Introduction

The spin valve, widely used in magnetic sensors and hard-disk read-heads, utilizes a spin-dependent transport scenario called the giant magnetoresistance (GMR)1,2,3. Its functional structure involves alternating thin films of ferromagnet/nonmagnetic spacer/ferromagnet, where the relative spin orientation of the two magnetic layers controls the scattering process and leads to the GMR. This, however, relies on nanoscale deposition and patterning of artificially tailored thin-film heterostructures, or mechanically stacking of van der Waals heterojunctions with precise layer counting3,4,5. There have been efforts to reproduce the spin-valve effect in granular magnetic solids and bulk ruthenates6,7,8, yet careful control of chemical distribution or composition is still needed. For instance, optimal Cr-doping is needed to form one Cr-O layer every 2 or 3 Ru-O bilayers in Ca3(Ru0.83Cr0.17)2O7, and the resultant GMR size is only 50%8.

The vast kagome materials can be a candidate for searching bulk spin valves. They contain two-dimensional kagome lattices comprised of corner-sharing triangles as shown in Fig. 1a, and have been intensely studied in the search for emergent quantum phenomena for over 70 years9,10,11,12,13. Due to the nontrivial band topology and electron correlations, this model family can sustain exotic quantum phases including the Chern insulator, the fractional quantum Hall state, electronic or magnetic instabilities, and unconventional superconductivity, etc, depending on the band filling, the spin-orbit coupling strength and magnetism14,15,16,17,18,19,20. In addition to the hopping within the kagome plane, the interaction along the stacking direction of kagome layers in real materials exerts further manipulation on the electrons.

Fig. 1: Realizing self spin valve in the kagome helimagnet.
figure 1

a The kagome lattice and frustrated interlayer exchange couplings in kagome helimagnets. b Proposed self spin valve in crystalline bulk kagome materials, and comparison with c Traditional giant magnetoresistance (GMR) in ferromagnet/nonmagnet/ferromagnet trilayers.

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In this work we demonstrate that frustrated interlayer exchange couplings in kagome helimagnets can induce a self spin-valve effect. By combined magnetic force microscopy (MFM) and transport measurements, we show in bulk TmMn6Sn6 the formation of stripe domains along the helical axis under an in-plane magnetic field, whose pattern mimics the artificial multilayered structure in traditional spin valves and gives rise to a large GMR ratio over 160% at low temperatures. Theoretical modeling also suggests a great tunability of the self spin-valve effect. Our discovery therefore paves a way to introduce spin-dependent transport phenomena in quantum magnets, and shows potential in spintronic applications.

Self spin valve in the kagome helimagnet

We firstly consider the situation where neighbouring magnetic kagome layers, with easy-plane anisotropy, are crystallographically equivalent as illustrated in Fig. 1a. If the exchange integral J3 for the next-nearest-neighbor layers has opposite sign with respect to the nearest-neighbor exchange integral J1 (J1 = J2 in this case), and the condition ∣J3∣ > 1/4∣J1∣ holds, the magnetic energy has a minimum for a spiral structure, with pitch angle between magnetic moments of nearest-neighbor layers being \(\phi=\arccos \left(-{J}_{1}/4{J}_{3}\right)\). This is the Yoshimori-type helimagnet stabilized by frustrated interlayer interactions21,22. If the magnetic kagome layers are separated by different building blocks (J1 ≠ J2), there can exist multiple sets of pitch angles, leading to the appearance of double or even triple spiral structure23. Experimentally, helical states with short periods (typically λ < 10 nm) have been observed in a wide range of Mn-based kagome magnets, including RMn6Sn6 (R = Er, Tm, Sc, Y, Lu), RMn6Ge6 (R = Tb, Dy), and their Ga-substitutes, etc23,24,25,26,27,28.

