Gate control of magnon spin transport in unconventional magnon transistors based on the van der Waals antiferromagnet CrPS4
Dennis K. de Wal Raul Luna Mena Muhammad Zohaib Bart J. van Wees


APS/123-QED


d.k.de.wal@rug.nl


Zernike Institude for Advanced Materials, University of Groningen,
Groningen, the Netherlands











Zernike Institude for Advanced Materials, University of Groningen,
Groningen, the Netherlands



§ ABSTRACT 
Magnon based spintronic devices require the modulation of magnon spin transport for their operations. We provide a proof-of-principle of two unconventional non-local magnon transport devices in which we modulate the diffusive magnon transport of incoherent magnons in the van der Waals antiferromagnet Chromium thiophosphate, CrPS4. The non-local signals generated electrically by spin injection via the spin Hall effect (SHE) and thermally via the spin Seebeck effect (SSE) are altered by a modulator electrode. The current through the modulator increases or decreases the magnon chemical potential via the SHE and changes the magnon temperature through Joule heating. We achieve up to η^1ω_SHE=25%/mA and η^2ω_SHE=16%/mA modulation efficiencies for the electrically and thermally generated magnon spin transport, respectively, for CrPS4 in the collinear state at in plane fields >7T at a temperature of 25K.



                              
Gate control of magnon spin transport in unconventional magnon transistors based on the van der Waals antiferromagnet CrPS4
    Bart J. van Wees
    September 9, 2024
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§ INTRODUCTION

In information processing technology, encoding, transport, and manipulation is crucial for its operation. Spin wave (magnon) based computing has been shown as a very suitable alternative to CMOS based electronics for encoding<cit.> and transport in three-dimensional ferro, ferri and antiferromagnets<cit.>. Also on investigating the novel two-dimensional (2D) van der Waals magnetic materials, significant efforts have been made with regards to thermally generated<cit.> and electrically generated magnon transport<cit.>. Yet, electrical control over and manipulation of magnon signals in these systems remains a challenge. In Yttrium Iron Garnet (YIG), the “workhorse” of magnonics, a magnon transistor in a conventional three-terminal non-local geometry is demonstrated and explored, showing that the magnon spin conductivity can be modulated both electrically and thermally<cit.>. In this geometry strong signal modulation is achieved up to 40%/mA<cit.>.

Efficient and scalable control over magnon spin transport in 2D van der Waals materials is also crucial for achieving a controllable 2D magnon gas. In the van der Waals magnets advances have been made in magnon valves, based on the non-local geometry, in MnPS3<cit.> and CrPS4<cit.>. Nevertheless, for both these experiments the magnon currents are generated thermally, by the SSE, for which only convoluted information about the magnon transport properties, such as magnon relaxation length and magnon conductivity, can be obtained. Also, in these works, neither via the SHE injected magnon transport, nor modulation of the magnon transport via the SHE, are reported. Moreover, the reported 'off' state, explained as the zero-crossing of the non-local spin Seebeck effect (SSE) voltages at specific gate dc-currents is, in fact, the sign change in magnon chemical potential at the detector as a function of thermal gradient, which is observed in YIG as a function of temperature, Joule heating and injector-detector spacing<cit.>. Although the proof of principle for these thermally controllable magnon transistors in <cit.> and <cit.> is highly relevant, only thermal control over the thermally generated magnon spin current, driven via Joule heating, is shown and not via the SHE. 

“All-electrical” non-local magnon transport, where the magnon spin is injected via the SHE, has been shown in the 2D van der Waals antiferromagnet CrPS4<cit.>, making this material very suitable for fully electrical (via the SHE) modulation of magnon spin transport. In this work, we demonstrate and explain the working of a magnon transistor based on CrPS4, similar to the magnon transistor on YIG<cit.>.  We elaborate on the effects on the magnon conductivity of electrical gating via the SHE and thermal gating via both injection of heat and through the SSE. which affect both the electrically injected and thermally injected magnon currents. Furthermore, we propose a two-terminal and an unconventional three-terminal non-local geometry instead of using the conventional three-terminal with the gate in the middle, to achieve a greater tunability of the magnon current.






§ EXPERIMENTAL CONCEPTS

For electron transport in metals and semiconductors, the electron conductivity (σ_e) depends on the free electron density (n_e). This Drude model for electrons follows: σ_e=e^2n_eτ_e/m_e, where e, m_e, and τ_e are the electron charge, effective mass, and the scattering time, respectively<cit.>. For magnons in a system at finite temperature (thermal equilibrium magnons) we can define a similar relation. For out-of-equilibrium magnons, such as electrically injected and thermally generated (SSE) magnons, the magnon spin conductivity becomes:

    σ_m=ħn_mτ_m/m_m,

where n_m is the magnon density, which depends on both the magnon chemical potential as well as the temperature, τ_m is the magnon scattering time and m_m=ħ^2/(2J_S) is the effective mass with J_S as the spin wave stiffness<cit.>. Therefore, σ_m can be directly tuned via n_m.





