A simplified method characterizing magnetic ordering modulated photo-thermoelectric response in noncentrosymmetric semimetal Ca3Ru2O7

Photo-Thermoelectric (PTE) response is usually one of the main working mechanisms for photodetectors. However, as another fast and easier way to measure thermoelectric characteristics of materials, it can also reveal important physics such as electric-phonon coupling, electron-electron correlation, etc. Recently, the spin entropy related to magnetic order transition which contributes to thermoelectric power is attracting more and more attention. Here, we demonstrate the PTE response can be reshaped when Ca3Ru2O7 undergoes meta-magnetic phase (MMP) transition driven by both temperature and magnetic field. Firstly, a sign change is observed crossing TS = 48 K and the linear polarization angle dependent PTE current maximizes along a-axis above TS while maximizes along b-axis below TS, which indicates that the antiferromagnetic spin order contributes to such spatial anisotropy. Secondly, in the temperature range of around 40 ~ 50 K, the PTE current is found to be sharply suppressed when external magnetic field is applied in plane along a-axis but is only gradually suppressed when applied field is along b-axis which gives out two critical fields. We attribute such suppression of PTE current under magnetic field to the suppression of the spin entropy in the phase transition between the antiferromagnetic state and the MMP state and the H-T phase diagrams of Ca3Ru2O7 is redrawn accordingly. Compared to previously work which trying to understand the magnetic phase transition in Ca3Ru2O7, such as neutron scattering, specific heat, and other advanced transport measurements, our work provides a more convenient yet efficient method, which may also find applications in other correlated spin materials in general.


Introduction
PTE effect has been exploited as a new method other than Photopyroelectric (PPE) effect to characterize the phase transition of materials since it can sense the thermal parameters variation during the phase transition. [1][2] Traditional PPE or recently developed PTE method uses normally three-or four-layer measurement configuration, [3][4][5] exploiting materials with well characterized and superior thermoelectric (TE) property as pyroelectric (PE) or TE sensor.
Dynamic thermo parameters such as thermo diffusivity, effusivity, and specific heat can be retrieved to portrait the phase transition. For instance, the antiferro-paramagnetic phase transition of Cr2O3 was successfully studied by PTE method by using Liquid TE sensor. [6] The LTE sensor is located between the metal electrode and the sample. A thin layer of silver is deposited on the backside of the sample, forming the second electrode for the PTE signal. Hence the thermal properties in the sample can be calculated given that thermoelectric coefficient of the LTE sensor is known. However, neither PPE or PTE method has simple and convenient measurement configuration since they both use external PE/TE sensors. One natural question is raised that weather PTE measurement can characterize phase transition without the assistance of external sensors. In this work, we demonstrate that the simplified PTE method can characterize the magnetic order and MMP in Ca3Ru2O7, which is a well investigated perovskite oxide material. [7] The actually measured photocurrent is mainly from PTE effect and it turns out to be wideband, zero-bias driven and stable. By combining cryogenic and magnetic field dependent PTE measurement, the sharp PTE current variation of Ca3Ru2O7 has been discovered when Ca3Ru2O7 undergoes phase transition from AFM-a to AFM-b state at ~ 48 K. The application of in-plane magnetic field along b-axis causes the MMP transition and leads to the drastic suppression of the PTE current which we attributed to suppression of the spin entropy contribution. Although our simplified PTE method cannot measure the thermal parameters directly, our work provides an alternative and more convenient way to characterize the phase transitions related to correlated electronic or spin materials.