In the chiral helimagnet, with Cr1/3NbS2 being a representative, the helimagnetic structure is protected by crystal chirality29. Under a magnetic field perpendicular to the helical axis, the ground state continuously evolves into a chiral soliton lattice29. In the Yoshimori-type centrosymmetric kagome helimagnet, however, chiral symmetry is preserved at the level of Hamiltonian in the absence of the Dzyaloshinskii-Moriya interaction. The helical spin structure here, therefore, has no symmetry protectorate and is easily fragmented into multidomains under external stimuli30. Especially, this instability, from competition between chiral magnetism and achiral Hamiltonian, leads to a discontinuous transition from a helimagnetic structure to a fan or forced-ferromagnetic structure under magnetic field perpendicular to the helical axis30. This can be seen from our numeric simulation of the magnetization curve for kagome magnets with the double-spiral ground state as shown in Supplementary Information (SI) Fig. S1. At some critical in-plane magnetic field, the rotation of one of the moments initiates an avalanche-like reorientation of the rest moments to reach the global energy minimum, which leads to a magnetic-history-dependent hysteresis between the field-sweep branches. An important consequence is that the field polarized states can be sustained during field-sweep branches in the form of alternating domains as illustrated in Fig. 1b. The upper bound of the ___domain wall thickness is also limited by λ, avoiding the damping of GMR size due to spin precession across the ___domain walls2,31. These features in kagome helimagnets are the key ingredients to realize a large, bulk spin-valve effect without the necessity of spacing layers; we thus dub it as a self spin-valve effect.

Material candidate

We demonstrate TmMn6Sn6 to be one such material candidate for self spin valves. As shown in Fig. 2a, it crystallizes in the centrosymmetric, hexagonal HfFe6Ge6-type structure consisting of kagome slabs [Mn3Sn] separated by two inequivalent [Sn3] and [TmSn2] slabs. The interlayer exchange parameters between [Mn3Sn] slabs fall into the Yoshimori-type frustration32, and TmMn6Sn6 behaves similarly to the non-magnetic R variants like YMn6Sn6 due to the relatively weak coupling between Tm and Mn27,33,34. According to the neutron scattering results27, the Mn sublattice displays an incommensurate double spiral structure below  ~330 K as shown in the phase diagram in Fig. 2b. The Tm sublattice also becomes magnetically ordered and forms another spiral structure which tends to be antiferromagnetically coupled with neighboring Mn moments. In this manner the Mn and Tm spirals are referred to as a triple-spiral structure, and can be roughly described together by a propagating vector of (0, 0,  ~0.16) below 50 K, which corresponds to a short helix period of 5.5 nm27. In the existence of an applied magnetic field in the ab plane, the Mn moments can be polarized with Tm moment antiparallel-aligned, forming a ferrimagnetic (FIM) state. Our density functional theory (DFT) calculations confirm a large spin polarization factor (81%) in the FIM state as shown in Fig. 2c, which is crucial for a spin-dependent process to dominate in transport35,36.

Fig. 2: Fragmented multidomains in TmMn6Sn6.
figure 2

a Crystal structure of TmMn6Sn6, which is composed of alternating slabs of [TmSn2], [Mn3Sn], [Sn3], and [Mn3Sn]. b Magnetic phase diagram of TmMn6Sn6 under an in-plane field, showing multiple phase areas including the low-field helical-ordered (Helix), antiferromagnetic (AFM) and paramagnetic (PM) regions, the high-field ferrimagnetic (FIM) and possible canted-FIM regions. c Calculated density of states (DOS) in the FIM state. d Magnetic force microscope (MFM) images of the spontaneous ___domain formation in TmMn6Sn6 at 5 K. Magnetic field is swept from −9 T to 5.1 T along the x (crystalline a) direction (perpendicular to the paper plane). The scale bar is 2 μm. In the first panel, three samples with length around 20 μm (along the z direction, or c axis), thickness around 1 μm, and different widths around 1.5, 3, 6 μm (left to right) in series are shown. The remaining 5 panels show local zoom-in. e Derivative of the MFM strength along the z (crystalline c) direction at representative fields. f Magnetization profiles from integration of the local MFM strength.

