Magnetic article and rotation of magnetic spins via spin-orbit effect in same

A nonvolatile memory cell includes: a first fixed magnetic layer; a first nonmagnetic electrode disposed on the first magnetic layer; a memory storage layer disposed on the first nonmagnetic electrode; a tunnel barrier layer disposed on the memory storage layer; a second fixed magnetic layer disposed on the tunnel barrier layer; and a second nonmagnetic electrode disposed on the second fixed magnetic layer.

BRIEF DESCRIPTION

Disclosed is a nonvolatile memory cell to store a memory bit, the nonvolatile memory cell comprising: a first fixed magnetic layer comprising a first fixed magnetic state and that conducts electrical current; a first nonmagnetic electrode disposed on the first magnetic layer and that conducts electrical current; a memory storage layer disposed on the first nonmagnetic electrode and comprising the memory bit, the memory bit being in a first magnetic state or a second magnetic state, the memory storage layer being switchable between the first magnetic state and the second magnetic state in response to a direction of electrical current present in the first nonmagnetic electrode, the memory bit being stored in the memory storage layer as the first magnetic state or the second magnetic state, the first nonmagnetic electrode being interposed between the first fixed magnetic layer and the memory storage layer, and the first fixed magnetic state being oriented orthogonal to the first magnetic state and the second magnetic state; a tunnel barrier layer disposed on the memory storage layer such that the memory storage layer is interposed between the tunnel barrier layer and the first nonmagnetic electrode; a second fixed magnetic layer comprising a second fixed magnetic state and that conducts electrical current, the tunnel barrier layer interposed between the memory storage layer and the second fixed magnetic layer, and the second fixed magnetic state being aligned with the memory bit in the memory storage layer; and a second nonmagnetic electrode disposed on the second fixed magnetic layer and that conducts electrical current, the second fixed magnetic layer being interposed between the tunnel barrier layer and the second nonmagnetic electrode.

Also disclosed is, in a memory system comprising a nonvolatile memory cell, a process for writing or reading the memory bit, the process comprising: subjecting the first nonmagnetic electrode to an electrical current flowing in a first direction through the first nonmagnetic electrode; and storing the memory bit as the first magnetic state in the memory storage layer, in response to the electrical current flowing in the first direction through the first nonmagnetic electrode, to write the memory bit in the nonvolatile memory cell.

DETAILED DESCRIPTION

Advantageously and unexpectedly, it has been discovered that a nonvolatile memory cell herein provides low power consumption, high speed, and extremely dense scalability. Moreover, electrical current flowing in a fixed magnetic layer switches magnetization in an adjacent memory storage layer that includes magnetic material. Here, magnetic spin rotation in combination with a magnetic spin Hall effect provide memory bit storage and retrieval in a ferromagnetic metal of the memory storage layer. The nonvolatile memory cell provides high endurance and high density in memory storage.

In an embodiment, with reference toFIG. 1, nonvolatile memory cell100includes first fixed magnetic layer102; first nonmagnetic electrode104disposed on first magnetic layer102; memory storage layer106disposed on first nonmagnetic electrode104; tunnel barrier layer108disposed on memory storage layer106; second fixed magnetic layer110disposed on tunnel barrier layer108; and second nonmagnetic electrode112disposed on second fixed magnetic layer110. Here, first fixed magnetic layer102includes first fixed magnetic state FM1and conducts electrical current. Also, first nonmagnetic electrode104conducts electrical current. Memory storage layer106includes the memory bit, and the memory bit is in first magnetic state M1or second magnetic state M2, wherein memory storage layer106is switchable between first magnetic state M1and second magnetic state M2in response to a direction of electrical current present in first nonmagnetic electrode104and first fixed magnetic layer102such that the memory bit is stored or written in memory storage layer106as first magnetic state M1or second magnetic state M2. First nonmagnetic electrode104is interposed between first fixed magnetic layer102and memory storage layer106, and first fixed magnetic state FM1is oriented orthogonal to first magnetic state M0and second magnetic state M1. Tunnel barrier layer108is disposed on memory storage layer106such that memory storage layer106is interposed between tunnel barrier layer108and first nonmagnetic electrode104. Further, second fixed magnetic layer110includes second fixed magnetic state FM2and conducts electrical current such that tunnel barrier layer108is interposed between memory storage layer106and second fixed magnetic layer110. Second fixed magnetic state FM2is aligned with the memory bit in memory storage layer106. Additionally, second nonmagnetic electrode112is disposed on second fixed magnetic layer110such that second fixed magnetic layer110is interposed between tunnel barrier layer108and second nonmagnetic electrode112.

