In the 5d layered perovskite material, Sr2IrO4, spin-orbit coupling and strong electron correlations combine to give rise to a spin-orbit coupled Mott insulator with a pseudospin J=1/2 antiferromagnetic (AFM) state1,2. It exhibits close structural3,4, electronic5,6 and magnetic3,4 similarities with the 3d layered perovskite material, La2CuO4, which evolves from a spin S=1/2 AFM Mott insulator to a high temperature superconductor upon doping. Doped Sr2IrO4 has then become a quite promising material to discover new states of matter, including unconventional superconductivity.

The crystal structure of the layered perovskite Sr2IrO4 is characterized by the stacking of IrO2 and SrO layers. The Ir4+ ion is at the centre of an oxygen octahedron, rotated by θ=11° in the basal ab plane. (Fig. 1c). For a long time, Sr2IrO4 has been described as possessing a tetragonal centrosymmetric structure with four-fold rotational symmetry about the c-axis, corresponding to a space group I41/acd7. However, a structural distortion exists even above room temperature as shown by optical second-harmonic generation (SHG) studies8 yielding to the space group I41/a where the c- and d-glide planes are lost. That gives rise to additional weak Bragg spots such as (1, 0, 2n+1) that have been reported using neutron diffraction3,4. In this material, crystal field effects, spin-orbit coupling, Coulomb repulsion and the bending of the Ir-O-Ir bonds play an important role to understand electronic and magnetic properties.

Figure 1: Magnetic phase diagram and LC order.
figure 1

(a) Magnetic phase diagram of Sr2(Ir,Rh)O4. The obtained transition temperatures, TN and Tmag in this study are represented by black and red empty circles for the conventional AFM and the hidden magnetism preserving the lattice translation, respectively. The hidden broken symmetry phase, TΩ, observed by SHG15 (orange squares) is also represented as well as the AFM phase determined by magnetization measurements11,12,13 (blue triangles) and by neutron diffraction3,14 (green diamonds). (b) A schematic picture for co-planar LC state in a single IrO6 octahedron. The blue and red arrows denote magnetic moments generated by circulating currents and the anapole, Ω, respectively. (c) Atomic and AFM structures of Sr2IrO4 with a space group I41/a (origin choice 2) (Ir atoms are represented in green, Sr in yellow and oxygen in red). (d) The co-planar LC ordered state in the basal plane. The red arrows denote the anapole vector, Ω, as shown in b, and the plus/minus signs correspond to the orbital magnetic moments perpendicular to the ab-plane. This nearly-ferro-toroidal order preserves translational symmetry of lattice but breaks parity inversion, four-fold rotational and time-reversal symmetries.

Within the octahedral crystal field, the Ir 5d electronic levels split into eg and t2g states. Under strong spin-orbit coupling, the t2g states split into a J=1/2 doublet and J=3/2 quartet, so that, among the five 5d electrons of the Ir4+ ion, only one remains in the J=1/2 doublet state. A large enough effective Coulomb repulsion finally localizes the J=1/2 electron and one is left with a J=1/2 pseudospin model. Below TN230 K (ref. 1), an AFM order develops, characterized by a magnetic propagation wavevector qm=(1, 1, 1) and magnetic moments at the Ir sites aligned in the basal ab-plane3,4,9 (Fig. 1c). The directions of the staggered magnetic moments are tied to IrO6 octaedra and follow their rotation, θ, giving rise to a canting of the AFM structure in each IrO2 layer with a ferromagnetic component along the b-axis. As shown in Fig. 1c, the magnetic structure of Sr2IrO4 has a staggered stacking along the c-axis of the canted AFM layers (defined as + or − depending of the sign ±θ of the tilt). In other words, the weak ferromagnetic component in each layer is stacked to give a −++− structure along c-axis (AF-I phase)3,4, so it cancels out globally. However, the AFM interaction along the c-axis is rather weak, thus it is easily transformed to the ++++ stacking order (AF-II phase) by applying an external magnetic field2. At variance with the AF-I order, the AF-II stacking is then characterized by a magnetic propagation vector qm=0 (ref. 10) and a net (but weak) ferromagnetic moment. Throughout the paper, we refer to these AFM phases, as the one depicted in Fig. 1c, as conventional AFM phases.

