Mesoscopic Spintronics

Transcription

1 Mesoscopic Spintronics Taro WAKAMURA (Université Paris-Sud) Lecture 5

2 Today s Topics 5.1 Spincaloritronics 5.2 Domain walls and skyrmions

3 Spin Caloritronics Basics of thermoelectric effects The gradient of electrochemical potential in the case of finite temperature gradient is written as S : Ohm s law S : SeebeckZeeffect (a: Seebeck coefficient) : Hall effect : Nernst effect (N: Nernst coefficient)

4 Spin Caloritronics Seebeck effect More carriers are excited for hotter side, and they diffuse to colder side. Temperature gradient Electric field Application: thermocouple E Y X

5 Spin Caloritronics Pertier effect (inverse of Seebeck effect) Inverse effect of the Seebeck effect. Electric field Temperature gradient Charge carriers are also heat carriers. Temperature gradient can be generated between two different materials (metals or semiconductors). Application: (e.g.) Wine cooler Maa maybe French people store wines in the cave...

6 Spin Caloritronics Nernst effect Temperature gradient + Magnetic field B Temperature gradient (x direction) Electric field (y direction) E Ettinghausen effect (inverse of Seebeck effect) Inverse effect of the Nernst effect Y Electric field (x direction) X Temperature gradient (y direction)

7 Spin Caloritronics Important equations for thermoelectric effects Figure of merit (Seebeck effect) (>1 for practical applications) s e : Conductivity, S: Seebeck coefficient, k L : Thermal conductivity For larger ZT ratio, large s e, large S and small k are necessary. According to the semiclassical Boltzman theory, S 2 s is at maximum when n ~10 19 cm -3 independent of materials. Semiconductors are candidates for high ZT materials!

8 Spin Caloritronics Typical thermoelectric devices Electrons type type SC n-type and p-type semiconductors (SCs) are connected: Hot Cold I In the n-type SC, electrons are excited and flow to the colder side. Electrode Holes type SC Electrode In the p-type SC, holes are excited and flow to the colder side. Structure of the typical thermoelectric device is shown in the right figure. Many thermoelectric elements make the structure complicated.

9 Spin Caloritronics Birth of spincaloritronics In conventional thermocouple Two different conductors with different Seebeck coefficients are connected. In ferromagnets, upspin and downspin have different conductivity, and different Seebeck coefficients. A net flow of spin angular momentum (spin current) Named as spin Seebeck effect Basic idea Temperature gradient + Inverse spin Hall effect K. Uchida et al., Nature 455, 778 (2008).

10 Spin Caloritronics First observation of the spin Seebeck effect Py/Pt simple structure (Fig. a) Finite voltages are observed as a function of the temperature gradient. Sign of the observed voltages is opposite for the hot and cold ends (Fig. b and c). No voltages are observed if no Pt wires are contacted with Py. Signature of spin currents detection by the inverse spin Hall effect K. Uchida et al., Nature 455, 778 (2008).

11 Spin Caloritronics Observed voltages follow sinusoidal relation as a function of the angle between the direction of magnetic field and the temperature gradient (figure a). Measured voltages are symmetric to the central line of the sample (figure b). K. Uchida et al., Nature 455, 778 (2008).

12 Spin Caloritronics Spin Seebeck effect in a magnetic semiconductor Ga 1-x Mn x As Magnetic semiconductor (T C ~ 135 K, when x = 0.158) Contribution of magnetism to observed signals can be revealed by taking data below and above T C. Sign change of voltages measured at hot and cold sign is again observed as the experiments for the Py/Pt system. C. M. Jaworski et al., Nat. Mater. 9, 898 (2010).

13 Spin Caloritronics Spin Seebeck effect in a magnetic semiconductor Linear dependence between DV y and DT x Spin Seebeck coefficient is defined as Quite different behavior of S xy,compared with T dep. of M and a xx (Charge Seebeck coefficient) C. M. Jaworski et al., Nat. Mater. 9, 898 (2010).

14 Spin Caloritronics Spin Seebeck effect in a magnetic semiconductor Even if the channel is scratched, generated voltage (V y ) and the spin Seebeck coefficients (S xy ) do not change. The observed voltage is generated from the global spin currents. Then what is the origin of the spin Seebeck effect? Phonons? Magnons? C. M. Jaworski et al., Nat. Mater. 9, 898 (2010).

15 Spin Caloritronics How to suppress spurious effects? To investigate effects from magnons or phonons, it is better to use ferromagnetic (or ferrimagnetic) insulators, by suppressing conventional thermoelectric effects mediated by electrons or holes(e.g. Seebeck effect, Nernst effect). Candidates Phonons Magnons (spin waves) Is the spin Seebeck effect originated from magnons? K. Uchida et al., Nat. Mater. 9, 894 (2010).