In an embodiment, with reference toFIG. 2, nonvolatile memory cell100includes intermediate layer114interposed between second fixed magnetic layer110and second nonmagnetic electrode112.

In an embodiment, with reference toFIG. 3, nonvolatile memory cell100includes power source152in electrical communication with first fixed magnetic layer102and first nonmagnetic electrode104via electrical wires (158,160,162,164,166,168). Power source152provides electrical current that flows through first fixed magnetic layer102and first nonmagnetic electrode104. When the electrical current flows in first direction I1in first nonmagnetic electrode104, the memory bit is in first memory state M0in memory storage layer106. When the electrical current flows in second direction I2in first nonmagnetic electrode104, the memory bit is in second memory state M1in memory storage layer106.

Nonvolatile memory cell100also can include resistance meter150in electrical communication with first nonmagnetic electrode104and second nonmagnetic electrode112nanowires156and154. Resistance meter150measures an electrical resistance across memory storage layer106. The electrical resistance across memory storage layer106can be relative to the little resistance of second fixed magnetic layer110. Here, memory storage layer106has first electrical resistance R0in first magnetic state M0, and memory storage layer106has second electrical resistance R1in second magnetic state M1as shown inFIG. 10.

In an embodiment, with reference toFIG. 4, computing system200includes storage drive180, first controller204, and second controller206. Storage drive180includes plurality of nonvolatile memory cells100arranged in an array and connected to first controller204via wires202and second controller206wires200. In this manner, electrical power can be supplied individual nonvolatile memory cells100and individual memory bets can be written to or read from individual nonvolatile memory cells100, wherein controllers (204,206) in combination address individual nonvolatile memory cells100. A number of nonvolatile memory cells100in storage drive180is not limited and can be any number selected to read and write memory bits. A size of storage drive180can be selected to be application of computing system200.

Nonvolatile memory cell100can have a size selected for a give application for storage of a memory bit. A volume of nonvolatile memory cell can be, e.g., from 2e1 nm3to 5e7 nm3, specifically from 2e1 nm3to 1e6 nm3, and more specifically from 2e1 nm3to 1e4 nm3. An amount of electrical current to store the memory bit in memory storage layer106and that flows through first nonmagnetic lecture104and first fixed magnetic layer102is an amount effective to change between first magnetic state M0and second magnetic state M1. It is contemplated that the amount of electrical current can be, e.g., from 1 μA to 1 mA, specifically from 10 μA to 100 μA, and more specifically from 10 μA to 50 μA. Further, an electrical resistance difference of memory storage layer106in first magnetic state M0and second magnetic state M1can be, e.g., from 10Ω to 1e4Ω, specifically from 50Ω to 1e3Ω, and more specifically from 50Ω to 200Ω.

First fixed magnetic layer102of nonvolatile memory cell100provides first fixed magnetic state FM1. A thickness of first fixed magnetic layer102can be can be from 0.5 nm to 100 nm, specifically from 1 nm to 20 nm, and more specifically from 1 nm to 5 nm. Exemplary materials for first fixed magnetic layer102include iron, nickel, cobalt, or a combination thereof.

First nonmagnetic electrode104provides an electrically conductive path of the electrical current and through spin-orbit coupling of electrons therein switches the memory bit in memory storage layer106between first magnetic state M0and second magnetic state M1. A thickness of first nonmagnetic electrode104can be can be from 0.5 nm to 100 nm, specifically from 1 nm to 20 nm, and more specifically from 1 nm to 5 nm. Exemplary materials for first nonmagnetic electrode104include nonmagnetic material such as Cu, Au, Ag, or a combination thereof.

Memory storage layer106provides storage of the memory bit in first magnetic state M0or second magnetic state M1. A thickness of memory storage layer106can be can be from 0.5 nm to 10 nm, specifically from 1 nm to 4 nm, and more specifically from 1 nm to 2 nm. Exemplary materials for memory storage layer106include cobalt, iron, nickel, or a combination thereof.