Interestingly, the AFM transition temperature is suppressed under the substitution of Rh for Ir. While the Rh substitution could be thought to be iso-electronic, it should be stressed that Rh is likely to play the role of an acceptor (Rh3+/Ir5+) and effectively give rise to a hole-doping of the material10. Figure 1a shows the magnetic phase diagram in Sr2Ir1−xRhxO4. From bulk magnetization11,12,13 and neutron diffraction measurements3,14, the conventional AFM transition decays almost linearly as a function of Rh substitution up to xc≈0.15. Actually, X-ray studies10 indicate a slightly larger critical doping xc≈0.17 with the occurence of another transition at lower temperature when the magnetic correlation lengths are effectively diverging. Further, upon Rh substitution, the AFM order undergoes a transition from the AF-I to the AF-II phase, even at zero magnetic field10,14.

Recently, a hidden broken symmetry phase, developing prior to the AFM state, has been reported in Sr2(Ir,Rh)O4 using rotational anisotropy optical SHG measurements15. The hidden broken symmetry phase was observed distinctively at a few K above TN for the pure sample and far above for the doped systems15. These data highlight an odd-parity hidden order as both the inversion and four-fold rotational symmetries are broken below a temperature TΩ distinct from the Néel temperature TN (Fig. 1a)15. From the symmetry analysis, the SHG results could be in principle explained by a triclinic distortion of the crystal structure. However, there is no experimental evidence using X-ray and neutron scattering of any structural distortion2,3,4. It should be nevertheless stressed that these diffraction studies use too modest spatial resolution to definitively prove a lack of symmetry lowering.

Alternatively, the SHG signal could be due to a magnetic ordering although there is no proof of time-reversal symmetry breaking at TΩ. Actually, the AF-I ground state of pure Sr2IrO4 preserves the parity inversion symmetry and thus cannot explain the SHG signal. Instead, a few magnetic point groups that preserve the translation symmetry of the lattice were proposed to account for the SHG signal, such as 2′/m or m1′ (refs 15, 16). In particular, a so far non-observed AFM state of 2′/m symmetry, corresponding to a stacking +−+− along the c-axis of AFM planes, would produce the SHG signal16.

Among the magnetic point groups, it is argued15 that the new broken symmetries can be caused by a loop-current (LC) phase17,18, theoretically proposed to account for the pseudogap physics of superconducting cuprates. The existence of such a magneto-electric state has gained support from the detection in several cuprate families of its magnetic fingerprint by polarized neutron diffraction19,20,21,22,23,24. Using the same technique for Sr2(Ir,Rh)O4, we here report at the temperature of the odd-parity order, TΩ, the appearance of a hidden magnetic order, which breaks time-reversal symmetry while preserving lattice translation invariance. Among the magnetic models inferred from the SHG data15, only the co-planar LC order17,18 produces a magnetic diffraction pattern consistent with our polarized neutron data. Our results show that exotic magnetic orders with the same symmetry properties as the LC phase exist in both iridates and cuprates.


Momentum location of LC and AFM orders

Let us first describe the co-planar LC order. It is characterized by two circulating currents turning clockwise and anticlockwise within the same plane inside the IrO6 octahedron (Fig. 1b) and belongs to a 2′/m point group symmetry. It breaks time-reversal and inversion symmetries but not their product. The LCs produce two opposite orbital magnetic moments within each IrO6 octahedron. A toroidal pseudovector, or anapole, is defined as an order parameter by , where ri and mi stand for the position and the orbital magnetic moment, respectively, in one octahedron (Fig. 1b). It is similar to the toroidal moment in multiferroic systems25. When the anapole vectors are stacking parallel along the c-axis (ferro-toroidal coupling) as shown in Fig. 1d, the ordered structure does not break translational symmetry but breaks parity inversion and four-fold rotational symmetries15. Since the direction of the anapole is bound to the orientation of each IrO6 octahedron, the resulting order is a nearly-ferro-toroidal order (that is, weakly distorted) (Fig. 1d).

