Transverse Spin Seebeck Effect versus Anomalous and Planar Nernst Effects in Permalloy Thin Films

Abstract

Transverse magnetothermoelectric effects are studied in Permalloy thin films grown on MgO and GaAs substrates and compared to those grown on suspended SiN(x) membranes. The transverse voltage along platinum strips patterned on top of the Permalloy films is measured versus the external magnetic field as a function of the angle and temperature gradients. After the identification of the contribution of the planar and anomalous Nernst effects, we find an upper limit for the transverse spin Seebeck effect, which is several orders of magnitude smaller than previously reported.

Energy repartition in the nonequilibrium steady state

“…We can model this situation by contacting the spin chain either at the two ends or at some intermediate site. The former configuration corresponds to the "longitudinal" spin Seebeck effect [36][37][38][39][40][41], while the latter one is referred to as "transverse" [35,[42][43][44][45][46] or "nonlocal" [47]. The spin dynamics at the interface pumps a spin current into the contact at site n given by…”

Dependence of transverse magnetothermoelectric effects on inhomogeneous magnetic fields

“…3 we show a typical set of experimental data of the voltages V y (H) (green lines) measured across the Pt strip for the following parameters: base temperature T str = 360 K; temperature difference on the sample ∆T The peaks visible in the V y (H) curves as well as the sin 2Θ H dependence of A(Θ H ) are related to the AMTEP, for details see [15,16]. The transverse voltage, associated with the AMTEP traces, can be described as: (1) where Θ 0 is the angle between the temperature gradient ∇ x T and the magnetization vector M ; A 0 is the (2) and is placed in the middle of the vacuum chamber (3) without contact to its walls.…”

“…3). Its amplitude ∆ 0 can be interpreted as a mixture of TSSE and ANE signals, where the ANE is produced by a spurious out-of-plane temperature gradient ∇ z T [15].…”

“…However, it turned out that the TSSE [3][4][5][6][7][8][9][10][11][12][13][14][15][16], especially when using metallic ferromagnets [3-7, 13, 15, 16], is under strong discussion. Other magneto-thermoelectric effects, like the anomalous Nernst effect (ANE) [6,7,[15][16][17] and the anisotropic magneto-thermopower (AMTEP, also known as the planar Nernst effect (PNE)) [4,15,16,18,19] play an important role in the TSSE measurements and contribute to the detected signals. ANE and TSSE signals are antisymmetric with respect to the external magnetic field, have the shape of hysteresis loops and both follow the cos Θ 0 dependence, where Θ 0 is the angle between the magnetization vector M and the temperature gradient ∇T .…”

“…The AMTEP can be identified by its sin 2Θ 0 angular dependence and symmetric shape. Thus, it was postulated that the ANE caused by an unintended outof-plane temperature gradient (due to heat flux into surrounding area by radiation [15] and through electrical contacts by thermal conductivity [16]) is the main effect masking TSSE in metallic ferromagnets. Small static environmental magnetic fields of the Earth magnetic field's order of magnitude and lower are typically not considered in experimental set-ups.…”