Tunnel barrier layer108provides magnetic contrast in the form of a magnetization dependent resistance for current flowing through the storage layer stack consisting of layers104through112. A thickness of tunnel barrier layer108can be can be from 0.3 nm to 3 nm, specifically from 0.5 nm to 2 nm, and more specifically from 0.5 to 1 nm. Exemplary materials for tunnel barrier layer108include magnesium oxide (MgO), aluminum oxide (Al2O3), carbon (C), or a combination thereof.

Second fixed magnetic layer110of nonvolatile memory cell100provides second fixed magnetic state FM2. A thickness of second fixed magnetic layer110can be can be from 100 nm to 1 nm, specifically from 20 nm to 2 nm, and more specifically from 10 nm to 5 nm. Exemplary materials for second fixed magnetic layer110include cobalt, iron, nickel, or a combination thereof.

Intermediate layer114provides exchange bias in order to stabilize and fix the magnetization of second fixed magnetic layer110. A thickness of intermediate layer114can be can be from 100 nm to 1 nm, specifically from 50 nm to 2 nm, and more specifically from 10 nm to 5 nm. Exemplary materials for intermediate layer114include nickel oxide (NiO), ruthenium (Ru), iridium manganese (IrMn), or a combination thereof.

Second magnetic electrode112provides additional stabilization and control of the free magnetic layer106via cancellation of any stray magnetic field from the fixed magnetic layer110. A thickness of second nonmagnetic electrode112can be can be from 0.5 nm to 100 nm, specifically from 1 nm to 20 nm, and more specifically from 1 nm to 5 nm. Exemplary materials for second nonmagnetic electrode112include magnetic material such as cobalt, iron, nickel, or a combination thereof.

Power source152provides voltage and current to drive the switching of magnetic layer106. Moreover, power source152can be controlled in terms of timing, duration, and current amplitude during the switching process.

Resistance meter150provides the ability to determine the magnetic-dependent tunnel magnetoresistance that impedes current flow through the storage stack. Moreover, resistance meter150provides a bias voltage for the measurement of the tunnel magnetoresistance.

Controllers (204,206) provides timing and power control for both the writing and reading process. Moreover, controllers (204,206) allow for selection of the particular bit in the array that should be written to or read from.

In an embodiment, with reference toFIG. 5,FIG. 6,FIG. 7,FIG. 8, andFIG. 9, a process for making nonvolatile memory cell includes deposition of all layers via sputtering, evaporation, or any other thin film deposition method.

In an embodiment, a process for making system200includes deposition of all materials via processing methods such as electrochemical platting, evaporation, sputter deposition, or molecular beam epitaxy, and subsequent patterning of the materials into devices via lithographic processing methods.

According to an embodiment, with reference toFIG. 10andFIG. 11, in a memory system including nonvolatile memory cell100, a process for writing or reading the memory bit includes: subjecting first nonmagnetic electrode104to an electrical current flowing in first direction I1through first nonmagnetic electrode104; and storing the memory bit as first magnetic state M0in memory storage layer106, in response to the electrical current flowing in first direction I1through first nonmagnetic electrode104, to write the memory bit in nonvolatile memory cell100. The process further can include measuring an electrical resistance of memory storage layer106relative to second fixed magnetic layer110to read the memory bit stored in memory storage layer106of nonvolatile memory cell100. The process also can include: subjecting first nonmagnetic electrode104to an electrical current flowing in second direction I2through first nonmagnetic electrode104; and storing the memory bit as second magnetic state M1in memory storage layer106, in response to the electrical current flowing in second direction I2through first nonmagnetic electrode104, to write the memory bit in nonvolatile memory cell100. The process further can include measuring an electrical resistance of memory storage layer106relative to second fixed magnetic layer110to read the memory bit stored in memory storage layer106of nonvolatile memory cell100.

It is contemplated that in the process, subjecting first nonmagnetic electrode104to the electrical current flowing in first direction I1includes use of a power supply to provide said current, and control electronics to determine both the timing, duration, and magnitude of said current.

Storing the memory bit as first magnetic state M0in memory storage layer106includes application of sufficient current of a selected strength and duration to allow for complete, deterministic switching of the magnetization in storage layer106.

Measuring the electrical resistance of memory storage layer106relative to second fixed magnetic layer110to read the memory bit stored as first magnetic state M0includes application of a bias voltage across the tunnel junction layer108of sufficient amplitude and duration to permit unambiguous determination of the magnetization state in layer106, e.g. by measurement of the tunnel barrier resistance.