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In order to trace possible ___domain structures in TmMn6Sn6, we have adopted the MFM method which is sensitive to the perpendicular stray field gradient of the detected surface (See Methods section). Interestingly, we observe stripe domains in focused-ion-beam (FIB) milled TmMn6Sn6 thin plates under an in-plane magnetic field. The ___domain pattern is apparently asymmetric with respect to field, appearing at around −1.5 T and persisting to 5 T during a sweep-up circle (Fig. 2d). Note that the orientation of the stripe domains is insensitive to the sample geometry or size, and the domains always stack along the helical c axis (SI Figs. S3 and S4). Typical ___domain width is on the order of 300 nm as shown in Fig. 2e. From the integration of the local MFM strength, we further obtained the relative magnetization profiles in Fig. 2f, which is similar to our calculated hysteresis in SI Fig. S1. The high spin polarization and the fragmented multidomains in TmMn6Sn6, therefore, pave the way for the appearance of the self spin-valve effect.

GMR in TmMn6Sn6

We have measured the resistance of TmMn6Sn6 thin plates in different directions with field H perpendicular to the current I (SI Fig. S5). For H∥c, I∥ab configuration, the change of resistance with respect to H is small and positive. For H⊥c, however, both the current perpendicular to ___domain plane (I∥c, CPP) and current in ___domain plane (I∥ab, CIP) designs exhibit a remarkable hysteresis as shown in Fig. 3a and b, which is typical for a spin valve and is in good accord with the measured magnetization profiles. In the region where the moments are polarized by the field, the MR ratio (defined as the relative change with respect to the minimal value in the polarized state) is small. However, in the region where the ___domain structures appear, the resistance is greatly enhanced, and MR in the CPP setup is as large as 164% at 2 K. Magnetic-history-dependent memory effect, similar to traditional spin valves37, also appears as shown in Fig. S7 in SI. Even in the CIP structure, the MR in TmMn6Sn6 device is still over 30%. We have compared the magnitude of GMR from different mechanisms in SI Fig. S8. The MR ratio in the CPP configuration is comparable to state-of-arts epitaxial GMR spin valves1,38, and much higher than those in granular Co20Ag80 and Cr-doped bulk Ca3Ru2O76,7,8. This value even competes with the tunneling magnetoresistance of many magnetic tunneling junctions4,5,39, yet maintaining a significant smaller resistance-area product, which is crucial for higher operating frequencies and lower Johnson and shot noises in practical devices40. We note that the observed GMR with apparent memory effect and the underlying ___domain-based physics are entirely distinguished from the results in ref. 34 and layered magnetic systems like the manganites41.

Fig. 3: Giant self spin-valve effect in TmMn6Sn6.
figure 3

a Self spin-valve effect for the current perpendicular to the ___domain plane (CPP) configuration at 1.5 K. b Self spin-valve effect for the current in ___domain plane (CIP) configuration at 1.5 K. c Temperature evolution of the magnetoresistance (MR) magnitudes. Solid circles represent the maximal MR size whereas the open circles compare the unpolarized, zero-field-cooled (ZFC) resistivity to the minimal resistivity under external fields. Inset shows temperature dependence of the hysteresis field ΔH between the sweep-up and down branches. d Upper panels: Sample configurations for field H rotating away from the current in the ca plane and perpendicular to the current, respectively. Lower panels: Corresponding angular dependence of GMR size and ΔH.

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As the temperature rises, the MR magnitudes monotonously decrease and the hysteresis field ΔH between the sweep-up and down branches vanishes above 100 K as shown in Fig. 3c, probably due to enhanced scattering probabilities and thermal fluctuations. We also compare the resistance in the multidomain states with respect to the one in the pure helical states obtained from a zero-field-cooled (ZFC) procedure in Fig. 3c. As expected, the multidomains generate a way larger GMR ratio than the helical states at low temperatures, suggesting that the alternating ___domain patterns are more efficient in tuning the spin-dependent transport.

The angle dependence of the self spin-valve effect is studied as well in Fig. 3d. For H rotating in the ca plane (θ = 0∘ when H∥c), ΔH shows a \(1/\sin \theta\) behavior, suggesting a strong easy-ab-plane anisotropy. The size of MR is almost unchanged at various angles except when the ab plane component of H is not enough to alter the ___domain orientations. For H rotating in the ba plane, ΔH possesses a six-fold symmetry from the Mn kagome lattice due to the crystal-field effect32. The maximal MR occurs when the field is along to the crystalline b axis for our setup, amounting up to 175%.