As explained in Supplementary Note 1, the Fourier transform of the magnetic correlation function associated with the LC phase is located in iridates at nuclear Bragg peaks, such as (1, 1, 2+4n). These Bragg peaks respect both the original body-centred tetragonal structure condition H+K+L=2n and the 2H+L=4m condition due to the (1/2, 0, 1/4) translation. (The wave-vector is denoted by Q=(H, K, L), see Methods section). This produces a very specific magnetic diffraction pattern, which can be probed by magnetic sensitive diffraction technique, such as neutron scattering technique.

We have investigated both the conventional AFM orders and the LC magnetic order using neutron scattering diffraction experiments. Note that the momentum transfers Q are different for both types of phase: (1, 0, L) for AFM peaks and (1, 1, L) for the LC peaks (see Supplementary Note 1 and Supplementary Fig. 1). Three major wave-vectors positions, Q, have been examined: their projection onto the reciprocal HK-plane are shown in Fig. 2a. We have then studied each phase in a different scattering plane: H00-00L for conventional AFM orders and HH0-00L to study the LC order (see Methods section). We have investigated two iridate samples: a pure Sr2IrO4 and a 7% Rh-doped one. Small single crystals have been co-aligned to get a large enough sample mass in order to perform the polarized neutron experiment. The sample preparation and magnetization measurements, which characterize the samples, are described in the Methods section (see also Supplementary Fig. 2).

Figure 2: AFM order in Sr2IrO4.
figure 2

(a) Momentum transfer Q positions (projected in the reciprocal HK-plane) investigated with neutron scattering: (1, 0, L=1, 2) corresponds to the AFM Bragg peaks, whereas (1, 1, 2) is where a magnetic scattering is expected for the LC phase. (b) Thermal evolution of the peak intensity at the AFM Bragg peak (1, 0, 2) measured by unpolarized neutron (black) and the full polarization analysis at T=100 and 250 K (red) (see text). (c,d) The (H, 0, L=1, 2) scans at 100 K for both the non-spin-flip (NSF) (empty symbols) and spin-flip (SF) (full symbols) channels (diamond symbols for L=1 and square symbols for L=2). While the (1, 0, 2) peak (black squares) shows purely magnetic behaviour, the (1, 0, 1) (green diamonds) shows a purely nuclear signal.

Conventional AFM orders

We have first studied the conventional AF-I order by repeating unpolarized neutron diffraction measurements3,4. We report in Fig. 2b the AFM Bragg peak at Q=(1, 0, 2) in the pure system where the magnetic Bragg intensity shows a sharp AFM transition at TN=232 K. The fitted critical exponent 2β≈0.41 is consistent to 0.36 in the previous report3. Next, we have performed polarized neutron experiment to study the Q=(1, 0, L) Bragg peaks to disentangle the magnetic and nuclear contributions of these peaks. The polarized neutron experiment setup is presented in the Methods section. It has been already used in previous measurements in cuprates and described in refs 19, 20, 21, 22, 23, 24. For a given neutron polarization P, the neutron intensities, ISF and INSF, are measured in both spin-flip (SF) and non-spin-flip (NSF) channels, respectively. Full magnetic signal appears in the SF channel when P||Q (refs 22, 24) whereas the nuclear intensity occurs in the NSF channel. Figure 2c,d shows the wave-vector scans along H across the magnetic peak Q=(1, 0, 2) for the NSF and SF channels. That proves the magnetic origin of the peak as it is only seen in the SF channel (Fig. 2d). In Fig. 2b, the magnetic intensity Imag=ISF−BG is determined at two temperatures, 100 and 250 K, below and above TN (where BG stands for the flat background of Fig. 2d). A clear magnetic intensity is sizeable at 100 K, whereas no magnetic intensity is seen at 250 K. Further, we report at 100 K in Fig. 2b the magnetic intensity for three different neutron polarization states: the polarizations P||Q and PQ are in the scattering plane (see Methods section), whereas P||z is perpendicular to the scattering plane. In the given geometry, zero magnetic intensity with P||z proves that the AFM moments are confined in the ab-plane. This is in agreement with the previous studies of the neutron structure factors3,4.

