Normal and inverse bulk spin valve effects in single-crystal ruthenates

Spintronic is a new generation of devices that exploit both charge and spin degrees of freedom compared with traditional semiconductor-based devices that solely rely on charge degrees of freedom.¹ More degrees of freedom provide opportunities for new and highly efficient devices, such as electro-optic modulators,² magnetic field sensors,³ and logic devices.^4,5 The underlying mechanism is more complex than in semiconductor electronics. Current-perpendicular-to-plane magnetoresistivity (CPP-MR) is one of the most widely used properties in spintronics, especially in magnetic hard disk drivers and magnetic random access memory based on giant magnetoresistance (GMR) or tunneling magnetoresistance (TMR) effects.^5–9 Both effects are related to spin-dependent scattering in layered structures. The difference between these two effects is whether the nonmagnetic layers between the ferromagnetic (FM) layers are metallic (GMR) or insulating (TMR).^10–12 

Ruddlesden–Popper type layered materials, A_n+1B_nO_3n+1, are built using alternating stacks of n-layer BO₂ and rock-salt layer A₂O₂ along the c-axis.^13,14 This type of material can be taken as quasi-two-dimensional structure. Some of these materials intrinsically form FM multilayers such as the double-layer manganites, La_2−2xSr_1+2xMn₂O₇ (x = 0.3), and double-layer ruthenates, Ca₃Ru₂O₇. These structures are similar to the FM/I/FM-type artificial multilayers used in read heads. CPP-MR in the former material was found to be extremely large at low fields and was explained by a spin-polarized TMR mechanism.¹⁵ The latter material, which serves as the pristine compound reported in this study, also has interesting magnetic and electronic behavior. It orders antiferromagnetically at Néel temperature T_N = 56 K.¹⁶ This antiferromagnetic (AFM) state is characterized by FM RuO₂ bilayers coupled antiferromagnetically along the c-axis with spins pointing in the a/−a directions.^17,18 A first-order metal-insulator transition (MIT) accompanied by a switch of the spin direction from the a-axis to b-axis and a Jahn–Teller type structure change occurs at MIT temperature T_MIT = 48 K.^16–18 Photoemission and photoconductivity measurements show that a charge gap opening is associated with the MIT.^19,20 Angle resolved photoemission spectroscopy (ARPES) measurements further indicated that small metallic pockets survived at non-nested Fermi surface below T_MIT.²¹ Below 30 K, the in-plane resistivity $(ρab)$⁠, measured on single crystals grown using the floating zone process returns to the metallic state, while out-of-plane resistivity $(ρc)$ remains insulating and becomes saturated at ∼10 K.^22–24 Ionic liquid Hall bar devices have been manufactured based on the CPP and in-plane transport behavior. This demonstrates that the MIT can be tuned using the electric field.²⁵ Additionally, a bulk spin valve featuring colossal magnetoresistance was discovered, which is tuned by an in-plane field, leading to a large resistance change as a function of field strength or field orientation.²⁶ These curious electronic and magnetic properties also attract the attention of theoretical physicists. Density function theory (DFT) calculations were performed by several groups: DFT calculations with local spin-density approximation resulted in a half-metallic ground state.²⁷ First-principles calculations including the spin-orbital coupling and on-site Coulomb interaction find that when the magnetic moments align along the b-axis, the band structure indicates an insulating phase. The compound is predicted to be a rather good metal when spins are aligned along the a-axis.²⁸ This band structure of this material is strongly related to the magnetic anisotropy.