Discussion

The above observations and analyses are not limited to the FIB-milled TmMn6Sn6 samples. We have also observed similar ___domain patterns and corresponding self spin-valve effect in millimeter-sized crystals (SI Fig. S12). Nevertheless, the GMR ratio in the latter is smaller (88% at 2 K) for the CPP configuration, and the critical field at which the domains are fully aligned decreases to 1.9 T. We attribute the discrepancies to an over-enlarged ___domain width with respect to the spin diffusion length in millimeter-sized samples (SI Fig. S12a) and the reduced pinnings from boundaries42,43. As the avalanche-like reorientation in Fig. 2f (also SI Fig. S1) depends on detailed exchange parameters, the Ga-inclusion during FIB milling might also have subtle influences on the critical field44. We leave these for future explorations.

Though we have treated the Mn and Tm spirals as a whole throughout our investigations, the rare earth site matters due to its anisotropy and its exchange coupling with the Mn kagome layers, offering an easy tunability of the transition temperatures, the detailed magnetic structures and band structures in RMn6Sn6 or RMn6Ge624,28,45,46. We have also considered the inclusion of Tm moment and its anisotropy in a triple-spiral model in the SI Note 3. Nevertheless, the magnetization profiles are very similar to the double spiral model due to the relative weak Tm-Mn interaction.

For practical account, the critical field to switch the spin valve should be small. Theoretically, this effect can be tuned to near-zero magnetic field by manipulating the magnetic interaction of kagome helimagnets in the parameter space as shown in Fig. S15. We have also taken the thermal effect into consideration in SI Note 2. It is shown in Fig. S16 that for the fixed exchange parameters, the overall effect of increasing temperature is to decrease the field needed to alter magnetic domains from parallel to antiparallel and antiparallel to parallel states. These findings therefore suggest that the kagome helimagnets, in principle, offer low-field controllability at room temperature.

In short, we have considered the ___domain degrees of freedom and put forward a self spin-valve effect in a wide range of kagome magnets with frustrated interlayer interactions, with the R166 family being a representative. Especially, we show that in TmMn6Sn6, the GMR ratio can surpass 160%. Considering the vast variety of material candidates and the great tunability from rare-earth engineering, our finding may assist the flourish of spintronic devices in quantum magnets.

Methods

Material growth and characterization

Single crystals of TmMn6Sn6 were synthesized via a standard tin flux method45. Tm lumps, Mn pieces and Sn grains with a molar ratio of 1: 6: 20 were packed into an alumina crucible which was then sealed in a fused quartz tube under vacuum. The mixture was heated to 1000 °C, cooled down to 600 °C over 3 days and then centrifuged to remove residual flux. Magnetic measurements on single-crystalline samples were performed in the Quantum Design PPMS-14 T and MPMS-3.

Device fabrication and transport measurement

Thin plates of TmMn6Sn6 were cut out from single crystals using the FEI Helios NanoLab FIB and patterned into standard Hall bars, with typical size around 8 × 1 × 1 μm3. Electrical contact was made by FIB-assisted platinum deposition onto a silicon stage with pre-patterned gold electrodes. Typical SEM picture of the device is shown in SI Fig. S4. Electrical transport measurements were performed in the 12 T C-MAG Teslatron PT system with the SynkTek multichannel Lock-in.

MFM measurement

The MFM experiments were conducted using an in-house-built cryogenic magnetic force microscope using commercial piezoresistive cantilevers (Quantum Design model PRSA-L400-F30-Si-sdPCB) which have a resonance frequency of about 35 kHz and a Q factor about 104 at 5 K). One side of the tips was coated with 5 nm Ti and 40 nm Co films using electron beam evaporation. The magnetic force microscope was controlled by a commercial RHK controller with a built-in phase-locked loop module. The signal used to image was a shift of the cantilever’s resonant frequency (dF), which is proportional to the out-of-plane stray field gradient. During each scan, a topographic image was first obtained using a contact mode to compensate the sample surface tilting along the fast and slow-scan axes, after which the tip was lifted by 100 nm and the MFM images were collected in a constant height mode. When the net magnetic moment of a ___domain lies parallel/antiparallel to the external field H, the magnetic force is attractive/repulsive, leading to a negative/positive dF (dark/light areas in MFM images). MFM images were analyzed using the Gwyddion software. MFM measurements were performed both on the FIB samples of different sizes and orientations (SI Figs. S2 and S3) and highly polished (100) surface of millimeter-sized bulk samples (SI Fig. S12).