3 Layered ruthenates in the Ruddlesden-Popper series family (Sr, Ca)n+1RunO3n+1 as a canonical complex transition metal oxide system has attracted great attention. [8][9][10] It has rich interactions among charges, spins, orbits, and crystal lattices resulting in a wealth of physical phenomena, including superconductors, ferromagnets, antiferromagnetic metals, structural phase transitions, magnetic phase transitions, etc. [11][12][13][14][15][16] In the Ruddlesden-Popper family (Sr, Ca)n+1RunO3n+1 as the reduction of cation radius, system change from the quantum magnet Sr3Ru2O7 to antiferromagnetic metal Ca3Ru2O7 ; [17][18][19] as well as the increase in the number of perovskite RuO2 layers that leads to the transition from a band-dependent Mott insulator Ca2RuO4 to the metallic Ca3Ru2O7 with a k-dependent gap. [20][21] Ruddlesden-Popper Ca3Ru2O7 has a rich phase diagram. Ca3Ru2O7 is a paramagnetic (PM) metal at room temperature. [22] At TN = 56 K, Ca3Ru2O7 exhibits a transition from PM order to antiferromagnetic order (AFM-a), which is characterized by the double layer is antiferromagnetically coupled along c-axis. The ferromagnetic perovskite bilayer with a-axis, which is the short axis of the crystal. [14] At TS = 48 K, the second magnetic transition occurs, from AFM-a to AFM-b; the easy axis switches from a-axis to b-axis. [23][24] The transition at TS is also accompanied by a sharp increase in inplane resistivity. Angle-resolved photoemission measurements reveal the destruction of a large hole-like Fermi surface upon cooling at 48 K. [9,16] With the appearance of an insulating-like pseudogap, Ca3Ru2O7 undergoes semimetal-semiconductor transition. [25] Coincident with TS, Ca3Ru2O7 undergoes a first-order isosymmetric transition marked by a discontinuous change in the lattice parameters: the c-axis lattice constant is shortened, while those of the a-and b-axis are enlarged. [26] At AFM-b phase, a higher field transition under the magnetic field along the b-axis is a transition into a canted antiferromagnetic (CAFM) phase in which the magnetic moments on Ru ions are partially polarized along the direction of the applied field. [27] In the temperature range of 40 K to 48 K, the lower boundary of the magnetic field strength required for MMP phase transition gradually decreases with temperature, from 5.23 T (40 K) to 1.95 T (48 K). [23] 2. Results and Discussions  Figure 1a shows the crystal structure of Ca3Ru2O7. Ca3Ru2O7 is composed of perovskite double layer (CaRuO3)2 and RuO6 octahedrons, separated by an additional CaO rock salt layer. The small ion size of Ca causes the large coupling rotation and tilt of the RuO6 octahedron that constitutes the perovskite-like member of the structure, resulting in a non-centrosymmetric crystal structure.
The crystal structure has the orthorhombic symmetry with Bb21m space group (No.36(C2v), lattice parameters are a = 5.37 Å, b = 5.52 Å, c = 19.53 Å) [26] with rotation and tilting of RuO6 octahedra. It has the magnetic moment ferromagnetically aligned within the RuO2 bilayers and 5 antiferromagnetically aligned between the bilayers. The x-ray diffraction patterns in Figure 1b show that Ca3Ru2O7 crystal possess pure bilayer phase. As shown in Figure 1c, the Raman spectrum of Ca3Ru2O7 has been measured in the range of 200-500 cm -1 at room temperature.