16 Magnons Spin waves = excited state from the ground state (e.g. ferromagnetic) Spin waves Quantized Magnons (quasiparticles) Spin waves (magnons)

17 Spin-wave spin currents Transfer of spin angular momentum is mediated not only electrons (conduction-spin current), but also magnons (spin-wave spin current). Excitation and Detection via the STT and ISHE Spin wave excitation by STT Pt/Y 3 Fe 5 O 12 (YIG)/Pt structure Spin currents generated in Pt exert a torque (spin-transfer-torque (STT)) on YIG and excite spin waves. Y. Kajiwara et al., Nature 464, 262 (2010).

18 Spin-wave spin currents Spin pumping into Pt Very small damping of spin waves in YIG enables long propagation of spin waves. Spin waves propagated to the other Pt induces spin currents inside Pt via the spin pumping effect, and via the inverse spin Hall effect a finite voltage can be detected. Depending on the relative angle between the transverse direction of the sample and the external magnetic field, voltage signals are observed above the threshold current. The angle dependence follows the relation: Y. Kajiwara et al., Nature 464, 262 (2010).

19 Spin Caloritronics Spin Seebeck effect in a insulator Spin Seebeck effect can occur in insulators via spin-wave spin currents However, in this experimental setup spin waves are excited by thermal gradients. Excited spin waves generates spin currents inside the Pt film on top of ferrimagnetic insulator (LaY 2 Fe 5 O 12 ), which are converted into charge currents via the inverse spin Hall effect. K. Uchida et al., Nat. Mater. 9, 894 (2010).

20 Spin Caloritronics Observed voltages well follow magnetic profile of LaY 2 F 5 O 12. Replacing Pt by Cu supresses the observed voltages. Observed voltages are originated from the inverse spin Hall effect Inserting SiO 2 between Pt and LaY 2 F 5 O 12 suppresses the voltages. Coupling between Pt and LaY 2 F 5 O 12 is significant Heating the sample grobally at 320 K suppresses the voltages. K. Uchida et al., Nat. Mater. 9, 894 (2010).

21 Spin Caloritronics Similar behaviors to the experiments with the Py/Pt system are observed. Magnons (spin waves) play a dominant role for the spin Seebeck effect! K. Uchida et al., Nat. Mater. 9, 894 (2010).

22 Output voltage Spin Caloritronics Future applications of spin Seebeck effect Longitudinal setup of the spin Seebeck effect is developed. Easier to fabricate Applicable to commercial devices Attempts to produce commercial devices Device DT from the technical report of the NEC company A. Kirihara et al., Nat. Mater. 11, 686 (2012).

23 Spin Caloritronics Spin dependent Seebeck effect Thermal spin injection in lateral spin valves Spin-dependent current density with temperature gradients can be expressed as Contribution from spin-dependent Seebeck effect Therefore spin currents can be written under the condition of no charge currents as where A. Slachter et al., Nat. Phys. 6, 879 (2010).

24 Spin Caloritronics Thermal spin injection Currents flowing only through Py Joule heating effect Since, the voltage originated from spin-dependent Seebeck effect is proportional to I 2. Magnetic field dependent signals are observed as a function of I 2! A. Slachter et al., Nat. Phys. 6, 879 (2010).

25 Spin Caloritronics Spin dependent Pertier effect Spin-dependent Pertier coefficients P s : Upspins and downspins carry different amount of heat currents In the case of pure spin currents Upspins and downspins flow in the counter direction accompanying with different heat currents. Heat flow is carried away from the interface resulting in cooling down the interface (in the right figure). k:thermal conductivity Spin accumulation at the interface J. Flipse et al., Nat. Nanotech 7, 166 (2012).

26 Spin Caloritronics Spin dependent Pertier effect Cu Parallel magnetization Spin accumulation at the interface Py Only charge Pertier effect (because of no spin accumulation) Thermocouple Antiparallel magnetization Charge + spin Pertier effect (because of spin accumulation) J. Flipse et al., Nat. Nanotech 7, 166 (2012).

27 Spin Caloritronics Spin dependent Pertier effect Depending on the parallel or antiparallel magnetization, different voltage is measured by the thermocouple. A few mk temperature difference by the spin-dependent Pertier effect Contribution from the spin-dependent Pertier effect J. Flipse et al., Nat. Nanotech 7, 166 (2012).

28 Brief summary Spincaloritronics is a new field where spin transport is intimately coupled with thermoelectric effects Spin Seebeck effect in the Py/Pt structure gave birth to spincaloritronics, but initial scenario based on conduction electrons was finally wrong, and magnons play a central role for the spin Seebeck effect. Thermal spin injection is possible by exploiting different Seebeck coefficients for upspin and downspin conduction electrons. Cooling a device is also possible via the spin-dependent Pertier effect.

