Origin of the spin Seebeck effect in compensated ferrimagnets

Abstract

Magnons are the elementary excitations of a magnetically ordered system. In ferromagnets, only a single band of low-energy magnons needs to be considered, but in ferrimagnets the situation is more complex owing to different magnetic sublattices involved. In this case, low lying optical modes exist that can affect the dynamical response. Here we show that the spin Seebeck effect (SSE) is sensitive to the complexities of the magnon spectrum. The SSE is caused by thermally excited spin dynamics that are converted to a voltage by the inverse spin Hall effect at the interface to a heavy metal contact. By investigating the temperature dependence of the SSE in the ferrimagnet gadolinium iron garnet, with a magnetic compensation point near room temperature, we demonstrate that higher-energy exchange magnons play a key role in the SSE.

Figure 1. Magnetic sublattices of GdIG.

(a) Iron garnet crystal structure. The tetrahedrally and octahedrally coordinated Fe³⁺ ions are highlighted. (b,c) The three different magnetic sublattices of GdIG shown for temperatures above (T>T_comp) and below (T<T_comp) the magnetic compensation temperature T_comp. Due to the strong temperature dependence of the magnetic Gd sublattice (c sites), the Gd sublattice dominates the magnetic behaviour for T<T_comp, while for T>T_comp it is mainly caused by the antiferromagnetically coupled Fe sublattices (d and a sites). In the presence of a finite magnetic field, the net magnetization M points along the external magnetic field H. The direction and length of the coloured arrows represent the direction and magnitude of the magnetizations of the three magnetic sublattices.

Figure 2. Experimental set-up.

(a,b) Sketches of the experimental configurations used to record the longitudinal spin Seebeck effect (SSE). Three different samples were investigated: Sample A and sample B consist of a GdIG(100 nm)/Pt(8 nm) and a GdIG(1 μm)/Pt(10 nm) bilayer fabricated on a (100)- and a (111)-oriented gadolinium gallium garnet (Gd₃Ga₅O₁₂, GGG) substrate, respectively. Sample C is composed of a GdIG(26 nm)/Pt(10 nm) bilayer fabricated on a (111)-oriented yttrium aluminium garnet (Y₃Al₅O₁₂, YAG) substrate. For sample A and B, the longitudinal SSE signal is determined by measuring the transverse voltage V_t perpendicular to an external magnetic field while modifying the magnetic field magnitude at a fixed magnetic field orientation . The temperature gradient required for SSE measurements is generated by two independently heated copper blocks or AlN ceramics, respectively. The longitudinal SSE signal of sample C is obtained by recording V_t as a function of the in-plane orientation of the external magnetic field α at a fixed magnetic field magnitude of 2 T. Here the temperature gradient across the GdIG/Pt interface is generated by driving a large current I_d along the Pt microstructure. The temperature-dependent resistance of the Pt is exploited for on-chip thermometry.

Figure 3. Magnetization and spin Seebeck effect in GdIG/Pt hybrids.

(a) Transverse voltage V_t of sample A plotted versus the applied magnetic field for selected temperatures. The hysteresis loop flips sign twice with decreasing temperature. (b) Temperature-dependent magnetization of sample A recorded at a magnetic field of 0.1 T. (c) Corresponding SSE signal I_SSE obtained from the difference in V_t at positive and negative saturation taking the temperature dependence of the Pt resistance R(T) into account. (d,f) Magnetization as a function of temperature of sample B and sample C measured at μ₀H=0.1 T and μ₀H=2 T, respectively. (e) I_SSE signal of sample B. (g) I_SSE signal of sample C obtained by recording the transverse voltage V_t as a function of the in-plane orientation of the external magnetic field with constant magnitude of 2 T while applying a heating current I_d of 6 mA across the Hall bar. The SSE signal I_SSE is then calculated from . The blue dashed lines mark the zero-crossing temperatures T_sign1 and T_sign2 of the I_SSE signal. The temperatures T_comp of the magnetic compensation points are indicated by the black dashed lines.

Figure 4. Calculated spin wave spectra of GdIG and sublattice spin currents injected by the SSE.

(a) Low-frequency spin wave spectra of GdIG calculated from an atomistic model for three different temperatures. The colour code indicates the power spectral density. For temperatures lower than 300 K, the SSE is dominated by two modes: a uniform precession mode in the GHz regime (α-mode) and a gapped, optical mode (β-mode). The two nearly dispersionless modes around 1 THz are the Gd moments precessing in the exchange field of the Fe moments. (b) Temperature dependence of the spin current (red) and (blue) caused by the respective magnon modes. The total spin current (black) determines the SSE. takes the different interface exchange couplings at the GdIG/Pt interface into account. The ratio between these couplings is given by η.