Anisotropic magnetoresistance in antiferromagnetic Sr2IrO4

We report point-contact measurements of anisotropic magnetoresistance (AMR) in a single crystal of antiferromagnetic (AFM) Mott insulator Sr2IrO4. The point-contact technique is used here as a local probe of magnetotransport properties on the nanoscale. The measurements at liquid nitrogen temperature revealed negative magnetoresistances (MRs) (up to 28%) for modest magnetic fields (250 mT) applied within the IrO2 a-b plane and electric currents flowing perpendicular to the plane. The angular dependence of MR shows a crossover from four-fold to two-fold symmetry in response to an increasing magnetic field with angular variations in resistance from 1-14%. We tentatively attribute the four-fold symmetry to the crystalline component of AMR and the field-induced transition to the effects of applied field on the canting of AFM-coupled moments in Sr2IrO4. The observed AMR is very large compared to the crystalline AMRs in 3d transition metal alloys/oxides (0.1-0.5%) and can be associated with the large spin-orbit interactions in this 5d oxide while the transition provides evidence of correlations between electronic transport, magnetic order and orbital states. The finding of this work opens an entirely new avenue to not only gain a new insight into physics associated with spin-orbit coupling but also better harness the power of spintronics in a more technically favorable fashion.

2 Antiferromagnetic (AFM) spintronics [1][2][3][4] is a new emerging field of material science and device physics aiming to explore unique properties of AFMs and implementing them as active ingredients in spintronic applications. AFM materials share a number of useful functionalities with ferromagnets (FM) such as spin-transfer torque [1,2], which is predicted to be even stronger in AFMs [1], and exhibit unique interactions with FMs as in the well-known effect of exchange bias [5]. Moreover, they are instrumental in minimizing the cross-talk between nanodevices as AFMs do not produce stray magnetic fields. One of the milestones of AFM spintronics is finding an efficient method for monitoring the magnetic order parameter in AFM materials. Anisotropic magnetoresistance (AMR) [6] and tunneling AMR [7,8]

observed in
AFMs are among very promising candidates for this purpose. The canted AFM iridate Sr2IrO4 (see Fig. S1 in Supplemental Material) is a particularly interesting material for such AMR studies. The strong spin-orbit interaction in this and other iridates drives many fascinating phenomena including the Jeff =1/2 Mott state [9], possible superconductivity [10], topological insulator [11] and spin liquid [12] behaviors, which makes them an attractive playground for studying physics driven by spin-orbit interactions. As AMR is known to be closely associated with spin-orbit interaction, the strong spin-orbit interaction in this 5d transition metal oxide may favor stronger AMR compared to 3d transition metal alloys and oxides. The recent magnetotransport studies in Sr2IrO4 single crystals [13,14] and thin films [6] revealed largely unexplored correlations between electronic transport, magnetic order and orbital states.
Here we present the first observation of the point-contact AMR in single crystals of the AFM Mott insulator Sr2IrO4 [13][14][15], which can potentially be used to sense the AFM order parameter in spintronic nanodevices. The point-contact technique allows to probe very small volumes and, therefore, measures electronic transport on a microscopic scale. Point-contact measurements with single crystals of Sr2IrO4 were intended to examine if the additional local resistance associated with a small contact area between a sharpened Cu tip and the antiferromagnet shows a magnetoresistance (MR) like that seen in bulk crystals. The measurements at liquid nitrogen temperature revealed large MRs (up to 28%) for modest magnetic fields (250 mT) applied within the IrO2 a-b plane. The angular dependence of MR revealed an AMR with an intriguing transition from four-fold to two-fold symmetry in response to an increasing magnetic field. We tentatively attribute the four-fold symmetry to the crystalline component of AMR and the fieldinduced transition to the effects of applied field on the canting of AFM-coupled moments in Sr2IrO4. These findings open an entirely new avenue to not only gain a quantum-mechanical insight into the new physics but also better harness the power of spintronics in a more technically favorable fashion.
