Quest for New Quantum States via Field-Editing Technology

We report new quantum states in spin-orbit-coupled single crystals that are synthesized using a game-changing technology that"field-edits"crystal structures (borrowing from the phrase"genome editing") via application of magnetic field during crystal growth. This study is intended to fundamentally address a major challenge facing the research community today: A great deal of theoretical work predicting exotic states for strongly spin-orbit-coupled, correlated materials has thus far met very limited experimental confirmation. These conspicuous discrepancies are due chiefly to the extreme sensitivity of these materials to structural distortions. The results presented here demonstrate that the"field-edited"materials not only are much less distorted but also exhibit novel phenomena absent in their"non-edited"counterparts. The field-edited materials include an array of 4d and 5d transition metal oxides, and three representative materials presented here are Ba4Ir3O10, Ca2RuO4, and Sr2IrO4. This study provides an entirely new paradigm for discovery of new quantum states and materials otherwise unavailable.

ground state to emerge [2,6,[16][17][18][19][20][21][22][23][24]. In particular, the applied magnetic field during crystal growth exerts a torque on the magnetic moments, which via strong SOI can change the bond angles, the overlap matrix elements of the orbitals and hence the physical properties. It is astonishing that all these drastic changes in physical properties are a consequence of field-editing with a very weak magnetic field no stronger than 0.06 Tesla, as exampled in Figs.1b-1c (discussed below). This is utterly inconsistent with conventional thermodynamics, according to which even an extremely strong magnetic field (e.g., 45 Tesla ~ 4 meV) would seem inconsequential to chemical reactions as magnetic contributions to the Gibbs free enthalpy are too small to be significant in terms of energy scale [25]. Indeed, effects of growing silicon in weak magnetic fields were limited [26].
This work puts forward an entirely new paradigm for an otherwise unavailable path to discovery of novel quantum states/materials based on competing interactions.
Here, we report results of our study on three representative single-crystal materials that are "field-edited" and our controlled study on their "non-edited" counterparts. These three representative materials are the 5d-electron based iridates Ba4Ir3O10 [27], Sr2IrO4 [28] and the 4delectron based ruthenate Ca2RuO4 [29]. This comprehensive investigation involves an array of 4d and 5d oxides, and results of other studied materials will be presented in a separate paper. The study of all these materials reveals a common empirical trend that the field-edited single-crystal materials are much less distorted than their non-edited counterparts, and exhibit quantum states that are either absent or vastly different from those in the non-edited materials (e.g. Figs.1b-1c).
Experimental details including the single crystal synthesis, single-crystal x-ray diffraction, energy dispersion x-ray and measurements of physical properties are presented in the Supplemental Material [30]. A few crucial details are worth mentioning here. The field-edited single crystals are grown in a 1500 o C-furnace carefully surrounded with two specially-made permanent magnets, each of which is of 1.4 Tesla (Fig.1a). Since the magnetic field of a permanent magnet decays with distance d as 1/d 3 , the actual strength of the magnetic field inside the furnace chamber is measured to be within a range of 0.02 -0.06 Tesla. The non-edited single crystals are synthesized without the applied magnetic field in otherwise identical conditions. All results reported here are repeatedly confirmed by samples from multiple batches of single crystals synthesized throughout the nearly one-year period of this study.
It is emphasized that the work presented here can serve as proof-of-concept results; the field-editing technology with much stronger magnetic fields and higher temperatures will undoubtedly result in more discoveries of novel quantum states and materials.
For contrast and comparison, the structural and physical properties of both field-edited and non-edited samples are simultaneously presented.