Subjecting first nonmagnetic electrode104to the electrical current flowing in second direction I2includes use of a power supply to provide said current, and control electronics to determine both the timing, duration, and magnitude of said current.

Storing the memory bit as second magnetic state M1includes application of sufficient current of a selected strength and duration to allow for complete, deterministic switching of the magnetization in storage layer106.

Measuring an electrical resistance of memory storage layer106relative to second fixed magnetic layer110to read the memory bit stored as second magnetic state M1includes application of a bias voltage across the tunnel junction layer108of sufficient amplitude and duration to permit unambiguous determination of the magnetization state in layer106, e.g. by measurement of the tunnel barrier resistance.

An exemplary process for writing the memory bit to memory storage layer106and reading the memory bit stored in memory storage layer106is shown in panel A ofFIG. 10, and panel B shows a graph of magnetic state versus time that corresponds to the read and write periods shown in panel A, wherein the solid curve corresponds the magnetic state, and the dashed curve corresponds to the electrical resistance of memory storage layer106relative to second fixed magnetic layer110. Here, during first read period between time T0and time T1, no current flows through first nonmagnetic electrode104, and memory storage layer106is in first magnetic state M0with first resistance R0. Panel A ofFIG. 11shows operation of nonvolatile memory cell100during the first read period. During first write period between time T1and time T2, current flows in first direction I1through first nonmagnetic electrode104, and memory storage layer106switches from first magnetic state M0with first resistance R0to second magnetic state M1with second electrical resistance R1. Panel B ofFIG. 11shows operation of nonvolatile memory cell100during the first write period. During second read period between time T2and time T3, current is at I0, and memory storage layer106maintains second magnetic state M1with second electrical resistance R1. Panel C ofFIG. 11shows operation of nonvolatile memory cell100during the second read period. During second write period between time T3and time T4, current flows in second direction I2through first nonmagnetic electrode104, and memory storage layer106switches from second magnetic state M1with second resistance R1to first magnetic state M0with first electrical resistance R0. Panel D ofFIG. 11shows operation of nonvolatile memory cell100during the second write period. During third read period between time T4and time T5, current is at I0, and memory storage layer106maintains first magnetic state M0with first electrical resistance R0. Panel E ofFIG. 11shows operation of nonvolatile memory cell100during the third read period. During third write period between time T5and time T6, current flows in first direction I1through first nonmagnetic electrode104, and memory storage layer106switches from first magnetic state M0with first resistance R0to second magnetic state M1with second electrical resistance R1. Panel F ofFIG. 11shows operation of nonvolatile memory cell100during the third write period. During fourth read period between time T6and time T7(not shown), current is at I0, and memory storage layer106maintains second magnetic state M1with second electrical resistance R1. Panel F ofFIG. 11shows operation of nonvolatile memory cell100during the fourth read period.

Nonvolatile memory cell100, system200, and processes herein have numerous advantageous and beneficial properties. Advantageously, nonvolatile memory cell100provides the coincident use of a perpendicular magnetized magnetic storage layer106with an in-plane write current that flows in proximity to, but not through, the magnetic storage and readout stack, consisting of layers106through112. By use of a proximate write current, one avoids passage of a large write current through the storage and readout stack that could otherwise cause catastrophic or subtle damage to the stack, e.g. via heating or electro migration effects. By use of a perpendicular magnetized storage layer106, device stability with respect to thermal fluctuations is maximized. Finally, the combination of a proximate write current and a perpendicular magnetized storage layer is accomplished with a minimal increase in device complexity.

The articles and processes herein are illustrated further by the following Example, which is non-limiting.

Example

Large rotation of spin-orbit torques in metallic layers with orthogonally magnetized ferromagnets.

The spin-orbit interaction occurs in nonmagnetic/magnetic multilayers and provides conversion between a spin current and a charge current. In the spin-orbit torque (SOT) and inverse spin Hall/Rashba-Edelstein effects (ISHE/IREE), the charge current, spin current and spin directions are orthogonal to each other in the nonmagnetic material. This Example provides generation of SOT and ISHE/IREE voltage in unconventional directions in a magnetic metal. In a spin valve-like multilayer with orthogonal magnetization configurations, we observe SOTs on the in-plane magnetized layer in the direction that is rotated 90° from the conventional SOTs around the out-of-plane magnetization of the other magnetic layer. We measure the ISHE/IREE generated by an out-of-plane temperature gradient in the same sample and observe the ISHE/IREE voltage with a similar rotated symmetry. Spin-orbit effects in magnetic multilayers can be used magnetic random access memories.

