  The origin of the high-frequency radio emission detected from several
magnetars is poorly understood. In this paper, we report the ~40 GHz properties
of SGR J1745-29 as measured using Jansky Very Large Array (JVLA) and Robert C.
Byrd Green Bank Telescope (GBT) observations between 2013 October 26 and 2014
May 31. Our analysis of a Q-band (45 GHz) GBT observation on 2014 April 10
resulted in the earliest detection of pulsed radio emission at high frequencies
(>20 GHz); we found that the average pulse has a singly peaked profile with
width ~75 ms (~2% of the 3.764 s pulse period) and an average pulsed flux
density of ~100 mJy. We also detected very bright, short (<10 ms) single pulses
during ~70% of this neutron star's rotations, and the peak flux densities of
these bright pulses follow the same log-normal distribution as measured at 8.5
GHz. Additionally, our analysis of contemporaneous JVLA observations suggest
that its 41/44 GHz flux density varied between ~1-4 mJy during this period,
with a ~2x change observed on ~20 minute timescales during a JVLA observation
on 2014 May 10. Such a drastic change over short time-scales is inconsistent
with the radio emission resulting from a shock powered by the magnetar's
supersonic motion through the surrounding medium, and instead is dominated by
pulsed emission generated in its magnetosphere.