In the same scattering plane, the Bragg peaks at Q=(1, 0, L) for L=1 and 3 were also measured using polarized neutrons. They correspond to the forbidden peaks of the original I41/acd structure giving rise to the space group I41/a where the glide planes are lost8. As it has been already discussed3,4, their temperature dependence exhibits no anomaly neither at the Néel temperature nor at the onset of the odd-parity hidden order (TΩ)15. The origin of that scattering is non-magnetic, as shown in Fig. 2c,d. For the Bragg peak at Q=(1, 0, 1), no signal is sizeable in the SF channel and only a NSF signal is observed above the background. These results exclude the possibility of an AFM arrangement of +−+− type, where the magnetic signal should be only at odd L-value. It casts serious doubts that such an AFM stacking can explain the origin of the SHG signal16. The same conclusion holds for the ++++ arrangement, not observed in pure Sr2IrO4, in full agreement with the literature3,4,9. To account for the occurrence of an odd-parity hidden order in SHG measurements in pure Sr2IrO4, we are left with two scenarios. Either the missing AFM orders are light-induced metastable states during the SHG measurements, as suggested in ref. 16, or another kind of magnetic order exists. Let us consider this second scenario now.

LC order

The overall experimental procedure to extract the magnetic signal associated with the LC order is detailed in Supplementary Note 2 and it follows methods established in previous works on superconducting cuprates19,22. The measured SF intensity, ISF at Q=(1,1,2), is reported as a function of temperature in Fig. 3a for the pure sample. It is compared with the background baseline determined from the measured NSF intensity (see Fig. 3a caption and Supplementary Fig. 3). While decreases monotonically as temperature decreases, the SF intensity instead departs from below Tmag≈240±30 K. The difference, ISF, evidences a spontaneous magnetic order whose magnetic intensity, Imag, is reported in Fig. 3b. It has a different symmetry compared to the conventional AFM phases discussed above and the position corresponds to where magnetic intensity is expected for the LC phase. For the 7% Rh-substituted sample, the same analysis is given in Fig. 3c,d. While the AFM transition is suppressed down to TN≈100 K, the novel magnetic order is observed at much higher temperature Tmag≈240±30 K. Within error bars, the transition temperature, Tmag and its normalized magnetic intensity do not show a significant difference between the pure system and 7% Rh substitution. This is consistent with the estimate of onset of the hidden order, TΩ, from SHG (orange squares in Fig. 1a)15, which does not change appreciably with Rh substitution. Using the calibration of nuclear Bragg peaks intensities (Supplementary Fig. 4), one can deduce the magnetic cross-section of the hidden magnetic order as 2 mbarns per f.u., which is <10−3 of the strongest nuclear Bragg peak. The normalized magnitude of Imag for the hidden magnetic order is similar in both samples and is 5 times smaller than the one for the AFM order, (as shown by the comparison of the vertical scale of Fig. 3b,d with the red vertical scale of Fig. 2b).

Figure 3: Hidden magnetic order in Sr2Ir1−xRhxO4.
figure 3

(a,c) Temperature dependence of ISF and a bare SF intensity =INSF/FR0(T) from the polarization leakage. The temperature-dependent bare flipping ratio FR0(T) is taken from the reference Bragg peak (2, 2, 0) and rescaled to correct the NSF intensity at (1, 1, 2) (see Supplementary Note 2). (b,d) Temperature dependence of the magnetic intensity Imag=ISFINSF/FR0(T) at the nuclear Bragg peak (1, 1, 2). Red curves are a guide to the eye and grey areas represent temperature uncertainty in the determination of Tmag.


To understand the spontaneous magnetic order at Tmag, a model is needed to explain the broken symmetries of the hidden order. Concomitant with the SHG data, time-reversal, parity inversion and four-fold rotational symmetries are broken. It preserves the translational symmetry of the underlying lattice, as the magnetic scattering appears on top of the nuclear Bragg peak. The LC model17,18 is a good candidate, since it can explain all these broken symmetries. Nevertheless, a more detailed and quantitative study is required to establish the exact order parameter in the hidden ordered phase. The weak magnetic cross-section shows how difficult it is to detect and why it was not reported with typical unpolarized neutron diffraction. Due to the experimental limitations, a precise determination of the direction of induced magnetic moments and the full magnetic structure requires further works.