A. Ba4Ir3O10: From Quantum Liquid to Correlated Antiferromagnet
The magnetic insulator Ba4Ir3O10 is recently found to be a novel quantum liquid [31]. As shown in Fig.2, Ba4Ir3O10, which adopts a monoclinic structure with a P21/c space group, is structurally a two-dimensional, square lattice with no apparent spin chains. Our recent study reveals the quantum liquid persisting down to 0.2 K that is stabilized by strong antiferromagnetic (AFM) interaction with Curie-Weiss temperature ranging from -766 K to -169 K due to magnetic anisotropy. The anisotropy-averaged frustration parameter, defined as f= |qCW|/TN, is more than 2000, seldom seen in other materials. Heat capacity and thermal conductivity are both linear at low temperatures, a defining characteristic for an exotic quantum liquid state. The novelty of the state is that frustration occurs in an un-frustrated square lattice which features Ir3O12 trimers of face-sharing IrO6 octahedra. It is these trimers that form the basic magnetic unit and play a crucial role in frustration. In particular, a combined effect of the direct (Ir-Ir) and superexchange (Ir-O-Ir) interactions in the trimers results in such a delicate coupling that the middle Ir ion in a trimer is only very weakly linked to the two neighboring Ir ions. Such "weak-links" generate an effective one-dimensional system with zigzag chains or Luttinger liquids along the c axis [31].
This intricacy is fundamentally changed in the field-edited Ba4Ir3O10. Structurally, the field-edited single crystal exhibits a significant elongation in the b axis with only slight changes in the a and c axis, compared to those of the non-edited sample. As a result, the unit cell volume V increases considerably by up to 0.54% at 350 K (see The heat capacity, which measures bulk effects, confirms the AFM order. In particular, the low-temperature linearity of the heat capacity C(T) (data in blue Fig.3e), which characterizes the gapless excitations in the non-edited sample, is replaced by the T 3 -dependence in the field-edited sample, which is anticipated for an insulating antiferromagnet (data in red in Fig. 3e). Along with the linearity of C(T), the sharp upturn in C(T) at T* = 0.2 K in the non-edited sample also disappears in the field-edited sample. These changes clearly illustrate that the ground state of Ba4Ir3O10 is fundamentally changed! Indeed, as temperature rises, two anomalies occur at TN2 = 12 K (Fig.3f) and TN = 125 K ( Fig.3g), respectively, confirming the robustness of the long-range magnetic order observed in the magnetic data in Fig.3a-3d.
The observed magnetic order in the field-edited sample is similar to that observed in slightly doped Ba4Ir3O10, in which a mere 2% Sr substitution for Ba produces long-range order at 130 K [31]. However, remarkable differences are in the details. Most notably, the anomaly at TN2 (= 12 K) in C(T) of the field-edited samples is absent in C(T) of the Sr-doped sample, and the metamagnetic transition for Ma occurs at Hc = 2.5 T and 4.2 T for the field-edited and Sr-doped sample, respectively. Furthermore, Mb for the Sr-doped sample shows an additional Hc at 6.5 T, which is absent in Mb for the field-edited sample.
In short, the quantum liquid in the non-edited Ba4Ir3O10, which is attributed to the reduced intra-trimer exchange and weakly coupled one-dimensional chains along the c axis [31], is replaced in the field-edited Ba4Ir3O10 by the strongly AFM state stabilized by three-dimensional correlations. As shown in Fig. 4, the crystal structure of Ca2RuO4 is significantly field-edited, becoming less distorted. A few changes are particularly remarkable. The first-order structural transition TMI is suppressed by about 25 K from 357 K to 332 K, which is marked by the vertical blue dashed and red solid lines, respectively, through Figs. 4a-4c. In the field-edited structure, the c axis gets longer (Fig. 4a); the b axis becomes shorter whereas the a axis changes very slightly (Fig. 4b),

B. Ca2RuO4: From Collinear Antiferromagnet to Weak Ferromagnet
thus leading to a reduced orthorhombicity (Fig. 4d). Furthermore, the O2-Ru1-O2 and Ru1-O2-Ru1 bond angles, which measure the octahedral rotation and tilt, get relaxed, in the field-edited structure (Fig. 4e-4f). All these lattice changes are critical to both transport and magnetic properties.
The crystal structure in the ac and ab planes and the schematic for the bond angles are shown in Fig.4g-4i.
Indeed, the a-axis electrical resistivity ra of the field-edited sample shows a much lower metal-insulator transition TMI at 324 K, 31 K lower than TMI for the non-edited sample, as seen in Fig. 5a. The suppressed TMI closely tracks the structural transition that is reduced by about 25 K in the field-edited sample (Fig.4).
Magnetically, the field-edited sample behaves vastly differently from the non-edited sample. In particular, the a-axis magnetic susceptibility ca of the field-edited sample shows a ferromagnetic-like behavior with the onset of the magnetic transition at TN = 135 K (red curves), in sharp contrast to that of the non-edited sample (blue curve) (see Fig. 5b). The increased TN is likely related to a sizable increase in the unit cell V below 200 K via the strong magnetoelastic coupling (see Inset in Fig. 4c). Moreover, a large hysteresis behavior of ca is observed in the field-edited sample (Inset in Fig. 5b), which is absent in the non-edited sample but expected in a ferromagnet or weak ferromagnet. In this case, the field-edited sample more likely becomes a weak ferromagnet or canted antiferromagnet; this is consistent with a metamagnetic transition, Hc = 2.4 T, observed in the isothermal magnetization M(H) illustrated in Fig. 5c. The non-edited Ca2RuO4 is a known collinear antiferromagnet without any metamagnetic behavior [3,29]. The magnetic changes are also in accordance with changes in the low-temperature heat capacity C(T). For an insulating antiferromagnet, C(T) ~ (a + b) T 3 , in which the first term a and the second term b are associated with magnon and phonon contributions to C(T), respectively. Here, C(T) shows a significant slope change defined by (a + b) in the plot of C/T vs T 2 in Fig. 5d. Such a slope change clearly points out that the emergent magnetic state is distinctly different from the native AFM state, consistent with the magnetic data in Figs.5b-5c.