Our sample is a single crystal of Sr2IrO4 (1.5 mm×1 mm×0.5 mm) synthesized via a selfflux technique [16]. The insert to Fig. 1a shows a schematic of our experiment: a point contact between a sharpened Cu tip and the single crystal (001) surface was made with a mechanically controlled differential-screw system described elsewhere [17]; an electrical current is injected through the point contact into the crystal and flows (primarily) along the [001] c-axis into a macroscopic Cu electrode on the back side of the crystal. The system enables us to produce point contacts on the sample's surface with a dimension a from microns down to a few nanometers [18]. The point-contact current-voltage characteristics exhibit largely ohmic behavior, as shown in Supplemental Material Fig. S2. The contact size a can be estimated from the measured contact resistance R with a simple model [18] for diffusive point contacts that  Both grey-density plots show qualitatively similar transitions in AMR from four-(at low fields) to two-fold symmetry (at higher fields). For the smaller contact (PC2), the symmetry transition occurs at a somewhat larger field (~ 60 mT) compared to that for the larger PC1 contact (~ 40 mT).
To further quantify the data in Fig. 1 Fig. 1b). Figure 2a shows that the magnitude of AMR is a non-monotonic function of H and peaks at around 120 mT. Finally the 'coercive' field H * where R(H) has a maximum exhibits small variations as a function of . Figure 2b shows that these variations in H * () are somewhat correlated with the four-fold variations in R() at low fields (grey trace) but have a predominantly two-fold character.
We would like to point out that the AMR observed in our experiments cannot be explained by the conventional AMR in polycrystalline magnetic conductors defined solely by the relative angle between the current direction and magnetic moments [19]. The current is being injected vertically through the point contact (perpendicular to the a-b plane; see experimental setup in inset to Fig. 1a) and is not expected to see any changes in its relative orientation with respect to the magnetic moments of Sr2IrO4 as the applied magnetic field is rotated within the sample's basal a-b plane. Instead, it is the relative angle between the moments and the crystal axes that may change as the field rotates. Therefore the observed anisotropy in resistance can be tentatively attributed to the crystalline component of AMR. This spin-orbit (SO) coupling induced effect arises from the crystal symmetries and reflects the effects of orbital degree of freedom on the magneto-electronic transport in Sr2IrO4. Note that the AMR observed in our point contacts can be as large as 14%, which is very large when compared to the crystalline AMRs reported previously in 3d transition metal alloys/oxides (0.1-0.5%) [20][21][22] and is also much larger than the crystalline AMRs observed to date in Sr2IrO4 [6].
It is known from the resonant x-ray [15] and neutron [20,21] scattering experiments that Sr2IrO4 exhibits a meta-magnetic transition in an external magnetic field: the order of uncompensated magnetic moments within IrO2 planes changes above the critical field 0Hc  200 mT. As illustrated in Fig. S1 the canting of Jeff =1/2 moments leads to an uncompensated (residual) moment within each of IrO2 planes, and these uncompensated moments can be aligned by an external magnetic field that results in a non-zero net (weakly ferromagnetic) moment at high fields. The observed point-contact MR -R(H) traces in Fig. 1a correlate very well with this transition and previously observed MRs in bulk Sr2IrO4 samples [14]. We thus attribute the observed variations in R(H) to the field-induced variations in the magnetic order of Sr2IrO4 while the observed angular variations in R() can be attributed to the crystalline AMR [6]. The latter is further confirmed by correlations between the observed symmetry of AMR and the crystal structure as we discuss next.
The intriguing magnetic field dependence of the AMR symmetry obtained in this work indicates yet unexplored entanglements of crystal structure, magnetic order and electron transport in this canted AFM Mott insulator. The range of external magnetic fields we applied in this study (up to ~ 0.3 T) covers the field-induced variations in the magnetic order of IrO2 planes, but is too small (compared with the exchange field) to significantly alter the underlying AFM order of the Sr2IrO4 crystal. The observed AMR transition from the four-to two-fold symmetry (see Fig. 3) occurs over the same field range suggesting its possible relationship with the magnetic transformations in IrO2 planes. As was pointed out in previous studies of the magnetic order in Sr2IrO4 [23][24][25], the magnetic moments tend to follow octahedral-site rotation because of a strong spin-orbit coupling and therefore a strong single ion anisotropy in Sr2IrO4.
