Butterfly-shaped magnetoresistance in triangular-lattice antiferromagnet Ag2CrO2

Spintronic devices using antiferromagnets (AFMs) are promising candidates for future applications. Recently, many interesting physical properties have been reported with AFM-based devices. Here we report a butterfly-shaped magnetoresistance (MR) in a micrometer-sized triangular-lattice antiferromagnet Ag2CrO2. The material consists of two-dimensional triangular-lattice CrO2 layers with antiferromagnetically coupled S = 3/2 spins and Ag2 layers with high electrical conductivity. The butterfly-shaped MR appears only when the magnetic field is applied perpendicularly to the CrO2 plane with the maximum MR ratio (≈15%) at the magnetic ordering temperature. These features are distinct from those observed in conventional magnetic materials. We propose a theoretical model where fluctuations of partially disordered spins with the Ising anisotropy play an essential role in the butterfly-shaped MR in Ag2CrO2.

www.nature.com/scientificreports www.nature.com/scientificreports/ According to the neutron 22 and muon spin resonance (μSR) experiments 23 , Ag 2 CrO 2 has a unique thermodynamic property, i.e., partially disordered (PD) state with 5 sublattices, at finite temperatures 24,25 [see Fig. 1(c)], which is different from the above 120° structure. In principle, the PD spin acts as a free spin since all the interactions from the nearest, the second nearest, and even the third nearest neighbors are canceled out. Thus, there should be negligibly small magnetization below T N . Nevertheless, this compound has a finite magnetization (≈ 0.08μ B per Cr atom) at zero field 21,24 . The origin of the small magnetization is still unclear. This system is also quite interesting from the perspective of spin fluctuations in the PD state.
In this work, we performed magnetotransport measurements in order to investigate the impact of the PD spin fluctuations on the electrical transport property using a micrometer-sized Ag 2 CrO 2 ; it is close to the single crystal. We find a butterfly-shaped magnetoresistance (MR) when the magnetic field is applied along the c-axis. Unlike the case of conventional magnetic systems, the amplitude of the butterfly-shaped MR is small at low temperatures and takes a maximum at around T N , and disappears above T * = 32 K. The result coincides with the MR by magnetic fluctuation, which is based on the 2D magnetic system with the uniaxial anisotropy.

Sample Fabrications and Experimental Setup
Polycrystalline Ag 2 CrO 2 samples were obtained by encapsulating a mixture of Ag, Ag 2 O, and Cr 2 O 3 powders in a gold cell, and by baking them at 1200 °C for 1 hour under a pressure of 6 GPa 21 . The polycrystalline samples were then pounded on a glass plate in order to obtain small pieces of Ag 2 CrO 2 . The small grains were picked up with a scotch tape and pasted onto a thermally oxidized silicon (SiO 2 /Si) substrate with several 100 nm thick gold marks. After removing the scotch tape from the substrate, another SiO 2 /Si substrate without any gold marks was pushed onto the substrate with the Ag 2 CrO 2 flakes and the 100 nm thick gold marks. In this process, Ag 2 CrO 2 flakes thinner than ≈100 nm are left on the SiO 2 /Si substrate with the gold mark, and relatively thick Ag 2 CrO 2 flakes are transferred to the substrate without the gold marks 25 . As a result, Ag 2 CrO 2 flakes with a few micrometer-size remain on the substrate with the gold marks. We have fabricated 10 different devices and always observed the butterfly-shaped structure as detailed in the next section. The thicknesses of these flakes (80~120 nm) were confirmed by a commercially available atomic force microscope.
To confirm if the Ag 2 CrO 2 flakes used for transport measurements are close to a single crystal, we took scanning transmission electron microscope (STEM) images shown in Fig. 2(a,b). As confirmed with the X-ray diffraction pattern for the polycrystalline samples, there is a single Ag 2 CrO 2 phase 21 ; no other phases such as AgCrO 2 26 , which is a ferroelectric material. The Ag 2 and Cr layers [see Fig. 1(a)] are alternatively stacked perpendicularly to the SiO 2 /Si substrate. On top and bottom of the Ag 2 CrO 2 flake, some Ag clusters segregated can be seen. However, inside the Ag 2 CrO 2 flake, there is no obvious cluster, indicating that the flake is close to a single crystal.
To perform the transport measurement, we deposited 150 nm thick Cu electrodes to the micrometer-sized Ag 2 CrO 2 films, using the standard electron beam lithography and a Joule heating evaporator 25 . A typical device is shown in the inset of Fig. 1(b). The lateral size and the thickness of the Ag 2 CrO 2 flake are a few μm and 100 nm, respectively. The contact resistance between Ag 2 CrO 2 and Cu is less than 1 Ω, which is comparable to a contact resistance for normal metallic junctions with almost the same junction area. This is also consistent with the STEM www.nature.com/scientificreports www.nature.com/scientificreports/ image in Fig. 2(c): the segregated Ag part on the left top side is continuously connected to the most top part of the Ag 2 CrO 2 flake, showing that the Ag layer is exposed after the fabrication. The transport measurements have been carried out using an ac lock-in amplifier and a 4 He flow cryostat.