Besides electronic field and magnetic field, the electronic state can also be tuned by chemical doping. Previous work showed that Ti doping on the Ru site tunes the ground state from a quasi-two-dimensional metallic phase with a layered AFM structure to a Mott insulating state with G-type AFM order through phase separation.^29–32 When increasing the Ti doping level, the G-AFM phase starts to appear at x ∼ 0.02 as a minor phase in the ground state and its volume fraction gradually increases. It becomes a dominant phase at x ≥ 0.03. Eventually, a pure G-AFM phase appears at x ≥ 0.05.²⁹ Because the magnetic ground state of this system is quite sensitive to Ti doping, every crystal used for measurements was checked carefully using energy-dispersive X-ray spectroscopy. The real compositions are in general consistent with the nominal ones.²⁹ While the AFM-a phase (T_MIT < T < T_N) always exhibits metallic behavior, the ground states for 0 < x < 0.03 compositions display a localized electronic state, in contrast with the quasi-two-dimensional metallic ground state of Ca₃Ru₂O₇. The localized state switches to the Mott insulating state for x > 0.03.³¹ The complex magnetic and electronic states in Ti-doped Ca₃Ru₂O₇ indicate a delicate balance between several competing energy scales. Exotic magneto-electronic coupling may arise from this soft electronic environment. In this paper, we focus on the normal and inverse spin valve effect in a 2% Ti-doped Ca₃Ru₂O₇ compound since that this is the composition with phase separation while its major phase is still ferromagnetic layers coupled antiferromagnetically along c-axis, a similar structure with artificial multilayers used in read heads.

High-quality single-crystalline samples of Ca₃(Ru_1−xTi_x)₂O₇ were grown using the floating zone process. All samples used for measurements were examined by X-ray diffraction. The magnetization was studied using a superconducting quantum interference device (SQUID, Quantum Design) to make sure crystals are composed of pure bilayered phase and twin-domain free. In-plane crystallographic directions were determined by Laue X-ray diffraction measurements. The CPP-MR measurements were performed on a thin plate-like crystal (thickness approximately 0.1 mm) with a four-probe contact in a physical property measurement system (PPMS, Quantum Design). The schematic diagram of CPP-MR measurements is shown in Figure 1.

Zero field $ρc(T)$ for the 2% Ti-doped sample is shown in Fig. 1. This composition orders antiferromagnetically at ∼61.5 K, followed by an MIT at approximately 46 K. Above the AFM ordering temperature, $ρc(T)$ changes from a metallic to a localized state. Below T_N, it remains in a metallic behavior. $ρc(T)$ exhibits a first-order transition with small hysteresis at T_MIT. The resistivity value increases by about one order of magnitude. However, it does not saturate at ∼10 K as observed in the pristine compound,^22–24 possibly because of impurity scattering.

The 2% Ti-doped samples show complex CPP-MR behavior at different temperatures and field orientations. Normalized $ρc(B)$ $(defined as ρc(B)−ρc(0)ρc(0)$⁠) at typical temperatures when the external field is applied along b-axis are shown in Fig. 2(a). At 5 K, for a field applied along the b-axis, $ρc$ decreases by greater than 50% at ∼6 T (Fig. 2(a)). We define the magnetic fields for these two transitions as B_c1-b. When the temperature increases, this transition moves to a lower field as indicated by down arrows. The decrease of transition field can be explained by classical thermodynamics that thermal fluctuation helps system to overcome the potential barrier between lower polarized and higher polarized state, and lower the transition field. Above 30 K, a second transition, manifested by a significant increase in $ρc(B)$⁠, is observed at higher fields (indicated by the up arrows). This field is defined as B_c2-b. The exact values of two transitions are decided by peaks/valleys' positions in $dρc(B)dB$ curves for B//b. The magnetic transition at B_c1-b annihilates at ∼40 K. The transition at B_c2-b becomes undetectable at T > 50 K. To explore the underlying mechanism of the non-monotonic CPP-MR in Ti-doped Ca₃Ru₂O₇, we compared the field dependent magnetization curves M(B) and $ρc(B)$ for 35 K < T < 45 K. A contour plot of the magnetization for a field applied along the b-axis is given in Fig. 2(c). The $ρc(B)$ curves are also given at the corresponding temperatures. The two transitions at B_c1-b and B_c2-b of $ρc(B)$ are marked by up and down arrows. These two transitions in $ρc(B)$ curves occurred near the discontinuous changes in M(B). B_c1-b occurred near the boundary of the blue- and green-colored regions. B_c2-b corresponds to the boundary of the green- and red-colored regions. Because that the orbital degrees of freedom are quenched in 4d transition metal oxides, the magnetization values are determined by the local spin configurations in a localized system. Therefore, each inflection point in the magnetization curves is caused by local spin rearrangement. We suggest that each transition in $ρc(B)$ for external field applied along b-axis (B//b) corresponds to a modification of the spin configuration. We then wanted to determine whether this rule is valid for a field applied along the a-axis (B//a).