Since the electronic properties of Sr2IrO4 are also known to be sensitive to lattice distortions [14,19], it is possible that the observed magnetic field dependence of AMR symmetry in our study can be associated with lattice distortions that originate from the magnetoelastic effect and spinorbit coupling.
To explain the different AMR symmetries observed at low (four-fold) and high (two-fold) fields, we note that our Sr2IrO4 sample has a tetragonal crystallographic structure as verified by X-ray diffraction (XRD). Based on the XRD data (not shown), we found that the minima of the four-fold AMR pattern observed at low fields, where the magnetoelastic effect is small, correspond to the applied field oriented along the Ir-O bonds, assuming small octahedral distortions. Note that the four-fold symmetry of AMR is most readily observed around 0H ~ 40 mT where we also see the maximum in R(H) traces (Fig. 1a). At this 'coercive' field, we expect to have no net magnetization in the crystal and the measured AMR to reflect the intrinsic electronic properties of Sr2IrO4. This correlation suggests that the four-fold AMR pattern observed at low fields can be associated with the intrinsic crystal structure, band structure and orbitals of 5d electrons with spin-orbit interactions.
The two-fold symmetry of AMR observed at higher fields can be tentatively associated with the uniaxial anisotropy of the canted antiferromagnetic configuration in Sr2IrO4. Although the crystal structure is tetragonal, the canted antiferromagnetic order is orthorhombic with twinning domains as confirmed by neutron scattering/diffraction [24]. The observed angular dependence of the coercive field H * () has a predominantly uniaxial character (see Fig. 2b) that is also consistent with the existence of orthorhombic magnetic structure in the a-b plane. We attribute the uniaxial symmetry of AMR observed at low fields to the effect of the applied magnetic field on the canting of AFM magnetic moments. When the field is applied along the spin axis (near the [100] a-axis) of Sr2IrO4 the canting is reduced, while a perpendicular (to the spin axis) field would promote a larger canting. Smaller canting corresponds to a 'more antiparallel' state which corresponds to a higher resistance and thus results in a two-fold symmetry. In light of the fact that the canting of magnetic moments can be locked to the distortions of octahedra, the proposed picture of AMR due to the field mediated canting is in good agreement with previously reported magnetoelastic effect on the resistivity of Sr2IrO4 [14,19]. The uniaxial magnetic anisotropy due to this reduced symmetry may be strengthened by the applied magnetic field, which aligns the uncompensated (residual) moments of IrO2 planes [15]. Note that the observed symmetry of AMR becomes mostly two-fold at a relatively low field (~ 60 mT), indicating the predominance of the anisotropy upon the breaking of AFM order between the uncompensated moments. After that, the magnetic order (dominated by the two-fold symmetry) continues to change up to a higher magnetic field of the order of the critical field where the two-fold symmetry finally stabilizes/saturates. Moreover, the lattice distortions induced by magnetoelastic coupling are expected to further enhance the uniaxial anisotropy because of the orthorhombic magnetic structure. All of the above suggests that the field-induced lattice distortions due to the magnetoelastic effect may dominate the AMR and result in the two-fold symmetry at high fields.
In summary, we observe a large (up to 14%) AMR in point contacts to a single crystal of antiferromagnetic Mott insulator Sr2IrO4. The observed AMR has an intriguing transition from four-fold to two-fold symmetry with increasing magnetic field, which provides an interesting insight into correlations between the orbital states, electronic properties and magnetic properties of this antiferromagnetic oxide. Finally, the observed large AMR effect in a purely antiferromagnetic system without interference of ferromagnetic materials supports the development of antiferromagnetic spintronics where antiferromagnets are used in place of ferromagnets. The observed AMR that originates from strong spin-orbit interactions in 5d transition metal oxides could be used in spintronics to monitor the AFM order parameter in a more technologically favorable fashion.