Spin-orbit interaction in nonmagnetic materials leads to interconversion between charge current and spin current. Related phenomena that have been studied are the spin Hall effect (SHE), the Rashba-Edelstein effect (REE) and their inverse effects, ISHE/IREE. The SHE/REE enables efficient control of magnetization by a charge current, which leads to potential applications in magnetic random access memories and racetrack memories. These effects can usually be described by the same symmetry in polycrystalline or amorphous samples. For example, in a ferromagnetic/nonmagnetic bilayer film, an in-plane electric current generates a damping-like SOT τDLand a field-like SOT τFLon the magnetization,
τDL∝{circumflex over (m)}×({circumflex over (m)}×(Î×{circumflex over (z)}))
τFL∝({circumflex over (m)}×(Î×{circumflex over (z)}))  (1)
where m^ is the unit magnetization direction of the ferromagnet, I^ is a unit vector along the electric current direction, and z^ is a unit vector perpendicular to the film.

Similarly, if a perpendicular temperature gradient is applied, an electric field is generated due to the ISHE/IREE, whose geometry can be described as
{right arrow over (E)}∝{circumflex over (m)}×∇{right arrow over (T)}(2)
where ∇T is the temperature gradient.

This Example shows that in magnetic multilayers with orthogonal magnetizations, there are spin-orbit effects that cannot be described by Eqs. (1) and (2). Instead, they exhibit a rotated geometry as if the spins have precessed around the magnetizations.

First, we demonstrate the detection of rotated SOTs by the magneto-optic-Kerr-effect (MOKE). We deposit a test sample consisting of Seed/PML/Cu(3)/Py(2)/Pt(3) and a control sample consisting of Seed/PML/Cu(3)/TaOx(3)/Py(2)/Pt(3), where Seed=Ta(2)/Cu(3), PML=[Co(0.16)/Ni(0.6)]8/Co(0.16), and the numbers in parentheses are nominal thicknesses in nanometers. At zero external magnetic field, the PML has perpendicular magnetization while Py has in-plane magnetization. As shown inFIG. 12(a), when an electric current is applied to the sample along the x-direction, a torque is generated in the Py layer with both field-like and damping-like symmetries. Present theory predicts the torque can be expressed in terms of an equivalent SOT field,
{right arrow over (h)}SOT=hDL({circumflex over (m)}Py×(Î×{circumflex over (z)}))+hFL_in(Î×{circumflex over (z)})+hFL_out{circumflex over (z)}(3)
where hDLis the magnitude of the damping-like field, hFL_inis the magnitude of the field-like field, including the in-plane Oersted field from the current and spin-orbit effective fields, hFL_outis the magnitude of the out-of-plane Oersted field from the current, and m^Pyis the unit magnetization direction of Py.

Assuming the initial magnetization of Py is aligned by an in-plane external magnetic field Hext, m^Pywill be tilted out-of-plane by the damping-like field. To the first order approximation, this tilting can be calculated as

mPy⁢_⁢z=hDL⁡(m^Py·I^)+hFL⁢_⁢ou⁢tHext+Meff(4)
where Meffis the effective demagnetizing field along the z-direction in Py.

The out-of-plane magnetization tilting is detected by the polar MOKE with normal light incidence, where the Kerr rotation Ψpolaris proportional to mPy_z. If I^ is applied parallel to Hext, the current-induced polar MOKE rotation is shown inFIG. 12(b). Here the hysteresis-like behavior is due to the hDL and the offset is due to the hFL_out, according to Eq. (4). The signal is independent on the initial direction of the PML magnetization m^PML. By comparing the contributions due to the hDLand hFL_outin a line scan measurement, we estimate that hDLis about 120±12 A/m when 30 mA electric current is applied through a 50 μm wide sample.