Four characteristic peaks of Ca3Ru2O7 can be observed at 244, 311, 386 and 435 cm -1 . The peak centered at 435 cm -1 can be assigned to the A2 phonon mode, while the other three Raman peaks can be attributed to the A1 phonon mode. All the observed Raman peaks are well in line with the phonon assignment reported earlier. [28] This indicates that high-quality Ca3Ru2O7 crystals are obtained using the FZ growth method. Figure 1d shows the temperature dependence of resistivity. At high temperatures, it shows metallic behavior (the resistivity decreases as the temperature decreases, show that the Ca3Ru2O7 is in the PM state. At TN = 56 K the resistivity drops sharply as the temperature continues to drop, which corresponds to the beginning of the AFM transition. While at TS = 48 K, the resistivity increases as the temperature decreases indicating the second magnetic transition occurs, from AFM-a to AFM-b. The transition at TN and TS agrees with the previous report. [29] The photocurrent response is measured on the bulk Ca3Ru2O7 single crystal fabricated device on silicon substrate with 300 nm Oxide layer. As shown in  of Figure 2b, the photocurrents reach two maxima and has opposite signs when the beam illuminated the two sides (Ca3Ru2O7-metal contacts), with no photocurrents induce when the beams focus on the center of channel, which are typical PTE effect. [30][31] The PTE effect arises when the laser causes local heating, generating a temperature difference between the two electrodes. Subsequently, the carriers diffuse from the hot region to the cold region, resulting in a photocurrent. Figure 2c   Previous work has revealed MMP transition at TS = 48 K in Ca3Ru2O7 by sophisticated transport measurements or neutron diffraction spectroscopy. However, those methods require complex techniques. Our PTE method is a simple one and can be easily combined with cryogenic and magnetic field environment. We expect our simplified PTE method is also efficient to characterize MMP. We studied the PTE response of Ca3Ru2O7 devices at 30-60 K, 8 paying particular attention to MMP transition region (around TS = 48 K) and found two characteristics. Firstly, as shown in Figure 3a, when temperature cools from 50 K to 40 K, the photocurrent has a sign change and a significant increasement in its amplitude under 0.2 mW power. From the I-V curve shown in the inset of Figure 3a, one can see at 40 K, photocurrent is linearly bias voltage dependent, which indicates that the semiconducting like behavior. This is consistent to previous finding that the Seebeck coefficient undergoes a sharp sign change across the phase transition and a small pseudogap opening. [9] Secondly, the PTE current peaks at TS where the value of 4.7 μm light is higher than that of 532 nm light as shown in Figure 3a.
Previous band-structure calculations based on density-functional theory (DFT) shows that: [16,32] At TS < T< TN the electron and hole bands at the zone center develop a strong hybridization with multiple bands crossing EF, this band structure is nearly semi-metallic. At TS = 48 K a pseudo-gap opens at EF, and total density of states (DOS) of Ca3Ru2O7 shows that the band is unoccupied near EF which mediated by spin-orbit coupling. A semimetal-semiconductor transition occurs as a pseudo-gap opens at EF in MMP transition. When the band is nearly full occupied (in AFM-a region), the probability of absorbing a photon to produce PTE response is reduced compared with that the band is unoccupied near EF when pseudo-gap exists (in MMP transition region). This was also seen in optical spectroscopy measurements upon cooling through TS = 48 K. [25] One can see from the inset of Figure 3b, the electrons can be photoexcited to contribute to PTE current directly without complicated electron phonon scattering for light of 4.7 μm since its photon energy matches the band energy difference while the visible light does not match, therefore, the PTE responsivity rate vs light power for 4.7 μm light is higher than the visible light as shown in Figure 3b. As shown in Figure 3c, a half-wave plate is used to rotate the normally incident light polarization to realize angle dependent PTE response measurement. In Figure 3d, the normalized photocurrent dependence on the azimuth angle θ of the incident linear polarized laser is plotted for different temperatures. An apparent anisotropy pattern emerges on the photocurrent PTE(θ), revealing an overall two-fold symmetry. This twofold symmetry is only observable for T<56 K, which indicate its magnetic origin. Most notably, a 90° shift is found between the PTE(θ) pattern at 46 K and 50 K. The major difference of the magnetic state at these two temperatures, as discussed before, was the AFM easy axis (a-axis for the high-T AFM-a state, b-axis for the low-T AFM-b state). Now the PTE(θ) reaches its maxima when the electric field of the incident photon aligns along the easy axis in both AFMa and AFM-b states (through assistence of polarized optical reflection method.) [33] This magnetization-dependent photocurrent carries important insight. In view of the entropic origin of the thermoelectricity, a plausible mechanism is that the enhancement of PTE(θ) consists the 9 contribution of spin entropy. [34][35][36][37] While at present it is difficult to seek for a quantitative assessment of the validity of the spin entropy contribution and its magnitude, especially in an partially itinerant d-electron system, the observed PTE(θ) patterns provide an tempting direction for further exploration and perhaps a feasible experimental probe for such mechanisms, which are typically elusive for other probes. Nevertheless, such photocurrent enhancement at the spin alignment direction in antiferromagnetic materials may be alternatively explained by the optical linear birefrangence, which the absortion of linearly polarized light maximizes at the direction of the antiferromagnetic spin alignment direction, [38][39] and hence the PTE current correspondingly demonstrates such linear polarization dependence. [40]  represents the data of neutron scattering and the blue pentagon dots represent the data from Hall measurement in (e), which are reproduced with permission. [23] 2019, Nature publishing group.