Normalized $ρc(B)$ values at different temperatures for an external field applied along the a-axis are presented in Fig. 2(b). They show a distinct behavior with H//b. For T < 25 K, $ρc(B)$ decreased gradually with increased field strength and showed no anomalous below 9 T. A sudden drop in $ρc(B)$ occurred at T > 25 K. The drop in field (defined as B_c1-a) decreased with increasing environmental temperature. It was inferred that this drop in $ρc(B)$ also occurs below 25 K at high fields, which is beyond our measurement limitations. This feature is similar to the $ρc(B)$ drop for B//a in the pristine compound and can be attributed to the spin-flip transitions from AFM-b to a more polarized state. For T ≥ 39 K, $ρc$(B) exhibits non-monotonic changes. It first suddenly increases at a certain field (defined as B_c2-a), followed by a decrease at B_c1-a. A contour plot of the magnetization values for a field applied along the a-axis is shown in Fig. 2(d). $ρc$(B) for B//a is also shown at the corresponding temperatures. Two critical fields, B_c1-a and B_c2-a, derived from $dρc(B)/dB$ are marked with arrows. The B_c2-a values occur when the contour plot color changed from light blue to green. B_c1-a can be fitted to the boundary of the green- and red colored regions. Therefore, each transition in $ρc(B)$ for B//a is also corresponds to a modification of spin configurations.

B-T phase diagrams based on M(B), M(T), and $ρc(B)$ measurements for a field applied along the b and a axes are shown in Figs. 3(a) and 3(b). Contour plots of the magnetization values at the corresponding temperature and magnetic field strength M(B, T) are also shown. Scale labels are listed on the right in units of $μB/Ru mol$⁠. Critical points derived from M(B), M(T), and $ρc(B)$ curves are shown in hollow, half-hollow, and solid symbols, respectively. Transition fields B_c1-b and B_c2-b derived from different field sweep measurements (M(B) and $ρc(B)$⁠) are almost identical as we discussed above. The small bifurcation may originate from the magnetic field orientations. As we state in the experimental part, M(B) measurements were performed on SQUID which do not combine a rotator sample holder due to small chamber size. The samples were aligned by Laure diffraction measurements and inserted into the Chamber after that $ρc(B)$ measurements were performed on PPMS which have a rotator sample stage. Therefore, the alignment can be adjusted after it is inserted into the Chamber. In general, the directions of samples for $ρc(B)$ measurements are more precisely aligned to a or b axis than M(B) measurements, resulting in a little bit smaller transition fields. T₁, T₂, and T₃ are characteristic temperatures observed in the zero field cooling magnetic susceptibility measurements, χ(T), for different magnetic fields.³³ These characteristic fields and temperatures separate the whole-phase diagram into five regions for the field applied along the b-axis. We will discuss the regions one by one.

M(B) and $ρc(B)$ curves show simple metamagnetic transitions at B_c1-b for T < 25 K. The transition from region I to region II is manifested by a jump in magnetization from ∼0.1 $μB/Ru mol$ to ∼1.5 $μB/Ru mol$ and a first-order drop in $ρc(B)$⁠. The GMR associated with this metamagnetic transition is almost identical to that observed in Ca₃Ru₂O₇. Elastic neutron diffraction measurements on single-crystalline Ca₃Ru₂O₇ revealed that the magnetic structures above the metamagnetic transition were in the canted AFM (CAFM) state instead of the fully polarized FM state. CAFM is a canted AFM state where the spins in the bilayers are canted 25° from the b-axis. The magnetic structure of regions I and II should be AFM-b (with G-AFM as minor phase) and CAFM, respectively.