When I^ is applied perpendicular to Hext, Eq. (4) suggests the out-of-plane magnetization tilting due to the damping-like field should vanish. Indeed, in the control sample with TaOxas seen inFIG. 12(c), very weak hysteresis-like signals independent on m^PMLare observed, which is likely due to small misalignment. However, in the test sample, large polar MOKE signals are observed indicating significant out-of-plane magnetization tilting due to some damping-like fields. The magnitude is estimated to be 25% of the magnitude of hDL, which is 30±4 A/m with the same current density described above. Strikingly, this damping-like field reverses as m^PMLswitches, suggesting such signals are not due to misalignment.

To understand the damping-like field that depends on m^PML, we first extract the contribution from the damping-like field by taking the difference of Ψpolar when m^Pyswitches. The obtained values will then be added or subtracted when m^PMLreverses, in order to separate damping-like fields depending on whether they are even or odd with m^PML,

Shown inFIG. 12(d), ΨP_evenexhibits a cos ϕ dependence, while ΨP_oddexhibits a sin ϕ dependence, where ϕ is the angle between Hextand I^. This suggests that a new damping-like field should be added to Eq. (3),
{right arrow over (h)}R_DL=hR_DL{circumflex over (m)}Py×((Î×{circumflex over (z)})×{circumflex over (m)}PML)  (6)
where hR_DLis the magnitude of the damping-like field of this rotated SOT.

We further measured the in-plane magnetization reorientation by using quadratic MOKE and observed similar symmetries. In-plane field hFL_inEq. (3) leads to in-plane magnetization tilting toward the y-direction.

mPy⁢_⁢⁢y=hFL⁢_⁢⁢in⁡(I^×z^)·y^Hext±Han(7)
where Hanis the in-plane anisotropy field of Py and the ±sign depends on whether m^Pyis parallel or anti-parallel with Hext. The in-plane magnetization reorientation gives rise to a quadratic MOKE signal Ψquadthat is proportional to ({circumflex over (m)}Py·ŷ)({circumflex over (m)}Py·{circumflex over (x)}). When ϕ=0°, as shown inFIG. 13(a), both the test and control samples exhibit 1/Hext-like quadratic MOKE response, as expected from Eq. (7). These signals are independent with the initial polarization of PML. As shown inFIG. 13 (b), when ϕ=90°, the control sample exhibits very weak quadratic MOKE signal independent on m^ PML, consistent with Eq. (7). However, the test sample exhibits significant quadratic MOKE signals, which depend on the initial polarization of m^PML.

Similar to Eq. (5), we separate Ψquaddepending on whether it is odd or even with m^PML,
ψQ_even=ψquad({circumflex over (m)}PML=+z)+Ψquad({circumflex over (m)}PML+z)
ψQ_odd=ψquad({circumflex over (m)}PML=+z)−Ψquad({circumflex over (m)}PML+z)  (8)

We further perform linear fitting of ΨQ_evenand ΨQ_oddwith a calibration signal Ψquad_calmeasured with an external calibration field, and plot the slopes as a function of ϕ inFIG. 13(c). The similar symmetry as the damping-like field inFIG. 12(d)suggests that there is also a rotated field-like field, which can be described as
{right arrow over (h)}R_FL=hR_FL(Î×{circumflex over (z)})×{circumflex over (m)}PML(9)

The magnitude of this field hR_FLis extracted to be 41±13 A/m when ϕ=90°, which is comparable to the rotated damping-like field hR_DL.

In order to further understand the rotation of spin-orbit effects, we use the same samples to perform a spin Seebeck effect-driven ISHE/IREE measurement. As shown inFIG. 14(a), when the samples are subject to an out-of-plane temperature gradient, we measure in-plane voltages along the x-direction as the in-plane external field Hextis swept with an angle ϕ from the x-direction. The voltage may arise from the anomalous Nernst effect in the magnetic layers, ISHE/IREE due to the spin current injected from the magnetic layers into the adjacent layers as well as the planar Nernst effect in PML,
V=ηPy({circumflex over (m)}Py×{circumflex over (∇)}T)·{circumflex over (x)}+ηPML({circumflex over (m)}PML×{right arrow over (∇)}T)·{circumflex over (x)}PNE_PML({circumflex over (m)}PML·{circumflex over (x)})({circumflex over (m)}PML·{circumflex over (∇)}T)  (10)
where ∇T is the temperature gradient in the z-direction, ηPy, and ηPMLare, respectively, the coefficients associated to the Py and PML layers due to the combination of the anomalous Nernst effect and the ISHE/IREE, ηPNE_PML is the coefficient associated to the planar Nernst effect of PML.