Experimental Results
In Fig. 1(b), we plot the longitudinal resistivity ρ xx of the Ag 2 CrO 2 device as a function of temperature. The overall temperature dependence is metallic and there is a large resistivity drop at around T N determined from the heat capacity measurements for polycrystalline Ag 2 CrO 2 samples 21 . This resistivity change can be explained by spin fluctuation: fluctuations of paramagnetic spins at the Cr sites above T N are strongly suppressed below T N and the scattering rate of the conduction electrons is reduced. We also note that ρ xx at 5 K obtained for the thin film device is about 10 times smaller than that for the polycrystalline bulk samples 21,25 . From this result, we can argue that the thin film devices obtained with the mechanical exfoliation technique include much less grain boundaries compared to the polycrystalline bulk samples, resulting in a much better quality of Ag 2 CrO 2 . This is also supported by the STEM image in Fig. 2.
For the Ag 2 CrO 2 device, we performed MR measurements with three different magnetic field (B) directions, i.e., x (in-plane along the current direction), y (in-plane perpendicular to the current direction), and z (out-of-plane along the c-axis, i.e., z || c) directions. Figure 3 , the MR shows the negative sign. This trend is explained by the competition of two different mechanisms for MR, i.e., the ordinary MR and the MR related to spin fluctuation. The positive MR at T <<T N is related to the ordinary MR by the Lorenz force because the magnetic fluctuation is suppressed in this temperature region. On the other hand, when T ~ T N , the magnetic scattering by thermal fluctuation of spins is enhanced. This contribution to the resistivity is suppressed by the magnetic field perpendicular to the plane, producing the negative MR. Another unique feature is the butterfly-shaped MR at B ≈ ±0.5 T. The amplitude of the butterfly-shaped MR is small when T << T N . As we approach T N , it becomes larger and takes a maximum at 25 K (≈T N ). The maximum value reaches more than 10% at B = 0.5 T, which is unusually large for conventional ferromagnetic materials 27,28 . As we raise the temperature further, the amplitude of the MR suddenly decreases and becomes zero above T * = 32 K.
In contrast to the MR along the z-direction, such a drastic temperature dependence of MR has not been observed when B || x and B || y, although a small negative MR can be seen below T N . The B-angle dependence of the MR has never been studied for polycrystalline bulk Ag 2 CrO 2 21,24 .
To evaluate the butterfly-shaped MR observed only for B || z, we define the amplitude of the buttery-shaped xx xx xx upper c lower c , and the corresponding magnetic field (B c ), as illustrated in the inset of Fig. 4(a).
Γ has a small value at low temperatures and takes a maximum (15%) at around T N . It still has a finite value even above T N and finally disappears at T * . B c in Fig. 4(b) is almost constant up to T ≈ 22 K, and starts to decrease with increasing temperature and disappears at T * . Similar MR effects are often observed not only in current-in-plane (CIP) giant-magnetoresistance (GMR) devices 27,28 but also in ferromagnetic 29,30 and even antiferromagnetic materials 31 . However, the present butterfly-shaped MR is essentially different from them. While commonly-used CIP-GMR devices have in-plane magnetization whose direction is the same as the current direction, Ag 2 CrO 2 has a perpendicular magnetization to the basal plane and the current direction. An MR in conventional magnetic materials depends on the relative angle of magnetic domains, which is tuned by B. The amplitude of the MR is at most less than 1% 30 at B = 0.5 T. It decreases with increasing temperature and becomes zero above the transition temperature. In the butterfly-shaped MR, however, Γ has a maximum value of 15% near the transition temperature, which cannot be www.nature.com/scientificreports www.nature.com/scientificreports/ expected in conventional magnetic materials [29][30][31] . These experimental facts indicate that spin fluctuations of the PD state are strongly related to the butterfly-shaped MR. To our knowledge, this is the largest MR value induced by spin fluctuations.