In transistors based on magnons, spin is carried by magnons. A current through a gate contact affects the magnon transport in three ways: 1. The current generates an electronic spin accumulation (μ_mod) at the Pt/CrPS4 interface via the SHE. By transfer of spin from the gate contact to the magnetic insulator, the magnon chemical potential μ_m is enhanced or depleted, in case the magnetization of CrPS4 is collinear to μ_mod. Since a change in μ_m changes n_m, hence it also changes σ_m between the injector and detector contacts. 2. The gate current generates heat by Joule heating, this alters the magnon temperature in the area of the CrPS4 flake in proximity to the gate, changing n_m via T. 3. Moreover, the increased temperature creates thermal gradients in the sample as well. These thermal gradients drive magnon currents via the SSE and therefore can lead to a change in μ_m.  

We studied two Pt/CrPS4 heterostructures (Device D1 and D2) where the CrPS4 flakes are exfoliated from bulk crystals of CrPS4 (HQgraphene). The 7 nm thick Pt electrodes are sputtered on top of a ∼100 nm thick flake. The contact spacing for the devices varies between 270 nm to 1400 nm edge-to-edge distance (see figure <ref>c) and the contacts have equal width (∼300nm). The length of the Pt strips is 20-40 μm. The Pt strips are contacted with Ti/Au leads to make electrical connections to the device. Angular dependent magnetoresistance (ADMR) measurements are performed for this non-local geometry as a function of in-plane angle α of the applied magnetic field w.r.t. the Pt strips (see figure <ref>). A low frequency (ω/(2π)<20 Hz) ac-current I=I_0sinω t is applied to the injector Pt strip. The first (V^1ω) and second (V^2ω) harmonic voltage responses are measured at the detector Pt strip. All CrPS4 flakes are exfoliated from the same bulk crystal.

First considering the conventional three-terminal magnon transistor, as given in figure <ref>a, we explore the effects of the modulation on the non-local magnon spin transport. The non-local voltages V^1ω_nl and V^2ω_nl in the detector correspond to the electrically and thermally generated magnon transport excited by the ac-current (I_AC) in the injector. Additionally, a modulating dc-current (I_DC) is applied to the gate electrode, affecting the magnon spin transport.

V^1ω and V^2ω will not be offsetted by I_DC as we employ the lock-in method. We can summarize the effect on both V^1ω and V^2ω by:

    V^1ω   =C_1I_ACσ_m(α)cos^2(α),
        
    
        V^2ω   =C_2I^2_ACσ_m(α)cos(α),

where C_1 and C_2 are the constants capturing the conversion of the charge currents to spin currents in the injector and detector<cit.>, for the electrical and thermal injection, respectively. The magnon conductivity σ_m depends on I_DC and is given by:

    σ_m(α) = σ_m^0 + Δσ_JI^2_DC + Δσ_SHEI_DCcos(α).

Here σ_m^0 is the spin conductivity without any modulation by I_dc, Δσ_J is the efficiency of modulation by Joule heating and Δσ_SHE for the magnons injected by the SHE. For the latter, the injection depends on the col-linearity of μ_mod and the net magnetization of the CrPS4 (𝐦=(𝐦_1+𝐦_2)/2, 𝐦_1,2 are the sub-lattice magnetizations) via the SHE, as is the case for equation <ref> and <ref>.

Substituting σ_m in equation <ref> and <ref> we arrive at the following responses:

    V^1ω   =A^1ωcos^2(α) + B^1ωcos^3(α),
        
    
        V^2ω   =A^2ωcos(α) + B^2ωcos^2(α),

for which the Joule heating affects the amplitudes A^1ω(2ω), scaling with I_DC^2, and the injected magnons via the SHE modify the amplitude B^1ω(2ω), scaling with I_DC. 