Actually, other magnetic orders, which could potentially account for the SHG data, are not consistent with our finding as they would give rise to distinct scattering patterns. For instance, the proposed structure with m1′ point group15 yields a different relation H+K+L=2n+1, as the configuration is opposite when one considers the (1/2, 1/2, 1/2) translation. This breaks the original body-centred nuclear structure7 and would give rise to magnetic superstructure peaks at (1, 0, L=2n) and no magnetic intensity at any (1, 1, L) position. With Rh doping, one also does not observe magnetic superstructures at (1, 0, L) with even L10,14. Both points dismiss the proposal of the m1′ point group15.

Alternatively, the SHG measurements have been reinterpreted considering conventional AFM orders16 with a different stacking along the c-axis. We detail in Supplementary Note 3 why the different AFM structures discussed in the literature cannot actually explain our observation. First, since the hidden order occurs at different Q positions compared to the AFM order, it is clearly distinct with the AF-I order. Second, the AFM state of 2′/m symmetry with a +−+− stacking along the c-axis of AFM planes is argued to explain SHG data16. This phase will give rise to magnetic contributions at positions such as (1, 0, L=2n+1) and nothing at (1, 1, L), where we observe the hidden magnetic intensity. Further, the non-magnetoelectric ++++ phase (AF-II) (described above) could also account for the SHG data16. This AF-II phase is reported in the Rh-doped system10,14 but is absent in the pure system3,4. It would also exhibit the largest magnetic contribution at (1, 0, L=2n+1) as well as tiny magnetic contributions at Bragg peaks, such as (1, 1, L=2+4n), due to its weak ferromagnetism. This interpretation can be excluded in both samples we have studied. First, in the pure sample, the ferromagnetic order is absent (see Fig. 1)3,4 and can be only induced by an applied magnetic field of about 0.2 T (2000 Oe)2. Second, under Rh substitution, such a ferromagnetic order indeed develops but only below TN (ref. 10), as it results from the canting of the AFM order, clearly lower than Tmag. Moreover, the neutron intensity due to ferromagnetism would be tan2θ≤10−2 smaller than the AFM one, that is, at least one order of magnitude smaller than the observed magnetic scattering we report here. All these arguments allow us to rule out the weak ferromagnetism derived from the canted AFM order as a candidate to account for the observed magnetic scattering at Q=(1, 1, 2). Therefore, our observation of a magnetic signal at Q=(1, 1, 2) is not consistent with any kind of stackings along the c-axis of the pseudospin AFM orders considered to explain the SHG signal in ref. 16.

Using polarized neutron diffraction, we have experimentally addressed all these alternative phases and found out evidence for a hidden magnetic order in Sr2Ir1−xRhxO4. It is a translation-invariant but time-reversal symmetry broken phase that is consistent with the LC order of 2′/m point group symmetry, concomitantly compatible with the SHG signal. In that model, all IrO6 octahedra, which are the building blocks of the material, are identically decorated by the same set of staggered magnetic moments, whose magnetism cancels out on each octahedron (as depicted in Fig. 1b). This magnetic order is then clearly distinct from the AFM one, where each octahedron has a single pseudospin on the Ir site and where the nearest octahedra have staggered moments.

In conclusion, we report the first evidence of an unconventional magnetic order in Sr2(Ir,Rh)O4, which breaks time-reversal symmetry but preserves translational symmetry of the underlying lattice. By analogy with superconducting cuprates, where a similar kind of order is observed, one can refer to it as an intra-unit-cell order. The new magnetic phase overlaps with parity inversion and rotational symmetry broken phase recently reported using SHG15. Both observations can be described by the LC order17,18 proposed for the pseudogap state in cuprates, where it is well supported by polarized neutron measurements19,22. Further, the neutron observation in cuprates is confirmed as well by recent SHG measurements that show a global broken inversion symmetry in YBa2Cu3O6+x (ref. 26). This may provide more analogy between the iridates and the high-Tc cuprates, in spite of a different nature of 5d and 3d orbitals. A noticeable difference here is that the loop order occurs in the insulating compounds at half-filling, whereas in cuprates it is observed in the doped metallic (superconducting) state. Our report generalizes the existence of LC electronic states in oxides.