DFT calculation

The bulk band structures of TmMn6Sn6 (Fig. S11) were computed using the projector augmented wave method as implemented in the VASP package47,48,49 within the GGA+U scheme50. The experimental lattice parameters and the in-plane ferrimagnetic (FIM) magnetic configuration were used. The spin-polarized calculation was included self-consistently in the calculations of electronic structures with a Γ-centered k-point mesh of 15 × 15 × 9. We employed the same methodology in ref. 46, utilizing the GGA+U approach with a UTm−4f value of 6.4 eV. The computed spin magnetic moment for Tm is 1.917 μB, consistent with the Hund’s rule prediction of 2 μB. The average spin magnetic moment for Mn is determined to be 2.38 μB, which is in close agreement with the results reported in ref. 46. The visualization of models was performed by using the VESTA code51.

Magnetic hysteresis calculation

A double-spiral model was adopted for the calculation of the magnetic hysteresis23, where the pitch angle ϕn for moment in the nth Mn layer in the zero-field spiral state is

$${\phi }_{n}=\left\{\begin{array}{ll}k\Phi,\quad &n=2k,\\ k\Phi+\delta,\quad &n=2k+1.\end{array}\right.$$
(1)

The pitch angle is modulated under an external in-plane magnetic field, and the total magnetic energy is

$$E= - \frac{1}{N}{\sum }_{k=0}^{N-1}\left\{B{M}_{s}\left[\cos ({\phi }_{2k})+\cos ({\phi }_{2k+1})\right]+{J}_{1}{M}_{s}^{2}\cos ({\phi }_{2k+1}-{\phi }_{2k})\right.\\ +\left.{J}_{2}{M}_{s}^{2}\cos ({\phi }_{2k+1}-{\phi }_{2k+2})+{J}_{3}{M}_{s}^{2}\left[\cos ({\phi }_{2k+2}-{\phi }_{2k})+\cos ({\phi }_{2k+3}-{\phi }_{2k+1})\right]\right\},$$
(2)

where Ms is the saturation magnetization, and the exchange parameters (x = J2/J1 = 0.243, y = J3/J1 = − 0.12) used here are similar to the reported values in ref. 23. The optimal magnetic moment angles during the field sweeps were solved numerically by minimizing the energy, and were subsequently converted into magnetization as shown in Fig. S1.

We also derived the exchange coupling values directly from a Heisenberg model52. The Heisenberg Hamiltonian is written in the following form:

$$H \,=\, {J}_{1}{\sum}_{ij}\vec{{S}_{i}}\cdot \vec{{S}_{j}}+{J}_{2}{\sum}_{ij}\vec{{S}_{i}}\cdot \vec{{S}_{j}}+{J}_{3}{\sum}_{ij}\vec{{S}_{i}}\cdot \vec{{S}_{j}},$$
(3)

where Si/j is the spin of each Mn ion. Considering two Mn layers associated with the exchange coupling J1 (as illustrated in Fig. 1a in the main text), we have \({\sum }_{ij}\vec{{S}_{i}}\cdot \vec{{S}_{j}}=\pm 3| {S}^{2}|\) for the parallel/antiparallel alignment. Consequently, this can be expressed as \({J}_{1}=\left({E}_{F,1}-{E}_{AF,1}\right)/6| {S}^{2}|\), where EF,1 − EAF,1 is the energy difference between the parallel and antiparallel alignments for a pair of nearest neighboring moments. J2 and J3 were calculated in the same methodology. The exchange parameters were found to be x = 0.2449 and y = − 0.1203 from the DFT calculation, in remarkable correspondence to the values used in our simulated hysteresis curves.