§ RESULTS

For our experiment employing the conventional three terminal magnon transistor (as given in Fig. <ref>a) we could not observe a signal for V^1ω_nl above the noise level of typically 5nVRMS. This is caused by two factors: Firstly, the injector-detector distance is comparable to the magnon relaxation length λ_m, meaning the magnons can already decay before they reach the detector. Secondly, the Pt gate contact in between the injector and detector contact functions as a spin sink, absorbing magnon spin by spin flip scattering in the Pt at the Pt/CrPS4 interface. Therefore, we combined the injector and gate into one contact, making a two terminal transistor (see Fig. <ref>b), with injector-detector spacing d=340nm. As the gate affects the magnon density over a distance λ_m from the gate, the working principle is of a two-terminal magnon transistor is similar to that of a three-terminal magnon transistor as long as d<λ_m. However, the two-terminal magnon transistor the coinciding injector and gate contact give rise to an additional I_ACI_dccosα cross term for V^1ω compared to equation <ref>, with D being a prefactor (see SI):

    V^1ω=A^1ωcos^2(α) + B^1ωcos^3(α) + Dcos(α).


In figure <ref> the non-local voltages as a function of in-plane angle α for an injector current I_AC= 60 μA and a dc-current of I_DC=-50μA and I_DC=-100μA are shown at a field of B= 7.5 T at T= 25 K. In <ref>a,c the symmetrized, around α=90^∘ see SI, (antisymmetrized) non-local voltage responses are shown for V^1ω (V^2ω). The fits correspond to the A^1ω (A^2ω) term in equation <ref> (<ref>). In figure <ref>b,d the antisymmetrized, (symmetrized) voltage responses for the first (second) harmonic are given. The fits correspond to the (Dcosα) term. 


In figure <ref>b the Dcosα cross term dominates over the B^1ωcos^3α term. Extraction of B^1ω only yielded values for B^1ω>A^1ω, which is nonphysical. 
Yet, in figure <ref>d the effect of I_DC via the SHE is clearly observed as the B^2ωcos^2α (the latter part of equation <ref>). As I_DC affects the magnon density via the SHE, we expect the same modulation via the SHE in the first harmonic signal B^1ω compared to the second harmonic signal B^2ω. 

Both A^1ω and A^2ω are given as a function of I_DC in figure <ref>a and <ref>b for I_DC between -200μA and +200μA. Fit results for A^1ω and A^2ω are indicated by the dashed lines and show a quadratic dependence on I_DC. The sign of the gate current dependence of A^1ω and A^2ω is equal, indicating that both the electrically and thermally generated magnon spin transport are reduced by an increased magnon temperature. In contrast to the magnon gate on YIG, in which the thermally generated magnon transport is enhanced by the enhanced temperature due to Joule heating by the modulator<cit.>, we only see a decrease in V^2ω_nl. Figure <ref>c, the fit results for B^2ω, shows a linear dependence on I_DC as expected. The slope dB^2ω/dI_DC expresses the modulation efficiency by the SHE injection by I_DC. At 25 K for a magnetic field of 7.5 T, we find dB^2ω/dI_DC=13±2 nV/mA for I_AC=60 μA and dB^2ω/dI_DC=5±2 nV/mA for I_AC=40 μA. These values are comparable to the values measured in the three-terminal magnon transistor on YIG<cit.>. Comparing the modulation to the zero-gating (I_DC=0) signals, where B^1ω(2ω) = 0, we can extract the relative efficiency of modulation:

    η_SHE = dB^1ω(2ω)/dI_DC/A^1ω(2ω)_0,

where A^1ω(2ω)_0=A^1ω(2ω) (I_DC=0). We find η_SHE=13±2%/mA for the second harmonic for I_AC=60μ A and η_SHE=5±2%/mA for I_AC=40μ A. 
The sign of dB^2ω/dI_DC is consistent, as a positive (negative) dc-current via the SHE corresponds to an increase (decrease) in μ_m and therefore in n_m (see Fig. <ref>d and Fig. <ref>c).

In short, the use of the conventional three terminal magnon transistor geometry for CrPS4 is restricted by the relatively short λ_m together with the middle gate contact functioning as a spin sink. However, by exploring a two terminal transistor, where the injector and gate coincide, we show clear modulation by both changing n_m by the SHE as well as by Joule heating. Yet, for the first we can only observe it for the thermally generated non-local magnon transport signal (V^2ω_nl). 