Similar to Eq. (8), we further separate the voltage according to its symmetry on the initial direction of m^PML,
Veven=V({circumflex over (m)}PML=+z)+V({circumflex over (m)}PML=−{circumflex over (z)})
Vodd=V({circumflex over (m)}PML=+z)−V({circumflex over (m)}PML=−{circumflex over (z)})  (11)

As shown inFIG. 14(b), Vevenmeasured when Hextis along the y-direction consists of two components: one resembles the hysteretic switching of Py (first term in Eq. (10)), and a linear slope related to the magnetization tilting of the PML under the influence of external field (second term in Eq. (10)). When Hextis applied along the x-direction, the first two terms in Eq. (10) shall vanish. Voddmeasured for the control sample yields a straight line, which is consistent with the planar Nernst effect described in Eq. (10). However, ∇Vodd measured for the test sample has an additional component related to the Py magnetization switching, which is not described in Eq. (10). The angle dependence of this component shown inFIG. 14(c)suggests that the voltage component can be described as
Vodd Py_Py=ηR({right arrow over (m)}Py×{right arrow over (m)}PML)×{right arrow over (∇)}T(12)
where ηRis the corresponding coefficient. Equation (12) bears the same rotated symmetry as in Eqs. (6) and (9).

We further studied the Py-thickness dependence of Veven_Pyand Vodd_Pymeasured in the two configurations, ϕ=90° and ϕ=0°, respectively. Shown inFIG. 3 (d), Veven_Py, which is due to the Anomalous Nernst effect and the ISHE/IREE, exhibits a monotonic increase with the Py thickness. This is because the Anomalous Nernst effect is a bulk effect that all Py contributes to the voltage. When the capping layer Pt is replaced with Ta, VANEchanges dramatically, which may be due to magnetic dead layer near the Ta/Py interface and that Ta contributes to a different ISHE/IREE signal than Pt. In sharp contrast, Vodd_Pyexhibits much weaker thickness dependence and is much less sensitive to the capping layer than VANE. This suggests Vodd_Pyhas a very short characteristic length scale.

Based on the comparison between the test and control samples, we think the spin current flowing between the two magnetic layers is essential for the observed rotated SOT and rotated ISHE/IREE-like voltage. Since the spin rotation and spin-orbit interactions at the Cu/ferromagnetic metal (FM) interface have been found to be weak, we speculate the phenomena may be related to the spin-orbit interaction of transverse spins in the FM itself. Taking the rotated SOT as an example, an in-plane electric current through PML, may generate a perpendicularly flowing spin current with spins polarized along I^. If we attribute the hR_DLmeasured inFIG. 12to solely arise from such a spin current, we can estimate an effective spin Hall angle that accounts for the rotated damping-like SOT to be

θR=hR⁢_⁢DL⁢μ0⁢Ms⁢dPyℏ2⁢e⁢I⁢⁢ζwdPML≈0.01(13)
where w=50 μm is the width of the sample, dPMLand dPyare respectively the thicknesses of PML and Py, ζ is the ratio of current flowing through PML, which is estimated to be 25%. It should be emphasized that in Eq. (13), we have assumed perfect spin transmission at the Cu/Py interface. In a more direct comparison, the effective spin Hall angle of Pt in Py(2)/Cu(3)/Pt(3) is found to be 0.04.

One possible mechanism that can lead to such a spin current is the spin swapping effect. The electric current I^ through PML generates a spin current along I^ with spins parallel with m^PMLdue to spin-dependent scattering. It may be that the spin-orbit interaction will lead to a new spin current that flows along m^PMLbut polarized along I^, as illustrated inFIG. 15(a). Alternatively, spin rotation may also lead to the spin current polarized along I^. As shown inFIG. 15 (b), conventional SHE gives rise to spin current polarized along I^×{circumflex over (z)}. As the spins exiting PML, they precess around m^PMLdue to the exchange interaction. This leads to spin current polarized along m^PML×(I^×{circumflex over (z)}), which is parallel with I^. The rotated ISHE/IREE-like voltage may be explained as the reverse process. Both mechanisms speculated here are related to transverse spins in a ferromagnet, which are often neglected due to the strong dephasing.