29 Domain walls and skyrmions

30 Birth of Spintronics Application of TMR to hard disk drives

31 Importance of domain wall for technology Racetrack memory Memory device as a long magnetic tape based on spin-transfer torque and tunnel magnetoresistance (TMR). Stuart Parkin S. S. P. Parkin et al., Science 320, 190 (2008).

32 Importance of domain wall for technology Problem Stuart Parkin To drive domain walls by STTs, very large current (~10 12 A/m 2 ) is needed. Large Joule heating effect occurs, which is not good for efficient energy consumption. S. S. P. Parkin et al., Science 320, 190 (2008).

33 Emergence of magnetic skyrmions Original skyrmions Skyrmion A quasiparticle with hedgehog spin configuration originally proposed as the theoretical model baryons in nuclear physics. Skyrmions in condensed matter physics Tony Skyrme Skyrmions in quantum Hall ferromagnets Skyrmions in atomic Bose-Einstein condensation Skyrmions in chiral magnets

34 Skyrmions Skyrmions Skyrmion number N k : Particle-like spin textures Topologically protected n(r): Unit vector parallel to the magnetization at r Magnetization vector of a skyrmion covers a whole surface, thus N k = ±1. (the sign depends on the direction of the magnetization at the core) On the other hand, other spin structures such as ferromagnetic, antiferromagnetic, helical alignent etc. give N k = 0. Topologically protected

35 Magnetic bubbles vs skyrmions Magnetic bubble memory Intensively investigated in 70 s as a future candidate for magnetic memory. Problems Large size (hundreds nm ~ mm) due to the origin of the bubble domains (dipolar interaction). Strong pinning effects by defects or impurities Skyrmions: smaller size (1 100 nm), less pinning effects, more stable owing to the topological protection.

36 Skyrmions What are ingredients for skyrmions? Exchange interaction Colinear alignment is favorable Dzyaloshinski-Moriya interaction (DMI) D 12 disappears when the system is inversion symmetric. Inversion symmetry breaking is essential to have DMI. A. Fert et al., Nat. Nanotech 8, 152 (2013).

37 Skyrmions Dzyaloshinski-Moriya interaction (DMI) This interaction can be considered when indirect exchange interaction via spin-orbit coupling (SOC) is taken into account. Materials which contain elements with large SOC have stronger DMI. Direction of D 12 is determined by (crystal) symmetry. A. Fert et al., Nat. Nanotech 8, 152 (2013). Canted spin alignment is favorable When J 0 ~ D 12, helical spin configuration emerges.

38 Skyrmions Anomalous A-phase of MnSi MnSi: Cubic but no inversion symmetry (chiral magnet) DMI plays an important role With small external magnetic field (B) Helical state is favored With relatively large external magnetic field (B) Conical state is favored The q vector favors the alignment parallel to the external magnetic field (B). q B Helical Conical

39 Skyrmions Helical (or conical) state: Defined by single wave vector q The anomalous A-phase was found in MnSi close to the phase transition to the conical state. S. Muhlbauer et al., Science 323, 913 (2009).

40 Skyrmions In this A-phase, there are three q vectors and these q vectors are on the plane perpendicular to the external magnetic field (B). Triple-q state : A superposition of three helices under 120 degrees Hexagonal alignment of the q vectors implies the hexagonal crystal formation. Skyrmion? However, magnetic structures are not clear only with these data. S. Muhlbauer et al., Science 323, 913 (2009).

41 Skyrmions Observation of topological Hall effect (THE) What happens if we measure the Hall effect for MnSi? Anomalous contributions to the Hall effect in the A-phase region. Attribute to the fictitious magnetic field generated by the Berry phase, due to nontrivial spin textures With the fictitious magnetic field, the Hall resistivity of the THE component can be expressed as A. Neubauer et al., Phys. Rev. Lett. 102, (2009).

42 Skyrmions Observation of topological Hall effect (THE) A For a single q state (like helical or conical) therefore. Suggestive for nontrivial topology existing in the A-phase. Nonzero D r xy is observed almost exactly in the A-phase region as a function of temperature (figure A). A. Neubauer et al., Phys. Rev. Lett. 102, (2009). B Similar anomalous contribution to s xy was observed for pressured MnSi (figure B). M. Lee et al., Phys. Rev. Lett. 102, (2009).

43 Skyrmions Real space observation of skyrmion crystal Semiconducting Fe 0.5 Co 0.5 Si Real space observation of Lorenz transmission Electromicroscope (LTEM) 0 T 50 mt X. Z. Yu et al., Nature 465, 901 (2010).

44 Skyrmions Real space observation of skyrmion crystal Skyrmion crystal (SkX) phase emerges at low temperatures and in a certain magnetic field region. Theoretical simulations reproduce well the experimental phase diagrams (the right figure). X. Z. Yu et al., Nature 465, 901 (2010).