For T > 25 K, the field corresponding to the metamagnetic transition (B_c1-b) decreases. A second-order transition occurred at a higher field (B_c2-b). At B_c2-b, both M(B) and $ρc(B)$ significantly increase. Region III is at the boundary between region I and region II. In region III, we observed zero or positive MR with an increased magnetization from approximately 0.4 $μB/Ru mol$ to approximately 1.0 $μB/Ru mol$⁠. The transition at B_c2-b cannot be explained using normal MR caused by the Lorentz force or an anisotropic MR mechanism because of its large amplitude and field. Another possible explanation is explored here. Schematics of spin configurations for each region are shown in Fig. 3(c). In region I, spins in one bilayer are pointing in the +b direction. In the neighboring bilayer, they point in the −b direction. Above the metamagnetic transition (region II), they form the CAFM structure. For region III, temperatures of 30 K ≤ T ≤ 40 K are close to the magnetic transition temperature from AFM-b to AFM-a. In this region, the spin directions may not be as constant. It is possible that the spins in one bilayer are partially polarized at a lower field. As shown in Fig. 3(c)–III, the spins in the upper layer are identical to the upper layer of Fig. 3(c)–II. Spins in the lower layer of Fig. 3(c)–III are not as polarized as the upper layer. This can explain the step-like polarization process of M(B) in this temperature range. A dual spin valve structure with alternating hard and soft magnetic layers forms at a field strength between B_c1-b and B_c2-b. In this structure, an inverse spin valve effect can be observed. An explanation based on the spin-dependent scattering model is illustrated in Fig. 4. For an FM/I/FM-layered structure, if the spin scattering asymmetry factor (⁠$α$⁠) of both FM layers is the same [$(α1>1$⁠, $α2>1)$ or $(α1<1$⁠, $α2<1)$], the MR is expected to be negative. If $α$ is different in neighboring FM layers [$(α1>1$⁠, $α2<1)$ or $(α1<1$⁠, $α2>1)$], as shown in Fig. 4(b), the low resistivity channel is formed for the low polarized state instead of the highly polarized state. Positive MR is therefore expected.

We will go back to the Ti-doped Ca₃Ru₂O₇ system. The B-T phase diagram for a field applied along the a-axis is also established. Critical points derived from the field-dependent magnetization, magnetoresistance, and susceptibility measurements meet at one critical point (3.7 T, 43 K). The inverse spin-valve effect occurs around this point (defined as region III). Region III in Fig. 3(b) is generally at a higher temperature than in Fig. 3(a). This is understandable because spins hesitate in a wide temperature range from 30 K to 50 K. They slowly rotate from the +b/−b axis to the +a/−a axis. Alternate hard/easy magnetic layers are then formed. This alternating hard/easy magnetic layered structure may also exist in pristine Ca₃Ru₂O₇ in a more narrow temperature range based on the following evidence: (1) the valley shape in $ρc$(B) for B//b was observed between 43 and 47 K in Ca₃Ru₂O₇; (2) the peak shape in $ρc$(B) for B//a was observed between 50 and 52 K.²⁶ Chemical doping effectively enhanced the amplitude of the negative spin valve effect. The peak height reached 40% in $ρc$(B) for B//a in the 2% Ti-doped Ca₃Ru₂O₇ sample. In the pristine compound, the amplitude is less than 10%. Temperature ranges are also extended from 4 K and 2 K in the pristine compound for B//b and B//a to 10 K and 11 K, respectively, with 2% Ti doping. The uneven distribution of doping content, which was thought to be the reason behind magnetic phase coexistence in Ti-doped Ca₃Ru₂O₇, may be responsible for the enhancement. A similar story was previously found in Cr-doped Ca₃Ru₂O₇.³⁴ Because the spin scattering asymmetry factor is strongly related to the polarized Fermi surface, calculations related to the band structures are desirable.

In summary, both normal and inverse spin valve effects are observed in 2% Ti-doped Ca₃Ru₂O₇. To understand this phenomenon, we established a B-T phase diagram based on M(B), M(T), and $ρc$(B) measurements for both B//b and B//a. Alternating hard and soft magnetic layers are formed in a certain temperature range in which the inverse spin valve effect is observed. Chemical doping can affect the softness of the magnetic layers. This exotic magnetoresistivity behavior highlights the strong spin-charge coupling in double-layer ruthenates, as well as providing inspiration for further applications in spintronic devices. Theoretical investigation is imperative to reveal the underlying physics of this intriguing phenomenon.

This work at Nanjing University was supported by the Natural Science Foundation of China (Nos. 11304149, U1332205, 11274153, 11204124, and 51202108). The Work at Tulane University was supported by the U.S. Department of Energy under EPSCOR Grant No. DE-SC0012432 with additional support from the Louisiana Board of Regents (support for crystal growth and magnetic measurements).