What's wrong with my diode SPICE model for the HSMS-2860?
While a practical design of an RF detector with the Schottky diode use distributed elements

(see, for example, the AVAGO Technologies datasheet HSMS-286x Series Surface Mount Microwave Schottky Detector Diodes, Figure 21 5.8 GHz Matching Network for the HSMS-286x Series at 3 µA Bias), and these circuits should be developed using specialized design tools, the origin of &quot;negative peaks&quot; can be traced with a general-purpose SPICE simulator.
Sure there is always a reverse current through a diode, even for DC current, only it can be very small and you would not see it in your simulation plots. With AC current, a reverse current has two components: the reverse leakage current, which can be high for Schottky diodes when compared with p-n diodes, and the reverse recovery current, which is much smaller for Schottky diodes when compared with p-n diodes but still reveals itself when the signal waveform period \$T_{sig}\$ is on the order of Schottky diode's reverse recovery time \$t_{rr}\$ (switching time). The voltage sensitivity of HSMS2860 is halved at the frequency of 5.8GHz (ref value at 915MHz). At this frequency, the reverse recovery time effects become noticeable in the waveform of detected signals (&quot;rectified&quot; waveforms).
To mitigate the visible &quot;negative peaks&quot; in your &quot;Half-Wave Rectifier&quot; simulations, you can decrease a load resistance (impedance) in order to provide a sufficient reverse current.
For reference, the &quot;Half-Wave Rectifier&quot; circuit to be simulated:

, to easily see the effects of load, I first simulate your &quot;Half-Wave Rectifier&quot; with a 0.58GHz V1 source and 100 Ohm (R1) load:

You see &quot;negative peaks&quot; in graphs of both a voltage across the load and a diode current.
With 10 Ohm (R1) load:

&quot;negative peaks&quot; are noticeable, but become much smaller.
With 5.8GHz frequency (V1 source) and 10 Ohm (R1) load,

&quot;negative peaks&quot; are here again, but the current is 40 mA and I do not know if we can decrease the load without a risk of diode damage.
Summing up: the &quot;negative peaks&quot; are a legitimate phenomenon, it is a manifestation of finite reverse recovery time. You cannot get rid of it entirely. You have to only be aware of this phenomenon when designing your circuits.