Figure 4a&c
shows the PTE response with the applied in-plane magnetic field at different temperatures. The main feature is the significant suppression of the PTE current at certain magnetic fields, which is only observed at 48 K and below. However, the suppresion behavior is in stark contrast when magnetic field is along a-axis and b-axis. For instance, when magnetic field along a-axis, there is only one sharp decrease appear in the PTE current curves. When magnetic field along b-axis, there are plateaus appear in the PTE current decrease process.
Taking TS = 48 K as an example, the PTE current starts to decrease at ~ 2.5 T, the whole process ends until about 5 T, while have a wide plateau in between. As the temperature lowered below TS, the magnetic field required to produce the PTE current suppression increases. By taking the differentiate point of d(PTE)/dH, we derive the turning points at different temperatures for magnetic field in both direction, as displayed in Figure 4b&d. These critical points can redraw the phase diagram partly as demonstrate in Figure 4e&f. For comparism, we replot the smallangle neutron scattering (SANS) experiments result by the light yellow dashed line, and the data of hall measurement result by dark blue shapes from previous work. [23] It can be found that our measurement results fit the two curves in the figure very well, which means that we can use the measurement of the PTE response to characterize the magnetic order phase transition.
We now turn to discuss why PTE current is suppressed significantly under external in plane magnetic field. This can also be probably explained with the scenary of spin entropy contribution mentioned above. While the magnetization is reported to be small at AFM-b state, it is dramatically increased and saturated at much higher value at the critical magnetic fields which draw the phase boundary between CAFM and AFM-b phase. [23] The increasement of magnetization means the alignment of spins, equally, the charge carriers lose their spin entropy.
This phenomenon is only obvious at the temperature region of AFM-b state which has localized carriers. [10] The magnetic field applied in either a-axis or b-axis direction tends to switch from AFM-b state to a canted AFM state, where the spin entropy of localized carriers in AFM-b will be lost during such switch process and hence the PTE current suppression. However, compared to the simple switch from AFM-b state to a canted AFM-a state under magetic field along aaxis, the switch process from AFM-b to canted AFM-b is more intricate, accomanying with a meta magnetic transition in between. [23] Our PTE current suppression process has an intermediate plateau when external magnetic field is along b-axis seems to be consistent with such scenaro.

Conclusion
In summary, we have constructed simple device of Ca3Ru2O7 single crystal, and measured its PTE response as a function of temperature and magnetic field. We find that the value of the 11 PTE response has changed nearly ten times under laser illumination of λ = 532 nm and λ = 4.7 μm, at temperature TS. The change in the PTE response coincides with the change in the energy band structure caused by the SOC in the MMP transition or alternatively, the contribution from spin entropy of the localized carriers. Applying magnetic field in different directions changes the magnetic order and suppresses the PTE response. Compared with traditional thermodynamic transport measurement, our simplified PTE method complements and confirms each other, and the difference between the two may be caused by different physics. Our simplified PTE method is convenient yet efficient while maintaining the measurement accuracy of phases evolution, which has great potential in investigation of other correlated electronic or spin materials.

Device Fabrication:
The photo-response based on bulk Ca3Ru2O7 were fabricated using 1 mm*1 mm*0.3 mm single domain Ca3Ru2O7 crystal on the Silicon substrate with 300 nm Oxide layer. Thin gold wires were connected to freshly cleaved surface by covering the silver paint completely to enable a good Ohmic contact.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.