Coaligned single crystals and magnetization measurements

We have investigated the pure and 7% Rh-doped Sr2(Ir,Rh)O4 single crystals grown by flux method at Laboratoire de Physique des Solides (Orsay). Owing to a rectangular cuboid shape of the crystals, several tiny crystals could be coaligned in order to increase the total mass, as shown in Supplementary Fig. 2a. To address the conventional AFM order, the magnetization was measured under a magnetic field H=1 T using Magnetic Property Measurement System. The pure system originally exhibits an AFM order, but it can easily show ferromagnetism, by applying a small external magnetic field H≈0.2 T (2,000 Oe)2. For instance, the reported magnetic moment deduced from magnetization measurements shown in Supplementary Fig. 2b corresponds to a net ferromagnetic moment under 1 T. This ferromagnetism originates from a canting of the AFM structure. The transition temperature is taken at the maximum slope in M(T) curve, that is, the minimum of the first derivative of magnetization, dM(T)/dT shown in Supplementary Fig. 2b. The pure system shows a sharp transition at TN≈232 K and the saturated ferromagnetic moment per Ir ion is 0.08μB at 1 T. On the other hand, the doped one shows a broad transition near TN≈100 K and the moment is also reduced to 0.04μB. To map out the phase diagram (Fig. 1), the transition temperatures for different doping levels were determined from the previous literatures12,14, following the same procedure.

Polarized neutron diffraction

The polarized neutron diffraction experiments were performed on the triple-axis spectrometer 4F1 located at the Orphée reactor in Saclay (France). The polarized neutron setup was similar to the one used previously for studying cuprates19,20,21. A polarized incident neutron beam with Ei=13.7 meV (ki=2.57 Å−1) is obtained by a polarizing supermirror (bender) and scattered neutrons are measured with a Heusler analyser, which determines as well the final neutron polarization. A pyrolytic graphite filter is put before the bender to remove high harmonics. A small magnetic field of typically 10 G is applied using a Helmholtz-like coil. It is used to change adiabatically the direction of the neutron polarization at the sample position. A Mezei flipper is located before the sample position to flip the neutron spin.

All measurements were done in two different scattering planes, either H00-00L or HH0-00L, where the scattering wave-vector is quoted as Q=H a*+K b*+L c*≡(H, K, L) with a*=b*=1.15 Å−1 and c*=0.24 Å−1. As emphasized in Supplementary Note 1, in Sr2(Ir,Rh)O4, the conventional AFM order is expected in the H00-00L plane and the LC phase in the HH0-00L plane. For each Bragg position, the scattered neutron intensity is measured in both SF and NSF channels that corresponds to two different states of the Mezei flipper, flipper-off and flipper-on, respectively. One defines the flipping ratio FR=INSF/ISF of the Bragg peaks intensities in both NSF and SF channels. It determines the polarization efficiency of the apparatus. Due to unavoidable neutron polarization leakage from the NSF to the SF channel (imperfect polarization), a value for FR was obtained between 30 and 50 for the pure sample and between 50 and 65 for the doped sample. In order to measure a small magnetic signal on top of the large nuclear peak, it is essential to keep very stable and homogeneous neutron polarization through the whole measurement. Thus all the data were measured at a fixed configuration of the spectrometer while changing the temperature. The neutron measurements were performed with a neutron polarization P||Q where the magnetic signal appears entirely in the SF channel19,22. The AF-I order was further studied with a polarization PQ (but still within the H00-00L plane) as well as with a polarization P||z, which is perpendicular to the scattering plane (along 0K0 in the given case).

Data availability

The data that support the findings of this study are available from the corresponding authors upon request.

Additional information

How to cite this article: Jeong, J. et al. Time-reversal symmetry breaking hidden order in Sr2(Ir,Rh)O4. Nat. Commun. 8, 15119 doi: 10.1038/ncomms15119 (2017).

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