45 Skyrmions How to enhance the critical temperature? Dimension of the system is an important factor to stabilize skyrmions. When the sample thickness is comparable or thinner than the conical periodicity, the conical state can no longer benefit from the energy gain of DMI. Skyrmion phase rather than conical phase becomes more stable. M. Mochizuki and S. Seki, J. Phys. Cond. Mater. 27, (2015).

46 Skyrmions How to enhance the critical temperature? Skyrmions are formed in helimagnets, below the critical temperature (T C ) of the helical magnetization. One solution Choice of helimagnets with higher T C. FeGe: helimagnet with T C ~ 280 K Skyrmion phase appears around 260 K! The area of the skyrmion phase becomes larger for thinner samples. Importance of the dimension of the system. X. Z. Yu et al., Nat. Mater. 10, 106 (2011).

47 Skyrmions above room temperature Co-Zn-Mn alloys: crystal structure with broken inversion symmetry DMI helimagnet High critical temperature (T C ~420 K for Co 10 Zn 10 ) Room temperature skyrmion phase is expected. Y. Tokunaga et al., Nat. Comm. 6, 7638 (2015).

48 Skyrmions above room temperature Skyrmion phase is observed in a narrow window above room temperatures for bulk. For thin films, skyrmion phase enlarges and becomes more stable. Importance of the sample dimension Multiple q-state is observed. Y. Tokunaga et al., Nat. Comm. 6, 7638 (2015).

49 Skyrmions at the interface Interface between ferromagnet and nonmagnet with strong SOI Broken inversion symmetry (BIA) and hosts strong DMI Spins can see the BIA via SOI Advantages compared with skyrmions in bulk crystals Smaller skyrmions are possible for large DMI Size of bulk skyrmions: nm Size of interface skyrmions: 1 - a few nm Skyrmions are observed as a ground state Bulk skyrmions: metastable state (magnetic field needed) Bulk skyrmions: spontaneous ground state (magnetic field needed) A. Fert et al., Nat. Nanotech 8, 152 (2013).

50 Influence of DMI on magnetic structures Mn on W(110) Mn Antiferromagnet Strong DMI induced at the interface induces canted spin structure (helical or cycloidal). Spin-polarized scanning tunnel microscopy (SP-STM) Tunneling currents between the spin-polarized tip and sample strongly depends on the magnetization of the sample. Powerful tool to investigate magnetic structure at the surface! Spin-polarized STM

51 Influence of DMI on magnetic structures Brightest part shifts depending on the orientation of the spin polarization of the tip. Rotation of magnetization of the sample as a function of position. Theoretical calculation including spin-orbit coupling (SOC) demonstrates lower energy at a finite spiral periodicity l. M. Bode et al, Nature 447, 190 (2007).

52 First experimental observation Spin-polarized STM measurements on Fe/Ir(111) interface Inversion symmetry is broken at the interface + strong spin-orbit interaction of Ir Multiple q state: two q vector (Q1 and Q2) is observed. Simulations assuming skyrmion crystals formation clearly reproduce the observed SP-STM image (see the inset of the figure B) S. Heinze et al., Nat. Phys. 7, 713 (2011).

53 Interface skyrmions at room temperature Pt/Co/Ir multilayer structures Additive DMI induces strong DMI in Co layer Room temperature skyrmions are expected. Applied perpendicular field Observations by magnetizationsensitive scanning X-ray transmission microscopy. 8 mt 38 mt 68 mt 83 mt C. Moreau-Luchaire et al., Nat. Nanotech 11, 444 (2016).

54 Interface skyrmions at room temperature Isolated skyrmions are stabilized around 70 mt (see the figure d). Micromagnetic simulations show the expected DMI is as large as 20 % of the exchange interaction of Co layer. 8 mt 38 mt 68 mt 83 mt C. Moreau-Luchaire et al., Nat. Nanotech 11, 444 (2016).

55 Interface skyrmions at room temperature Skyrmions can be confined in disks and also long tracks. Applicable to the skyrmions train memory like race track memory simulated in the figure below. J. Sampaio et al., Nat. Nanotech 8, 839 (2013). C. Moreau-Luchaire et al., Nat. Nanotech 11, 444 (2016).

56 Brief Summary Skyrmions are promising candidates for future high density memory device Skyrmions are roughly categorized into the two types, bulk skyrmions and interface skyrmions. For both of them the Dzyaloshinskii-Moriya interaction (DMI) induced by symmetry breaking plays a crucial role to generate this chiral magnetic structure. Skyrmions were initially observed at low temperatures, but now both types of skyrmions can already be measured at room temperatures by appropriate choice of materials. To realize commercial skyrmion devices, there are still problems (e.g. speed of skyrmions driven by STT), but intensive research is ongoing.