C. Sr2IrO4: Towards Novel Superconductivity
Sr2IrO4 is an archetype of the spin-orbit-driven magnetic insulator [45,46], an extensively studied material in recent years [2,3,[6][7][8][9][10][11][12]. It is widely anticipated that with slight electron doping, Sr2IrO4 should be a novel superconductor [2,[9][10][11][12]24]. However, there has been no experimental confirmation of superconductivity, despite many years of experimental effort [2]. We believe that the absence of the predicted superconductivity is due to inherently severe structural distortions that suppress superconductivity [2,[16][17][18]47]. This point is also supported by a recent theoretical study, which attributes the lack of superconductivity to the octahedral rotation [24]. In fact, it is precisely because of this early realization that we initiated the development of the field-editing technology and investigations of field-edited materials. Indeed, the structural, magnetic and transport properties of the field-edited Sr2IrO4 and 3% La doped Sr2IrO4 or (Sr0.97La0.03)2IrO4 are either drastically improved or changed, compared to those of the non-edited samples. In particular, the field-edited structure is more expanded and less distorted (Ir-O-Ir bond angle becomes larger) (Figs.6a-6b), and the AFM transition TN is suppressed by astonishing 90 K (Fig.6c); the isothermal magnetization is reduced by 50% and much less "saturated" compared to that for the non-edited Sr2IrO4 (see Supplementary Fig.1[30]). That the Ir-O-Ir bond angle dictates TN and magnetization suggests a critical role of the Dzyaloshinskii-Moriya interaction, consistent with early study of the iridate [6]. Indeed, such magnetic changes are clearly reflected in Raman scattering. One-magnon Raman scattering measures the anisotropy field that pins the magnetic moment orientation. It broadens with increasing temperature and vanishes at TN. At 10 K, this peak in the non-edited Sr2IrO4 occurs near 18 cm -1 (data in blue in Fig.6d) [48] but is absent in the field-edited Sr2IrO4 for the measured energy range (data in red Fig.6d). This conspicuous disappearance of the peak clearly indicates that the anisotropy field is drastically reduced and, consequently, the one-magnon peak is either completely removed or suppressed to an energy below the energy cutoff of 5.3 cm -1 (0.67 meV) in the field-edited sample. On the other hand, two-magnon scattering remains essentially unchanged (see Supplementary Fig.2 [30]). (Figs.6e-6f)! Also note that there is an anomaly corresponding to TN = 150 K (see Inset in Fig.6e), indicating a close correlation between the transport and magnetic properties that is noticeably absent in the nonedited Sr2IrO4 (Figs 6c, 6e-6f) [2]. This is consistent with the fact that the drastically improved conductivity (Figs.6e-6f) is accompanied by the equally drastically weakened magnetic state (Figs.6c-6d). It is therefore not surprising that the resistivity for the field-edited (Sr0.97La0.03)2IrO4 exhibits an abrupt drop below 20 K by nearly three orders of magnitude, suggesting that the long-elusive superconductivity in the iridate may be finally within reach (these results are to be reported in a separate paper).

Furthermore, the resistivity is reduced by up to seven orders of magnitude and shows a nearly metallic behavior at high temperatures in the field-edited Sr2IrO4
All results presented above have clearly demonstrated that the field-editing technology is extraordinarily effective for generating new quantum states in correlated and spin-orbit-coupled materials. It is particularly astonishing that all this is achieved via an applied magnetic field no stronger than 0.06 Tesla during materials growth. This is a game-changing technology, and with stronger magnetic fields, it will overcome more materials challenges, leading to more discoveries of novel quantum states and materials that cannot be produced otherwise.