before, and the material specific information resulting from the microscopic calculations, was not available before. The new insights from LDA+DMFT calculation restricts the effective theory enough to result in a large number of consequences that can be compared with experiment, as for example the response of the system to pressure, uniaxial stresses and weak external magnetic field. In addition, the simplifications offered by the low-energy effective Hamiltonian of Landau-Ginzburg type allow us to obtain analytical expressions which cannot be obtained in the full LDA+DMFT solution. We take the symmetry of the low-lying crystal field sequence from LDA+DMFT calculation |∅〉= i √ 2 (|4〉− |− 4〉), and |1〉= cos(φ) √ 2 (|4〉+ | − 4〉)− sin(φ)|0〉, with φ∼ 0.372π and ∆≈ 35K. The value of φ in the “pseudo-atomic” picture used here is modified from the LDA+DMFT value φ∼ 0.23π, to take into account renormalization from higher-lying f configurations. A low-energy many-body Hamiltonian, generating this sequence of levels, is sketched in the appendix. While