Our results show interesting spin-orbit effects with rotated symmetry in magnetic multilayers. Although allowed by symmetry, the magnitudes of these effects are expected to be weak due to transverse spin dephasing. The significant signals observed here suggest that there are more sophisticated mechanisms associated with the interplay between spin-orbit interaction and magnetism. Being able to generate spin-orbit torque in unconventional geometry is useful for the development of spin-torque magnetic random access memory.

The samples used in this Example are fabricated by magnetron sputtering. In the thermal measurement, the samples are typically cut into a 2 mm×25 mm strip. The samples are sandwiched in between two aluminum plates. The aluminum plates are attached to Peltier elements to create a typical temperature difference across the sample. The typical temperature difference measured on the two aluminum plates is 50 K. The voltage across the sample is measured by a Keithley nano voltmeter 2182. We typically measure the hysteretic loops for 10-20 times and take the average. Possible drifts in the measurement are removed mathematically by assuming the drift is linear with measurement time. In the MOKE measurement, the sample is patterned into a 50 μm×50 μm square.

Computers suitable for the execution of a computer program include, by way of example, can be based on general or special purpose microprocessors or both, workstations, or any other kind of central processing unit. Generally, a central processing unit will receive instructions and data from a read-only memory or a random access memory or both. The essential elements of a computer are a central processing unit for performing or executing instructions and one or more memory devices for storing instructions and data. Generally, a computer will also include, or be operatively coupled to receive data from or transfer data to, or both, one or more mass storage devices for storing data, e.g., magnetic; magneto-optical disks, optical disks, USB drives, and so on. However, a computer need not have such devices. Moreover, a computer can be embedded in another device, e.g., a mobile telephone, a personal digital assistant (PDA), a microwave oven, mobile audio or video player, a game console, a Global Positioning System (GPS) receiver, or a portable storage device (e.g., a universal serial bus (USB) flash drive), to name just a few. Devices suitable for storing computer program instructions and data include all forms of nonvolatile memory, media and memory devices, including by way of example semiconductor memory devices, e.g., EPROM, EEPROM, and flash memory devices; magnetic disks, e.g., internal hard disks or removable disks; magneto-optical disks; and CD-ROM and DVD-ROM disks. The central processing unit and the memory can be supplemented by, or incorporated in, special purpose logic circuitry.

Reference throughout this specification to “one embodiment,” “particular embodiment,” “certain embodiment,” “an embodiment,” or the like means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment. Thus, appearances of these phrases (e.g., “in one embodiment” or “in an embodiment”) throughout this specification are not necessarily all referring to the same embodiment, but may. Furthermore, particular features, structures, or characteristics may be combined in any suitable manner, as would be apparent to one of ordinary skill in the art from this disclosure, in one or more embodiments.

All ranges disclosed herein are inclusive of the endpoints, and the endpoints are independently combinable with each other. The ranges are continuous and thus contain every value and subset thereof in the range. Unless otherwise stated or contextually inapplicable, all percentages, when expressing a quantity, are weight percentages. The suffix “(s)” as used herein is intended to include both the singular and the plural of the term that it modifies, thereby including at least one of that term (e.g., the colorant(s) includes at least one colorants). “Optional” or “optionally” means that the subsequently described event or circumstance can or cannot occur, and that the description includes instances where the event occurs and instances where it does not. As used herein, “combination” is inclusive of blends, mixtures, alloys, reaction products, and the like.

As used herein, “a combination thereof” refers to a combination comprising at least one of the named constituents, components, compounds, or elements, optionally together with one or more of the same class of constituents, components, compounds, or elements.

All references are incorporated herein by reference.

The use of the terms “a” and “an” and “the” and similar referents in the context of describing the invention (especially in the context of the following claims) are to be construed to cover both the singular and the plural, unless otherwise indicated herein or clearly contradicted by context. “Or” means “and/or.” Further, the conjunction “or” is used to link objects of a list or alternatives and is not disjunctive; rather the elements can be used separately or can be combined together under appropriate circumstances. It should further be noted that the terms “first,” “second,” “primary,” “secondary,” and the like herein do not denote any order, quantity, or importance, but rather are used to distinguish one element from another. The modifier “about” used in connection with a quantity is inclusive of the stated value and has the meaning dictated by the context (e.g., it includes the degree of error associated with measurement of the particular quantity).