Discussions
What is the origin of the butterfly-shaped MR? As mentioned in the introduction, Ag 2 CrO 2 is basically an antiferromagnetic metal and the PD spin behaves as a free spin. Thus there should be no spontaneous magnetization, but it has been established that the polycrystalline Ag 2 CrO 2 has a small but finite spontaneous magnetization below T N [21][22][23][24] . The origin of the spontaneous magnetization is still an unsolved problem, but the PD spins should play an essential role in the butterfly-shaped MR. Here we assume the same magnetic state for the thin film device as the bulk sample, although the magnetization measurement has not been performed. We also recall that the butterfly-shaped MR in the present work appears only when B || z. These features imply that the uniform magnetic moment is along the z-axis and has a strong uniaxial anisotropy. As illustrated in Fig. 5, we assume that the PD spin is canted and has a small magnetic moment along the c-axis. In addition, we also assume that the magnetic fluctuation of the PD spin is relatively large, since the PD spin flips only at 0.5 T. In such a situation, B suppresses the spin fluctuations when it is parallel to the moment direction, while B causes a spin flip when it is antiparallel to the moment direction. Thus, a negative and butterfly-shaped MR can be explained by the suppression of spin fluctuation and the spin-flip process induced by B, respectively.
As one of the possible models to explain the butterfly-shaped MR, we consider a 2D ferromagnetic spin system with the Ising anisotropy. Under a small magnetic field ≤1 T, we assume that the ferromagnetic magnon well approximates the low-energy magnon states of Ag 2 CrO 2 . The Hamiltonian is given by where k F is the Fermi wave number, μ eff is the effective ferromagnetic moment, a 0 is the lattice constant between the neighboring effective ferromagnetic moments, = − F x ( ) (2) is shown in Fig. 3(e); the butterfly-shaped MR near T N is well-reproduced by our theoretical model. We have roughly estimated both J and Δ to be about 10 K, which is reasonable for the present case (See Supplementary Information for details on our theoretical model, which includes refs. [32][33][34][35][36] ).
Finally, let us mention the relation between T N and T * . In the present experiment, the butterfly-shaped MR takes a maximum at around T N and vanishes at T * = 32 K. Originally, T N is determined from the peak position of the heat capacity measurement as shown in ref. 21 . A long range ordering emerges below T N (~24 K), but some short range ordering with magnetic fluctuations may grow even above T N . This was already pointed out by Sugiyama et al. from zero-field μ + SR measurements 23 . They argued that the phase with the PD spins already grows above T N and vanishes T * = 28 K. Those tendencies are indeed consistent with our experimental data. In addition, it is also known that T N is slightly shifted to the higher temperature side, by applying the magnetic field 21 . Thus, it seems to be reasonable that T * determined from the present MR measurement is higher than T * Figure 5. Schematic drawing of the spin configuration on the b-c plane (see Fig. 1(a)) expected from the experimental result. www.nature.com/scientificreports www.nature.com/scientificreports/ determined from the zero-field μ + SR measurement. However, we cannot make a further statement about the relation between T N and T * because it is difficult to perform standard measurements such as heat capacity and magnetization measurements for a tiny crystal. Further experimental and theoretical works are highly desirable to unveil the relation between the two characteristic temperatures.

Conclusions
In summary, we observed a butterfly-shaped MR in triangular-lattice antiferromagnetic Ag 2 CrO 2 devices. The butterfly-shaped MR can be seen only when the magnetic field is applied along the c-axis. This fact indicates a strong uniaxial anisotropy in Ag 2 CrO 2 . The butterfly-shaped MR takes a maximum value of 15% at around the transition temperature, suggesting that spin fluctuations are essential. The result is well explained by the theoretical model based on the 2D magnetic system with the Ising anisotropy. Rich physics is further expected in such a magnetically frustrated system coupled to conducting electrons. In addition, the large MR at small switching fields obtained in the frustrated spin system would be useful for future device applications.