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We use inelastic neutron scattering to study the temperature dependence ofmagnetic excitations (for energies up to 100 meV) in the cuprateLa$_{1.875}$Ba$_{0.125}$CuO$_4$. This compound exhibits stripe order below atemperature of ~50 K; previous measurements have shown that the magneticexcitations of the stripe-ordered phase have an hour-glass-like dispersion,with a saddle point at ~50 meV. Here we compare measurements in the disorderedphase taken at 65 and 300 K. At energies on the scale of $k_{\rm B}T$, there issubstantial momentum-broadening of the signal, and the low-energyincommensurate features can no longer be resolved at 300 K. In contrast, thereis remarkably little change in the scattered signal for energies greater than$k_{\rm B}T$. In fact, the momentum-integrated dynamic susceptibility is almostconstant with temperature. We suggest that the continuity of higher-energymagnetic excitations is strong evidence for dynamic stripes in thehigh-temperature, disordered phase. We reconsider the nature of the magneticdispersion, and we discuss the correspondences between the thermal evolution ofmagnetic stripe correlations with other electronic properties of the cuprates

physical review. b, condensed matter and materials physics

High-energy magnetic excitations from dynamic stripes in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">La</mml:mi><mml:mn>1.875</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">Ba</mml:mi><mml:mn>0.125</mml:mn></mml:msub><mml:mi mathvariant="normal">Cu</mml:mi><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:mrow></mml:math>

High-energy magnetic excitations from dynamic stripes inLa1.875Ba0.125CuO4