In addition to this we measured a second device D2. As a proof of principle we investigated another unconventional magnon transistor geometry, where the injector-detector contacts are directly adjacent and the gate contact is located on the opposite side of the detector compared to the injector. This is illustrated in figure <ref>c. Both the electrically and thermally generated magnon transport channels can be modulated by the gate contact as the injected magnon spin and heat can diffuse towards the magnon transport channels, even though the gate contact is outside these channels, as long as d_g≪λ_m (where d_g is the distance between the detector and gate). In figure <ref>a and <ref>b the first and second harmonic non-local voltages at an in plane field of 10 T in the y-direction at 25 K, with I_AC=100μA for device D2, are shown as a function of I_DC with the modulator strip as depicted in figure <ref>c. The edge-to-edge distance d between the injector and detector contact is 270 nm and the distance d_g between the detector and gate contact is 480 nm. Both d≪λ_m and d_g≪λ_m, where λ_m is the magnon relaxation length of CrPS4. At 10 T the sub-lattice magnetizations of CrPS4 are saturated in plane and aligned with the magnetic field (see <cit.>). The first harmonic voltage response is fitted (solid red line in Fig. <ref>a) and shows a quadratic dependence of A^1ω on I_DC, as is the case for device D1 (Fig. <ref>a). 

In contrast, the second harmonic voltage response, given in figure <ref>b, show a very different modulation as a function of I_DC. To our surprise, V^2ω_nl is strongly enhanced by I_DC up to one order of magnitude at I_DC≈|370μ A| and at larger I_DC, V^2ω_nl decreases. This is different than has been observed in conventional three terminal magnon valve systems on MnPS3<cit.>, CrPS4<cit.>, and even in the two-terminal geometry in device D1 (Fig. <ref>b), where only a strong suppression of the V^2ω_nl is observed and at sufficiently large I_DC the zero crossing is realized. Although the temperature dependence of the non-local SSE in CrPS4 is not fully understood, such a strong enhancement of nl-SSE voltage is at least striking and possibly opens up a completely new route towards the control of magnon spin transport. The absence of this enhanced transport in V^1ω_nl shows that the enhancement in V^2ω_nl is likely a combined effect of changing n_m via the temperature and the SSE both originating from the Joule heating by I_DC.

Lastly, we compared the effect of I_DC via the SHE altering the B parameters in equations <ref> and <ref>. In figure <ref>d the dependence of B^1ω(2ω) for the first harmonic (second harmonic) at an external field of 12 T is plotted as function of I_DC (extracted from field dependent measurements, see SI). The fit shows a linear dependence on I_DC which is consistent with the results on device D1. Albeit, the modulation efficiency dB/dI_DC achieved is larger. Moreover, we found dB/dI_DC depends on the magnitude of the magnetic field applied, which is likely caused by the not fully saturated V^1ω_nl for larger I_DC, due to the Joule heating, and the not understood behavior of the nl-SSE as a function of temperatures (see SI). For the efficiency of modulation at 12 T in device D2, we found η^1ω_SHE=25%/mA (η_SHE^2ω=16%/mA) for the first (second) harmonic. These values are slightly larger than found for device D1 which is likely caused by the stronger magnetic field. Compared to the modulation efficiencies found in YIG, the values here are 3-5 times larger for device D1 and 5-8 times larger for device D2<cit.>. 



§ CONCLUSION

Summarizing, we demonstrate control over the magnon spin transport in two magnon transistors with unconventional non-local geometries. 
In these transistors we modulated the electrically and thermally generated magnon spin currents, by using a Pt gate contact which injects magnon spins via the SHE, and by altering the magnon temperature and via the SSE, both by Joule heating. Moreover, we separate the effects of modulation on both the electrically and thermally generated magnon spin currents. In device D1, a two terminal transistor where the injector and gate contact coincide, we find a modulation efficiency by the SHE of η_SHE^2ω=13±2%/mA for the thermally generated magnon current at 7.5 T, 25K. In device D2, a three terminal magnon transistor with the gate electrode on the opposite side of the detector compared to the injector, we find modulation efficiencies by the SHE of η^1ω_SHE=25%/mA and η^2ω_SHE=16%/mA at 12 T, 25K, for the electrically and thermally generated magnon currents, respectively. These values are 3-8 times larger than modulation efficiencies found in YIG<cit.>. Moreover, we show that via altering the temperature of device the thermally generated magnon current can be enhanced by one order of magnitude. These results, pave the way for valorization of magnon spin transport in antiferromagnets in technological applications and contribute to our understanding of controlling magnon spin transport. 



We acknowledge the technical support from J. G. Holstein, H. Adema, H. H. de Vries, and F. H. van der Velde. We acknowledge the financial support of the Zernike Institute for Advanced Materials and the European Union’s Horizon 2020 research and innovation program under Grant Agreements No. 785219 and No. 881603 (Graphene Flagship Core 2 and Core 3). This project is also financed by the NWO Spinoza prize awarded to B.J.W. by the NWO and has received funding from the European Research Council (ERC) under the European Union’s 2DMAGSPIN (Grant Agreement No. 101053054). 


























































